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Stable32 User Manual - Hamilton Technical Services

1. E Press OKto print selected data e Controls The Print dialog box contains the following controls Control Type Description Data Type Group Data type Phase Radiobutton Select phase data Frequency Radiobutton Select frequency data Data Range Group Data range Start Edit Enter first point to print End Edit Enter last point to print Timetags Checkbox Print timetag data All Data Checkbox Print all data OK Pushbutton Perform the Print function amp close dialog box Cancel Pushbutton Abort the Print function amp close dialog box Help Pushbutton Invoke the Print help topic e Operation Choose Phase or Frequency data and enter the Start and End points to print or check All Data to print all the data Check Timetags to also print the corresponding timetag data Then press OK to print or Cancel to abort 151 STABLE32 USER MANUAL 152 EDITING FUNCTIONS Edit Function e Purpose Use the Edit function to display search and edit the current phase or frequency data The primary purpose of this function is to examine phase or frequency data for gaps outliers and other anomalous values relating them to their point number or timetag For example this function can be used to quickly find the date and time of an outlier in a set of frequency data outlier identification is not available for phase data The Edit function is not intended for manual data entry or heavy editing tasks Use Windows Note
2. 269 Time Domain Stability 1 5 4 deterret ie deeper ariris niesi i ide 55 Time Variance 63 184 ND CE O M 27 211 Timetags Function ise ede ete ree reet aei eet doeet dod in ob e enano n ese de vale Pado reel de den en aa eda 211 Timing Solutions Corporation TSC esses eere 23 117 TRE Plot Files 5 5 ug aevo ten eec tede tee tae dated otii a ien ei ed 25 253 301 Toolbar Total Variance ost SAA O 55 65 U User Interfaces ooa e bte de d m n E timui 7 V Validation Variances Viewpoint W WED Site M PC 2 MTA t 228 STABLE32 USER MANUAL WinBatch ss ita tiere a tt D de deae entes 33 302 Witidows Metatil s wmb 3 i e seda eire ed ees edet dag eee dee s 301 X x Phase Data ooh de nM ML bM ka 7 Y ry Prequency Data ii ee ese te e ote t he e HERR eee eH De sev dene cate A Z Zero Frequency aaa c e e re e Cd Aisa gina tu tesevesbtass 17 Zero Mean ope bebe eni M Pe oq dime o reps 163 312 Notes INDEX 313
3. X Axis 30 sec div Y Axis 1 917e 11 to 1 770e 12 3 480e 12 div Avg Freg 9 99261e 12 2 711e 13 scaled e Condensed Operating Instructions 1 Connect the TSC 5110A to a PC COM port using a null modem cable 2 Launch the 5110Comm program directly or from within Stable32 3 Verify that the COM port is open by observing the Open indicator or status message in the List box 4 Enter the desired filename for the data file Note If there is an existing file with this name it will be overwritten each time a new run is started 5 Enter the scale factor to convert cycles of the A channel frequency into seconds This is equal to the period of the A channel frequency e g 100 nsec or 1e 7 for 10 MHz 6 Press the Start button Data capture will begin immediately at 1 second intervals or as soon as the TSC 5110A is started 7 The captured data can be displayed as a listing a phase plot or a frequency plot by selecting the desired Radiobutton above the display area 8 The data listing shows the data point number the raw TSC 5110A data in cycles of the A channel frequency and the scaled data file values in seconds of phase difference as labeled below the listing 305 306 10 11 12 13 14 15 16 STABLE32 USER MANUAL For plots the annotation in the first line below the display shows the plot scales The X axis scale is shown in sec div The Y axis scale is shown as the maximum a
4. where x 1 is the ith of N M 1 phase values at averaging time t Like the Allan variance the Hadamard variance is usually expressed as its square root the Hadamard deviation HDEV or Ho t Note The Picinbono variance is a similar 3 sample statistic It is identical to the Hadamard variance except for a factor of 2 3 69 70 STABLE32 USER MANUAL TIME DOMAIN STABILITY Overlapping Hadamard Variance e Overlapping Hadamard Variance In the same way that the overlapping Allan variance makes maximum use of a data set by forming all possible fully overlapping 2 sample pairs at each averaging time t the overlapping Hadamard variance uses all 3 sample combinations It can be estimated from a set of M frequency measurements for averaging time t mto where m is the averaging factor and ty is the basic measurement interval by the expression 2 1 M 3m 1 j m 1 Ho r une Dy o 7 6m M 3m 1 2 2 Viam Yam Xil gt where y is the ith of M fractional frequency values at each measurement time In terms of phase data the overlapping Hadamard variance can be estimated from a set of N M 1 time measurements as N 3m Ho 1 gnome 3m y T LiL ton SX 3x Xo E x where x is the ith of N M 1 phase values at each measurement time Computation of the overlapping Hadamard variance is more efficient for phase data where the averaging is accomplished by simply choosing the appropriate interval For frequenc
5. 0 22 STABLE32 USER MANUAL References J A Barnes Tables of Bias Functions B1 and B2 for Variances Based on Finite Samples of Processes with Power Law Spectral Densities NBS Technical Note 375 January 1969 J A Barnes and D A Allan Variances Based on Data with Dead Time Between the Measurements NIST Technical Note 1318 1990 P Tavella and M Leonardi Noise Characterization of Irregularly Spaced Data Proceedings of the 12th European Frequency and Time Forum pp 209 214 March 1998 C Hackman and T E Parker Noise Analysis of Unevenly Spaced Time Series Data Metrologia Vol 33 pp 457 466 1996 W J Riley Gaps Outliers Dead Time and Uneven Spacing in Frequency Stability Data Hamilton Technical Services web site GENERAL Archive File Format e TSC Archive File Format Timing Solutions Corporation TSC now Symmetricom archive files have lines that start with either a or symbol The lines have 1 additional field the MJD for the data on the following lines The MJD is a 18 character string comprised of a 5 digit integer part a decimal point and a 12 digit fractional part A sample line is as follows where the is in 1st column and is followed by a single space 48888 612500000000 The lines have 5 additional fields a 1 or 2 digit channel 4 between 1 and N the of channels in the system a 20 character clock ID string and 3 numerical fields The 1st number is the nominal clock
6. Window ing s List Select window ing s Avg or BW Factor List Select AF 4 or BW J Factor PSD Std Dev or Text Standard deviation of PSD 96 PSD Max Text Maximum PSD data value PSD Min Text Minimum PSD data value Scale Max Edit Maximum PSD scale Scale Min Edit Minimum PSD scale PSD File Edit Enter PSD filename Smooth Checkbox Smooth PSD results Max AF Text Maximum AF Options Group Plot options Date Checkbox Show date on plot Box Checkbox Draw box around plot Cursor Checkbox Activate mouse cursor for plot Fit Checkbox Draw power law line fit Pts Checkbox Show FFT points on plot Info Checkbox Show windowing amp freq info on plot Wide Checkbox Draw wide lines on plot Plot Pushbutton Plot power spectrum Close Pushbutton Close Power Spectrum dialog box Help Pushbutton Invoke the Power help topic Reset AII Pushbutton Reset all plot attributes to defaults e Operation Enter the desired Title Sub Title Message message Position and Options Select the desired PSD Type Windowing Type Windowings or Windows and Avg or BW J Factor Enter the Carrier Frequency value for S f or f PSD types Use the Date Box Cursor Fit Pts and Info checkboxes to select the desired options Then press Plot to plot the power spectrum or Close to close the Power Spectrum dialog box The Auto Avg Factor selection uses a variable averaging factor for the periodogram PSD as described below Display of the FFT po
7. lt gt Pushbutton Swap data type Plot Title Text Plot type and scale factor Statistics Text Basic statistics for data see above Plot Graphic Data plot Scrollbar Scrollbar Data selection Point Text Data display Zoom Text Box Zoom factor Track Checkbox Enable scroll tracking Copy Pushbutton Copy plot to clipboard Timetags Combo Select timetag type All Pushbutton Select all data Close Pushbutton Close the Statistics dialog box Help Pushbutton Invoke the Statistics help topic 173 STABLE32 USER MANUAL e Operation Use the mouse cursor to select data points for numeric display and the scrollbar to select them for statistics and plotting Zoom and un zoom the plot with the R and L mouse buttons The Track checkbox determines if the plot updates during scrolling Disable tracking for large data sets and or slow computers Use the Timetags box to select the timetag display for data that has them The All button selects all the data and disables the scrollbar and the lt gt button switches between phase and frequency data if equivalent data exists Press the Close button to close the Statistics dialog box e Zooming The plot and statistics can be zoomed in and out by clicking the R and L mouse buttons while the cursor is in the plot The zooming is centered on the mouse position The width of the scroll box thumb indicates the relative span of the plot and the zoom factor is shown in its text box The status bar
8. o a simplex fnt iC y U 84 o m V 135 12 V 169 ses dud A n T D as U 102 19 36 Q 153 U 170 e7 E Q lt x D g I Th N C c 3 do Ds uy S C I a Q a p nu p a ID Re O Oe E k 43 O R3 co 3 a 5 KO O i o 98 2 E amp o gt O A 3 q R O 5 z c pen gt co U J O EN o oo O Le i CN nae b es a st al A 98 9 5 gt 12 C 1499 O 166 83 A Simplex Font Numeric Code 0203 287 STABLE32 USER MANUAL 288 APPENDICES Appendix III Editing Keys e Editing Keys The Stable32 program uses the standard Windows editing keys except that the Enter key can generally be used to terminate edit control entries This causes the entry to be reformatted and checked for validity The following special editing keys that apply to the Edit dialog box F2 The existing data may be edited by first pressing the F2 key It is necessary to delete a portion of the existing data to make room for the new entries Ese The original value may be restored with the Esc key Enter The changes are accepted with the Enter key 289 STABLE32 USER MANUAL 290 APPENDICES Appendix IV Configuration File Default None None None None None None None e Files The Files section of the STABLE3
9. e Gaps Jumps and Outliers It is not uncommon to have gaps and outliers in a set of raw frequency stability data Missing or erroneous data may occur due to power outages equipment malfunctions and interference For long term tests it may not be possible or practical to repeat the run or otherwise avoid such bad data points Usually the reason for the gap or outlier is known and it is particularly important to explain all phase discontinuities Plotting the data will often show the bad points which may have to be removed before doing an analysis to obtain meaningful results Frequency outliers are found by comparing each data point with the median value of the data set plus or minus some multiple of the absolute median deviation These median statistics are more robust because they are insensitive to the size of the outliers The outliers can be replaced by gaps or filled with interpolated values Frequency jumps can also be a problem for stability analysis They are an indication that the statistics are not stationary and it may be necessary to divide the data into portions and analyze them separately e Data Plotting Data plotting is often the most important step in the analysis of frequency stability Visual inspection can provide vital insight into the results and is an important preprocessor before numerical analysis A plot also shows much about the validity of a curve fit Phase data is plotted as line segments connecting the data
10. e Operation The Sigma function begins with the selection of the Variance Type and the Avg Factor the of to measurement intervals averaged to form the averaging time t Entering an m or M will give the maximum allowable averaging factor The Cale button will then calculate the desired Sigma value The Show Details checkbox will change the dialog box to a more detailed format as described below The Help button invokes this Help screen while the Close button closes the dialog box A change in either the Variance Type or Avg Factor clears the results e Detailed Sigma Dialog Box The detailed Sigma dialog box provides additional options and results The Variance Parameters group box adds a BW Factor entry and a display of the Tau value The BW Factor is equal to 27f t9 where f is the upper cutoff frequency of the measuring system in Hz and applies only to flicker PM noise The Sigma Results group box adds a display of the Std Dev standard deviation The Noise Type group box shows several parameters associated with the power law noise type based on the B1 or R n Ratio This ratio is used to estimate the Noise type and corresponding Alpha Mu and for normal AVAR Kn values as described below The a value is the exponent of the S f noise process and the p is the o t log log slope See the Noise Processes and Noise Spectra Help screens for more information about those subjects Confidence Interval information is displayed in the
11. General help information is available via the F1 key or by accessing the Help menu or toolbutton while context sensitive help is available by pressing the Help button within a particular function Complete information about the Stable32 program is available in the User Manual Stable32 uses the GraphiC scientific plotting package under the terms of a royalty license agreement with Scientific Endeavors Corporation Kingston TN 37763 It may include the PlayW program for replaying the TKF graphics files produced by GraphiC e Features E Stable32 Welcome to the Stable32 program for frequency stability analysis Date 05 04 98 MID 50937 C Phase Data Total Freq Data Total File zx No Phase Data File No Freq Data Tau Start End Tau Start End Stable32 file manipulations include entering and opening phase and freguency files combining data files and storing all or a portion of a data array Data is stored in space or comma delimited multicolumn ASCII format with gaps denoted by a value of zero Editing features include displaying printing changing correcting converting scaling inserting or deleting data or removing outliers filling gaps and adding timetags STABLE32 USER MANUAL Plotting can be done for all or a portion of the data with automatic or user defined scales titles and annotations Stable32 includes provisions for the generation
12. The calendar opens to the current month with the current day highlighted Use the Year Up Year Down Month Up and Month Down auto repeating buttons to move to the month desired Use the Today button to return to the current month When finished Close the calendar dialog box 249 STABLE32 USER MANUAL e MJD The Modified Julian Date MJD is based on the astronomical Julian Date the of days since noon on January 1 4713 BC The MJD is the Julian Date 2 4000 000 5 it starts at midnight on November 17 1858 MJD 50 000 was on October 10 1995 e GPS Week The GPS week number is displayed at the top left of the calendar when applicable This number is used by the Global Positioning System to measure its system time It has an origin time zero of 00 00 00 UTC 6 January 1980 Julian Day 2 444 244 500 MJD 44244 A GPS week cycle is 1024 weeks 250 MISCELLANEOUS FUNCTIONS Pad e Purpose Use the Pad function to invoke Windows Notepad or an alternative text editor program El phase dat Notepad Ol x File Edit Search Help p 000000000000000e 00 8 511601033439709e 02 204754825860608e 01 470741798514836e 01 417563029461325e 01 145763378402094e 01 512799857208863e 01 798670993851792e 01 938636382882760e 01 840701657650369e 01 3555465081033 78e 01 856719903110837e 01 581741624819895e 01 525590220324474e 01 229270669 703960et 00 172310267951015e 00 892151893271170e 01 160605940601602e 00 753391
13. Timetag Static Start and end timetag data Timetag Type Combo Choose timetag type OK Pushbutton Perform the Part function amp close dialog box Cancel Pushbutton Abort the Part function amp close dialog box Help Pushbutton Invoke the Part help topic e Operation Enter the Start and End data points to be selected If timetags are available choose the desired Timetag Type to help select the desired data points Use the Press OK to delete the data outside these limits or Cancel to abort e Timetag Display Timetags can be displayed for the start and end data points in MJD DOY Date or general exponential format 171 STABLE32 USER MANUAL 172 ANALYSIS FUNCTIONS Statistics Function e Purpose Use the Statistics function to display basic statistics for and a simple plot of phase or frequency data The full filename and the following statistics are displayed Point Range Points Gaps Minimum Maximum Average Median Std Dev Sigma Noise Type File PHASE gt Phase Data le 00 div Zoom 2 0X Points 228 730 Points 503 Gaps 0 Maximum 2 794732e 00 Minimum 3 609595e 00 Average 4 963155e 01 Median 5 13300 e 01 Std Dew 2 881059e 02 Sigma 2 913097e 02 W FM a 0 i Copy All Pa e lt lt gt Basic Statistics Timetags en re for Plotted Data None e Controls The Statistics dialog box contains the following controls Control Type Description File Text Data filename
14. B1 ratio Bias 6 Total Lag 1 ACF TOTMVAR X TOTMVAR Modified B1 plus EDF Bias 7 TOTMVAR R n fora for m gt 8 else 1 2 EDF 5 Total Lag 1 ACF TOTMVAR X TOTMVAR Time B1 plus EDF Bias 7 TOTTVAR R n for a for m gt 8 else 1 2 EDF 5 Th ol Lag 1 ACF Th ol EDF x Th ol Bias B1 plus 17 17 or R n for a Th oBR 1 2 18 Th oH Lag 1 ACF Th o1 EDF x Th oBR B1 plus 17 18 R n for a 1 2 TIE rms N A N A None N A MTIE N A N A None N A The Lag 1 ACF noise ID method is used when the of analysis points is 2 30 93 STABLE32 USER MANUAL References The following references apply to the Stable32 edf and bias functions 1 2 10 11 12 13 14 15 16 17 18 94 IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology Random Instabilities JEEE Std 1139 1999 July 1999 C A Greenhall Estimating the Modified Allan Variance Proc IEEE 1995 Freq Contrl Symp pp 346 353 May 1995 D A Howe amp C A Greenhall Total Variance A Progress Report on a New Frequency Stability Characterization Proc 1997 PTTI Meeting pp 39 48 December 1997 C A Greenhall private communication May 1999 D A Howe private communication March 2000 D A Howe Total Variance Explained Proc 1999 Joint Meeting of the European Freq and Time Forum and the IEEE Freq Contrl Symp pp 1093 1099 April 1999 D A How
15. Bregni Clock Stability Characterization and Measurement in Telecommunications IEEE Trans Instrum Meas Vol 46 No 6 pp 1284 1294 Dec 1997 2 P Tavella A Godone amp S Leschiutta The Range Covered by a Random Process and the New Definition of MTIE Proc 28th PTTI Meeting Dec 1996 pp 119 124 3 P Tavella and D Meo The Range Covered by a Clock Error in the Case of White FM Proc 30th PTTI Meeting Dec 1998 to be published 4 S Bregni and S Maccabruni Fast Computation of Maximum Time Interval Error by Binary Decomposition IEEE Trans I amp M Vol 49 No 6 Dec 2000 pp 1240 1244 80 TIME DOMAIN STABILITY TIE rms e TIE rms The rms time interval error TIR rms is another clock statistic commonly used by the telecommunications industry TIE rms is defined by the expression 1 N n gt nc bii x A ia TIE MS where n 1 2 N 1 and N phase data points For no frequency offset TIE rms is approximately equal to the standard deviation of the fractional frequency fluctuations multiplied by the averaging time It is therefore similar in behavior to TDEV although the latter is better suited for divergent noise types e References The following reference applies to the TIE rms statistic S Bregni Clock Stability Characterization and Measurement in Telecommunications JEEE Trans Instrum Meas Vol 46 No 6 pp 1284 1294 Dec 1997 81 82 STABLE32 USER MANUA
16. Checkbox Print Table 8 Checkbox Close X Checkbox Add Delay 9 Checkbox msec Edit Script Name Edit Go Pushbutton OK Pushbutton Cancel Pushbutton Help Pushbutton e Manual Use The Auto functions may be used manually by setting the desired analysis steps and either saving them by pressing OK or executing them by pressing Go Pressing Cancel aborts any changes made The analysis functions are the same as provided for a non automated Stable32 analysis The automation script options are interlocked so as to simplify their selection All reasonable combinations are allowed but their order may not be changed Default timetag and data columns are used for multicolumn data The Close checkbox determines whether the last result remains on the screen Extra delay may be added with the Add Delay and msec Description Open data file for analysis Browse for data file Label Choose phase data Choose frequency data Enter name of data file Convert to other data type Use timetags to insert gaps Remove bad freq data Enter outlier criterion Use part of data Enter starting point 1 1 Enter ending point 0 last Combine data for longer t Enter averaging factor Normalize data Remove drift Select drift fit type Plot data on screen Select data plot type s Print data plot Run stability analysis Select variance type Plot stability on screen Print stability plot Print stability table Close at end of script A
17. For color surface plots the Grid control selects the grid type 0 No Grid 1 Full Grid 2 9 of x and y mesh lines skipped The preferred Message Position is Top Right where there is the most space The character sequence n backslash and lower case n will insert a carriage return line feed into the message to allow a longer more vertical format 234 ANALYSIS FUNCTIONS The dynamic stability analysis options and settings can be saved in the STABLE32 INI configuration file with the Save Config button recalled with the Read Config button and restored to their default settings with the Reset button e Dynamic Stability Plot The dynamic stability plot is a 3D surface plot of ADEV or HDEV log sigma versus averaging time log tau or log averaging factor AF as a function of time window Sigma is calculated using fully overlapping samples at all possible averaging factors up to one quarter of the window size In the axes orientation used the tau scale is opposite to that usually used AF and tau increase toward the left which is the convention for a dynamic stability plot and has the advantage of best showing the sigma tau surface that usually has lower sigma at longer tau The y axis and z axis are labeled as log sigma and log AF respectively and a log log grid is shown in the back x plane while the linear x axis is labeled as window The dynamic stability plot includes annotations that show the sigma range tau range win
18. Help eene ListFiles of Type Drives C Frequency Data Files dat y c drive c M Archive e Controls The Add dialog box contains the standard Windows file open controls plus the following custom controls Control Type Description Data Type Group Box Controls to choose the data type Phase Radiobutton Read additional data into the phase array Frequency Radiobutton Read additional data into the frequency array e Operation Select Phase or Frequency data type and perform the usual Windows file dialog box operations Attempting to add excessive data will be trapped with an error message The results of an Add operation will be displayed in a File Opened box if this feature is activated with the Show File Opened option of the Configure function e Caution Overlength data files cannot be added 131 STABLE32 USER MANUAL 132 FILE FUNCTIONS Database Function e Purpose Use the Database function to select read and save clock data from a Symmetricom previously Timing Solutions Corporation Multichannel Measuring System MMS database TSC MMS Database Ei m Reference Measurement Glock Name Cesium 1 Clock Name Decription Cs Clock Decription Rb Clock m Records Reference Measurement IMMS Ch Start Time EndTime IMMS Ch Start Time EndTime 01 03 2005 10 14 22 41 42 Run Continuing 02 0 2005 10 14 22 41 58 Run Continuing 01 2005 10
19. However the plot can be redrawn with different options without repeating the calculation e XYZ Data File A data file comprising 3 columns of x Averaging Factor y Window and z Sigma data named XYZ dat is written to the Stable32 working directory each time a dynamic stability plot is generated This file must be manually renamed before the next plot to save it The XYZ dat data is the actual stability analysis results before log scaling and interpolation An example of the first 5 lines of an XYZ dat file is shown below 1 000000e 000 1 000000e 000 2 952219e 001 2 000000e 000 1 000000e 000 1 895182e 001 3 000000e 000 1 000000e 000 1 582051e 001 4 000000e 000 1 000000e 000 1 422213e 001 5 000000e 000 1 000000e 000 1 354947e 001 235 STABLE32 USER MANUAL 236 ANALYSIS FUNCTIONS Regularize Function e Purpose Use the Regularize function to find interruptions and missing points in time tagged phase or frequency data and optionally insert gaps as required to provide a regular sequence of data points The regularize function is not available for data that does not have timetags Regularize x Interruptions Missing Pts 3 Data Interval 9 0000000000e 02 2 Press OK to use timetag info to insert 222 gaps where data is missing Help e Controls The Regularize dialog box contains the following controls Control Type Description Interruptions Text Display of interruptions in the dat
20. Normalize Remove median from data Remove Remove fit Choose fit type Residual data Drift Run Stability Choose variance Stability plot analysis type Stability table Close Close last Leave open for Add delay to screen manual analysis Observe steps Script M Open File Browse Data Type Phase Freg 1 Filename CADateAFM202 phd Select functions desired f M Convert Analysis of Freq Data Iv Regularize SURE Iv Remove Outliers Sigma Factor 5 000 processing Part Q Start End p Script 1 Name Average 1 Avg Factor E Normalize AutoScriptt Remove Drift 2 Drift Type 3 Linear Iv Data Plot Type 4 Original Run Variance Type D Overlapping E K 7 Stability Plot I Print Stability Plot 7 Print Table 8 CETERI Close X Add Delay 9 msec eos Help dd 243 STABLE32 USER MANUAL e Controls The Auto dialog box contains the following controls Control Type Open File Checkbox Browse Pushbutton Data Type Text Phase Radiobutton Freq Radiobutton Filename Edit Convert Checkbox Regularize Checkbox Remove Outliers Checkbox Sigma Factor Edit Part 0 Checkbox Start Edit End Edit Average 1 Checkbox Avg Factor Edit Normalize Checkbox Remove Drift 2 Checkbox Drift Type 3 Listbox Data Plot Checkbox Type 4 Listbox Print Data Plot 5 Checkbox Run 6 Checkbox Variance Combobox Stability Plot Checkbox Print Stab Plot 7
21. OK Pushbutton Perform the Clear function amp close dialog box Cancel Pushbutton Abort the Clear function amp close dialog box Help Pushbutton Invoke the Clear help topic e Operation Select the Phase Data Phase Timetags Frequency Data or Frequency Timetags to be cleared Then press OK to clear the selected data or Cancel to abort e Caution There is no confirmation after OK is pressed the selected data is cleared and cannot be recovered It is possible to clear the phase or frequency data and retain the corresponding timetags but this is an unusual thing to do 217 STABLE32 USER MANUAL 218 ANALYSIS FUNCTIONS Run Function e Purpose Use the Run function to calculate and optionally plot or print Allan total or Hadamard variance statistics for the selected portion of the current phase or frequency data over a series of averaging times The averaging times may be selected in octave or sub decade increments or at every possible tau out to a reasonable fraction of the record length The Sigma function is available for performing this calculation at a single averaging time Frequency drift may be removed and 1 of 2 unit scaling may be applied as options Variance Type Overlapping gt Alpha Automatic Confidence Factor 0 683 AF Tau Alpha Min Sigma Sigma Max Sigma Close 1 1 0000e 00 999 0 28458801 2 9223e 01 3 0054e 01 2 2 0000e 00 997 0 19535e 01 2 0102e 01 2 0721e 01 Print 4 4 0000e
22. Read Config N Pushbutton Read config data from INI file Save Config G Pushbutton Save configuration data to INI file ACF File F Edit Enter ACF data filename Plot File E Edit Enter ACF plot filename Lag Edit Scatter plot lag X Axis Groupbox X axis parameters X Label Text X axis label Lag Lags L Edit of autocorrelation lag points Y Axis Groupbox Y axis parameters Y Label Text Y axis label Autocorrelation Options Groupbox Plot options 193 STABLE32 USER MANUAL Date D Checkbox Show date on plot Box X Checkbox Draw box around plot Cursor U Checkbox Activate mouse cursor for plot Zero Z Checkbox Draw horizontal line at zero Lagk K Checkbox Show lag k scatter plot Wide W Checkbox Use wide lines for spectrum plot Reset All R Pushbutton Reset all parameters to defaults Help H Pushbutton Invoke this help topic Close C Pushbutton Close ACF dialog box e Operation Enter the desired plot Title SubTitle Message Message Position and Options and select the desired Avg Factor and Lags Then press Plot to plot the autocorrelation sequence or Scatter to plot a lag scatter plot for the selected lag When done press Close to close the Autocorrelation dialog box Autocorrelation plot configurations may be read saved and reset with the Read Config Save Config and Reset All buttons The lag to be used for the scatter plot normally 1 can be entered in the Scatter Plot Lag box Display of the zero
23. Stones 48 dH decede ANALYSIS FUNCTIONS Autocorrelation Function e Purpose Use the Autocorrelation function to plot the autocorrelation function ACF of the current phase or frequency data The primary purpose of the Autocorrelation function is to provide insight into the degree of correlation or non whiteness of the phase or frequency fluctuations and to provide an estimate of the power law noise type Title AUTOCORRELATION gj Plot Sue PHASE DAT f Scatter Message White FM Estimated alpha 0 05 gg Close Message Position Topet E Avg Factor i Save Config Help Scatter Plot Lag po Tau 1 000008 00 Read Config Reset All ACF File C Stable32 AUTODAT PlotFile CAStable32AUTO TKF rane r Y Axis X Label Lag Lags 500 of 500 All Y Label Autocorrelation 1 0 987 Options E Date M Box M Cursor V Zero W Lagk Wide EN Press Plotfor Autocorrelation plot e Controls The Autocorrelation dialog box contains the following controls Dialog Box ALT Control Control Control Key Type Description Plot P Pushbutton Plot autocorrelation Scatter S Pushbutton Plot lag scatter plot Title T Combo Edit or select plot title SubTitle B Combo Edit or select plot subtitle Message M Combo Edit or select plot message Position O List Select message position Avg Factor V Edit Avg factor for autocorrelation Tau Text Averaging time for autocorrelation
24. at long tau e 3 Cornered Hat Error Bars The error bars of the separated variances may be set using X statistics by first determining the reduced number of degrees of freedom associated with the 3 cornered hat process see References 11 and 12 below The fraction of remaining degrees of freedom for unit i as a result of performing a 3 cornered hat instead of measuring against a perfect reference is given by T 2 0 Q 0 o2 0 02 021 0 0 The ratio of the number of degrees of freedom is 0 4 for three units having the same stability independent of the averaging time and noise type 97 STABLE32 USER MANUAL References The following references apply to the 3 cornered hat method for frequency stability analysis 1 10 11 12 13 98 The term 3 cornered hat was coined by J E Gray of NIST J E Gray and D W Allan A Method for Estimating the Freguency Stability of an Individual Oscillator Proceedings of the 28th Annual Symposium on Frequency Control May 1974 pp 243 246 J Groslambert D Fest M Oliver and J J Gagnepain Characterization of Freguency Fluctuations by Crosscorrelations and by Using Three or More Oscillators Proceedings of the 35th Annual Frequency Control Symposium May 1981 pp 458 462 S R Stein Frequency and Time Their Measurement and Characterization Chapter 12 Section 12 1 9 Separating the Variances of the Oscillator and the Reference pp 216 217 Precision
25. noise It is particularly useful for measuring the stability of a time distribution network It is usually given as its square root o t TDEV e Total Time Variance The total time variance TOTTVAR is a similar measure of time stability based on the total modified variance It is defined as o total 1 E 3 Mod total T It is usually given as its square root Ox totalt TOTTDEV 63 64 STABLE32 USER MANUAL TIME DOMAIN STABILITY Total Allan Variance e Total Allan Variance The total Allan variance TOTAVAR is similar to the 2 sample or Allan variance and has the same expected value but offers improved confidence at long averaging times Work on total variance began with the realization that the Allan variance can collapse at long averaging factors because of symmetry in the data An early idea was to shift the data by 1 4 of the record length and average the two resulting Allan variances 1 The next step was to wrap the data in a circular fashion and calculate the average of all the Allan variances at every basic measurement interval t 2 3 This technique is very effective in improving the confidence at long averaging factors but required end matching of the data A further improvement of the total variance concept was to extend the data by reflection first at one end of the record 4 and then at both ends 5 This latter technique called TOTAVAR gives a very significant confidence advantage at long averagin
26. ttti este pite etse EN EE E 7 Menu Tree Elle c 25 jurc M 27 TAUNOKIMG C 29 Command Line Options eerte rettet tette SAT 31 Automated Operation rri natalia 33 Copy COMMA e MP 35 lupra 37 io 39 Eog Fie 43 Special Versions m licitar AS 45 Configure Functioft ierit tidad 47 Configuration File TIME DOMAIN STABILITY Time Domain Stability PARU nto f o 57 Overlapping Allan Variance oai nere tereti roter e arae rr ds 59 Modified Allan Var ia 61 Tine Varane eS T t 63 STABLE32 USER MANUAL Total Allan Variance Total Modified Variance etm temario Ian tados asis 67 Hada Mardi 69 Overlapping Hadamard Variance eene 71 Total Hadamard Variance i iecit iret tiet ri dieere tee 73 Dynamic Stability cet od e d to de eee e ERR Te Rer 83 Confidence Interyalss RR NS RR REESE 85 Bias Functions iaee t 91 Dead Time lee otii inii et EROR TE rts E TET 95 3 Corniered nia 93 Autocorrelation e dol 99 FREQUENCY DOMAIN STABILITY Frequency Domain Stability seen 101 Noise Processes oon 107 DOMAIN COnVErSi viii ia RIED SERO IGI RYE NARI EE TESI 109 FILE FUNCTIONS File EUNGEONS 44 retention inestsecessasdedergaceetantobcectsqdeineseat ee 111 Filename
27. 00 993 0 13961e 01 1 4479e 01 1 5059e 01 8 8 0000e 00 985 0 11 0060e 01 1 0570e 01 1 1158e 01 16 18000801 989 0 57798e 02 6 1915e 02 6 7057e 02 32 3 2000e 01 937 0 43715e 02 4 8082e 02 5 4088e 02 Copy 64 6 4000e 01 873 0 31771e 02 3 6237e 02 4 3338e 02 Pane 128 1 2800e 02 745 0 2 3073e 02 2 7674e 02 3 69118 02 Options Lines Notes Help C Decade Octave T NoDrit Freq Drift Day 5 608146e 01 Dead Time roo Press Calc to calculate F 1of2 T Tau selected variance type All Tau e Controls The Run dialog box contains the following controls Control Type Description Variance Type Combo Choose variance type Alpha Combo Choose automatic or selected alpha value Conf Factor Edit Enter desired confidence factor Results Group Text Display results of stability run Drift Day Text Display linear frequency drift Plot Pushbutton Plot stability results Copy Pushbutton Copy analysis results to clipboard Options Pushbutton Open Run Options dialog box Lines Pushbutton Open Run Lines dialog box Notes Pushbutton Open Run Notes dialog box Print Pushbutton Print stability results No Drift Checkbox Remove linear frequency drift from data lof2 Checkbox Scale results forlof 2 identical units T Tau Edit Enter dead time ratio Decade Radiobutton Use decade tau increments Octave Radiobutton Use octave tau increments All Tau Radiobutton Use all tau increments Calc 1 Pushbutton Calc
28. 1 69e 01 o 1 83e 01 a 2 49e 01 o 3 43e 01 3 82e 01 icc 6 32e 01 F E 1 03e 00 1 38e 00 b ee EER 109 2 10 2 10 2 103 Averaging Time t Seconds 229 STABLE32 USER MANUAL 230 ANALYSIS FUNCTIONS Run Notes Function e Purpose Use the Run Notes function to add annotations to a stability plot Run Plot Notes E Note fi y Up Point Size e OK Down Iv Border M Opaque E Text Cance Note 1 um Clear All ig Position Notes 1 x 0 00000e 00 NE 0 00000e 00 m FT e Controls The Run Notes dialog box contains the following controls Control Type Description Note Edit Enter the of the note to edit Up Pushbutton Increment the note f Down Pushbutton Decrement the note Point Size Edit Enter the point size for the note Text Edit Enter the text of the note Position Group Note position values X Edit Enter the x position of the note Y Edit Enter the y position of the note Notes Text notes entered Border Checkbox Draw a border around the note Opaque Checkbox Hide grid in note area Clear All Pushbutton Clear all notes Read Pushbutton Read line information from INI file Save Pushbutton Save line information in INI file OK Pushbutton Accept the settings amp close dialog box Cancel Pushbutton Abort the changes amp close dialog box Help Pushbutton Invoke the Run Notes help topic Operation Enter the desired plot annotations an
29. 14 21 54 19 2005 10 17 15 46 20 Meas Info measurement Details Reset C UTC C MJD r Read Times Tau sec Read UTC MJD Meas Start 2005 10 14 22 41 58 53657 345810 Tau ETS um clocks choose their End Both Runs Continuing AE ep records and press 6 i ance Read to extract data Real hi from MMS database Tau Help Span 83d Gh 59m 42s 72071 82 e Controls The Database function main dialog box contains the following controls Dialog Box ALT Accel Control Control Control Key Key Type Description Reference Group Box Reference clock info Clock Name C Combo Shows list of clocks Description Text Shows description of selected reference clock Measurement Group Box Measurement clock info Clock Name N Combo Shows list of clocks Description Text Show description of selected measurement clock Records Group Box Clock measurement records Reference Data Table List of ref clock records Measurement Data Table List of meas clock records Meas Info Text Information about measurement record Details D Pushbutton Open Details box with database info Reset R Pushbutton Reset clock amp record lists UTC U Radio button Show date time as timestamp MJD M Radio button Show date time as MJD 133 STABLE32 USER MANUAL Read Times Group Box Start amp stop times of data to be read Start UTC S Edit Read start date time or message Start MJD Edit Read start M
30. 2 CAStab e321AUTO DAT Path csteb le 32A e Controls The Filenames dialog box contains the following controls Control Type Plot Filenames Group Box Phase Edit Freq Edit Sigma Edit Histo Edit Spectrum Edit ACF 1 Edit DAVAR Edit Data Filenames Group Box Phase Edit Freq Edit Stability Edit PSD Edit ACF 2 Edit Path Edit OK Pushbutton Set Pushbutton Reset Pushbutton Description Controls to set plot filenames Enter phase plot filename Enter frequency plot filename Enter sigma plot filename Enter histogram plot filename Enter power spectrum plot filename Enter autocorrelation plot filename Enter dynamic stability plot filename Controls to set data filenames Enter phase data filename Enter frequency data filename Enter stability data filename Enter power spectrum data filename Enter autocorrelation data filename Enter the filename path Apply filenames amp close Set all filenames to new path Reset all filenames to default path 113 STABLE32 USER MANUAL Cancel Pushbutton Abort Filenames function amp close Help Pushbutton Invoke the Filenames help topic e Operation Enter the path for the filenames and press the Set button Then enter the individual plot and data filenames Press OK to apply the new filenames Reset to use the default path or Cancel to restore the original filenames e Note A valid filename cannot be blank or contain the characters 1 lt gt
31. 67 T The N sample or standard variance is not recommended as a general purpose measure of frequency stability because it is not convergent for some types of noise commonly found in frequency sources It is used primarily in the calculation of the B1 ratio for noise recognition Allan Variance 0 T The Allan variance is given by o 1 A p t where t averaging time seconds It is the most common measure of the fluctuations of the fractional frequency y t v t vo vo Av vo x t It may be calculated by the non overlapping or overlapping method Modified Allan Variance Mod 0 T The modified Allan variance employs phase averaging and is given by Mod 0 t B u t where u a 1 Total Allan Variance O ota T The total Allan variance is similar to the Allan variance but uses a doubly reflected method that improves its statistical confidence at large averaging factors Total Modified Allan Variance Mod 67 ota1 The total modified Allan variance is similar to the modified Allan variance but uses an uninverted even reflection method that improves its statistical confidence at large averaging factors Time Variance 0 T The time variance is based on the modified Allan variance It has units of seconds is given by 62 7 C t 17 3 Mod o x sec where n B 1 Total Time Variance O 1 The total time variance in units of seconds is given by 02 1 C n T 12 3 Mod o totai t sec where
32. Allan variance with dead time ratio r T t to the 2 sample Allan variance without dead time r 1 B2 r 4 o Q T T o 2 T x e B3 Bias Function The B3 bias function is the ratio of the N sample standard variance with dead time ratio r T t at multiples M t t of the basic averaging time t to the N sample variance with the same dead time ratio at averaging time t B3 N M r 1 o N M T 1 N T 1 e R n Function The R n function is the ratio of the modified Allan variance to the normal Allan variance for n phase data points Note R n is also a function of a the exponent of the power law noise type R n Mod 0 1 027 e TOTVAR Bias Function The TOTVAR statistic is an unbiased estimator of the Allan variance for white and flicker PM noise and for white FM noise For flicker and random walk FM noise TOTVAR is biased low as t becomes significant compared with the record length The ratio of the expected value of TOTVAR to AVAR is given by the expression B TOTAL l a vT 0 lt rt lt T 2 where a 1 3 In2 0 481 for flicker FM noise a 3 4 0 750 for random walk FM noise and T is the record length At the maximum allowable value of t T 2 TOTVAR is biased low by about 24 for RW FM noise 91 STABLE32 USER MANUAL The Stable32 program applies this bias function automatically to correct the reported TOTVAR result e TOTMVAR Bias Function The TOTMVAR statistic is a biased
33. Allan Variance o 1 Based on square of 1st differences of fractional frequency deviation values Modified Allan Variance Mod o t Based on square of 2nd differences of averaged phase deviation values Total Allan Variance O viai T Based on square of 1st differences of fractional frequency deviations of an extended data set Total Modified Variance Mod Based on square of 2nd differences of averaged O tiat phase deviations of an extended data set Time Variance 07 7 Equal to t 3 Mod Allan variance Total Time Variance Total version of time variance Hadamard Variance Ho t Based on square of 2nd differences of fractional frequency values Total Hadamard Variance Ho y t Total version of Hadamard variance Theoretical Variance 1 Theol Allan estimator for large avg factor Bias Removed Th ol Th oBR Same expected value as Allan variance Allan amp Th ol Hybrid Th oH Combined Allan and Th oBR RMS Time Interval Error TIE rms RMS value of time deviations Max Time Interval Error MTIE Max time deviation within window e Allan Variances The most common time domain stability measure is the Allan variance AVAR o x which gives a value for the fractional frequency fluctuations as a function of averaging time t The other common time domain statistics are the modified Allan variance MVAR Mod o t and the time variance o x The modified Allan variance is better able to distinguish between white and flicker phase noi
34. Frequency Control Vol 2 Edited by E A Gerber and A Ballato Academic Press New York 1985 ISBN 0 12 280602 6 P Tavella and A Premoli Characterization of Frequency Standard Instability by Estimation of their Covariance Matrix Proceedings of the 23rd Annual Precise Time and Time Interval PTTI Applications and Planning Meeting December 1991 pp 265 276 J A Barnes The Analysis of Frequency and Time Data Austron Inc May 1992 P Tavella and A Premoli A Revisited Tree Cornered Hat Method for Estimating Frequency Standard Instability JEEE Transactions on Instrumentation and Measurement IM 42 February 1993 pp 7 13 P Tavella and A Premoli Estimation of Instabilities of N Clocks by Measuring Differences of their Readings Metrologia Vol 30 No 5 1993 pp 479 486 F Torcaso C R Ekstrom E A Burt and D N Matsakis Estimating Frequency Stability and Cross Correlations Proceedings of the 30th Annual Precise Time and Time Interval PTTI Systems and Applications Meeting December 1998 pp 69 82 C Audoin and B Guinot The Measurement of Time Cambridge University Press ISBN 0 521 00397 0 2001 Section 5 2 8 C Ekstrom and P Koppang Three Cornered Hats and Degrees of Freedom Proceedings of the 33rd Annual Precise Time and Time Interval PTTI Systems and Applications Meeting November 2001 pp 425 430 C R Ekstrom and P A Koppang Error Bars for Three Cornered Hats JEEE Trans UFFC Vol 53
35. Greek letters etc to data plot titles subtitles and labels e Time Scales The X Axis Label control offers several choices for the data plot x axis time scale as shown in the following table X Axis Label Units Remarks Data Point Data point Data Point x1000 Data point 1000 Time Seconds Seconds Tau Time Minutes Minutes Tau 60 Time Hours Hours Tau 3600 Time Days Days Tau 86400 Time Weeks Weeks Tau 604800 DOY Days Same as days if no timetags DOY with year if timetags MJD Days Same as days if no timetags MJD coarse MJD if timetags Timetag Point Regularized data point Selecting the x axis label automatically sets the x axis offset and multiplier If there are timetags they are automatically used to annotate the year and MJD The units for the x axis offset are those of the data points The x axis start and end controls may be used to select a portion of the data for plotting The Timetag Point option is available only for data with associated timetags It offers a preview of how the data will look if regularized to show gaps indicated by the timetags The Timetag Point x axis scale automatically changes to the x1000 mode as necessary The plot lines are not available for this option but the fit lines may be used Use the Regularize function to prepare the data for further analysis e Curve Fits The Options Type control offers several choices for curve fits as shown in the following table The Fit checkbox c
36. Keyword Host Database User Password e Auto APPENDICES Description Host ID address Database name User name Password Default 1 tsc postgres tsc tsc encrypted The Auto sections where 1 3 of the STABLE32 INI file can contain the following parameters that define the three automation scripts Keyword FileOpen Convert Outliers Average Drift PhaseDataPlot FreqDataPlot Run StabPlot StabTable Close DataPlot DataPrint PrintOriginal PrintCorrected PrintSelected PrintAveraged PrintResidual RunPlot Part Delay Script PhaseVariance FreqVariance Filename PhaseDriftType FreqDriftType AvgFactor DataType AnalysisType SigmaFactor DelayTime Start End Description Flag to open data file Flag to convert data type Flag to remove outliers Flag to average data Flag to remove drift Flag to plot phase data Flag to plot frequency data Flag to run stability analysis Flag to print stability plot Flag to print stability table Flag to close Auto dialog box Flag to plot data Flag to print data Flag to print original data Flag to print corrected data Flag to print selected data Flag to print averaged data Flag to print residual data Flag to plot stability Flag to use part of data Flag to add extra delay Script name Variance type for phase data Variance type for freq data Data filename to open Drift fit type for phase data Drift fit type for freq data Averaging factor Data t
37. Line type 0 5 0 None X axis start point X axis end point Y axis start point Y axis end point Line slope 0 5 Default 0 0 0 0 0 0 0 0 0 0 295 STABLE32 USER MANUAL e PhaseLines The PhaseLines section of the STABLE32 INI file can contain the following parameters the items are repeated for each line as indicated by the index 1 i 1 to 12 Keyword Description Default Type i Line type 0 5 0 None 0 X Start 1 X axis start point 0 0 X End i X axis end point 0 0 Y Start i Y axis start point 0 0 Y End i Y axis end point 0 0 Slopeli Line slope 0 5 0 e SigmaLines The SigmaLines section of the STABLE32 INI file can contain the following parameters the items are repeated for each line as indicated by the index i i 1 to 12 Keyword Description Default Typeli Line type 0 5 0 None 0 X Start 1 X axis start point 0 0 X End i X axis end point 0 0 Y Start i Y axis start point 0 0 Y End i Y axis end point 0 0 Slope 1 Line slope 0 5 0 MaskFile i Mask filename Null e FreqNotes The FreqNotes section of the STABLE32 INI file can contain the following parameters the items are repeated for each note as indicated by the index 1 i 1 to 8 Keyword Description Default Size i Font point size 8 Border i Border flag 0 X Position i X axis position 0 0 Y Position i Y axis position 0 0 Text 1 Note text Null e PhaseNotes The PhaseNotes section of the STABLE32 INI fi
38. M Opaque Text 7 Help Clear All d Position Notes 0 x 0 000006 00 Se 0 00000e 00 Read Save e Controls The Plot Annotations dialog box contains the following controls Control Type Description Note Edit Enter the of the note to edit Up Pushbutton Increment the note Down Pushbutton Decrement the note Point Size Edit Enter the point size for the note Text Edit Enter the text of the note Position Group Note position values X Edit Enter the x position of the note Y Edit Enter the y position of the note Notes Text notes entered Border Checkbox Draw a border around the note Opaque Checkbox Hide grid in note area Clear All Pushbutton Clear all notes Read Pushbutton Read line information from INI file Save Pushbutton Save line information in INI file OK Pushbutton Accept the settings amp close dialog box Cancel Pushbutton Abort the changes amp close dialog box Help Pushbutton Invoke the Plot Notes help topic e Operation Enter the desired plot annotations and press OK to accept them or Cancel to abort Select the Border and Opaque options as desired Press Clear All to clear all annotations or use the Read and Save buttons to retrieve and store note information The X and Y positions are in user units that are the same as the plot scales 209 STABLE32 USER MANUAL 210 ANALYSIS FUNCTIONS Timetags Function e Purpose Use the Timetags functi
39. Reset All Table Position Top Right Stability File CAProgram Files DevStudio Append Axis Y Axis Label Averaging Time EtE Secon Label Overlapping Allan Deviatio TauMax 1 28000e 02 Sigma Max 2 92198e 01 Scale Max 1 00000e 03 Scale Max 1 00000e 00 Tau Min 1 00000e 00 Sigma Min 2 76603e 02 Scale Min fi 00000e 00 Scale Min fi 00000e 02 Options v Date V Box1 V Bars2 v Table 3 4 F4 Wide PlotFile CxProgram Files DevSt e Controls The Run Options dialog box contains the following controls Control Type Description Title Edit Enter plot title Sub Title Edit Enter plot subtitle Message Edit Enter plot message Msg Position Combo Choose message position Table Position Combo Choose table position X Axis Group X Axis parameters Label Edit Enter x axis label Tau Max Text Display maximum tau value Scale Max Edit Enter x axis scale maximum Tau Min Text Display minimum tau value Scale Min Edit Enter x axis scale minimum Y Axis Group Y Axis parameters Label Edit Enter y axis label Sigma Max Text Display maximum sigma value Scale Max Edit Enter y axis scale maximum Sigma Min Text Display minimum sigma value Scale Min Edit Enter y axis scale minimum Options Group Plot options Date Checkbox Show date on plot Box 1 Checkbox Draw box around plot Bars 2 Checkbox Show error bars on plot Table 3 Checkbox Show stability table on plot 22
40. S f one sided power spectral density of the fractional frequency fluctuations 1 Hz f Fourier or sideband frequency Hz h a intensity coefficient a exponent of the power law noise process The most commonly encountered noise spectra are White Random Walk f Flicker f Flicker Walk f For examples showing the appearance of these noise types use the Play program to display the file NOISEPIX TKF Power law spectral models can be applied to both phase and frequency power spectral densities PSD Phase is the time integral of frequency so the relationship between them is as 1 f S f S f 2nfy where S f PSD of the time fluctuations sec Hz Two other quantities are also commonly used to measure phase noise SoA PSD of the phase fluctuations rad Hz and its logarithmic equivalent f dBc Hz The relationship between these is Sy Cavo S f f 10 logis S O where vo is the carrier frequency Hz The power law exponent of the phase noise power spectral densities is B a 2 These frequency domain power law exponents are also related to the slopes of the following time domain stability measures Allan variance o T u a l a lt 2 Modified Allan variance Mod 0 t p a l a lt 3 Time variance o x n a l a lt 3 107 STABLE32 USER MANUAL e Phase Noise Diagram The following diagram shows the slope of the SSB phase noise f dBc Hz versus log f Fourier freque
41. Stable32 identical in all respects to the standard version may be available for a free 30 day evaluation period Please contact Hamilton Technical Services for further information 45 46 STABLE32 USER MANUAL GENERAL Configure Function e Purpose Use the Configure function to set certain options of the Stable32 program These options are stored in the STABLE32 INI configuration file The Configure function has six property sheet pages as shown and described below e Property Sheet Controls The main Configure property sheet contains the following controls Control Type Description OK Pushbutton Accept the configuration changes amp close dialog box Cancel Pushbutton Abort the Configure function amp close dialog box Help Pushbutton Invoke the Configure help topic configure E General Tootbuttons Plots Data Inputs Options butions Plots Data Inputs Options r General Settings v Write Sigma File v AutoCalc M Autoinc Filename Ext V AutoPlot Y Show Eile Opened 7 Show Status Plots No Greek Plot Labels v Show Splash Screen Text Editor Notepad Notepad exe Select the toolbuttons you 541 prefer The number shown will depend on the width of your screen X Select general Stable32 settings All are recommended except No Greek Plot Labels AutoCalc and AutoPlot are optional Page 1 General Page 2 Toolbuttons e General Page Controls The
42. Trans UFFC Vol 52 No 8 August 2005 T N Tassert D A Howe and D B Percival Th ol Confidence Intervals Unpublished paper 2004 T N Tasset Th oH Unpublished private communication July 2004 TIME DOMAIN STABILITY Dead Time e Dead Time Dead time can occur in frequency measurements because of instrumentation delay between successive measurements or because of a deliberate wait between measurements It can have a significant effect on the results of a stability analysis especially for the case of large dead time e g frequency data taken for 100 seconds once per hour Stable32 includes provisions for making dead time corrections in the Sigma and Run functions for normal and overlapping Allan deviations where the noise type is known These corrections use the B2 and B3 bias functions to handle single and multiple distributed measurement dead time respectively The dead time is entered as the ratio r T t where t is the measurement time and T is the longer time between measurements r 1 for no dead time Measurement Dead Measurement Dead Time Time Time Time The corrections are applied by dividing the calculated sigma by the square root of the product of B2 and B3 These corrections are particularly important for non white FM noise with a large dead time ratio Restricting the dead time corrections to Allan deviations is a conservative approach based on the B2 and B3 definitions These bias functions depend critical
43. a del ak gea Clear Timetags Command Line Options Commas Instead of Decimal Points 16 Confidence Intervals smoren naiean een tete reet eee eher po e epe epa tepida exe gute reete ev eee eques 85 Configuration File E Configure Function Convert Function oooocococccononononononcnoncnononncononn nono nonnnn neon nn ennt tnen teens nn neon rre nor ran nt tette terrent enne nntn nen Copy to ChpbOdId oo cette ii Data ATTAYS M NN T STABLE32 USER MANUAL Data Ford ibas 15 Data Plot Eunctions ii dis 201 Data Tabs Database Functions 23 3 ida dO per e rd Te dens 133 Day of Year DO Viminale 249 Dead Time Demo Version Dialog Boxes Directo x isse reco co e e co ia co o i D can cdas Domain Conyersions one hd rea oi n te oan reos ato awa ee teet ei Pee e doas e de 109 239 Domain Function Drift Functions cu SE d A SR ES Eee d ru E Edit Function coooccconoconnnononononoconoconnnonn nono nccnnnonnnono nono nn nonn nono nnnn nn no trennen entiers etes n rennen trennen 153 E Mail welll 2 Error Bars a nd a dH o So E AID t Metti e Sd E s 85 Example e m 267 F FAX cr A dy Gdvcdh Uo dabuas Saas boas te NGM anedon ase ees daveecas deeds dus teeh vets li 2 FOC AD ACK 255 555 C 277 Fil E nctl ns ti eo a ica PY E qe 111 File Opened as FAME ik Ea e AESA EAE AIEEE ANA TERA GOR Fill
44. by uninverted even reflection Next the modified Allan variance is computed for these 9m points Finally these steps are repeated for each of the N 3m 1 subsequences calculating TOTMVAR as their overall average These steps are shown in the diagram below Phase Data x i 1 to N 3m gt N 3m 1 Subsequences ecco X eco i n to n 3m 1 Linear Trend Removed x X x C c freq offset 9m gt Extended Subseguence 0 4 0 o 4 0 0 3 Xu 7 Xia X Xeamsa T Kn 3ma 1 lt 1 lt 3m Uninverted Even Reflection ecco Lg ee 9 m Point Averages 6m 2nd Differences L1 LE mod oy 1 1 27 z m where Calculate Mod c KO for Subsequence B z m x m 2X sm m x 5 m Computationally the TOTMVAR process requires 3 nested loops e An outer summation over the N 3m 1 subsequences The 3m point subsequence is formed its linear trend is removed and it is extended at both ends by uninverted even reflection to 9m points 67 STABLE32 USER MANUAL e An inner summation over the 6m unique groups of m point averages from which all possible fully overlapping 2 differences are used to calculate MVAR e A loop within the inner summation to sum the phase averages for 3 sets of m points The final step is to scale the result according to the sampling period to averaging factor m and number of points N Overall t
45. center group box The Kn value is used to determine the confidence limits for the nno overlapping sigma Chi squared statistics are used for the overlapping modified time and total sigmas and the X value is displayed A bias correction is applied automatically as needed to the total sigma and Th ol value Activating the Set Noise checkbox opens a Noise combo box that allows selection of a particular noise type or the r1 and Alpha lag 1 ACF noise ID parameters are shown and may be Appl y ied to determine the noise type 183 STABLE32 USER MANUAL e Allan Variance The non overlapping Allan variance function calculates the original o t and the standard deviation and uses their ratio to estimate the noise type and the confidence interval of the Allan deviation e Overlapping Allan Variance The overlapping Allan variance function also calculates and displays o t using fully overlapping samples It also estimates the noise type and uses that to determine the of degrees of freedom It then establishes single or double sided confidence intervals for the Allan deviation based on a certain confidence factor e Modified Allan Variance The modified Allan variance function requests the averaging factor and bandwidth factor for the measuring system BW 2nf to where fh is the upper cutoff frequency in Hz It then calculates o t and Mod o t and uses their ratio to estimate the noise type This function then continues with the deter
46. conversions may be made for power law noise models by using the following conversion formulae Noise Type o y t Sq RW FM Af Sif t Ad ot f FFM B f S 1 B mt W FM Cf sua Ci af F PM D ETSA r Dos oS f WPM E f Sy f E 7 041 f where A 47 6 B 2 1n2 C 12 D 1 038 3 In 2nf to dn E 3f 412 and f is the upper cutoff frequency of the measuring system in Hz and tp is the basic measurement time The fj factor applies only to white and flicker PM noise 109 STABLE32 USER MANUAL 110 FILE FUNCTIONS File Functions e Purpose Stable32 offers several functions for setting opening adding saving and reading data files The Open function applies to phase frequency and archive data files the Add and Save functions apply to phase and frequency data files and the Read function is used to read a stability file e Controls The Stable32 Open Add and Save file functions use the standard Windows file open and save dialog boxes except that the Open and Add dialog boxes contain the following additional controls Control Type Description Data Type Group Select data type Phase Radiobutton Use phase data array Frequency Radiobutton Use frequency data array The Open function also has a radiobutton to select archive data and an edit control to set the averaging factor to be used when reading the data The Save function has a checkbox to save timetags along with the phase or frequen
47. data file header tau entry 3 a STABLE32 INI Inputs value 4 the first timetag interval and 5 the default 1 0 125 STABLE32 USER MANUAL e Data Scaling The data scaling option uses phase or frequency data addend and multiplier values from the Inputs section of the STABLE32 INI configuration file Those values can be entered manually by editing the configuration file with a text editor such as Notepad or by pressing the Inputs button They default to 0 and 1 respectively and in that case the scaling option is disabled e Timetag Scaling The timetag scaling option uses the tag scale and tag offset values from the Inputs section of the STABLE32 INI configuration file Those values can be entered manually by editing the configuration file with a text editor such as Notepad or by pressing the Inputs button They default to 1 and 0 respectively Timetag scaling is done as the data file is read 126 FILE FUNCTIONS Inputs e Purpose Use the Inputs function to set the tau data addend and multiplier values and the timetag offset and scale factors for the current data type e Controls The Inputs dialog box contains the following controls Tau 0000000000000e 00 Addend 0 0000000000000e 00 Beneal Multiplier 0000000000000e 00 EE Tag Scale 8 6400000000000e 04 Tag offsetis applied as file Tag Offset 0 0000000000000e 00 dal Press OK to setvalues stored in Inputs section of Stable32 ini configur
48. data for analysis This can also be done by moving between the tabs with the left or right arrow keys or using the Home and End keys move between the first and last tabs respectively and pressing the spacebar To select a tab without loading its data press the CTRL key while clicking the tab The only significant disadvantage of the data tabs is that they require allocated memory to hold their data and this can take a significant amount of RAM for many tabs with large data sets 13 STABLE32 USER MANUAL e Tab Toolbutton The Tab toolbutton can be used to activate the data tabs and store the current data to a new tab 14 GENERAL Data Format e Data Format Stable32 data files are comprised of essentially any number 513 in Student Version of lines of numeric data in ASCII format with each line terminated by a carriage return line feed Such a file can be read and edited with Windows Notepad The data may be in integer floating point or exponential format Each line can have 1 or more space or comma delimited columns and up to 8 columns can be processed A value of zero is treated as a gap in the data Stable32 reads processes and stores data in double precision 15 digit floating point format The Stable32 file reading routine is quite robust It will read an input file with any number of columns and will allow selection from up to 8 columns of data Additional columns are simply ignored One or more spaces or commas must
49. data points with a value of zero except the 1st and last points of phase data The Previous and Next Gaps and Outliers can be found using the Find controls More elaborate searching is supported by the Find and Replace functions of the Detailed Search controls Simple editing can be done with the usual editing keys directly in the data display including changing adding and deleting data No adjustments are made in the timetags when data is added or deleted and the timetag column is not editable Insertion or Deletion of a certain of points is facilitated by the Edit After Highlighted Point controls The editing changes can be accepted with the OK button or aborted by pressing Cancel e Navigation A cell may be selected with a mouse click the scroll bars or the arrow keys A cell may also be selected by using one of the Go To Find or Search functions If status bar plots are enabled the corresponding plot is dynamically updated during editing and a small cursor appears above the plot to indicate the position of the currently selected point e Editing Data A new value can be entered directly into the selected cell with the numeric keys The existing data may be edited by first pressing the F2 key It is necessary to delete a portion of the existing data to make room for the new entries The usual editing keys apply The original value may be restored with the Esc key and the changes are accepted with the Enter key e Caution Ed
50. entren tren testen Es 61 Modified Julian Date MJD 249 250 Modified Total Variance 67 MTIE uestis 79 M ulticolumn Data adi ii ia init 121 Multiple Stability Plots iie iei eree etse neo eo teie tn Fel ed san eaae eben ohver ed 142 N Noise FUNGUON os deklarant lehmakell teet detiene e EP ERATES 213 Noise Identifica vn dc SEE 86 Nos Bi id iodo RIA PEENS 228 NOISE pecado tv ie DT dede UDIN MD MESE 107 Non Numeric Characters cccccccccssccessecssecssecessceeseecssecsseceeeeeeseecsseceseceeseeessecseeeeeseeseeesseeseeeees 15 STABLE32 USER MANUAL Normalize B netion airi abad 163 Notepad caca di a ees 251 One of Two Scaling oocooonccnccnononononononnconocnnonononnconoonnon nono nnnn enne ennt nre nennen nennen enne enne 221 Open Function Outliers eee Overlapping Allan Variance sese enne nennen tnnt en rennen 59 Overlapping Hadamard Variance cocooccocnicnonicnnononnnnnoncnnnonononononnon nono eene ennemi ener 71 PO A ls visa Part Function Phase Noise Diagram Picinbono Variance ES EN A RO Play um M Plot Annotatiotis a idas Plot PUM Ct OM oue cisco tiec er A Ad cie Plot Inserts Plot Lines Plot Options Power Function Power Law NOISE si 5 55 A ees ce aree cos ustonnd dad s siseastesescovagsiocesueusveak oe sis canlesoeedaaes Power Spectral Density PSD s
51. estimator of the modified Allan variance The TOTMVAR bias factor the ratio of the expected value of TOTMVAR to MVAR depends on the noise type but is essentially independent of the averaging factor and of data points as shown in the following table Noise Bias Factor Note The Stable32 program applies this bias WPM 1 06 factor automatically to correct the reported F PM 1 17 TOTMVAR result W FM 1 27 F FM 1 30 RWFM 131 e Th o1 Bias See the Th ol section of this User Manual for a discussion of the Th ol bias e Summary of Stable32 EDF and Bias Functions The following table summarizes the use of the equivalent degrees of freedom confidence intervals and bias corrections in the variance calculations of the Stable32 Sigma and Run functions 92 TIME DOMAIN STABILITY Stable32 Noise ID EDF CI Bias Methods Variance Noise ID EDF Calc CWError Bars Bias Calc Type Method Allan Lag 1 ACF N A o N and K N A AVAR B1 ratio Can t set CI Overlapping Lag 1 ACF CDF 1 x N A Allan B1 ratio AVAR Modified Lag 1 ACF HEDF 2 11 x N A Allan B1 plus w modified MVAR R n for a arguments 1 2 Time Lag 1 ACF HEDF 2 11 x N A TVAR B1 plus w modified R n for a arguments 1 2 Hadamard Lag 1 ACF N A Sigma None N A HVAR Run o VN and K Can t set CI Overlapping Lag 1 ACF HEDF 3 X N A Hadamard B1 ratio HVAR Total Allan Lag 1 ACF TOTEDF 4 X TOTVAR TOTAVAR
52. for Approximating Confidence on the Modified Allan Variance and the Time Variance Proc 28th PTTI Meeting pp 215 224 Dec 1996 F Vernotte and M Vincent Estimation of the Uncertainty of a Mean Frequency Measurement Proc 1 1th European Freq and Time Forum pp 553 556 March 1997 D A Howe Methods of Improving the Estimation of Long Term Frequency Variance Proc 11th European Freq and Time Forum pp 91 99 March 1997 W J Riley Confidence Intervals and Bias Corrections for the Stable32 Variance Functions Hamilton Technical Services 2000 C Greenhall and W Riley Uncertainty of Stability Variances Based on Finite Differences Proc 35th PTTI Meeting Dec 2003 T N Tasset D A Howe and D B Percival Th ol Confidence Intervals Proc 2004 Joint FCS UFFC Meeting pp 725 728 Aug 2004 Drift Estimation and Removal C A Greenhall Removal of Drift from Frequency Stability Measurements Telecommunications and Data Acquisition Progress Report 42 65 July Aug 1981 Jet Propulsion Laboratory Pasadena CA pp 127 132 1981 J A Barnes The Measurement of Linear Frequency Drift in Oscillators Proc 15th PTTI Meeting pp 551 582 Dec 1983 M A Weiss D W Allan and D A Howe Confidence on the Second Difference Estimation of Frequency Drift Proc 1992 Freq Contrl Symp pp 300 305 June 1992 M A Weiss and C Hackman Confidence on the Three Point Estimator of Frequency Drift Proc 24th PTTI Me
53. frequency source itself Stable32 includes provisions for handling gaps in phase or frequency data and for finding and removing outliers by replacing them with gaps see the Data Format and Check Function help topics for more details It can accept timetags along with the data and use them in the Regularize function to add gaps as placeholders for missing data The corrected and regularized data can then be analyzed e Gap Handling Stable32 supports four basic methods for handling gaps as described in the table below Stable32 Gap Handling Methods Description Use the Edit function or another text editor to omit gaps from the data Omit This eliminates the gaps but also changes the time sequence of the data It is best suited to removing a few isolated gaps Use the Part function to exclude gaps from the beginning or end of the Exclude data or use the analysis limits to exclude the gaps from the analysis This eliminates the gaps but also shortens the record It is best suited to removing gaps near the start or end of the record i Gaps are automatically skipped by some variance functions P see table below This is the preferred method where applicable Use the Fill function to fill gaps with interpolated values Gaps are automatically filled by some variance functions see table below This method is satisfactory as long as there are fewer than about 5 gaps in the record see Reference 1 Fill The Stable
54. in 1980 When the IBM PC was introduced in 1981 a DOS version of Stable was written for it in 1982 The name besides its obvious implications for frequency stability came from the name of a bar in Nashua NH Its initial application was to support the development of rubidium clocks for the GPS navigation satellites Stable was ported to Microsoft Windows as Stable Win in 1992 and then to its current Stable32 form in 1997 when Windows evolved to 32 bits e Acknowledgments The author wishes to acknowledge the contributions of many colleagues in the Time and Frequency community who have contributed the analytical tools that are so vital to this field Some of those persons are listed in the References help topic David W Allan has had a major impact on this field and has been a source of much inspiration and encouragement for the Stable programs The work of the late J A Barnes influenced the drift analysis and noise recognition techniques while that of C A Greenhall C Ekstrom and P Koppang has helped with the numerical methods and confidence limits T Walter has contributed particularly toward the noise simulation as has G Winkler toward outlier detection Credit also goes to M A Weiss for work regarding modified and time sigma and D A Howe for the new total variances and for contributing many beneficial suggestions toward this program More recently important work was done by D A Howe C A Greenhall F Vernotte and T K Peppler on impl
55. in the Case of White FM Proc 30th PTTI Meeting Dec 1998 S Bregni and S Maccabruni Fast Computation of Maximum Time Interval Error by Binary Decomposition JEEE Trans I amp M Vol 49 No 6 pp 1240 1244 Dec 2000 10 11 OTHER INFORMATION Dynamic Stability L Galleani and P Tavella The Characterization of Clock Behavior with the Dynamic Allan Variance Proc 2003 Joint FCS EFTF Meeting pp 239 244 L Galleani and P Tavella Tracking Nonstationarities in Clock Noises Using the Dynamic Allan Variance Proc 2005 Joint FCS PTTI Meeting Confidence Intervals P Lesage and C Audoin Characterization of Frequency Stability Uncertainty due to the Finite Number of Measurements JEEE Trans Instrum Meas Vol 22 No 2 pp 157 161 June 1973 P Lesage and C Audoin Estimation of the Two Sample Variance with a Limited Number of Data Proc 31st Freq Contrl Symp pp 311 318 June 1977 K Yoshimura Degrees of Freedom of the Estimate of the Two Sample Variance in the Continuous Sampling Method IEEE Trans Instrum Meas Vol 38 No 6 pp 1044 1049 Dec 1989 C A Greenhall Recipes for Degrees of Freedom of Frequency Stability Estimators IEEE Trans Instrum Meas Vol 40 No 6 pp 994 999 Dec 1991 M A Weiss and C Hackman Confidence on the Three Point Estimator of Frequency Drift Proc 24th PTTI Meeting pp 451 460 Dec 1992 M A Weiss and C A Greenhall A Simple Algorithm
56. log or diffusion drift type is selected for frequency data The averaging factor for these fit calculations can be set larger than the normal value of to provide a better fit in the presence of noise This is especially useful for large data sets having a short measurement interval where both the short term noise and drift are high compared with the flicker floor In that case an averaging factor sufficient to show the drift is suggested perhaps up to VN where N is the of data points A larger averaging factor also speeds up the iterative fit calculation 178 ANALYSIS FUNCTIONS Phase Data Three drift methods are available to analyze frequency drift in phase data 1 The first is a least sguares guadratic fit to the phase data x t a bt ct where y t x t b 2ct slope y t 2c This method is optimum for white PM noise It is the default and is also the method used for drift analysis when plotting phase data The second method is the average of the 2nd differences of the phase data y t x t t x t t slope y t t y t t t 21 2x t t x t 1 This method is optimum for random walk FM noise The third method uses the 3 points at the start middle and end of the phase data slope 4 x end 2x mid x start Mt where M data points It is the equivalent of the bisection method for frequency data Frequency offset may be calculated in phase data by either of three m
57. not displayed in the timetag and data column fields of that dialog box e Data Entry Data entry is generally done within edit controls in dialog boxes A default entry is usually presented and it generally represents an acceptable choice or a way to abort the current function The usual Windows editing keys apply e Gaps amp Outliers Stable32 includes provisions for handling gaps and outliers that often occur in time and frequency stability data A value of zero 0 is treated as a gap in a Stable32 data file unless it is the first or last point of phase data Stable32 data files are simple vectors of equally spaced phase seconds or fractional frequency dimensionless values Gaps should be included to maintain the proper implied time interval between measurements The Stable32 analysis functions will then produce meaningful results for data having gaps The analysis functions simply skip those points that involve a gap For example in the calculation of the Allan variance for frequency data if either of the two points involved in the first difference is a gap that Allan variance point is skipped in the summation Stable32 also has provisions for filling gaps in phase or frequency data by replacing them with interpolated values Use the Fill function for this purpose Fill first removes any leading and trailing gaps It then uses the two values immediately before and after any interior gaps to determine linearly interpolated values withi
58. of simulated power law clock noise with the desired offset stability and drift It also has a function for the conversion between time and frequency domain measures of frequency stability e License A license is hereby granted to the purchaser for the use of this program Stable32 may be installed on any number of computers within the immediate user group that purchased it and backup copies may be made but only one copy of the program may be used at any time Additional copies may not be distributed to others This program has been extensively tested but it is never possible to declare a program completely bug free No warranty is made nor is any liability assumed in connection with the use of the program e Release Notes These notes describe the latest changes to the Stable32 program as of the version and date shown on the cover of this User Manual Please see the User Manual Supplement pages if any for more recent changes and the Readme txt file for a more complete revision history Please use the context sensitive help topics for more detailed information about new features Release 1 50 Version 3 0 of FrequenC Library HTML Help Enhanced dynamic stability function Weighted stability plot noise fit lines Tab toolbutton Error bars for Th ol and Th oH in Read function PSD plot auto AF and smoothing with semilog noise fit Avg factor selection for log and diffusion drift fits Configure property sheet pages PSD and Sigma pl
59. of the 1st line of the data file OK Pushbutton Perform the read operation amp close dialog boxes Cancel Pushbutton Abort the read function amp close dialog boxes Help Pushbutton Invoke Multicolumn Read help topic e Operation Select the desired column for the optional Timetags and Data and then press OK to read the data or Cancel to abort e Limits Up to 8 columns may be processed from the data file 121 STABLE32 USER MANUAL 122 FILE FUNCTIONS Large Data File e Purpose The Large Data File function supports the reading of large data files It is a sub function of the Open function Use the Large Data File function to select the desired option for handling a large data file This dialog box opens automatically during an Open operation whenever such a data file is detected The user then has the options of 1 averaging the data as it is read 2 using only the first portion of the data 3 using only the last portion of the data Large Data File x Data file is too big to load Choose one ofthe following options or press Cancel to abort Average Data As ltls Read C Use First Portion Of Data Points 27552 C Use Last Portion Of Data Avg Factor 4 e Controls The Large Data File dialog box contains the following controls Control Type Description Average Radiobutton Average the data as it is read First Radiobutton Use the first portion of the data Last Radiobutton Use the las
60. of the user s client area and copy it to the Windows clipboard for importing into another application The Edit menu s Copy Metafile command will make a metafile of the current plot and copy it to the Windows clipboard for importing into another application Note The Copy Metafile can be used only once after Stable32 is launched and a Copy Metafile not available message will appear thereafter Use the Convert Metafile function instead The Draw menu s Draw Next command is used to start the drawing of the next plot in the currently opened TKF file A return key from the keyboard will also generate a Draw Next command Note This does not apply to Stable32 plots The Draw menu s Redraw command is used to redraw the currently displayed TKF plot When the users Windows is enlarged the current plot will automatically be redrawn A space entered from the keyboard will generate a Redraw command and is a useful way to return to the original plot size after zooming in or out The Draw menu s Go To Plot command opens the Go To Plot dialog box to allow the user to input the number of the plot to draw in the currently open TKF file The user enters an integer number for the index of the plot and that plot in the TKF file is drawn in the Play window Only TKF files with an accompanying OFF file TKF offset file are enabled for specifying a particular plot to draw Note This does not apply to Stable32 plots The Draw menu s Zoom In command i
61. or 114 FILE FUNCTIONS Open Function e Purpose Use the Open function to read a phase or frequency data file from disk Open Data File xl Lookin Stable32 Jj et eke 122100 dat PHASENOHEAD DAT 523808 DAT J FREONOHEAD DAT EQPSD DAT Ex da Archive dat CQFREQTAG DAT ES Random Walk dat data8 dat gd GAP DAT gd SAMPLE DAT error dat Cd messages DAT Eg Sine dat Flicker dat CI NBS DAT Ef tour dat Flicker1 dat GA NEW DAT E TSC DATA DAT Flicker2 dat gd PHASE DAT CQTST_SUIT DAT n File name PHASEDAT Files of type Data Files day y Cancel Data Type Phase C Freq C Archive Avg By h Help e Controls The Open dialog box contains the standard Windows file open controls plus the following custom controls Control Type Description Data Type Group Box Controls to choose the data type Phase Radiobutton Read data into the phase array Frequency Radiobutton Read data into the frequency array Archive Radiobutton Read TSC archive file Avg By Edit Averaging factor to apply when reading data e Operation Select Phase Frequency or Archive data type and perform the usual file dialog box operations Opening a data file with multiple columns will invoke the Multicolumn Data function The data may be averaged as it is read by entering a non unity Avg By value Attempting to open an oversize data file as set by the Max Data File Size configuration parameter will invoke the Lar
62. plots are not affected by Statistics plot zooming and if set to the full range can serve as a guide to the overall data e Scrolling The usual horizontal scrolling operations apply Dragging the scroll box scrolls the plot Clicking on the L and R arrows or pressing the left up or right down arrow keys moves the plot one point in the corresponding direction Clicking on the L and R scrollbar shaft regions or pressing the page up or page down keys moves the plot one plot width in the corresponding direction Pressing the home or end keys moves the plot to the first or last point The scrollbar must have the input focus be blinking for the keyboard inputs to work During scrolling the point range is shown in the text box below the scrollbar e Plot Scale The plot is scaled to a standardized value at the top of the plot During scrolling the plot scale and or of divisions may change e Average A green horizontal line is drawn to show the average value of a frequency plot e Data and Timetag Readout Data point s and their corresponding values are shown in the text box below the plot when the mouse cursor is in the plot region Phase data is read at the points while freq data is read on the horizontal lines that show the averaging time Timetags can also be displayed for the selected data point in MJD DOY Date or general exponential formats e Data Type Switching Use the lt gt button to switch between equivalent phase and fr
63. points This presentation properly conveys the integral nature of the phase data Frequency data is plotted as a horizontal line between the frequency data points This shows the averaging time associated with the frequency measurement and mimics the analog record from a frequency counter As the density of the data points increases there is essentially no difference between the two plotting methods Missing data points are shown as gaps without lines connecting the adjacent points 274 OTHER INFORMATION e Variance Selection It is the user s responsibility to select an appropriate variance for the stability analysis The overlapping Allan variance is recommended in most cases especially where the frequency drift is small or has been removed The Allan variance is the most widely used time domain stability measure and the overlapping form provides better confidence than the original non overlapping version The total variances and Th ol can be used for even better confidence at large averaging factors at the expense of longer computation time The modified Allan variance is recommended to distinguish between white and flicker PM noise and again a total form of it is available for better confidence at long tau The time variance provides a good measure of the time dispersion of a clock due to noise while MTIE measures the peak time deviations TIE rms can also be used to assess clock performance but TVAR is generally preferred Finally th
64. removed will be displayed as the default message The original data is not affected The Fill control can be used to eliminate the filled histogram bars for better printouts Then press Plot to plot the histogram or Close to close the Histogram dialog box e Example An example of a histogram plot is shown below E GraphiC Win histo tkf File Edit Draw Convert Help Dole 02 77 30 Ime 701073 Dota Palms 1 thru 1007 af 001 auc HISTOGRAM phase dat Fhe ohose dol 150 E m a E amp 198 ANALYSIS FUNCTIONS Plot Function e Purpose Use the Plot function to control the plotting of the current phase or frequency data Plot Options Lines Notes Bm Spor Lines _Notes Heb EE e Controls The Plot dialog box contains the following controls Control Type Description Plot Pushbutton Plot the current phase or frequency data Options Pushbutton Select plot options Lines Pushbutton Add lines to the plot Notes Pushbutton Add notes to the plot Close Pushbutton Abort the Plot function amp close dialog box Help Pushbutton Invoke the Plot help topic e Operation Simply press the button for the desired plotting function e Auto Plot Plotting can be done automatically bypassing the Plot function dialog box by setting the AutoPlot item in the Configure function 199 STABLE32 USER MANUAL 200 ANALYSIS FUNCTIONS Data Plot Function e Purpose Use the Data Plot functio
65. row of data Use Comma as Decimal Point Use comma instead of decimal point for input data Warn for Zero Freq Data Display warning if two adjacent phase data points are equal 116 FILE FUNCTIONS Read Archive Function e Purpose Use the Read Archive function to extract clock data from a TSC archive file This function will read the information produced by a Timing Solutions Corporation now Symmetricom clock measuring system and convert it into time tagged phase and frequency data for analysis by the Stable32 program Controls are available for selecting the desired data file measurement channels and time span for analysis Read Archive XI File archive dat Tau 900 m Last MJD 51078 51041667 Display Channel Index Measurement E E Configure Reference E EER Time Span dii Record amp V Last C Start MJD 51 026 00000000 End MJD 51 078 51041667 e Controls The Read Archive dialog box contains the following controls Control Type Description File Text Archive filename Tau Text Measurement interval First MJD Text First MJD in archive file Last MJD Text Last MJD in archive file Channel Group Channel controls Measurement Edit Enter measurement channel Reference Edit Enter reference channel 0 LO reference Time Span Group Time span controls Record Radiobutton Select record time span Record Edit Enter record to read 117 STABLE32 USER MA
66. smart y axis data plot scales Flag to use lag 1 ACF noise ID method Left main window screen position Top main window screen position Right main window screen position 0 main window fills the desktop area Bottom main window screen position Type of data last opened Flag to scale input data Flag to write header in data file Avoid Greek characters in stability plot labels Flag to show welcome screen Flag for detailed check box Flag for detailed drift box Flag for detailed sigma box Flag for wide edit box Flag to normalize frequency during conversion Flag to transfer timetags during conversion Flag for many tau run Many tau parameter Flag to use timetags for tau Flag for weighted stability plot noise fit lines Flag to apply smoothing to PSD plot Relative max PSD automatic averaging factor Absolute max PSD automatic averaging factor low frequency PSD points to skip PSD smoothing points octave Flag to weight smoothed PSD semilog fit Description Default Plot title text Null Plot subtitle text Null Message text Null X axis time label text Null Y axis freq label text Null TKF filename Null Message position 0 ooocoocr ooo SESE EOS OD ded O m A N ON Qu A R APPENDICES X Div x axis divisions 5 Y Div y axis divisions 5 Y Tic y axis tics 5 Line Line type 0 Mouse Mouse flag 0 Date Data annotation flag 0 Box Draw box around plot flag 0 Wide Use wide plot line flag 0 X Offset X axis scal
67. the highest Fourier frequency is 1 2t If averaging is done the value of n is reduced by the averaging factor The PSD fit is a least squares power law line through octave band PSD averages 190 ANALYSIS FUNCTIONS The Stable32 Power function is intended primarily for the analysis of noise not discrete components and includes the qualitative display of power law noise in common PSD units with weighted least squares fits a power law noise process The PSD line fit weighting is based on the of unaveraged PSD points used to determine each octave band average shown as circles on the PSD plot Amplitude corrections are made for the noise response of the windowing functions The amplitude of discrete components should be increased by the log of the BW Fourier frequency spacing in Hz which is a negative number for typical sub Hz bandwidths The PSD plot will fail and an error message will be shown if there are too few data points to produce a plot An AF 1 periodogram or multitaper spectrum requires at least 6 data points and an Auto AF periodogram at least 10 data points The cursor can be used to help identify the frequency and amplitude of discrete components on the PSD plot Press the ESC key to deactivate it before closing the plot A spectral analysis involves many non parsimonious choices which depend on the analyst s objective judgment and taste Stable32 offers several PSD types and calculation methods The choice of PSD ty
68. the lag k autocorrelation 194 ANALYSIS FUNCTIONS The lag scatter plot is a cluster of uncorrelated points for white noise and has a linear shape for the more correlated flicker and random walk noises It will assume a circular form for noise having a sinusoidal component when the lag is at or near one quarter of its period Boxes showing the one two and three sigma error bounds are drawn on the lag scatter plot with dashed lines Not all of these boxes may be visible The lag scatter plot can take a considerable time to draw and the normal filled dot symbol is replaced with a cross when the of analysis points is 10 000 and higher The subtitle of the lag scatter plot is the same as the autocorrelation plot e ACF Data File A data file comprising rows of 2 columns of lag and ACF values is written each time a dynamic stability plot is generated This file which has a default name AUTO DAT and must be manually renamed before the next plot to save it An example of the first 5 lines of an AUTO dat file is shown below 0 9 99654114e 01 1 1 59891486e 01 2 5 67231514e 02 3 4 17460054e 02 4 4 83987387e 03 e Notes The autocorrelation sequence is calculated using the Fast Fourier Transform FFT which produces autocorrelation points at lags up to one half of the data length The phase or frequency data is averaged by the entered averaging factor to the corresponding tau before the autocorrelation is calculated Gaps in the data ar
69. timetag itself but only its interpretation as a tau value e Tag Offset Use the tag offset to make time zone corrections or to convert general timetag dates to MJD For example if the timetags are the default dates used by Microsoft Excel that start at zero at midnight on December 31 1899 the Tag Offset value should be set to 15018 to convert them to MJD Note Excel incorrectly treats 1900 as a leap year The tag offset is applied as the timetags are read 128 FILE FUNCTIONS Save Function e Purpose Use the Save function to save phase or frequency data to disk Save Data File CAstable32Xphase dat 3 col dat Sci archive dat y stable32 arcindex dat clkplt dat freq dat freq x dat messages DAT nbs dat Data Files da e Controls The Save dialog box contains the standard Windows file save controls plus a Save Timetags checkbox to choose whether or not to also save the timetags e Operation Perform the usual Windows file save dialog box operations 129 STABLE32 USER MANUAL 130 FILE FUNCTIONS Add Function e Purpose Use the Add function to append phase or frequency data from disk to the end of the current data in memory Append Data File x File Name Directories OK C stable32 phase dat cAstable32 3 col dat 3 c archive dat 3 stable32 arcindex dat clkpltdat freq dat freq x dat messages DAT r Data Type nbs dat El Phase Network
70. to multiply frequency data by in 1 0 Scale function PhaseTagScale Timetag scale multiplier for phase data 1 0 FreqTagScale Timetag scale multiplier for freq data 1 0 PhaseTagOffset Timetag scale multiplier for phase data 1 0 FreqTagOffset Timetag scale multiplier for freq data 1 0 If there is no corresponding item in the Inputs section of the INI file the default value is used Otherwise the one in the INI file overrides that value The tau number can be changed in the Opened dialog box or by editing the value in the status bar The addend and multiplier values do not take effect unless the Scale function is executed These items are very useful for setting the tau to a standard measurement interval time for adding a frequency offset and for scaling the data by a particular factor e g microseconds If there is timetag data and no tau Input then the spacing of the first two timetags scaled by the TagScale value is used as the default tau when a data file is opened The TagOffset is applied as the data file is read e Archive The Archive section of the STABLE32 INI file can contain the following parameters Keyword Description Default Num Channels 4 Meas Measurement Channel 2 Ref Reference Channel 1 The Archive section of the INI file contains the default values set by the Read Archive Configure function 298 e Database The Database section of the STABLE32 INI file can contain the following parameters
71. unless another message has been entered The PSD standard deviation at the upper Fourier frequencies is equal to 100 VMax AF e Multitaper PSD Analysis The Stable32 Power function also includes a multitaper PSD analysis method that offers a better compromise between bias variance and spectral resolution Averaging is accomplished by applying a set of orthogonal windowing tapering functions called discrete prolate spheroidal sequences DPSS or Slepian functions to the entire data array The 1st function resembles a classic window function while the others sample other portions of the data The higher windows have larger amplitude at the ends that compensates for the denser sampling at the center These multiple tapering functions are defined by two parameters the order of the function J which affects the resolution bandwidth and the of windows which affects the variance A higher J permits the use of more windows without introducing bias which provides more averaging lower variance at the expense of lower spectral resolution This is shown in the following table Order J Windows 2 0 1 3 2 5 1 4 3 0 1 5 3 5 1 6 4 0 1 7 4 5 1 8 5 0 1 9 189 STABLE32 USER MANUAL An example of seven of these functions for order J 4 is shown below Slepian DPSS Taper Functions J 4 7 Taper Amplitude 400 600 800 1000 0 200 Data Point The resolution BW is given by 2J Nt where N is the of data points sampled at tim
72. useful for data editing but are not needed for analysis STABLE32 USER MANUAL e Results Display Results are displayed in static edge text controls e Parameter Entry Parameter entries are made in edit controls denoted by boxes Default values are offered for most entries and these often provide the desired result Entry error trapping is done either by correcting the value or displaying a dialog box showing the allowable range The program then restores the previous value and positions the caret in the field for editing GENERAL Menu Tree e Menu Tree The Stable32 program uses the following menu tree Open Edit Statistics Phase Noise Calendar Show Tabs Save Convert Check Frequency Timetags Domain Configure About Filenames Index Add Normalize Drift Inputs Status Bar Using Help Read Average Sigma Inserts Auto File Tabs Stable on the Web Database Fill Run Play Auto Change Tabs Feedback Print Regularize DAVAR T8C5110A Auto File Tabs Exit Scale Power Stable32 ini Auto Noise Tabs Part Histogram Log Save Current Data Clear Autocorrelation Pad Rename Selected Tab 3 Cornered Hat Auto1 Wirite Selected Tab Auto2 Close Selected Tab Auto3 Close All Tabs Item Function Description File Open Open phase or frequency data file Save Save current phase or frequency data Add Add data file to current phase or frequency data Read Read stability data file Database Read data from TSC MMS database Print Print phase or fre
73. user interface bug reports Tom Parker Doug Hogarth and John Hartnett for bug reports Richard Hambly and Tom Clark for suggesting Excel date compatibility Tom Van Baak for the many tau idea Dave Howe and Tiffany Tasset for Th ol Th BR and Th oH Nino De Falcis for suggesting the stability plot masks Robert Lutwak for suggesting the weighted stability plot noise fits Thanks all those who have contributed ideas toward and reported bugs for the Stable program I hope this latest version will also prove useful 280 APPENDICES Appendix I Stable32 Functions e Sta The Stab File Fun ble32 Functions le32 program includes the following functions ctions Open Function Read Archive Multicolumn Data Large Data File Data File Opened Add Function Save Function Database Function Read Function Print Function Editing Functions Convers Edit Function Find Function Replace Function Fill Function Scale Function Part Function Regularize Function Timetags Function Normalize Function Average Function Clear Function ion Functions Convert Function Domain Function Plot Functions Plot Function Plot Options Plot Lines Plot Notes Analysis Functions Sigma Function Run Function Run Options Run Lines Run Notes Dynamic Stability Function Check Function Statistics Function Drift Function Plot Function 281 STABLE32 USER MANUAL Analysis Functions Con t Autocorrelation Function Powe
74. width will cause the status plots to be eliminated and a very narrow setting will make it difficult to operate the status bar controls The toolbutton and status bar controls automatically update whenever the Windows system colors are changed e Caution Be certain to enter the correct tau value for the phase and frequency data Many of the conversion and analysis functions depend on this value to obtain the correct results so enter the tau value immediately after the data is opened 12 GENERAL Tabs e Data Tabs Stable32 has a data tab feature that supports the saving of phase or frequency data and their optional timetags in a row of up to 12 tabs buttons above the status and message bars at the bottom of the main screen These data tabs operate independently for phase and frequency data and can be created to save the current data manually or automatically whenever it changes Clicking on a tab then restores the data that it holds This is a convenient way to analyze and compare multiple data sets and it also serves as an undo feature to restore data after it has been changed The data tabs are labeled with the filename of the corresponding data An example of Stable32 data tabs is shown below Noise01 frd Noiset2 ird Noise03rd Noise041ra Noise05 frd Noise06 frd Date 11 18 06 MJD 54057 C PhaseData N Total amp 513 ar PN ak 5 Freq Data E Total 512 File Noise06 phd 513 a oe oies06 rai iecit Tau 000000808 Sta
75. 1e 02 5 780e 02 6 706e 02 9 121e 01 3 200e 02 937 4 808e 02 4 372e 02 5 409e 02 4 478e 01 6 400e 02 873 3 624e 02 3 177e 02 4 334e 02 2 141e 01 1 280e 03 745 2 767e 02 2 307e 02 3 691e 02 9 710e 00 The stability file items for the Both sigma case are Tau Std Dev Sigma Mod Sigma and DF No DF information is available for Normal and Hadamard variances or for MTIE and TIErms and the DF value is set to zero The stability file contains no header or other text It is comprised of space delimited columns of ASCII characters in any numeric format Examine the files written by the Run function for more examples These stability files may be edited and combined as required to produce a composite stability plot The Tau values should be in numerical order The TIE rms and MTIE stability files do not contain Min amp Max Sigma or DF columns The Th oH stability file has a format comprising the columns Tau Sigma Th oBR Sigma Min and Sigma Max where Tau is the ADEV tau Sigma is the AVAR value Th oBR is the bias corrected Th ol value and Sigma Min amp Sigma Max are the error bars for either ADEV or Th oBR e Multiple Data Sets The Stable32 Read function includes provisions for reading and plotting multiple sets of stability data A new data set is started whenever the tau value is less than the previous one The points between multiple data sets are not connected Multiple data sets are plotted with up to five different sym
76. 2 INI file can contain the following parameters Keyword Description LastFile Full filename of last file opened PhaseFilel Full filename of last phase file opened FregFile1 Full filename of last freq file opened PhaseFile2 Full filename of 2nd from last phase file opened FreqFile2 Full filename of 2nd from last freq file opened PhaseFile3 Full filename of 3rd form last phase file opened FreqFile3 Full filename of 3rd from last freq file opened Ext Additional file extension patterns None The Ext parameter takes the form Ext Label ext ext where the Label part defines the label for the pattern and ext defines the filename extension Both parts must end with a character These filename patterns will be added to the standard ones in the Open and Save functions e Preferences The Preferences section of the STABLE32 INI file can contain the following parameters Keyword ShowFileOpened UseFregPlotlni UsePhasePlotlni UseSigmaPlotIni UseHistoPlotIni UseSpectPlotIni UseAutoPlotIni Description Show the Opened dialog box whenever a data file is opened Use INI file data for frequency plot parameters Use INI file data for phase plot parameters Use INI file data for sigma plot parameters Use INI file data for histogram plot parameters Use INI file data for spectrum plot parameters Use INI file data for ACF plot parameters UseDAVARPlotIni Use INI file data for DAVAR plot parameters DataType LabelPlot PlotLabel I
77. 2 USER MANUAL GENERAL Automated Operation e Purpose Stable32 operation can be fully automated by using the WinBatch package from Wilson WindowWare Inc 5421 California Ave SW Seattle WA 98136 800 762 8383 www winbatch com e Operation WinBatch uses Windows Interface Language WIL WBT scripts These scripts can be created with a text editor or recorded automatically from a sequence of keystrokes They are then invoked from the command line or a menu to automate Stable32 operation by sending the series of keystrokes to the program An example of a WBT script to plot frequency data is shown below Main menu Plot Frequency command ALT P F SendKey PF Plot Frequency function Plot command P If WinExist Plot Then WinActivate Plot SendKey P Wait for plot to be drawn on screen Delay 5 GraphiC menu File Plot command ALT F P If WinExist Stable32 Main Then WinActivate Stable32 Main SendKey FP Wait for plot to be sent to printer Delay 15 Graphic menu File Exit command ALT F X SendKey FX Close Plot function with Escape ESC If WinExist Plot Then WinActivate Plot SendKey ESCAPE Keystrokes corresponding to the ALT keyboard access codes for the Stable32 functions are sent via SendKey statements The prefix denotes an ALT key WinActivate statements are used to direct these keystrokes to the appropriate window The Delay statements a
78. 32 variance functions automatically handle gaps by either skipping or filling them as shown in the table below Stable32 Variance Function Gap Handling Variance Type Gaps Skipped Gaps Filled Overlapping Allan Modified Allan Hadamard Overlapping Hadamard 19 STABLE32 USER MANUAL Variance Type Gaps Skipped Gaps Filled Total Allan Total Modified Total Hadamard TIE rms e Analysis of Data with Gaps The Stable32 analysis functions include provisions for handling gaps in the data These provisions have limitations however and it is important to understand those limitations to avoid errors see Reference 1 The general process is to use the Open function to read timetagged phase data use the Regularize function to insert gaps for missing points use the Convert function to convert the data to frequency data use the Check function to replace any outliers with gaps and then analyze the regularized and corrected frequency data The same process can be followed by reading timetagged frequency data and using the Regularize function on it Some of the analysis functions have speed or other limitations associated with data having gaps and the Fill function can sometimes be useful to replace gaps with interpolated values For phase data having gaps but no outliers it is better to perform a stability analysis directly on the phase data In all these cases judgment is needed to assure a correct result It
79. 5 STABLE32 USER MANUAL Fit 4 Checkbox Show fit parameters on plot Wide Checkbox Use wide lines for stability plot Plot File Edit Enter plot file name Read Config Pushbutton Read plot configuration data from STABLE32 INI Save Config Pushbutton Save plot configuration data in STABLE32 INI Stability File Edit Enter stability file name Append Checkbox Append stability file data Reset All Pushbutton Reset all plot attributes to defaults OK Pushbutton Set plot attributes amp close dialog box Cancel Pushbutton Abort changes amp close dialog box Help Pushbutton Invoke the Plot Options help topic e Operation Enter the desired plot attributes and press OK to accept them or Cancel to abort The plot defaults may be restored with the Reset All button and the plot options may be saved and recalled in the STABLE32 INI configuration file between program runs with the Save Config and Read Config buttons These configuration data contain additional parameters such as axis labels and scale factors for each plot type The configuration file is read and saved automatically if the corresponding box is checked in the Configure dialog box When using the default directory the new Stable32 GraphiC sigma plot SIGMA TKF and stability file SIGMA TAU will overwrite the previous ones If it is desired to keep the previous file rename it either from within the Run Options dialog box before plotting or manually from the command line after the p
80. 5 4 12050 i a z A E SR a cm EU i Sideband Freguency hi Hz 7 Av nipus Time 1 Seconds i E PSD Plot Sigma Plot e Caution The domain conversions use simple closed form expressions for the 5 most common power law noise processes and their summation depends on the noise PSD slope decreasing toward higher sideband frequencies Better results may be obtained by numerical integration for real noise data and other expressions are required to handle particular cases such as a filter where the noise slope increases above a certain SB frequency 241 STABLE32 USER MANUAL 242 MISCELLANEOUS FUNCTIONS Auto Functions e Purpose Use one of the Auto functions Autol Auto2 or Auto3 to automate a stability analysis The Auto functions execute automation scripts that describe the steps of a frequency stability analysis These steps are arranged in a standard order and can be individually selected or skipped Plots and tables can be drawn and printed to show the results The available options are as follows Step Description Options Plot Print Open File Open data file Phase or freq data Original data Browse for file Convert Convert data To other analysis Converted data type Remove Remove bad Frequency only Corrected data Outliers data Set sigma factor Part Use part of data Set start end points Selected data End 0 last point Average Combine data Set averaging Averaged data for longer t factor
81. 71939900557e 01 575908768589536e 01 019178375517534e 01 555233845694533e 01 e Operation The current data file is automatically opened when the Pad function is invoked Consult the Notepad help topics for information regarding that program Use the Notepad item in the Preferences section of the STABLE32 INI configuration file to set the name of the text editor program to be invoked e Caution Opening of the current data file may be prohibited as a file sharing violation 251 STABLE32 USER MANUAL 252 MISCELLANEOUS FUNCTIONS Play e Purpose Use the Play function to invoke the Play W program to redisplay a previous GraphiC TKF plot RA Playw32 CAstable32Ynoisepixtkf e Operation Consult the Play W help topics for information regarding that program e Note The Play W program is not included with all versions of the Stable32 software package 253 STABLE32 USER MANUAL 254 Glossary e Glossary OTHER INFORMATION The following terms are used in the field of frequency stability analysis and the Stable32 program Aging Allan Variance Averaging Averaging Time BW Confidence Limit Drift Dynamic Stability Frequency Data Hadamard Variance f MJD Modified Sigma MTIE The change in frequency with time due to internal effects within the device The 2 sample variance o t commonly used to measure frequency stability The process of combining phase or frequen
82. 79 D A Howe D W Allan and J A Barnes Properties of Signal Sources and Measurement Methods Proc 35th Annu Freq Control Symp pp A1 A47 June 1981 V F Kroupa Editor Frequency Stability Fundamentals and Measurement IEEE Press Institute of Electrical and Electronic Engineers New York 1983 ISBN 0 87942 171 1 S R Stein Frequency and Time Their Measurement and Characterization Chap 12 Precision Frequency Control E A Gerber and A Ballato Eds Academic Press Inc Orlando 1985 ISBN 0 12 280602 6 Vol 2 Proc IEEE Vol 74 Jan 1986 C A Greenhall Frequency Stability Review Telecommunications and Data Acquisition Progress Report 42 88 Oct Dec 1986 Jet Propulsion Laboratory Pasadena CA pp 200 212 Feb 1987 D W Allan Time and Frequency Time Domain Characterization Estimation and Prediction of Precision Clocks and Oscillators JEEE Trans Ultrasonics Ferroelectrics and Freq Contrl Vol UFFC 34 No 6 pp 647 654 Nov 1987 D W Allan et al Standard Terminology for Fundamental Frequency and Time Metrology Proc 42nd Annu Freq Control Symp pp 419 425 June 1988 Characterization of Clocks and Oscillators NIST Technical Note 1337 D B Sullivan D W Allan D A Howe and F L Walls Eds U S Dept of Commerce National Institute of Standards and Technology March 1990 Special Issue on Time and Frequency Proc IEEE Vol 79 July 1991 D W Allan Time and Frequency Metrol
83. 94 e AutoPilot APPENDICES The AutoPlot section of the STABLE32 INI file can contain the following parameters Keyword Title Subtitle Message Position Wide Date Box Zero Lagl Lag Lags Mouse AutoFile PlotFile AF AXDefault Description Plot title text Plot subtitle text Message text Message position Use wide plot line flag Date annotation flag Draw box around plot flag Draw horizontal line at 0 flag Show lag k scatter plot flag Scatter plot lag lags on plot Mouse flag ACF data filename ACF TKF plot filename Averaging factor Flag to set x axis scale to default e DAVARPlot The DAVARPlot section of the STABLE32 INI file can contain the following parameters Keyword Position Date Box SigmaType WindowSize StepSize Colors Title Subtitle Message Grid e FreqLines Description Message position Date annotation flag Draw box around plot flag Allan or Hadamard sigma type Analysis window size Analysis step size Use colors flag Plot title text Plot subtitle text Plot message text Show plot grid flag Default Null Null Z E OrreareeaRoo Null Null 1 Default oooo 100 10 Null Null Null The FreqLines section of the STABLE32 INI file can contain the following parameters the items are repeated for each line as indicated by the index i 1 1 to 12 Keyword Typeli X Start 1 X End i Y Start i Y End i Slope 1 Description
84. A Greenhall D A Howe and D B Percival Total Variance an Estimator of Long Term Frequency Stability IEEE Trans Ultrasonics Ferroelectrics and Freq Contrl Vol UFFC 46 No 5 pp 1183 1191 Sept 1999 D A Howe Total Variance Explained Proc 1999 Joint Meeting of the European Freq and Time Forum and the IEEE Freq Contrl Symp pp 1093 1099 April 1999 261 10 262 STABLE32 USER MANUAL D A Howe The Total Deviation Approach to Long Term Characterization of Frequency Stability ZEEE Trans Ultrasonics Ferroelectrics and Freq Contrl Vol UFFC 47 No 5 pp 1102 1110 Sept 2000 D A Howe and T K Peppler Definitions of Total Estimators of Common Time Domain Variances Proc 2001 Freq Cont Symp pp 127 132 June 2001 Modified Total Variance D A Howe and F Vernotte Generalization of the Total Variance Approach to the Modified Allan Variance Proc 31st PTTI Meeting pp 267 276 Dec 1999 Time Total Variance M A Weiss and D A Howe Total TDEV Proc 1998 IEEE Freq Cont Symp pp 192 198 June 1998 Total Hadamard Variance D Howe R Beard C Greenhall F Vernotte and W Riley A Total Estimator of the Hadamard Function Used for GPS Operations Proc 32nd PTTI Meeting pp 255 268 Nov 2000 D A Howe R L Beard C A Greenhall F Vernotte W J Riley and T K Peppler Enhancements to GPS Operations and Clock Evaluations Using a Total Hadamard Deviation JEEE
85. AII Tabs Options Configure Filenames Status Bar Help About Index Using Help Stable on the Web Feedback 10 Generate simulated power law clock noise Generate timetag data Display a DOY MJD calendar Perform frequency time domain conversions Set input file scaling values Replay a TKF plot file Invoke the 5110Comm applet Open Stable32 INI file Open Stable32 log file Invoke Windows Notepad or another text editor program Execute automatic analysis script 1 Execute automatic analysis script 2 Execute automatic analysis script 3 Activate the Tabs feature Activate automatic file opening tab creation Activate automatic file change tab creation Activate automatic file editing tab creation Activate automatic noise generation tab creation Save current file data in new tab Rename selected tab data file Write selected tab data to disk Close remove selected tab Close remove all tabs Set Stable32 program configuration options Set filenames Opens submenu to access status bar controls Display information about the Stable32 program Display the general Help index Display information about using Help Access the Hamilton Technical Services web site Send feedback re Stable32 via e mail GENERAL Status Bar e Purpose The Status Bar is a permanent area at the bottom of the screen that displays status information about the current phase and frequency data arrays Some of this information is editable T
86. All Tau runs if the full results are not needed at longer averaging factors The maximum size data file that can be read is set by the Max Data File Size item in the Configure function The purpose of this setting is to automatically activate the data averaging dialog box when a large data file is read Set this parameter to a value appropriate to your computer s speed and RAM The Stats Edit and Check functions can be very slow when processing frequency data having many repeated values This is because of the qsort function used in finding the median value One way to work around this problem is to add a very small slope to the data with the Scale function in order to eliminate exactly identical data points Convenience Features Use the Inputs section of the STABLE32 INI configuration file to automatically set the tau and scale factor you use most often Use the stored text in the plot options drop down combo controls to avoid having to reenter labels between plots Use the Save and Read buttons to store and recall complete plot configurations Associate the dat filename extension with the Stable32 program to automatically launch it by clicking on a data file with the Open command on the Explorer File menu or by dragging the data to the Stable32 icon on the desktop Use the Copy command of the Drift Sigma Run and Domain functions to write their results to the clipboard The File Opened dialog box can be eliminated with the Show File Op
87. Functio sisser onenn aia aE E RE E A AS 167 Fill Gaps 30 A E ti a 16 167 Find Function 5197 Find Interruptions 4237 First Difter ence mera er erreur GENRE VY TUE DE APER VERTES SES TEES Ab Eee geo dex 86 EredguenC EE ke shee 37 Frequency Domain Stability eese eene eerte etre 101 Gaps siet pletri des Christie po te Un iis pits ahuslkdesake 16 19 Generate Simulated Clock Noise nusen aniani nanas anr aaas a Eaa rE NAAS ennt 213 Generate Timeta siriene OO RU paid E re EKEN EO E iD Ede 211 GlOSSaty o see eem rated do i ea eee qe tem db pe omnit GPS Week Graphis suede os D OC it eee E a RN Graphics Interchange Format gif Files sese 301 H Hadamard Variance eere RETO RING IO mE 55 69 181 219 308 Hamilton Technical Services cec nec c ern p MT s ii 2 Help Els eoioqee teme eq eme p ei a PO ME 3 Hints and Notes si Histogram Function ii el AULA teadama Dha liz 197 I Inputs from Configuration File wennrenreenenentenrenre een eneenest 298 302 Insert Gaps Insert Plot Installation J Julian Date eie A a aated a 250 K Keys Edi o Al Si 289 L ECT A ETA 89 Large Data Pd siria 123 Launching License ees Log File Main WindOWw en WERT HE o ie E REY OE ER NER E as 7 MIL 0 5531 DIT RE 180 Modified Allan Variance esee ener entren enne
88. G FUNCTIONS Normalize Function e Purpose Use the Normalize function to remove the average value from phase or frequency data This normalizes the data to have a mean value of zero Average 5 403683e 01 E Press OKto normalize data by X 0 removing the average value from each point e Controls The Normalize dialog box contains the following controls Control Type Description Average Text Display the mean value OK Pushbutton Perform the normalize function amp close dialog box Cancel Pushbutton Abort the normalize function amp close dialog box Help Pushbutton Invoke the Normalize help topic e Operation Press OK To abort press Cancel 163 STABLE32 USER MANUAL 164 EDITING FUNCTIONS Average Function e Purpose Use the Average function to combine groups of phase or frequency data into values corresponding to a longer averaging time t Note The entire phase or frequency data array is averaged regardless of the analysis limits Avg Factor fi ol OK Cancel Press OK to average data by combining points for longer tau Help e Controls The Average dialog box contains the following controls Control Type Description Avg Factor Edit Enter averaging factor default 1 OK Pushbutton Perform the Average function amp close dialog box Cancel Pushbutton Abort the Average function amp close dialog box Help Pushbutton Invoke the Average help topic e Operat
89. General property sheet page contains the following controls Control Type Description General Settings Group General program flag settings Write Sigma File Checkbox Check to write stability file after run Autoinc Filename Checkbox Check to increment filename extension when data changes Show File Opened Checkbox Check to show data plot and information when data phase or frequency file opened No Greek Labels Checkbox Don t use Greek axis labels on plots AutoCalc Checkbox Check to automatically calculate when function opened AutoPlot Checkbox Check to automatically plot when function opened Show Status Plots Checkbox Show mini data plots in status bar Show Splash Checkbox Show splash screen when Stable32 opens 47 STABLE32 USER MANUAL Choose text editor to use Enter filename of test editor program Text Editor Group Notepad Edit e Toolbuttons Page Controls The Toolbuttons property sheet page contains the following controls Control Type Description Select Active Group Select desired toolbuttons to appear on toolbar Toolbuttons List Multiple selection list box General Toolbuttons Plots Data Inputs l Options General Toolbuttons Plots data Inputs Options m Read Plot Information r Piot Settings Phase M Use Smart Plot Scales Erequency Weight Sigma Plot Noise Fit Sigma Phase and Freq Data Reading Settings Max Data File Size 393999 Non Numerics to Skip ONE Us
90. IS FUNCTIONS e Data Entry It is generally best to work from the top down setting constants like carrier frequency and BW first To activate the BW edit boxes enter a non zero PM noise value The PSD and sigma noise values can be entered at any convenient Fourier frequency or averaging time The PSD and sigma plot ranges should be set consistently approximately reciprocal frequency and tau ranges and within the range where the noise parameters apply e Title and Subtitle The PSD and Sigma plot titles are Frequency Domain Stability and Time Domain Stability respectively Their subtitles show the values of the non zero noise intensity parameters h of the spectral density of the fractional frequency fluctuations Sy f h f where a is the power law noise exponent In addition the carrier frequency and system bandwidth are shown at the bottom of the plots e Notes The averaging factor AF is t to where t is the analysis averaging time and ty is the basic measurement time The bandwidth factor is 2nf to where f is the upper cutoff frequency of the measuring system in Hz It applies only to white and flicker PM noise e PSD and Sigma Plots Examples of PSD and sigma plots are shown below FREQUENCY DOMAIN STABILITY TIME DOMAIN STABILITY s 7 y2008 22 h 2006 26 EM 4 O 80 4 85 al e 8 90 s A Li 95L Ne i i id 4 3 S 100 eb bd 3 K i A Z 05 i d EB 2 S a RN Led E 1
91. It is the basis of much of the underlying Stable32 functionality The following is a list of the functions in the FrequenC Library FrequenC Functions ACFNoiseID AddPSD AddSigma AutocorrelationCalc AverageFregData AveragePhaseData BasScale BreakDate Ca Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Cal Ca Ca Ca Ca Cal Cal Cal Cal Ca Ca Ca lcBiasl LcBias2 LcBias3 LcBias LcBisectionDrift LcChiSgrProb LcDegFree LcDiffusionFregDrift LcDomain LcFastMTIE LcFastModSigma lcFirstDiff LcFregHadamardDev LcFregModSigma lcFreqOffset lcFreqOverlapHadamardDev lcFreqOverlapSigma LcFregSigma LcFregStdDev LcGreenhallModSigma LcHadamardB1 LcHadamardDev LcInvChiSgr LcLinFregDrift LcLogFregDrift LcMTIE LcMean lcNormalProb lcPhaseHadamardDev lcPhaseModSigma lcPhaseOverlapHadamardDev LcPhaseOverlapSigma lcPhaseSigma LcPhaseStdDev LcOuadraticDrift lcRatio lcSecondDiff lcStarBl Cal lcThreePointDrift 37 STABLE32 USER MANUAL CheckFrequenC CombinedEDF ConvDomain ConvFreqToPhase ConvPhaseToFreq ConvPhaseToFreqUsingTimetags CountEqualTimetags CountGaps DateConv DateToJulian DateToMJD DayOfWeek EDF FillFloatGaps FillGaps FindFreqOutliers FindMedian FindMinMax FindPlotScale GenNoise GetMJD HadTotvarBias HadTotvarCalc HadTotvarEDF HadamardEDF HistoCalc JulianToDate JDToDate
92. JD End UTC E Edit Read end date time or message End MJD Edit Read end MJD Span Text Read span days hrs mins secs Text data points in read span Tau sec Group Box Measurement amp sampling interval Meas Tau Text MMS measurement interval AF F Edit Averaging factor applied during read Read Tau Text Sampling interval of read data No Name Progress Bar Read progress indication No Name Text Program instructions amp messages Read A Pushbutton Read data from database Abort button during read Configure O Pushbutton Open Configure dialog box Stable32 T Pushbutton Launch Stable32 Close L Esc Pushbutton Close program Help H Fl Pushbutton Invoke this help topic In addition the right amp left arrow keys will move the focus up and down through the pushbuttons and the spacebar can be used to press them e Operation Begin by selecting the Reference and Measurement clocks which will display their descriptions and load their measurement records into the tables under their names Then select the desired reference and measurement clock Records Measurement clock records shown in red are from a different MMS system than the reference record and cannot be read The time format for the start and end time in the clock records table can be chosen as a UTC timestamp or MJD Details about the clock database records can be displayed with the Details button Measurement record pairs without overlapping time spans cannot be read The Start and End tim
93. JDtoDOY JDtoGPS akeDate edDev odTotvarBias odTotvarCalc odTotvarEDF ultiTaperSpectrumCalc NoiseID NormalizeData RemoveDiffusionFreqDrift RemoveFregOffset RemoveLinFreqDrift RemoveLogFreqDrift RemoveQuadraticDrift RoundAxes ScaleData SpectrumCalc TIErms Theol TheolBias TheolBiasToAlpha TheolEDF TotvarBias TotvarCalc TotvarEDF i ni The FrequenC Library its functions and their documentation are available for purchase by special arrangement with Hamilton Technical Services 38 GENERAL GraphiC e GraphiC GraphiC is a library of scientific plotting functions used by the Stable32 program for its phase frequency stability power spectrum autocorrelation histogram and dynamic stability plots The GraphiC plotting package also includes the Play program for replotting the TKF graphics files produced by Stable32 not available in the Student Version of Stable32 e Controls The GraphiC plot screen contains the following menu items and commands the commands marked with an apply only to the Play program GraphiC and Play Commands The File menu s Open command will display a dialog box for the Open user to select a new TKF file to open and display When the file is opened the first plot will be drawn in the user s window The File menu s Print Setup command calls the printer driver s Printer Setup setup dialog box to allow
94. L TIME DOMAIN STABILITY Dynamic Stability e Dynamic Stability A dynamic stability analysis uses a sequence of sliding time windows to perform an Allan DAVAR or Hadamard DHVAR analysis thereby showing changes nonstationarity in clock behavior versus time It is able to detect variations in clock stability noise bursts changes in noise level or type etc that would be difficult to see in an ordinary overall stability analysis and it can also show the portion of a run that has the best or worst stability The results of a dynamic stability analysis are presented as a 3D surface plot of log sigma versus log tau averaging factor as a function of time window Stable32 implements the DAVAR and DHVAR dynamic stability analyses in its Dynamic Stability function An example of a dynamic stability plot is shown below DYNAMIC STABILITY Analysis Windows 91 Windows of Size 100 amp Step Size 10 Time Spon 9 1008 01 sec e References 1 L Galleani and P Tavella The Characterization of Clock Behavior with the Dynamic Allan Variance Proc 2003 Joint FCS EFTF Meeting pp 239 244 2 L Galleani and P Tavella Tracking Nonstationarities in Clock Noises Using the Dynamic Allan Variance Proc 2005 Joint FCS PTTI Meeting 83 84 STABLE32 USER MANUAL TIME DOMAIN STABILITY Confidence Intervals e Confidence Intervals Stable32 uses several different methods for setting the confidence intervals and
95. M Alpha 0 Mu H I Apply m Dead Time T Tau fi 00 B2 B3 SD Press Calcto calculate sigma e Variance Types The Allan and Hadamard variances are the principal method for describing the stability of a frequency source in the time domain Those variances and other statistics may be calculated as shown in the table below Type Variance Abbreviation Symbol Allan Allan AVAR o T Overlap Allan Overlapping Allan AVAR T Mod Allan Modified Allan MVAR Mod 1 Time Time TVAR o Hadamard Hadamard HVAR Ho t Overlap Had Overlapping Hadamard HVAR Ho t 182 ANALYSIS FUNCTIONS Total Total Allan TOTAVAR 0 ota T Mod Total Total Modified Allan TOTMVAR Modo totai t Time Total Total Time TOTTVAR 07 totai T TIE rms RMS Time Interval Error TIE rms MTIE Maximum Time Interval Error MTIE Th ol Theoretical Variance 1 Th ol The Type column shows the variance types of the Sigma function list These short original Stable32 names are retained to avoid breaking batch files The currently accepted names and abbreviations for these variance types are shown in the Variance and Abbreviation columns These are all functions of the averaging time t and are usually expressed as their square roots the deviation or sigma oy x Mod o x o x Hoy t Stota t Mod ojotai t and abbreviated as ADEV MDEV TDEV HDEV TOTADEV TOTMDEV and TOTTDEV respectively The TIE rms MTIE and Th ol statistics apply only to phase data
96. MAIN STABILITY Modified Allan Variance e Modified Allan Variance The modified Allan variance Mod o 1 MVAR is another common time domain measure of frequency stability It is estimated from a set of M frequency measurements for averaging time t m1 where m is the averaging factor and tp is the basic measurement interval by the expression 2 1 M 3m 2 j m l f i m 1 Modo r odo T 2m M 3m 2 2 2 Eb J In terms of phase data the modified Allan variance is estimated from a set of N M 1 time measurements as 2 1 N 3m4 j m l Modo 7 X 2x Ex gt a 2mMT N 3m 1 2 2 i 2m i m A The result is usually expressed as the square root MDEV or Mod o t the modified Allan deviation The modified Allan variance is the same as the normal Allan variance for m 1 It includes an additional phase averaging operation and has the advantage of being able to distinguish between white and flicker PM noise The confidence interval of a modified Allan deviation determination is also dependent on the noise type but is often estimated as 0 t VN 61 62 STABLE32 USER MANUAL TIME DOMAIN STABILITY Time Variances e Time Variance The time variance TVAR is a measure of time stability based on the modified Allan variance It is defined as 07 7 1 3 Mod o 1 The time Allan variance is equal to the standard variance of the time deviations for white PM
97. MJD to the end of the file Archive File Indexing Locating the correct file and channel for a certain clock is easier with an index of the various measuring system transactions a list of the test start and end times channel s and record s for each clock under test Use the Index option of the Read Archive function to generate an index for TSC archive files This generates and displays an ASCII file named ARCINDEX DAT that may be printed and or searched for the desired clock data 24 GENERAL Filenames e Data Filenames Stable32 data filenames follow the usual DOS conventions While any names can be used the preferred extensions are DAT PHD and FRD for general phase and frequency data respectively A function that changes the data in memory optionally alters the extension to a number which is then incremented each time that the data is changed Phase data numerical extensions are even and those for frequency data are odd Automatic filename extension incrementing helps keep track of changes and avoid overwriting previous data It is controlled by the Autoinc Filename Ext checkbox of the Configure function The filename of the current phase or frequency data file can be changed by editing it directly in the corresponding edit control of the status bar at the bottom of the screen e Plot Filenames A TKF plot file in Tektronix 4105 format is automatically written to the current disk directory after each plot The default na
98. N is the of phase or frequency data points raised to the next higher power of 2 Stable32 is intended primarily for time domain frequency stability analysis but the Power function is included to provide additional insight into the noise properties under investigation as well as to assist in the detection of discrete and or periodic components e Caution The PSD results are based on time units of seconds 191 STABLE32 USER MANUAL References W H Press B P Flannery S A Teukolsky and W T Vetterling Numercial Recipes in C Cambridge University Press 1988 ISBN 0 521 35465 X Chapter 12 D J Thomson Spectrum Estimation and Harmonic Analysis Proc IEEE Vol 70 No 9 Sept 1982 pp 1055 1096 D B Percival and A T Walden Spectral Analysis for Physical Applications Cambridge University Press 1993 ISBN 0 521 43541 2 J M Lees and J Park A C Subroutine for Computing Multi Taper Spectral Analysis Computers in Geosciences Vol 21 1995 pp 195 236 Help File for the AutoSignal program for spectral analysis AISN Software Inc 1999 Example An example of a power spectrum plot is shown below 192 I GraphiC Win spectrum tkf File Edit Draw Convert Help Ode 02 27 30 ilme 13 07 20 Dota Palms 1 they 1 POWER SPECTR M T TIT phass dat H HERES t E 3 lt x g E i Window Hanning Carrier Freg 1 000e 007 i 3 i 3 Fourier Frequency f Hz Pamer Law Fris LM X53 BB dBe Hz
99. NUAL Last Checkbox Select last record Start MJD Radiobutton Select MJD time span Start MJD Edit Enter start MJD End MJD Checkbox Select optional end MJD instead of all data End MJD Edit Enter optional end MJD OK Pushbutton Perform Read Archive amp close Cancel Pushbutton Abort Read Archive function amp close Display Pushbutton Display the archive file Index Pushbutton Show an index of the archive file Configure Pushbutton Configure the Read Archive function Help Pushbutton Invoke the Read Archive help topic e Operation Choose the desired TSC archive file with the Archive option of the Open function Then observe the resulting File Tau and Start MJD Use the Display button to display the contents of the archive file or the Index button to show a listing of all clock transactions in the archive file Enter the desired Measurement and Reference channel s that correspond to the clock to be analyzed Entering a Reference channel of 0 will select the offset LO as the reference Entering a negative Measurement channel will cause the sense of the measurement and reference channels to be reversed this is useful in the case of a LO that is above rather than the below the nominal frequency as is normal Reversal of the Measurement and Reference channel s will also accomplish this but the ID information displayed after processing the data will be that of the other channel Then select either the Record or Start MJD button as the
100. No 5 pp 876 879 May 2006 W J Riley Application of the 3 Cornered Hat Method to the Analysis of Frequency Stability Hamilton Technical Services TIME DOMAIN STABILITY Autocorrelation e Autocorrelation The theoretical autocorrelation function is defined as EGG HZ 7 1 0 o where E is the expectation operator z is the time series m is its mean and s is its variance A common estimate of the autocorrelation function is 1 Mok NE De 2 V IE us F ge N 2 where 1 N 2 254 and where the lags are k 0 1 2 K and K is lt N 1 An equivalent and faster estimate can be made for the summation in the numerator as the product of the Fourier transforms of the two terms based on the fact that convolution in the time domain is equivalent to multiplication in the frequency domain e Noise Identification The lag 1 autocorrelation can provide an estimate of the power law noise type as described in Reference 5 below e References 1 W H Press B P Flannery S A Teukolsky and W T Vetterling Numercial Recipes in C Cambridge University Press 1988 ISBN 0 521 35465 X Section 13 2 2 G Box and G Jenkins Time Series Analysis Holden Day Inc 1976 ISBN 0 8162 1104 3 3 D B Percival and A T Walden Spectral Analysis for Physical Applications Cambridge University Press 1993 ISBN 0 521 43541 2 4 C A Greenhall Another Power Law Identifier That Uses Lag 1 Autocorrelation private communic
101. PTTI Meeting Dec 1997 pp 39 48 6 D B Percival and D A Howe Total Variance as an Exact Analysis of the Sample Variance Proc 1997 PTTI Meeting Dec 1997 pp 97 105 7 C A Greenhall D A Howe and D B Percival Total Variance an Estimator of Long Term Frequency Stability August 11 1998 to be published available on the Hamilton Technical Services web site 8 D Howe and T Peppler Definitions of Total Estimators of Common Time Domain Variances Proc 2001 Intl Freq Cont Symp June 2001 pp 127 132 66 TIME DOMAIN STABILITY Total Modified Variance e Total Modified Variance The total modified variance TOTMVAR is another new statistic for the analysis of frequency stability It is similar to the modified Allan variance MVAR and has the same expected value but offers improved confidence at long averaging times It uses the same phase averaging technique as MVAR to distinguish between white and flicker PM noise processes A TOTMVAR calculation as described in the reference below begins with an array of N phase data points time deviates x with sampling period t which are to be analyzed at averaging time t mty TOTMVAR is computed from a set of N 3m 1 subsequences of 3m points First a linear trend frequency offset is removed from the subsequence by averaging the first and last halves of the subsequence and dividing by half the interval Then the offset removed subsequence is extended at both ends
102. Save Sigma 1 1 00157e 02 Lines 1 e Controls The Read Lines dialog box contains the following controls Some parameters do not apply to all line types Control Line Up Down Type Tau Start End Sigma Start End Slope Sigma 1 Lines Type Edit Pushbutton Pushbutton Combo Group Edit Combo Edit Combo Group Edit Edit Combo Text Text Description Enter of line to edit Increment line Decrement line Select line type X Axis line parameters Enter x axis start of line Enter x axis end of line Y axis line parameters Enter y axis start of line Enter y axis end of line Noise type for fit Noise line fit parameter of lines entered 147 STABLE32 USER MANUAL OK Pushbutton Perform Read Lines function amp close dialog box Cancel Pushbutton Abort Read Lines function amp close dialog box Help Pushbutton Invoke the Read Lines help topic Print Pushbutton Print line parameters Clear All Pushbutton Clear all lines Read Pushbutton Read line information from INI file Save Pushbutton Save line information in INI file e Operation Select the desired Line and Type Enter the applicable Tau Start Tau End Sigma Start and Sigma End parameters Choose the applicable Slope for a Noise Line and press OK to accept the lines or Cancel to abort Press Clear All to remove all lines 148 READ FUNCTIONS Read Notes Function e Purpose Use the Read Notes function
103. TY File PHASE DAT 10 tion Ho t 1a 107 Hadamard Dev w o e Averaging Time t Seconds 103 a MN Dele 03 13 99 Time 11 55 30 Data Polnis 1 inry 1001 of 1001 Teu 1 0000000e4 00 FREQUENCY STABILITY PHASE DAT 3 File PHASE DAT He Hadamard Deviation 10 101 pping Overla 103 0 10 2 10 2 10 Averaging Time t Seconds e References The following references apply to the overlapping Hadamard statistic 1 T Walter A Multi Variance Analysis in the Time Domain Proc 24 PTTI Meeting pp 413 424 December 1992 2 S Hutsell Relating the Hadamard Variance to MCS Kalman Filter Clock Estimation Proc 27 PTTI Meeting pp 291 302 December 1995 72 TIME DOMAIN STABILITY Total Hadamard Variance Total Hadamard Variance The total Hadamard variance TOTHVAR is total version of the Hadamard variance that rejects linear frequency drift and offers improved confidence at long averaging times The algorithm for calculating the total Hadamard variance from a set of N fractional frequency values y at an averaging time t mr is very similar to that used to calculate TOTMVAR from phase data 1 Select a 3m point subsequence y of the frequency data y i n n 3m n 3m 1 2 Remove the linear trend c frequency drift from the subsequence obtaining y y ci where c is found by averaging the Ist and last halves of th
104. The full analysis limits may be restored by clicking on the small button next to the analysis limit bitmap A blue bitmap at the top center of the status bar indicates when the two data arrays contain corresponding data CAstable32phase dat Date 02 26 98 MJD 50870 Phase Data DEI Total 1001 C Freq Data Total 1000 ia File PHASE DAT 1000 File PHASE 001 1000 Tau 9 00000e 02 Stet 1 End 1000 Tau 9 00000e 02 Start 1 End 1000 Li e Controls The Status Bar contains the following controls Control Type Description Phase Data Radiobutton Select the phase array as the active data array Freq Data Radiobutton Select frequency array as the active data array Total Text Display the total of points in the data array File Text Display the current phase or freq data file title Text Display the of analysis points Tau Edit Enter the averaging time t for the current data Start Edit Enter the analysis start data point End Edit Enter the analysis end data point Plot Graphic Show data plot between analysis limits Unmarked Button Restore full analysis range 11 STABLE32 USER MANUAL e Bitmaps Several bitmaps appear on the status bar beside the Phase and Freq Data buttons to indicate when the changed data is unsaved when there are timetags and whether the analysis limits are either restricted or too small The latter bitmap changes when the of analysis poi
105. Timetags as Tau The Use Timetags for Tau option allows the time difference between adjacent timetags to be used as the tau for each point s phase to frequency conversion This is not normally used except for non uniformly spaced data The tau units must be in seconds Timetags in other units e g MJD fractional days must be scaled to seconds e g 86400 by the PhaseTagScale multiplier in the STABLE32 INI which can be entered from the Inputs function accessed via the Data File Opened dialog box or the Utilities menu The average timetag interval is used as the tau value for the converted frequency data e Notes The conversion of phase data having two equal adjacent values results in a fractional frequency value of zero While this is correct it would subsequently be treated as a gap in the frequency data That problem can be avoided by using the Adjust Zero Frequency option during the phase to frequency conversion which will adjust the frequency value to 1e 99 e Cautions Gaps in frequency data are converted to phase data by linear interpolation using the average frequency value which can cause a discontinuity in the resulting phase data The Use Timetags for Tau option will fail generating an error message if two adjacent timetags are equal Frequency data converted from unequally spaced phase data using the Use Timetags for Tau option will be correct but must have approximately the same tau to support subsequent analysis 162 EDITIN
106. Trans UFFC Vol 52 No 8 Aug 2005 Th o1 Th oBR and Th oH D A Howe and T K Peppler Very Long Term Frequency Stability Estimation Using a Special Purpose Statistic Proc 2003 IEEE Freq Contrl Symp pp 233 238 May 2003 D A Howe and T N Tasset Th 01 Characterization of Very Long Term Frequency Stability Proc 2004 EFTF D A Howe Th oH A Hybrid High Confidence Statistic that Improves on the Allan Deviation Metrologia 43 2006 S322 S331 D A Howe J McGee Taylor and T Tasset Th oH Bias Removal Method Proc 2006 IEEE Freq Contrl Symp pp 788 792 June 2006 MTIE G Zampetti Synopsis of Timing Measurement Techniques Used in Telecommunications Proc 24th PTTI Meeting pp 313 326 Dec 1992 Bregni Measurement of Maximum Time Interval Error for Telecommunications Clock Stability Characterization JEEE Trans Instrum Meas Vol IM 45 No 5 pp 900 906 Oct 1996 P Tavella A Godone amp S Leschiutta The Range Covered by a Random Process and the New Definition of MTIE Proc 28th PTTI Meeting Dec 1996 pp 119 124 M J Ivens Simulating the Wander Accumulation in a SDH Synchronisation Network Master s Thesis University College London UK November 1997 S Bregni Clock Stability Characterization and Measurement in Telecommunications IEEE Trans Instrum Meas Vol 46 No 6 pp 1284 1294 Dec 1997 P Tavella and D Meo The Range Covered by a Clock Error
107. UAL e Initial or Failed Launch When the Database function is launched the first time it is unlikely that the default database access parameters will be correct and the connection will fail This will bring up an error message followed by the Database Configure dialog that will allow the user to enter the correct access parameters Then after another error message the function can be restarted and the connection should succeed The same procedure can be followed any time a change is required in the access parameters e Configuration File A typical Stable32 configuration file contains the following database items Database Host 192 168 1 100 Database tsc User Bill Password A1B2C3D4 The password is encrypted in the Stable32 configuration file each password ASCII character becomes two hex characters The Database section of the STABLE32 INI file contains four parameters associated with database access Name Description Default Value Remarks Host IP address 1 Blank for localhost Database Database name tsc postgres Required User User name tsc Required Password Password tsc Not always required Encrypted These items of the Stable32 configuration file may be manually edited with a text editor but the preferred method is to use the Database Configue dialog within the Stable32 program If no STABLE32 INI file or Database item exists in the Stable32 exe program folder the program will almost certainly follow the failed connec
108. USER MANUAL Stable32 Frequency Stability Analysis E KAMA z pea mq as S ia ts EA k E bm U Hamilton Technical Services 650 Distant Island Drive N Beaufort SC 29907 USA 03 02 2007 Copyright Notice O 2007 Hamilton Technical Services All Rights Reserved The information in this document is subject to change without notice and is provided without any warranty of any type Please report any errors or corrections to the address below No part of this document may be reproduced or retransmitted in any form or by any means electronically or mechanically including photocopying or scanning for any purpose other than the purchaser s personal use without the express written permission of Hamilton Technical Services The software described in this document is licensed and may be used only in accordance with the terms of the Stable32 license agreement It may not be copied on any medium except as specifically allowed therein Stable32 User Manual Version 1 50 03 02 2007 Printed manual available from www lulu com as ID 212944 Hamilton Technical Services Phone 843 525 6495 650 Distant Island Drive Fax 843 525 0251 Beaufort SC 29907 1580 E Mail stable32 wriley com USA Web www wriley com ii TABLE OF CONTENTS Table of Contents FRONT MATTER Copyright Notice M M HM ii Wil EA ETA E D AS iii GENERAL Stable m 1 hti 3 Directories Program Model
109. a Missing Pts Text Display total missing points in the data Data Interval Text Display time interval between data points OK Pushbutton Perform the Regularize function amp close dialog box Cancel Pushbutton Abort the Regularize function amp close dialog box Help Pushbutton Invoke the Regularize help topic e Operation Observe the Interruptions Missing Pts and Data Interval displays If there are missing points that you wish to remove verify that the Data Interval is correct Then press OK to regularize the data To abort press Cancel or OK if interruptions 0 e Caution The Data Interval must indicate the proper time spacing It is determined by the difference between the first two timetags If this value is not correct edit the data file with a text editor before executing the Regularize function The Regularize function operates on the full data array 237 STABLE32 USER MANUAL 238 ANALYSIS FUNCTIONS Domain Function e Purpose Use the Domain function to perform basic time and frequency domain conversions for power law noise processes Domain x Frequency Domain Time Domain Close PSDType L dBc Hz v Sigma Type Normal y Copy1 SB Freg Hz 00000e 00 Tau Sec fi 00000e 00 Clear All Carrier Freq ooe PA Hel Mrs 1 00000e 01 Avg Factor fi Help BW Hz 1000 000 EWFactor 6283 186 24 Enter Power Law Noise Power Law Noise Type dB dec PSD Type Mu Sigma paramet
110. a inserted are simply interpolated values using the closest non gap data points at either side of each gap No attempt is made to simulate noise and the resulting statistics are not necessarily valid It is generally better practice to leave gaps unfilled 167 STABLE32 USER MANUAL 168 EDITING FUNCTIONS Scale Function e Purpose Use the Scale function to modify the selected phase or frequency data by an additive or multiplicative factor or by adding a linear slope Remove Addend 0 0000000000000e 00 OK ist Value Multiplier 1 0000000000000e 10 Ayerage Slope 0 0000000000000e 00 tine X Press OK to modify data by an additive or multiplicative factor or by adding a linear slope e Controls The Scale dialog box contains the following controls Control Type Description Addend Edit Enter addend default 0 Multiplier Edit Enter multiplier default 1 Slope Edit Enter slope per t interval default 0 Remove Group Insert values to be removed from data 1st Value Pushbutton Insert 1st value into Addend Average Pushbutton Insert average value into Addend Line Pushbutton Insert linear slope value into Slope OK Pushbutton Perform the Scale function amp close dialog box Cancel Pushbutton Abort the Scale function amp close dialog box Help Pushbutton Invoke the Scale help topic e Operation Enter the value of the Addend Multiplier and or Slope to
111. a set More data provides finer frequency resolution not lower noise while the data sampling time determines the highest Fourier frequency Without averaging for white noise each spectral result has only 2 degrees of freedom Some sort of filtering or averaging is usually necessary to provide less noise in the PSD results This is accomplished in Stable32 by dividing the data into sections performing an FFT analysis on each section separately and then averaging those values to obtain the final PSD result The averaging factor can be selected in integer power of 2 increments which improves the PSD standard deviation by the square root of the averaging factor The tradeoff in this averaging process is that each section of the data is shorter yielding a result with coarser frequency resolution that does not extend to as low a Fourier frequency The Auto AF periodogram PSD plot option uses a variable power of 2 series of averaging factors that increase from 1 to a default maximum of N 64 or 256 whichever is less where N is the of data points raised to the next higher power of 2 as the Fourier frequency increases The sequence of PSD points have averaging factors of 1 2 4 8 up to that maximum unless the first points are skipped see below This allows the analysis to extend down to the lowest possible Fourier frequency while reducing the PSD variability at higher frequencies The maximum AF used for the PSD plot is shown in the message box
112. aging factor m even and 10 m lt N 1 where N is the number of phase data points It consists of N m outer sums and m 2 inner sums The Th ol deviation has the same power law noise tau dependence as the Allan deviation It is an unbiased estimator of the Allan deviation for white FM noise but requires bias corrections for the other power law noises An example of the sampling technique used by Th ol is shown in the figure below This figure shows the m 2 5 pairs of inner summation terms for N 11 phase data points at the largest averaging factor m 10 for its single outer summation 1 1 Theo1 Schematic for nz11 m 10 1ton m 1 5 0tom 2 1 4 MIN ASADAS g 0T In general there are m 2 pairs of samples with spans ranging from m 2 to 1 all weighted the same The averaging time t associated with a Th ol value is t 0 75 m to where to is the measurement interval Stable32 offers the Th ol deviation alone and in combination with the Allan deviation which provides stability data over the whole range of averaging times from the basic measurement interval to 75 of the record length 75 STABLE32 USER MANUAL e NewTh o1 The NewTh ol algorithm of Reference 2 provides a method of automatic bias correction for a Th ol estimation based on the average ratio of the Allan and Theol variances over a range of averaging factors from 10 to N 30 3 where N is the of phase samples 1 Y Avar m 9 3i To N n 1 E T
113. al and overlapping Allan variances when the noise type is manually selected Enter the T Tau dead time ratio where tau is the measurement time and T is the time between measurements Dead time corrections are made using the B2 and B3 bias ratios which handle cases of single and multiple distributed measurement dead time respectively e Auto Calc A run can be done automatically when the Run function is invoked by setting the AutoCalc item in the Configure function 221 STABLE32 USER MANUAL e Stability File A stability file with a default name of sigma tau is written to disk after each run This file contains sigma tau and errorbar data as described in the Read Function help topic and may be used to document or replot the stability results It may even be used to create a stability plot with another program such as Gnuplot as shown below Frequency Stability E 1e 12 Sigma 1e 13 1 10 100 1000 10000 Tau The following wgnupl32 exe Gnuplot script was used for this stability plot set grid xtics ytics mxtics mytics 2 set nokey set logscale set title Frequency Stability set xlabel Tau set ylabel Sigma set zero 1e 20 plot sigma tau using 1 3 4 5 with yerrorbars Detailed Stability Data File A detailed stability data file with a fix
114. alue close to zero e g le 99 The Find and Replace feature of the Edit function may be used to make that substitution A zero value in frequency data can also occur as the result of the conversion of two equal adjacent phase data points perhaps because of limited measurement resolution and an optional warning message is available to flag this possibility when phase data is read This situation can be handled in the Convert function by activating the option to adjust the value of the converted frequency point from zero to 1e 99 A certain number of zeros gaps can be inserted into or deleted from phase or frequency data with the Edit After Highlighted Point feature of the Edit function This can be used to insert gaps that correspond to an interruption in the data record That process can be accomplished automatically for time tagged data with the Regularize function e Caution Header rows in a data file are not read and will be lost if the file is overwritten Unexpected results can occur if two adjacent phase data points are exactly the same This corresponds to zero frequency and can cause anomalies in the resulting stability analysis If converted to frequency data the resulting zero frequency data point will be treated as a gap unless the Adjust Zero Frequency option is activated 17 18 STABLE32 USER MANUAL GENERAL Gaps e Gaps Gaps and outliers can occur in clock data due to problems with the measuring system or the
115. am supports the limited use of timetags to help manipulate phase and frequency data Timetag arrays are associated with each of the phase and frequency arrays e Timetag Usage Timetags may be read from a file or they may be generated automatically with the Timetags function Actual timetags may be used to identify interruptions in the data with the Regularize function which can also insert gaps into the data at these points Generated timetags are suitable only for data inspection and editing The presence of timetags is indicated by a small yellow tag next to the filename in the status bar Timetags are not required for any of the analysis functions They may be stored to disk along with their corresponding data If there is timetag data and no tau input from the STABLE32 INI file then the spacing of the first two timetags scaled by the TagScale configuration file value is used as the default tau when a data file is opened For example MJD timetags scaled by 86400 can be used to automatically set the tau value e Timetag Editing Timetag editing is not supported by the Stable32 program but may be accomplished by an external ASCII text editing program such as Windows Notepad e Timetag Processing Timetags are processed automatically by the Average and Part functions to yield the correct values that correspond to the averaged or remaining data 27 28 STABLE32 USER MANUAL GENERAL Launching e Launching The Stable32 pro
116. ance to MCS Kalman Filter Clock Estimation Proc 27th PTTI Meeting pp 291 302 Dec 1995 S T Hutsell Operational Use of the Hadamard Variance in GPS Proc 28th PTTI Meeting pp 201 213 Dec 1996 D N Matsakis and F J Josties Pulsar Appropriate Clock Statistics Proc 28th PTTI Meeting pp 225 236 Dec 1996 W J Riley The Hadamard Variance Hamilton Technical Services Modified Hadamard Variance S Bregni and L Jmoda Improved Estimation of the Hurst Parameter of Long Range Dependent Traffic Using the Modified Hadamard Variance Proceedings of the IEEE ICC June 2006 Total Variance D A Howe An Extension of the Allan Variance with Increased Confidence at Long Term Proc 1995 IEEE Int Freq Cont Symp pp 321 329 June 1995 D A Howe and K J Lainson Simulation Study Using a New Type of Sample Variance Proc 1995 PTTI Meeting pp 279 290 Dec 1995 D A Howe and K J Lainson Effect of Drift on TOTALDEV Proc 1996 Intl Freq Cont Symp pp 883 889 June 1996 D A Howe Methods of Improving the Estimation of Long term Frequency Variance Proc 1997 European Frequency and Time Forum pp 91 99 March 1997 D A Howe amp C A Greenhall Total Variance A Progress Report on a New Frequency Stability Characterization pp 39 48 Proc 1997 PTTI Meeting Dec 1997 D B Percival and D A Howe Total Variance as an Exact Analysis of the Sample Variance Proc 1997 PTTI Meeting Dec 1997 C
117. as of the measured stability and the reduced number of degrees of freedom for the processed data The former requires maximum and minimum sigma data while the latter requires that the number of measured degrees of freedom be available The availability of these data are indicated by their respective MM and DF indicators e Reference Noise Removal The 3 Cornered Hat function can also be used to remove the contribution of a reference whose noise is known apriori either from its specification or by a separate determination Denote the device under test as unit A and the known reference as units B and C Enter the measured data as both A B and A C multiply the stability data for the reference by 2 and enter it as B C After the 3 cornered hat calculation the corrected stability data for the unit under test will be in column A e Results Data Files Three data files containing the results of a 3 cornered hat calculation are written to disk in the same folder as the original data These files named UnitA sig UnitB sig and UnitC sig have the same stability file format as the input file see Read Function e Caution Do not use results that contain negative variances The 3 cornered hat method is not a substitute for a low noise reference It is best used for units having similar stability e g to determine which unit is best Negative variances are a sign that the method is failing because it was based on insufficient measurement data or
118. ased on the astronomical Julian Date the of days since noon on January 1 4713 BC The MJD is the Julian Date 2 4000 000 5 it starts at zero at midnight on November 17 1858 Stable32 handles MJDs over the span of the 21st century and it has provisions for displaying them in several formats The MMS system usually takes data on each clock at a rate of once per second and each resulting row in the measurements table has a source id INT a pps count INT a utc TIMESTAMP and a meas NUMERIC 30 10 as shown in character format below 3 1129343209 2005 10 15 02 26 16 9814320 4886926900 These rows require 42 bytes The database for a 12 channel system taking data a once per second grows in size by about 1 million points day or 42 MB day This is a large amount of data to store read and analyze The meas value which represents phase in cycles has a resolution of 1e 8 cycle When divided by a nominal frequency of 5e6 this provides a resolution of 2e 15 sec The actual system resolution is limited by white phase noise to about 0 5 psec 5e 13 sec rms for a 1 second measurement interval The Database function automatically generates a phase data filename based on the measurement clock name with a phd extension 135 STABLE32 USER MANUAL e MMS Database Connection The computer on which the Stable32 program is run must be connected to the MMS database server via a network before the Database function can be used Follow the directions for th
119. ation August 28 2003 5 W J Riley and C A Greenhall Power Law Noise Identification Using the Lag 1 Autocorrelation Proc 18th European Frequency and Time Forum EFTF April 2004 Session 6B 99 STABLE32 USER MANUAL 100 FREQUENCY DOMAIN STABILITY Frequency Domain Stability e Frequency Domain Stability Stable32 uses the following frequency domain measures of frequency stability Formula Units Description Sy f 1 Hz PSD of fractional frequency fluctuations S f sec Hz PSD of time fluctuations So rad Hz PSD of phase fluctuations f dBc Hz SSB phase noise to carrier power ratio where PSD Power Spectral Density SSB Single Sideband dBc Decibels with respect to carrier power The most common frequency domain stability measure is f dBc Hz the SSB phase noise to signal ratio in a 1 Hz BW as a function of sideband frequency f Other frequency domain stability measures are S f 1 Hz the power spectral density of the fractional frequency fluctuations S f sec Hz the power spectral density of the time fluctuations and S f rad Hz the power spectral density of the phase fluctuations The Stable32 program can plot any of these from the appropriate phase or frequency data 101 STABLE32 USER MANUAL 102 FREQUENCY DOMAIN STABILITY Noise Processes e Power Law Noise Processes The spectral characteristics of the power law noise processes commonly used to describe the performance of freq
120. ation file for phase data i Control Type Description Tau Edit Enter the tau value Addend Edit Enter the addend scaling value Multiplier Edit Enter the multiplier scaling value Tag Scale Edit Enter the timetag scale multiplier Tag Offset Edit Enter the timetag offset value OK Pushbutton Store values amp close dialog box Cancel Pushbutton Abort amp close dialog box Help Pushbutton Invoke this help topic e Operation Invoking the Inputs dialog box displays the current Tau Addend Multiplier Tag Scale and Tag Offset values from the Inputs section of the STABLE32 INI configuration file for the current phase or frequency data type These values may be edited and saved by using the corresponding edit control s and pressing OK or any changes made may be aborted by pressing the Cancel button 127 STABLE32 USER MANUAL e inputs Values There are separate Tau Addend Multiplier Tag Scale and Tag Offset inputs values for phase and frequency data The Tau value should be set to the measurement interval of the data in seconds The Multiplier value should be set to scale the data for analysis generally to seconds and fractional frequency The Addend value is then added to the scaled values e Tag Scale Use the tag scale multiplier to convert the timetag units to seconds For example if the timetags are MJD in whole and fractional days the Tag Scale value should be set to 86400 The tag scale does not affect the
121. be added to the data Or automatically insert the negative of the Ist Value or Average into the Addend or the negative of the Linear slope into the Slope Then Press OK to scale the data or Cancel or OK with defaults to abort e Scaling Equation The data is scaled according to the following equation Scaled Value Original Value Multiplier Addend Slope Data Point e Caution It is possible to scale only a portion of a data array but this is unlikely to produce a satisfactory overall result 169 STABLE32 USER MANUAL 170 EDITING FUNCTIONS Part Function e Purpose Use the Part function to clear all except a portion of the current phase or frequency data The Part function changes the data in memory Use the analysis limits on the status bar to temporarily change the range of the data to be analyzed Part EI Data Range A OK Point Timetag Start fi m Date 2001 05 07 Time 14 35 10 Close End 25751 E Date 2001 05 18 Time 19 21 50 Help di Timetag Type AS Press OK to remove all except selected Date part of data e Controls The Part dialog box contains the following controls Control Type Description Data Range Group Controls for entering data range to select Point Static Start and end point s Start Edit Start data point 7 Pushbuttons Increment decrement start point End Edit End data point Pushbuttons Increment decrement end point
122. because the units under test have disparate stability Plots containing negative variances will have off scale points 248 MISCELLANEOUS FUNCTIONS Calendar Function e Purpose Use the Calendar function to display a monthly calendar showing the Day of Year DOY and Modified Julian Date MJD The MJD can be used as a timetag for phase or frequency data It is common to append the decimal fraction of a day to the MJD integer to indicate the exact date date and time When this is done the time is usually UTC Calendar x GPS Weeks 171 176 December 2002 Erg Year Up Wed Thu i Year Down 236 337 4385 539 e ES 52611 52612 52613 62614 PEDE 243 fiofsaa 1 345 fejas 13 Month Down 52617 52618 52619 52620 52821 Today He as0 i7 a581 refas2 i3 a53 e0 354 2 52624 62625 52526 525627 52628 Copy dd idi 3 357 24 358 esfasa 25 360 27 361 Close 52631 62632 52633 52634 52635 30 364 81 365 52638 52639 e Controls The Calendar dialog box contains the following controls Control Type Description Year Up Pushbutton Advance the calendar by 1 year Y ear Down Pushbutton Retard the calendar by 1 year Month Up Pushbutton Advance the calendar by 1 month Month Down Pushbutton Retard the calendar by 1 month Today Pushbutton Go to current month amp highlight current day Close Pushbutton Close the Calendar dialog box Help Pushbutton Invoke the Calendar help topic e Operation
123. bert D Fest M Oliver and J J Gagnepain Characterization of Frequency Fluctuations by Crosscorrelations and by Using Three or More Oscillators Proc 35th Freq Contrl Symp pp 458 462 May 1981 S R Stein Frequency and Time Their Measurement and Characterization Chapter 12 Section 12 1 9 Separating the Variances of the Oscillator and the Reference pp 216 217 Precision Frequency Control Vol 2 Edited by E A Gerber and A Ballato Academic Press New York 1985 ISBN 0 12 280602 6 OTHER INFORMATION P Tavella and A Premoli Characterization of Frequency Standard Instability by Estimation of their Covariance Matrix Proc 23rd PTTI Meeting pp 265 276 Dec 1991 P Tavella and A Premoli A Revisited Tree Cornered Hat Method for Estimating Frequency Standard Instability JEEE Trans Instrum Meas IM 42 pp 7 13 Feb 1993 C R Ekstrom and P A Koppang Error Bars for Three Cornered Hats JEEE Trans UFFC Vol 53 No 5 pp 876 879 May 2006 W J Riley Application of the 3 Cornered Hat Method to the Analysis of Frequency Stability Hamilton Technical Services Domain Conversion A R Chi The Mechanics of Translation of Frequency Stability Measures Between Frequency and Time Domain Measurements Proc 9th Annu PTTI Meeting pp 523 548 Dec 1977 J Rutman Relations Between Spectral Purity and Frequency Stability pp 160 165 R Burgoon and M C Fisher Conversion Between Time and Freq
124. bols The first symbol is a circle e followed by a down triangle v diamond up triangle and square M and they repeat thereafter The symbols are filled for normal variances and open for modified ones One application for multiple data sets is to show both stability data and its corresponding specification limit e Other Options By default all data points are shown with symbols and are included in the data table If however the of analysis points is made zero for the first row of a set that data will be plotted without symbols This may be desirable for showing spec limits In addition all data rows having 0 are excluded from the data table Thus spec limits can be excluded from the table by setting the analysis points to zero and placing them at the end of the data file 142 READ FUNCTIONS Read Plot Function e Purpose Use the Read Plot function to generate a stability plot IE GraphiC Win cAstable324sigma tkf Eile Edit Draw Convert Help Dole 09 24 98 Time 15 07 41 File SIGMA TAL Tau Sigma g 9 00e 02 3 25e 10 1 80e 03 2 23e 10 3 60e 03 1 61e 10 1 17e 10 6 88e 11 5 34e 11 5 76e 04 4 03e 11 115e 05 3 07e 11 ion 1010 Allan Deviat i 10 10 Averaging Time t Seconds 143 STABLE32 USER MANUAL 144 READ FUNCTIONS Read Options Function e Purpose Use the Read Options function to control the attributes of the stability plot Read Plot Option
125. ch as Notepad to change those and other parameters In particular the number of listing and plot points can be set with the ListSize and PlotSize items in the Preferences section Because the plots have 8 X axis divisions it is best if the PlotSize value have a round number after division by 8 e g PlotSize 240 will provide a scale of 30 sec div Note The 5110Comm program is not included with all versions of the Stable32 software package INDEX Index 3 Cornered Hab 1 nimii lic iei eoe o det oer E EEE ELE EEEE EEE 97 Zeknowledgnenis sce be ftne ie M aaa Add Function Allan Variance Analysis Limits Analysis Procedure YI LUU Archive Elle inen epe i eph Des aida on eee AutoCalc Autocorrelation sel ETE Autocorrelation Function viii luik ii radar iaa 193 Automated Operation AutoPlot Average Function Averaging Time tau Ayeraging Dalai rota eite be nn d ePi de REO e ERO Sa US Averaging LargeFileS o ite ee ere oe tera mt Siegen oe 15 123 Bias PUN Chong A E TD Bisection Bitmap bmp Files Bitmap tH Calendar EUnCLtOtb uee oen ee etie eret eate rtt iode elo dta pest Er E ea SEN EE ke akude obice edd 249 Check Function ACA eire EAEE E vat v he Sia Laat udu Saleh loetectansebdetaecstvenchertest os Cleat FUNC OON
126. cker FM noise coefficient o 1 White FM Edit Enter white FM noise coefficient o 1 Flicker PM Edit Enter flicker PM noise coefficient o 1 White PM Edit Enter white PM noise coefficient o 1 Points Group points and t interval Num Edit Enter points default 513 Tau Edit Enter t interval seconds default 1 Freq Params Group Fractional frequency parameters Offset Edit Enter fractional frequency offset Drift Edit Enter fractional frequency drift per t interval Sine peak Edit Enter peak value of sine term Sine Period Edit Enter period of sine term OK Pushbutton Perform the Noise function amp close dialog box Cancel Pushbutton Abort the Noise function amp close dialog box Copy Pushbutton Copy noise parameters to clipboard Help Pushbutton Invoke the Noise help topic 213 STABLE32 USER MANUAL e Operation Enter the Number of data points wanted and their Tau interval Then enter the o 1 Noise Parameters for the desired power law clock noise At least one noise parameter must be non zero Next enter any fractional frequency Offset and Drift and or the peak value and Period of any Sine term that may be wanted Then press OK to generate the simulated clock noise or Cancel to abort e FFM Noise Generation The long term phase excursions of the generated flicker FM noise are too small on average see Reference 2 below This does not affect the Allan deviation results and can be avoided by generating twice as
127. controls The numeric value also determines the search precision Enter the value that it is to be Replaced With Set the search direction with the Up and Down buttons and press one of the Find Next Replace Next or Replace All buttons The result of a successful search is displayed in the Edit dialog box Additional searches may be conducted with the Find Next button and additional replacements with the Replace Next or Replace All buttons Close the Replace dialog with the Cancel button or by closing the Edit dialog box 159 STABLE32 USER MANUAL 160 EDITING FUNCTIONS Convert Function e Purpose Use the Convert function to convert between phase and frequency data Conversion OK Phase to Frequency Frequency te Phase Cancel fv Adjust zero Frequency Help Transfer Timetags Use Timetags for Tau 4 Press OK to convert between phase and frequency data e Controls The Convert dialog box contains the following controls Control Type Description Conversion Group Choose conversion type Phase to Frequency Radiobutton Select f conversion Frequency to Phase Radiobutton Select f conversion Normalize Frequency Checkbox Remove average frequency before f conversion Adj Zero Frequency Checkbox Adjust zero freq to 1e 99 in b f conversion Transfer Timetags Checkbox Transfer timetags along with data Use Timetags for Tau Checkbox Use timetags as tau for conversion OK Pu
128. ctor t t Tau Averaging time t analysis points Alpha Estimated noise exponent a Min Sigma Lower confidence limit as applicable Sigma Nominal sigma Max Sigma Upper confidence limit as applicable e Stability Results Plot Use the Plot button along with the Options Lines and Notes functions to plot the results of a stability run Many aspects of the plot can be customized as desired The individual stability points of a run are indicated by closed normal or open modified circles which are automatically made smaller when the number of points exceeds 100 e g an all tau run e Variance Types See the Sigma function for a list of the variance types that can be found with the Run function In addition both the overlapping and modified Allan deviations can be calculated and plotted during the same run 220 ANALYSIS FUNCTIONS e Drift Removal The Run function allows linear frequency drift to be removed from phase or frequency data before performing the stability analysis Simply check the No Drift checkbox The drift day will be reported but the original phase or frequency data is not changed e 1of2 Scaling The Run function allows scaling the results for one of two identical units Simply check the 1 of 2 checkbox to scale the resulting sigma values by V2 e Dead Time Bias correction for measurement dead time Dead_Time is available for the normal and overlapping Allan variances when the noise type is manually selec
129. cy data e Operation Select Phase Frequency or Archive data type enter the desired Avg By factor if applicable and perform the usual Windows file dialog box operations Opening a data file with multiple columns will invoke the Multicolumn Data function Attempting to open an oversize data file as determined by the Max Data File Size configuration value will invoke the Large Data File function and attempting to add excessive data will be trapped with an error message The results of an Open or Add operation will be displayed in a File Opened box if this feature is activated with the Show File Opened option of the Configure function 111 STABLE32 USER MANUAL 112 FILE FUNCTIONS Filenames Function e Purpose Use the Filenames function to set the names of the various Stable32 data and plot files It is good practice to preset all the relevant filenames within this function before beginning an analysis m Plot Filenames Phase Freq Sigma Histo C Stable32 PHASETKF 0 OK fC Stable32 FREQTKF ss fC Stable32 SIGMATKF 0000 fC Stable32 HISTOTKF SS Spectum C Stable32 SPECTRUMTKF 09090000 Reset Cancel Help gt Hi ACF 1 CAStab e32XAUTO TKF DAYAR CAStab e321DAVAR TKF r Data Filenames Phase csteb e321PHASE DAT E 3 Enter plot 8 Freg CAStab e324FREO DAT Sis SA Y names Set Stability CAStab e324SIGMA TAU leis PSD Cxstab e321PSD DAT Resetthem to x defaults ACF
130. cy data into samples at a longer averaging time See Tau Bandwidth Hz The uncertainty associated with a measurement Often a 6896 confidence level or error bar The change in frequency with time due to all effects including aging and environmental sensitivity A form of the Allan variance showing the stability versus time A set of fractional frequency values y i where 1 denotes equally spaced time samples A 3 sample variance HVAR that is similar to the 2 sample Allan variance It uses the 2nd differences of the fractional frequencies and is unaffected by linear frequency drift The ratio of the SSB phase noise power in a 1 Hz BW to the total carrier power dBc Hz The Modified Julian Date is based on the astronomical Julian Date the of days since noon on January 1 4713 BC The MJD is the Julian Date 2 4000 000 5 A modified version of the Allan or total variance that uses phase averaging to distinguish between white and flicker PM noise processes The maximum time interval error of a clock 255 Normalize Phase Data Phase Noise Sampling Time Sigma Slope SSB Si f Sx f Sy f Tau Total Th o1 Th oBR Th oH TIE 256 STABLE32 USER MANUAL To remove the average value from phase or frequency data A set of time deviates x i with units of seconds where i denotes equally spaced time samples Called phase data to distinguish them from the independent time var
131. d Archive Configure help topic e Operation Use the Channels Meas Ch and Ref Chan edit controls to set default values for the Read Archive function Then press OK to accept or Cancel to reject these values The new of channels will take effect immediately in the Read Archive function 119 STABLE32 USER MANUAL 120 FILE FUNCTIONS Multicolumn Data e Purpose The Multicolumn Data function supports the reading of data files with multiple columns It is a sub function of the Open and Add functions Use the Multicolumn Data function to select the desired columns of phase or frequency and optional timetag data This dialog box opens automatically during an Open or Add operation whenever multicolumn data is detected The contents of the last line of the data file are displayed at the bottom of the dialog box to assist in selecting the desired timetags and data column Multicolumn Data x Select destination array s for multicolumn data OK Destination Array Column lo 2 3 4 6 b wq E Timetags 2 80 046 8 04 8 e e Help Data INE E EE ME NE LastLine 1 400000 2 400000 3 400000 4 400000 5 40 ofFile 0000 6 400000 7 400000 8 400000 e Controls The Multicolumn Data dialog box contains the following controls Control Type Description Timetags Radiobutton Choose column of timetag data to be read Data Radiobutton Choose column of phase or frequency data to be read Ist Line of File Text Display
132. d press OK to accept them or Cancel to abort Press Clear All to clear all annotations 331 STABLE32 USER MANUAL 232 ANALYSIS FUNCTIONS Dynamic Stability Function e Purpose Use the Dynamic Stability DVAR function to perform a dynamic Allan or Hadamard variance DAVAR or DHVAR stability analysis A dynamic stability analysis is useful to show stability changes nonstationarity noise bursts and other aspects of clock behavior Title JDYNAMICSTABLITY He Pot SubTitle JPHASEDAT o O Reset All Close Message El Plot Calc Message Position Top Right Read Config Save Config Plot Filename CADAVAR TKF AGA Axis Label Y Axis Label Z Axis Label Vert View Log AF Window Log Sigma E Up Settings Variance Hariz View AVAR C HVAR Dm om edere co us eth Window Size 100 H j Options Left Right a Step Size fi 0 v Date FF Colors Reverse 1 5 Down A Enter Settings choose Variance amp Windows 91 v Box Grid h D Options and set Views Then press Plotfor DAVAR plot e Controls The Dynamic Stability dialog box contains the following controls Dialog Box ALT Control Control Control Key Type Description Plot L Pushbutton Plot dynamic stability Title T Combo Enter or select plot title SubTitle U Combo Enter or select plot subtitle Message E Combo Enter or select plot message Msg Position M List Select message locat
133. data plots have defaults that give reasonable plots automatically Common changes are to modify the Subtitle Title to add a Message and to Scale and re Label the axes Standard and previous titles subtitles and messages may be selected from their combo box controls Several curve fits are available from the Options box as described in the Drift function The x axis is rescaled automatically when new time units are selected Since the x axis time scale is determined automatically use the X Divs to adjust an awkward x axis scale It is common to adjust the y axis Multiplier e g le 12 when the units e g pp10 are changed When this done for frequency data entering a pp10 label automatically adjusts the multiplier value The plot options when accepted with OK stick between dialog box openings User entered titles subtitles and messages are pushed onto their respective list boxes with a CR Tab or other focus change Up to six such options are automatically saved recalled and linked between the various plot option dialog boxes The plot options may be saved and recalled in the STABLE32 INI configuration file between program runs with the Save Config and Read Config buttons These configuration data contain additional parameters such as axis labels and scale factors for each plot type The configuration file is read and saved automatically if the corresponding box is checked in the Configure dialog box The Keep box may be checked to re
134. dd delay between steps Enter delay in msec Enter name of auto script Execute automation script Save automation script Abort Auto function Invoke Auto help topic controls to allow viewing of the intermediate results 244 MISCELLANEOUS FUNCTIONS e Command Line Use The Auto functions may be invoked from the command line with the o autol o auto2 or o auto3 options When invoked in this way the automation script is executed immediately without requiring that it be started with the Go button e Automation Scripts Three separate automation scripts are stored in the STABLE32 INI configuration file under the Auto sections Each of these sections has the same items that define the analysis steps for each automated analysis While it is possible to edit these configuration file items directly it is recommended that the corresponding Auto dialog box be used to avoid errors e Analysis Methods The Stable32 automation script feature is intended as a convenient way to quickly produce basic stability analysis information It is not intended to replace either manual analysis or complete batch files The former has the advantage of close user integration and insight while the latter can harness the full capabilities of the program including plot customization and annotation e Caution While considerable effort has been taken to make this automation process robust and useful many factors including data size hardware spe
135. dow parameters and time span A plot title can be included at the top a sub title at the bottom and a message can be shown in any of 9 positions Date time data analysis limits and data filename can be included at the top and an optional plot label e g organization name can be included at the bottom The dynamic stability 3D surface plot can be shown as a full red mesh or as a sigma dependent multicolor display with or without an adjustable density mesh The mesh density also depends on the window and step sizes For a large of analysis windows it is desirable to use the grid control to reduce the number of mesh points shown this does not affect the underlying surface plot The dynamic overlapping Allan and Hadamard deviation calculations are performed from phase data after frequency to phase conversion if necessary All zero values including the first and last data points of an analysis window are treated as gaps If all the data points within an analysis window are gaps then there will be a corresponding gap in the stability data which is shown as having a sigma value at the bottom of the plot Thus a group of missing data points will appear as a trough in the dynamic stability plot and will have z values equal to the minimum sigma value The dynamic stability plot requires an All Tau overlapping Allan or Hadamard deviation calculation for each of its analysis windows which can take a considerable time for a large data set
136. ds were used to validate the Stable32 frequency stability analysis software 1 Manual Analysis The results obtained by manual analysis of small data sets such as NBS Monograph 140 Annex 8 E were compared with the program output 2 Published Results The results of published analyses were compared with the program output 3 Other Programs The results obtained from other specialized stability analysis programs such as that from a previous generation computer or operating system were compared with the program output 4 General Programs The results obtained from industry standard general purpose mathematical and spreadsheet programs such as MathCAD and Excel amp were compared with the program output 5 Consistency Checks The program was verified for internal consistency such as producing the same stability results for phase and frequency data The standard and normal Allan variances should be approximately equal for white FM noise and the Allan variance should be approximately equal to 1 5 times the standard variance for white PM noise The normal and Modified Allan variances should be identical for an averaging factor of 1 For other averaging factors the Modified Allan variance should be approximately one half the normal Allan variance for white FM noise The normal and overlapping Allan variances should be approximately equal The various methods of drift removal should yield similar results 6 Simulated Data Simulated cl
137. e MMS database system to establish this connection which should be verified before running the Stable32 Database function When it is run for the first time a Database Configure dialog box will appear to enter the necessary access parameters host IP address database name user name and password Those settings will be saved for subsequent use by the program the password is encrypted e Database Queries The MMS database is queried when the program is opened to gather a list of all the clocks it contains which is put into both the reference and measurement combo boxes This represents a snapshot of the clocks in the database which is not updated again unless the Reset button is pushed or the program is restarted When the user selects a clock from one of these boxes all of the records for that clock are put into the corresponding table Again this represents a snapshot of the database if a continuing run is subsequently ended the table contents will not dynamically reflect that change Records for MMS systems different from the one selected as the reference are flagged in red and cannot be read Finally after the user has selected the records and the start amp end times to be read the corresponding data is read from the database For a continuing run for both clocks the current date time is used for the end of the record which will change each time the Read button is pushed If data collection on one or both of the clocks has stopped wit
138. e private communication March 2000 C A Greenhall Recipes for Degrees of Freedom of Frequency Stability Estimators IEEE Trans Instrum Meas Vol 40 No 6 pp 994 999 December 1991 D A Howe Methods of Improving the Estimation of Long Term Frequency Variance Proc 11th European Freq and Time Forum pp 91 99 March 1997 J A Barnes and D W Allan Variances Based on Data with Dead Time Between the Measurements NIST Technical Note 1318 1990 C A Greenhall private communication May 2000 D Howe R Beard C Greenhall F Vernotte and W Riley A Total Estimator of the Hadamard Function Used for GPS Operations Proceedings of the 32nd Annual Precise Time and Time Interval PTTI Systems and Applications Meeting pp 255 268 November 2000 C Greenhall and W Riley Uncertainty of Stability Variances Based on Finite Differences Proc 2003 PTTI Meeting December 2003 D A Howe and T K Peppler Very Long Term Frequency Stability Estimation Using a Special Purpose Statistic Proceedings of the 2003 IEEE International Frequency Control Symposium pp 233 238 May 2003 W J Riley and C A Greenhall Power Law Noise Identification Using the Lag 1 Autocorrelation Proc 18th European Frequency and Time Forum EFTF April 2004 Session 6B D A Howe R L Beard C A Greenhall F Vernotte W J Riley and T K Peppler Enhancements to GPS Operations and Clock Evaluations Using a Total Hadamard Deviation IEEE
139. e comma as decimal point Dynamic Stabili Selecting the read plot info items aiii ur will cause their stored settings to Warn for Zero Freq Data E be loaded automatically The T Eistogram plotlabel can show your Ph d Freq Data Writing Setti T Spectrum organization name jase ana he es rg Senos Restore Default Values i 7 Write Header P Autocorrelation XI _Beset m Plot Label a a These parameters control the reading and writing of phase or v Label Plots Label Stable32 DX freq deta files The Max Data File Size is not an absolute program limit but determines when the averaging box opens automatically See Help file for more information Page 3 Plots Page 4 Data e Plots Page Controls The Plots property sheet page contains the following controls Control Type Description Read Plot Info Group Select plots for which to read configuration info Phase Checkbox Check to read config information for phase data plot Frequency Checkbox Check to read config information for freq data plot Sigma Checkbox Check to read config information for stability plot Dynamic Stab Checkbox Check to read config info for dynamic stability plot Histogram Checkbox Check to read config information for histogram plot Spectrum Checkbox Check to read config information for spectrum plot Autocorrelation Checkbox Check to read config info for autocorrelation plot Plot Settings Group Select settings for plots Use Sma
140. e data file from disk Examine the phase data in the Data File Opened box and enter the averaging time tau value Convert the phase data to frequency data Check the frequency data for outliers Plot the frequency data Remove the frequency drift Plot the frequency residuals Run a stability analysis Plot the stability data CANADA WwW The results of an analysis can be documented by printing a table plotting a graph copying values to the Windows clipboard reading a stability file replaying a plot or reading or pasting a converted plot into another application In addition a log file is produced that documents all the analysis steps performed e Data Precision There are relatively few numerical precision issues relating to the analysis of frequency stability data One exception however is phase data for a highly stable frequency source having a relatively large frequency offset The raw phase data will be essentially a straight line representing the frequency offset and the instability information is contained in the small deviations from the line A large number of digits must be used unless the frequency offset is removed by subtracting a linear term from the raw phase data Similar considerations apply to the quadratic phase term linear frequency drift Many frequency stability measures involve averages of first or second differences Thus while their numerical precision obviously depends upon the variable digits of t
141. e data has an even filename extension number while frequency data has an odd extension number The Show File Opened checkbox controls the option to show a data plot and other information when a data file is opened This also allows the data file to be displayed and the data and timetags to be scaled as it is read The AutoCalc checkbox controls the option to automatically perform a default calculation upon entry to the Sigma and Run function The AutoPlot checkbox controls the option to automatically do a default phase or frequency data plot upon entry to the Plot function The Show Status Plots checkbox controls the option to display small phase and frequency data plots on the status bar at the bottom of the screen This option is offered because it can take a significant amount of time to redraw these plots for large data files e Toolbuttons The Toolbuttons Configure page contains a multiple selection list box to select the Toolbuttons that are shown on the toolbar below the menu Select as many of these as will fit across your screen omitting those least used as necessary The order of the toolbuttons cannot be changed Menu items are also available to access all toolbutton functions e Plots The Phase Frequency Sigma Dynamic Stability Histogram Spectrum and Autocorrelation checkboxes control automatic reading and saving of plot options lines and notes when the Stable32 program is opened and closed This can be convenient for repet
142. e filled with interpolated values before the analysis which can result in linear features on the lag scatter plot for a group of gaps The autocorrelation plot can be restricted to fewer points to better show values at smaller lags The autocorrelation sequence is most useful for determining the non whiteness of data or residuals for detecting periodic components and for identifying the dominant power law noise type The autocorrelation results are available in a data file for further analysis Deselect the inserted lag scatter plot to print or convert an autocorrelation plot or use the Play program to replay and plot or convert an autocorrelation plot with the inserted lag scatter plot 195 STABLE32 USER MANUAL 196 ANALYSIS FUNCTIONS Histogram Function e Purpose Use the Histogram function to plot a histogram of the current phase or frequency data Histogram Plot EI Title HISTOGRAM SubTitle phase dat y Close Message Help Message Position Top Left Read Config Save Config Plot Filename CAstable321HISTO TKF BesetAll Axis Y Axis Label Data Value Label Points Per Bin Options Y Date M Box M Cursor M Fit Normalize e Controls The Histogram dialog box contains the following controls Control Type Description Plot Pushbutton Plot histogram Title Combo Enter or select plot title Default is HISTOGRAM Sub Title Combo Enter or select plot subtitle Default is filena
143. e interval t An adaptive algorithm is used to weight the contributions of the individual tapers for lowest bias The multitaper PSD has a flat topped response for discrete spectral components that is nevertheless narrower than an averaged periodogram with the same variance It is therefore particularly useful for examining discrete components along with noise e PSD Data File A data file comprising a header and rows of 2 or 3 columns of Fourier frequency PSD and optionally AF values is written each time a power spectrum plot is generated This file which has a default name PSD DAT must be manually renamed before the next plot to save it An example of the first few lines of a PSD dat file is shown below File Date Type Avg Factor Auto Points 63 C Program Files Hamilton Technical Services Stable32 PSD DAT 01 27 07 13 24 08 Fourier Freq Hz amp Phase Noise L f dBc Hz Window 1 Hanning Carrier Freg 1 000e 7 Fourier Freq PSD Avg Factor 1 95312500e 03 1 83080795e 02 2 00000000e 00 3 90625000e 03 1 84696045e 02 4 00000000e 00 7 81250000e 03 1 79434464e 02 8 00000000e 00 1 56250000e 02 1 72444656e 02 8 00000000e 00 2 34375000e 02 1 63880249e 02 8 00000000e 00 Notes The carrier frequency parameter applies only to the Sf f and f PSD types Fourier frequency points is always the power of 2 greater than or equal to 1 2 of the of time domain data points n The spacing between Fourier frequency points is 1 nt and
144. e offset 0 0 FPlotX Frequency data plot x axis label 0 X Mult X axis scale multiplier 1 0 Y Offset Y axis scale offset 0 0 Y Mult Y axis scale multiplier 1 0 Y Min Y axis scale minimum value 0 0 Y Max Y axis scale maximum value 1 0 Fit Draw fit line flag 0 FXDefault Flag to set x axis scale to default 1 e PhasePlot The PhasePlot section of the STABLE32 INI file can contain the following parameters Keyword Description Default Title Plot title text Null Subtitle Plot subtitle text Null Message Message text Null X Label X axis time label text Null Y Label Y axis phase label text Null PlotFile TKF filename Null Position Message position 0 X Div x axis divisions 5 Y Div y axis divisions 5 Y Tic y axis tics gt Line Line type 0 Mouse Mouse flag 0 Date Date annotation flag 0 Box Draw box around plot flag 0 Wide Use wide plot line flag 0 Fit Draw fit line flag 0 X Offset X axis scale offset 0 0 X Mult X axis scale multiplier 1 0 Y Offset Y axis scale offset 0 0 Y Mult Y axis scale multiplier 1 0 Y Min Y axis scale minimum value 0 0 Y Max Y axis scale maximum value 1 0 PPlotX Phase data plot x axis label 0 PXDefault Flag to set x axis scale to default 1 e SigmaPlot The SigmaPlot section of the STABLE32 INI file can contain the following parameters Keyword Description Default Title Plot title text Null 293 STABLE32 USER MANUAL Subtitle Plot subtitle text Null Message Message text Null PlotFi
145. e overlapping Hadamard variance is recommended over its non overlapping form for analyzing stability in the presence of divergent noise or frequency drift In all cases the results are reported in terms of the deviations The choice of tau interval depends mainly on whether interference mechanisms are suspected which cause the stability to vary periodically Normally octave spacing will be used with decade spacing available to analyze tau multiples of ten The all tau option can be useful as a form of spectral analysis to detect cyclic disturbances such as temperature cycling 275 STABLE32 USER MANUAL 276 OTHER INFORMATION Validation e Validation Considerable effort has been taken to insure that the results obtained from Stable32 are correct In particular each of the six validation methods listed below have been employed Stable32 uses the same basic analysis functions of Stable DOS and the FrequenC Library both of which have been used extensively by a number of individuals and organizations for over ten years In addition feedback and peer review has been and still is encouraged Please report any suspected discrepancies A convenient way to do this is via the Feedback item under the Help menu One important validation method is comparison of the program results against the test suite described above Copies of the NBS and 1000 point test data are included with the Stable32 distribution e Validation Methods Several metho
146. e sequence divided by the interval Extend the subsequence at both ends by uninverted even reflection to form the 9m point subsequence y having the tripled range from i n 3m to n 6m 1 The extended subsequence can be constructed by the expressions yn k y 4 and Ynt3m k 1 Y n 3m x for k 1 to 3m Calculate the Hadamard 3 sample variance for this extended subsequence by forming the 6 m point frequency averages and finding the square of their 2nd differences Find TOTHVAR as the simple average of the N 3m HVAR subestimates References The following references apply to the total Hadamard statistic l 2 D A Howe et al A Total Estimator of the Hadamard Function Used For GPS Operations Proc 32 PTTI Meeting Nov 29 2000 pp 255 268 D A Howe R L Beard C A Greenhall F Vernotte W J Riley and T K Peppler Enhancements to GPS Operations and Clock Evaluations Using a Total Hadamard Deviation JEEE Trans UFFC Vol 52 No 8 August 2005 73 74 STABLE32 USER MANUAL TIME DOMAIN STABILITY e Th o1 The Theoretical Variance 1 Th ol is a special purpose statistic for the estimation of long term frequency stability It produces results similar to the Allan variance for averaging factors out to nearly the full data length The Th o statistic is defined as follows i 2 1 N m m 2 1 1 N 2 my mz y 0 75 2 4 m 2 9 i l Theol m To N x Kim Xinm 7 Xuan Ji for aver
147. e to reject comments but can also prevent the reading of actual data Thus if the data lines start with non numeric characters this configuration variable can help when reading them The Use Comma checkbox allows commas to be substituted for decimal points in data files The Warn for Zero Frequency checkbox activates a warning message when two identical adjacent values occur in a phase data file that result in a zero fractional frequency value that is also used to indicate a gap in the data Note that the Adjust Zero Frequency option in the Convert function can be used to adjust those zero fractional frequency values to 1e 99 in order to avoid their treatment as gaps The Write Header option causes a header that includes the filename date amp time data type points and tau to be written at the top of a data file The Reset pushbutton restores the Max Data File Size and Non Numerics to Skip to their default values e Inputs The Inputs Configure page contains edit controls for entering parameters that are applied to set and scale input data Separate sets of input values apply to phase and frequency data The Tau input value sets the measurement interval of the data in accordance with the following order of precedence It must have units of seconds 1 Manual entry 2 Command line 3 File header 4 INI Inputs 5 Timetag interval 6 Default 1 second 51 STABLE32 USER MANUAL The Addend and Multiplier values modi
148. ear Show Clear function toolbutton 0 Power Show Power function toolbutton 0 Edit Show Edit function toolbutton 0 Sigma Show Sigma function toolbutton 0 Fill Show Fill function toolbutton 0 Scale Show Scale function toolbutton 0 Play Show Play program toolbutton 0 Tag Show Timetag function toolbutton 0 Reg Show Regularize function toolbutton 0 Dom Show Domain function toolbutton 0 Part Show Part function toolbutton 0 Help Show Help function toolbutton 0 Pad Show Notepad function toolbutton 0 DVAR Show DAVAR function toolbutton 0 Autol Show Autol function toolbutton 0 Auto2 Show Auto2 function toolbutton 0 297 STABLE32 USER MANUAL Auto3 Show Auto3 function toolbutton 0 ACF Show ACF function toolbutton 0 Conf Show Configure function toolbutton 0 File Show Filenames function toolbutton 0 Comm Show 5110Comm program toolbutton 0 DBase Show Database function toolbutton 0 Tab Show Tab function toolbutton 0 e Inputs The Inputs section of the STABLE32 INI file can contain several read only items that serve as user selectable default values for the following parameters Keyword Description Default PhaseTau Tau value for phase data 1 0 FreqTau Tau value for frequency data 1 0 PhaseAddend Default value to be added to phase data in 0 0 Scale function FregAddend Default value to be added to frequency data in 0 0 Scale function PhaseMultiplier Default factor to multiply phase data by in 1 0 Scale function FregMultiplier Default factor
149. ease examine the README TXT file for any supplementary information It may be read with Notepad Executables STABLE32 EXE PLAYW EXE 5110COMM EXE Dynamic Link Libraries DTBL32 DLL FREQUENC DLL GPCWDLL DLL GPCWDRVN DLL LICENS32 DLL CGM DLL HPGL DLL POSTSCR DLL TIFF DLL SCODL DLL PIC DLL GEM DLL LIBPQ DLL LIBEA Y32 DLL LIBINTL 2 DLL LIBICONV 2 DLL SSLEAY32 DLL GraphicC Fonts BLOCK FNT COMPGRMA FNT COMPITAL FNT COMPLEX FNT COMSCR FNT DUPLEX FNT ENGOTH FNT MATRIX FNT MICROB FNT MICROG FNT NEWS FNT NEWSGRM FNT RUSSIAN FNT SIMGRMA FNT SIMPLEX FNT SIMSCR FNT SWISS FNT SWISSBIT FNT SWISSBLD FNT SWISSITL FNT SWISSN FNT TRIPITAL FNT TRIPLEX FNT Help Files STABLE32 CHM GRAPHICW HLP 5110COMM CHM HONH CHM Sample Data FREQ DAT PHASE DAT SAMPLE DAT TST SUIT DAT NBS DAT NOISEPIX TKF Stability Masks G 811PRC MTIE MSK G 824PRC MTIE MSK Miscellaneous MESSAGES TAB HDRI POS README TXT Documentation MANUAL150 PDF FUNCTIONS PDF STABLE32 USER MANUAL G 811PRC TDEV MSK TISTRATUMG TDEV MSK TEST MSK MESSAGES DAT HDR2 POS 5110COMM INI WELCOME PDF TECHNIQUES PDF STABILITY ANALYSIS SOFTWARE PDF Optional File TISTRATUM2 3E TDEV MSK HDR TIF STABLE32 INI STABILITYCHART PDF Play and 5110Comm files not included with Student Version GENERAL Directories e Directories The Stable32 program support and data files are normally located in a single disk directory folder as described below e Installat
150. easurement is negligible Or if the noise of the reference is known it can be removed by subtracting its variance A special case is that of two identical units where half of the measured variance comes from each and the measured deviation can be corrected for one unit by dividing it by 2 Otherwise it may be useful to use the so called 3 cornered hat method for separating the individual variances Given a set of three pairs of measurements for three independent frequency sources a b and c whose variances add 0 c ap O 0 Oac 0 0 O yc 0 0 The individual variances may be separated by the expressions 02 Y ab m ac i Orc ar Y Sab s be 7 ac 0 Y ac a be O72 Although useful for determining the individual stabilities of units having similar performance the method may fail by producing negative variances for units that have widely differing stabilities if the units are correlated or for which there is insufficient data The three sets of stability data should be measured simultaneously The 3 cornered hat method should be used with discretion and it is not a substitute for a low noise reference It is best used for units having similar stability e g to determine which unit is best Negative variances are a sign that the method is failing because it was based on insufficient measurement data or because the units under test have disparate or correlated stability This problem is most likely to arise
151. ed n0 1234567890 it produces the sequence n 395529916 n 1209410747 n 633705974 etc These numbers may be divided by 2147483647 to obtain a set of normalized floating point test data ranging from 0 to 1 Thus the normalized value of ny is 0 5748904732 A spreadsheet program is a convenient and reasonably universal way to generate this data The frequency data set may be converted to phase data by assuming an averaging time of 1 yielding a set of 1001 phase data points Similarly frequency offset and or drift terms may be added to the data These conversions can also be done by a spreadsheet program The values of this data set will be uniformly distributed between 0 and 1 While a data set with a normal Gaussian distribution would be more realistic and could be produced by summing a number of independent uniformly distributed data sets or by the Box Muller method 24 this simpler data set is adequate for software validation 270 OTHER INFORMATION Table III 1000 Point Frequency Data Set Averaging Factor Data Points Maximum Minimum Average 1 Median Linear Slope 2 3 Intercept 3 Bisection Slope 2 1st Diff Slope 2 Log Fit 2 4 a y t a In bt 1 c b y t ab bt 1 c Slope at end Standard Dev 5 Normal Allan Dev 6 Overlap Allan Dev 8 Mod Allan Dev 7 8 Time Deviation 8 Hadamard Deviation Overlap Had Dev Hadamard Total Dev Total Deviation Total modified Dev Time Total Devia
152. ed Allan Variance Proc 1992 IEEE Freq Contrl Symp pp 262 264 May 1992 C A Greenhall Estimating the Modified Allan Variance Proc IEEE 1995 Freq Contrl Symp pp 346 353 May 1995 C A Greenhall The Third Difference Approach to Modified Allan Variance JEEE Trans Instrum Meas Vol IM 46 No 3 pp 696 703 June 1997 OTHER INFORMATION Time Variance D W Allan and H Hellwig Time Deviation and Time Prediction Error for Clock Specification Characterization and Application March 1981 D W Allan D D Davis J Levine M A Weiss N Hironaka and D Okayama New Inexpensive Frequency Calibration Service From NIST Proc 44th Annu Symp on Freq Contrl pp 107 116 June 1990 D W Allan M A Weiss and J L Jespersen A Frequency Domain View of Time Domain Characterization of Clocks and Time and Frequency Distribution Systems Proc 45th Freq Contrl Symp pp 667 678 May 1991 Hadamard Variance R A Baugh Frequency Modulation Analysis with the Hadamard Variance Proc 25th Freq Contrl Symp pp 222 225 April 1971 B Picinbono Processus a Accroissements Stationnaires Ann des telecom Tome 30 No 7 8 pp 211 212 July Aug 1975 K Wan E Visr and J Roberts Extended Variances and Autoregressive Moving Average Algorithm for the Measurement and Synthesis of Oscillator Phase Noise Proc 43rd Freq Contrl Symp pp 331 335 June 1989 S T Hutsell Relating the Hadamard Vari
153. ed and concurrent programs can affect the script execution and successful operation cannot be guaranteed 245 STABLE32 USER MANUAL 246 MISCELLANEOUS FUNCTIONS 3 Comered Hat Function e Purpose Use the 3 Cornered Hat function to with discretion to separate variances from 3 sets of stability data e Controls The 3 Cornered Hat dialog box contains the following controls 3 Cornered Hat EI r Stability Files A B CAProgram Files A C CAProgram Files B C CAProgram Files Browse Bead 1 000e 01 1 427e 11 1 443e 11 1 291e 11 2 000e 01 1 031e 11 1 023e 11 9 733e 12 4 000e 01 7 241e 12 7 163e 12 7 113e 12 8 000e 01 5 606e 12 4 692e 12 5 119e 12 1 600e 02 4 065e 12 3 471e 12 3 720e 12 3 200e 02 2 699e 12 1 851e 12 2 895e 12 Calc Close Help 6 400e 02 2 031e 12 1 479e 12 2 217e 12 Plot 1 280e 03 1 377e 12 6 038e 13 1 962e 12 Options Lines Notes did Enter filenames read stability data ia Sigma Type Copy aeee st or sony dao ET Pint with the same sigma type amp tau range Unit an E OMM ODE Control Type Description Stability Files Group Choose stability filenames A B Edit Enter A B stability data filename A C Edit Enter A C stability data filename B C Edit Enter B C stability data filename Browse Pushbutton Invoke file open dialog box to select data file Tau etc Table Table of tau and stability data Read Pushbutton Read stability data Calc Pushbutt
154. ed name of STAB dat is also written to disk during each stability plot This file contains values related to the stability analysis with rows corresponding to each averaging factor and 9 columns as follows Tau Analysis Points Minimum Sigma Maximum Sigma Nominal Sigma Standard Deviation Degrees of Freedom Alpha Averaging Factor Two sets of rows are included for the Overlap amp Mod and Th oH variance types e Notes Printing of the stability results is not available for the All Tau option The TIE rms MTIE Th ol and Th oH statistics are only available for phase data TIE rms and MTIE do not include confidence intervals 222 ANALYSIS FUNCTIONS Run Plot Function e Purpose Use the Run Plot function to generate a stability plot ES GraphiC Win sigma tkf ol x File Edit Draw Convert Help Dole 3 Fhe ohose 02 27 30 ilme BL o ai o Ki 5 E To E lo Palms 1 thru 1007 of TO REQUENCY STABILITY Gaya i E ms 16 32 64 123 10 2 10 2 Averaging Time 1 Seconds Sigma 2 92e 01 2 05e 01 1 49e 01 1 10e 01 5 24e 02 f 5 62e 02 3 25e 02 f 3 59e 02 223 STABLE32 USER MANUAL 224 ANALYSIS FUNCTIONS Run Options Function e Purpose Use the Run Options function to control the attributes of the stability plot Title FREQUENCYSTABILITY OOO x Sume PHASEDAT OO gy 7 Message O m Hep Message Position Top Left Read Config Save Config
155. ed with successive averaging may reduce the With gaps the can depend on exactly where the gaps are In all cases the is counted dynamically during the calculation as the statistical sums are accumulated References 1 WJ Riley and C A Greenhall Power Law Noise Identification Using the Lag 1 Autocorrelation Proc 18 European Frequency and Time Forum April 2004 2 D Howe R Beard C Greenhall F Vernotte and W Riley A Total Estimator of the Hadamard Function Used for GPS Operations Proceedings of the 32nd Annual Precise Time and Time Interval PTTI Systems and Applications Meeting pp 255 268 November 2000 89 90 STABLE32 USER MANUAL TIME DOMAIN STABILITY Bias Functions e Bias Functions Several bias functions are defined and used in the analysis of frequency stability These bias functions are defined below The Stable32 program uses the B1 the standard variance to Allan variance ratio and R n the modified Allan variance to normal Allan variance ratio bias functions for the identification of noise types e B1 Bias Function The B1 bias function is the ratio of the N sample standard variance to the 2 sample Allan variance with dead time ratio r T t where T time between measurements t averaging time and u exponent of x in Allan variance for a certain power law noise process BIN r u 07 N T t o Q2 T x e B2 Bias Function The B2 bias function is the ratio of the 2 sample
156. edf for the modified Allan variance MVAR is determined by the same expression as the overlapping Hadamard variance see below with the arguments changed as follows valid for 2 lt a lt 2 MVAR and TVAR edf for N m and MVAR edf for N 1 m and a 2 e TOTVAR EDF The edf for the total variance TOTVAR is given by the formula b T t c where T is the length of the data record t is the averaging time and b amp c are coefficients that depend on the noise type as shown in the following table Power Law TOTVAR edf coefficients Noise Type b c W FM 1 50 0 F FM 1 17 0 22 RW FM 0 93 0 36 e TOTMVAR EDF The edf for the total modified variance TOTMVAR is given by the same formula b T 1 c where T is the length of the data record t is the averaging time and b amp c are coefficients that depend on the noise type as shown in the following table 87 STABLE32 USER MANUAL Power Law TOTMVAR edf Noise Type coefficients b c WPM 1 90 2 10 F PM 1 20 1 40 W FM 1 10 1 20 F FM 0 85 0 50 RW FM 0 75 0 31 e HVAR EDF The edf for the fully overlapping Hadamard variance HVAR can be found by an algorithm developed by C A Greenhall based on its generalized autocovariance function The HVAR edf is found either as a summation for small m cases with a small number of terms or from a limiting form for large m where 1 edf 1 p a0 al p with the coefficients as foll
157. eeting pp 255 268 Nov 2000 W J Riley and C A Greenhall Power Law Noise Identification Using the Lag 1 Autocorrelation Proc 18th European Freq and Time Forum April 2004 Bias Functions J A Barnes Tables of Bias Functions BI and B2 for Variances Based on Finite Samples of Processes with Power Law Spectral Densities NBS Technical Note 375 Jan 1969 W J Riley Confidence Intervals and Bias Corrections for the Stable32 Variance Functions Hamilton Technical Services Dead Time J A Barnes and D W Allan Variances Based on Data with Dead Time Between the Measurements NIST Technical Note 1318 U S Department of Commerce National Institute of Standards and Technology 1990 D B Sullivan D W Allan D A Howe and F L Walls Editors Characterization of Clocks and Oscillators NIST Technical Note 1337 U S Department of Commerce National Institute of Standards and Technology TN 296 335 March 1990 J A Barnes The Analysis of Frequency and Time Data Austron Inc Dec 1991 D A Howe and E E Hagn Limited Live Time Measurements of Frequency Stability Proc Joint FCS EFTF pp 1113 1116 April 1999 W J Riley Gaps Outliers Dead Time and Uneven Spacing in Frequency Stability Data Hamilton Technical Services 3 Cornered Hat J E Gray and D W Allan A Method for Estimating the Frequency Stability of an Individual Oscillator Proc 28 Freq Contrl Symp pp 243 246 May 1974 J Groslam
158. effective method for identifying power law noises based on the properties of discrete time fractionally integrated noises having spectral densities of the form Q sin nf 1 For 8 Y the process is stationary and has a lag 1 autocorrelation equal to p 9 1 6 and the noise type can therefore be estimated from 6 r 1 r For frequency data white PM noise has p 1 2 flicker PM noise has p 1 3 and white FM noise has p 0 For the more divergent noises first differences of the data are taken until a stationary process is obtained as determined by the criterion 6 lt 0 25 The noise identification method therefore uses p round 28 2d where round 28 is 26 rounded to the nearest integer and d is the number of times that the data is differenced to bring 6 down to lt 0 25 Ifz is a t average of frequency data y t then a p if z is a t sample of phase data x t then a p 2 where a is the usual power law exponent f thereby determining the noise type at that averaging time When there are a sufficient number of data points this method has excellent discrimination for all common power law noises for both phase and frequency data including difficult cases with mixed noises The dominant power law noise type can also be estimated by comparing the ratio of the N sample standard variance to the 2 sample Allan variance of the data the B1 bias factor see below to the value expected of this ratio for the pure
159. ementing the modified and Hadamard total variances while D B Percival amp A T Walden s book and J M Lees amp J Park s code supported multitaper spectral analysis D A Howe and T N Tasset have contributed significantly with the Th ol statistic Perkin Elmer Inc supported the development of the Database function and Matthew Phillips of Timing Solutions Corporation assisted in its writing 279 STABLE32 USER MANUAL Contributors Many people have contributed to the development of Stable32 reporting problems and offering ideas for new features Some of those persons are as follows Jim Barnes Dave Allan and Dave Howe for the statistical foundations Sam Stein for suggesting the GraphiC library Ed Powers for early evaluation and suggestions Ken Lyon for user interface suggestions Gernot Winkler for pratical robust statistics Todd Walter for power law noise generation Steve Kelley for GraphiC support Dave Howe for total statistics Trudi Peppler for programming collaboration Chuck Greenhall for many contributions related to edf Jack Kusters for the TDEV loci on MDEV plots Paul Koppang for suggesting the 1 of 2 option Paul Koppang and Chris Ekstrom for the 3 cornered hat edf Robert Lutwak for many many suggestions including the automation feature Ken Senior for careful checking of the Sigma and Run results Patrizia Tavella for unequally spaced data suggestions and dynamic stability analysis Tom Becker for
160. en to record a synopsis of all program activity during each run This ASCII text file contains a line for each major function called It gives a summary of the operation performed and thus can be used to document the steps performed during an analysis An example of a STABLE32 LOG file is shown below 01 17 99 01 17 99 01 17 99 01 17 99 01 17 99 The first two 11 11 11 115 114 08 Stable32 Version 1 46 Log File 08 Freg Data Opened FREO DAT 09 Freq Sigma Type Overlapping AF 1 Sigma 2 922319e 01 09 Freq Data Plot C Stable32 FREQ TKF 09 Stable32 Closed columns show the date and time in MM DD YY and HH MM format respectively The text on each line describes the operation performed and as appropriate a summary of the results obtained A new log file is written each time Stable32 is started so the previous one must be renamed in order to preserve it 43 44 STABLE32 USER MANUAL GENERAL Special Versions e Student Version A Student Version of Stable32 is available at a significantly reduced price It is identical in all respects to the standard version except for the following differences 1 No printed User Manual is included 2 The maximum data array size is limited to 513 points 3 The Play and 5110Comm programs are not included 4 The automation function is not supported 5 Printouts cannot be made of data stability power spectrum and histogram plots e Demo Version A Demo Version of
161. ened configuration item to speed data file entry Ne APPENDICES Batch Files The WinBatch batch language program for Windows from Wilson WindowWare Inc is highly recommended to automate repetitive analysis procedures with Stable32 Information is available at http www windowware com Screen Setup Use 1024 x 768 XGA screen resolution or higher if possible in order to support the mini data plots on the Stable32 status bar This resolution also supports the use of all toolbar buttons With lower than XGA resolution use the Configure function to select the toolbar buttons that you want The phase and frequency mini data plots can be eliminated by deselecting the Status Plots box in the Configure function This can save screen space and reduce update time on older systems Data Output The results of an analysis can be documented or captured in several ways for use in another analysis or application The results of a Check or Run can be printed The results of a Sigma or Drift calculation a stability Run or a Domain conversion can be copied to the clipboard with the Copy button Software such as the Microsoft ClipBook Viewer can be used to capture multiple outputs The results of a Run are written to a stability file that can be read by the Read function or another application All of the GraphiC plots can be printed copied to the clipboard or converted and saved in a number of file formats And finally a synopsis of a Stable32 ana
162. equency Control Symposium pp 274 283 May 1992 2 C A Greenhall FFT Based Methods for Simulating Flicker FM Proceedings of the 34th Annual Precise Time and Time Interval PTTI Systems and Applications Meeting December 2002 pp 481 492 214 ANALYSIS FUNCTIONS Example An example of the frequency stability of simulated data with a combination of white PM noise and a sinusoidal term is shown below 0 1 Shee ee 2 ot Rt 2 quee 101 2 Averaging Time t Seconds 3999 o 3999 FREQUENCY STABILITY Vibration Induced Allan Deviation Degradation 10 a Points 1 thru e i liiiiii i liiiii i 5 or 0T 101 z1 OT E 2 o uorierAeq uey urdde 19A0 215 STABLE32 USER MANUAL 216 ANALYSIS FUNCTIONS Clear Function e Purpose Use the Clear function to clear phase or frequency data or the corresponding timetags Note It is not necessary to clear the data array before reading another data file Data To Clear Iv Phase Data Iv Phase Timetags Frequency Data Ere BUE meten W Press OK to clear selected data Controls The Clear dialog box contains the following controls Control Type Description Data To Clear Group Choices for data to clear Phase Data Checkbox Clear phase data Phase Timetags Checkbox Clear phase timetags Frequency Data Checkbox Clear frequency data Frequency Timetags Checkbox Clear frequency timetags
163. equency data at the same zoom factor e Caution The Statistics function can be slow when processing frequency data having many repeated values because of the function used to find the median value 174 ANALYSIS FUNCTIONS Check Function e Purpose Use the Check function to check for and remove outliers from frequency data e Controls The Check dialog box contains the following controls Control Type Description Sigma Factor Edit Enter desired outlier criterion Outliers Text Display the of outliers Remove All Checkbox Remove all frequency outliers Show Details Checkbox Show detailed Check dialog box Calc Pushbutton Perform Check function amp close dialog box Close Pushbutton Abort Check function amp close dialog box Help Pushbutton Invoke the Check help topic Activating the Show Details option adds the following controls to the Check dialog box 175 STABLE32 USER MANUAL Control Type Description Sort Order Group Choose sort order Position Radiobutton Sort outliers by position Size Radiobutton Sort outliers by size Sigma Factor Edit Enter sigma factor Med Abs Dev Text Display MAD value Remove Outliers Group Choose type of outlier removal None Radiobutton Don t remove any outliers All Radiobutton Remove all outliers Largest Radiobutton Remove the largest outlier Selected Radiobutton Remove the selected outlier PrintPushbutton Print outliers Copy Pushbutton Copy o
164. er For now exit the Edit function by pressing Cancel 11 Select the Plot function by clicking on its toolbutton 12 Press the Plot button to produce a GraphiC plot of the frequency data The plot shows white frequency noise plus drift Close the plot by double clicking on its system menu icon If you wish you can try pressing the plot Options button to change the plot title or add a linear regression line and slope message to the plot Then leave the overall plot function 3 GraphiC Win freq tkf olx Eile Edit Draw Convert Help Dote 01 08 06 Time 16 327 0000000e 00 File SAMPLE DAT FREQUENCY DATA AMPLE DAT 6 00 T 3 T T 550L Slope Tau Interval 1 014e 00 0 350 100 150 200 250 300 350 400 450 500 550 Data Point Lineor Pi y t 0 bt intereepi 0 4 5868560e 01 Slope b 1 0135908 00 Siena 13 Select the Drift function from the Analysis menu or toolbar Notice that you have the option to Show Details for this function 267 14 15 16 17 18 19 20 21 22 268 STABLE32 USER MANUAL Choose Linear drift and check the Remove Drift box Then press Calc to calculate and remove the linear drift of about 1 0 per tau interval from the frequency data Notice that the unsaved symbol has appeared in the status bar indicating that the data has changed Also if enabled in the Configure box the filename extension will have been changed to 001 Close t
165. error bars in its stability analysis and plotting functions The confidence interval of an Allan variance estimate depends not only on the Allan variance type non overlapping overlapping modified or time and nominal value and on the averaging factor and number of data points but also on the statistical confidence factor desired and the type of noise e Simple Confidence Intervals The simplest confidence interval approximation with no consideration of the noise type sets the 10 68 error bars at 0 1 VN where N is the number of frequency data points used to calculate the Allan deviation e Kn Noise Factor A more accurate determination of this confidence interval can be made by considering the noise type which can be estimated by the B1 bias function the ratio of the standard variance to the Allan variance That noise type is then be used to determine a multiplicative factor Kn to apply to the confidence interval These are the error bars shown by the Stable32 Variance and Run functions for the non overlapping Allan deviation Noise Type Kn Random Walk FM 0 75 Flicker FM 0 77 White FM 0 87 Flicker PM 0 99 White PM 0 99 e Overlapping Samples Better statistical confidence can be obtained by making maximum use of the available data by forming all possible frequency differences for a given averaging time Although these fully overlapping samples are not all statistically independent they nevertheless help to improve the co
166. ers B1 R n Ratio Text Display B1 or R n ratio Noise Text Display estimated noise type Alpha Text Display estimated a value Mu Text Display estimated u value Kn Text Display Kn value 181 STABLE32 USER MANUAL Dead Time Group Dead time parameters T Tau Edit Enter deadtime ratio B2 Text Display B2 value B3 Text Display B3 value Conf Limits Group Confidence limit parameters Analysis Pts Text Display analysis points Max Sigma Text Display maximum sigma value Min Sigma Text Display minimum sigma value Copy Pushbutton Copy analysis results to clipboard Show Details Checkbox Deselect detailed Sigma dialog box format Set Noise Checkbox Set noise to user selected type ACF Noise ID Group Lag 1 autocorrelation noise ID params rl Text Lag 1 autocorrelation value Alpha Text Estimated power law noise type Apply Checkbox Use ACF noise ID method Noise Combo Select noise type when Set Noise is checked r Variance Parameters r Confidence Limits Calc Variance Type Overlap Allan Analysis Pts 998 Avg Factor fi ChiSqrDF 781248 Copy BW Factor Net Applicable Single C Double Sided Cl Help Welt 1 000000e 00 ConfEactor 0 950 Show Deteils r Sigma Results 22 717 533 SetNoise Sigma 2 921983e 01 Max ADEV 3 048956e 01 i ACF Noise ID Std Dev 2 885205e 01 Min ADEV Not Applicable E 20987 Noise Type Alpha 0 05 B1 Ratio 0 975 Noise WF
167. ers to perform domain conversion for BWFM 4 None BWFM 1 f0 0000e 00 EFM 30 None JEM o o 00000e 00 WFM 20 eo wrM a f1o000De 11 FEM 10 None FEM 2 o 00000e 00 WPM 0 WPM 1232818 12 All 00 All 1 00757e 11 PSD Plot Sigma Plot E StertFreg 1 000008 00 StartTau 1 000008 03 PetPsp End Freg 1 00000e 03 End Tau 1 000008 00 power law noise An Lif value of 0 denotes none BW applies only to W amp F PM noise e Controls The Domain dialog box contains the following controls Control Type Description Sigma Type Combo Choose sigma type normal modified or time Tau Sec Edit Enter basic averaging time To in seconds Avg Factor Edit Enter averaging factor AF t t where tis the analysis averaging time BW Factor Edit Enter bandwidth factor 27f t where f is the upper cutoff frequency of the measuring system in Hz and applies only to white and flicker PM noise PSD Type Combo Choose power spectral density PSD type SB Freq Hz Edit Enter the sideband frequency in Hz Carrier Freq Edit Enter the carrier frequency in MHz BW Hz Edit Enter the measuring system bandwidth in Hz PSD Label Use to select PSD entries from keyboard PSDRWFM Edit Enter or read the random walk FM noise PSD parameter PSD FFM Edit Enter or read the flicker FM noise PSD parameter PSD WFM Edit Enter or read the white FM noise PSD
168. es of measurement record pairs with overlapping time spans will be shown in the Read Times section along with their time Span and of data points Records that are continuing are denoted by Run Continuing and if both records are continuing the end time will be the current time Enter the desired AF averaging factor for the read data Then press Read to read the selected data from the MMS database and write it to a file The read operation can take a considerable time if the span is long and or the database connection is slow and can be aborted with the Abort button during a read The data read prior to the abort is valid and may be analyzed by any of the Stable32 analysis functions The parameters for the database access can be set by pressing the Configure button see the Database Configure Help topic These settings will take effect the next time the Database function is opened The clock names and records can be reset with the Reset button useful if the database may have changed since opening the Database function 134 FILE FUNCTIONS e Symmetricom MMS System The Symmetricom previously Timing Solutions Corporation Multi Channel Measuring System MMS is a multiple mixer clock measurement system It measures the phase differences between the clocks under test and an offset reference that is common to all measurment channels These phase differences and the time of the measurement are stored in the MMS database When data is read from t
169. ethods l The first optimum for white PM noise uses a least squares linear fit to the phase data x t a bt where slope y t b The second method optimum for white FM noise uses the average of the first differences of the phase data y t slope x t t x t t The third method simply uses the difference between the first and last points of the phase data slope y t x end x start M 1 where M phase data points This method is used mainly to match the two endpoints Frequency Data Four drift methods are also available for frequency data 1 The first the default is a least sguares linear regression to the freguency data y t a bt where a intercept b slope y t This is the optimum method for white FM noise 179 STABLE32 USER MANUAL 2 The second method computes the drift from the frequency averages over the first and last halves of the data slope 2 y 2nd half y 1st half Nt where N points This bisection method is optimum for white and random walk FM noise 3 The third method a log model of the form see MIL O 55310B y t a In bt 1 where slope y t ab bt 1 which applies to frequency stabilization It is available in the Plot function for frequency data 4 The last frequency drift method is a diffusion Vt model of the form y t a b t c where slope y t 4 b t cy It is also available in the Plot functio
170. eting pp 451 460 Dec 1992 G Wei Estimations of Frequency and its Drift Rate IEEE Trans Instrum Meas Vol 46 No 1 pp 79 82 Feb 1997 C A Greenhall A Frequency Drift Estimator and Its Removal from Modified Allan Variance Proc 1997 IEEE Freq Contrl Symp pp 428 432 June 1997 F Vernotte and M Vincent Estimation of the Measurement Uncertainty of Drift Coefficients Versus the Noise Levels Proc 12th European Freq and Time Forum pp 222 227 March 1998 263 264 STABLE32 USER MANUAL Noise Identification J A Barnes The Generation and Recognition of Flicker Noise NBS Report 9284 U S Department of Commerce National Bureau of Standards June 1967 J A Barnes Effective Stationarity and Power Law Spectral Densities NBS Frequency Time Seminar Preprint Feb 1968 J A Barnes and D W Allan Recognition and Classification of LF Divergent Noise Processes NBS Division 253 Class Notes circa 1970 J A Barnes Models for the Interpretation of Frequency Stability Measurements NBS Technical Note 683 U S Department of Commerce National Bureau of Standards Aug 1976 C A Greenhall and J A Barnes Large Sample Simulation of Flicker Noise Proc 19th PTTI Meeting pp 203 217 Dec 1987 and Proc 24th Annu PTTI Meeting p 461 Dec 1992 D Howe R Beard C Greenhall F Vernotte and W Riley A Total Estimator of the Hadamard Function Used for GPS Operations Proc 32nd PTTI M
171. frequency in MHz for that channel It is expressed as a 1 or 2 digit integer part a decimal point and a 15 digit fractional part thus forming a 17 or 18 character string The 2nd and 3rd numbers are clock phase in cycles with respect to the offset reference oscillator The 2nd number is a rounded integer tag while the 3rd has the full precision with a decimal point and a 12 digit fractional part The integer parts of these numbers grow with the beat note cycles of the offset oscillator about 10 per second so a 9 digit field is sufficient for about 3 years Thus the 2nd number string can have 9 characters and the 3rd number string can have 22 characters The number fields are each separated by 2 spaces Including spaces the maximum length of a line is 79 characters A sample line is as follows where is in 1st column and is followed by a single space Clock S N 0123456789 5 000000000000000 12007355 12007354 000000000000 Raw clock time data in seconds is calculated by dividing the phase number by the nominal frequency in MHz Corrected clock time is obtained from that value by subtracting the corresponding value for the reference channel This subtraction removes the contribution of the common offset local oscillator Fractional frequency is of course the difference between two adjacent time values divided by the time interval between them e Archive File Processing Clock data for a certain time span can be extracted directly
172. from TSC archive files by choosing the desired measurement and reference channels and then reading an archive file that has data for those sources during that period TSC archive file data can be processed either by using data from two measurement channels one serving as the reference or by using the common offset local oscillator LO as the reference In the former case the contribution of the offset LO cancels out Using the LO as the reference usually requires that it be synthesized from a standard source rather that being a free running crystal oscillator but measurements against a low noise crystal source can be an advantage for short averaging times An important feature of the TSC clock measuring system is that the reference for a particular measurement channel can be chosen after the fact and a single archive file can provide data versus several references Stable32 can process TSC archive data either between two measurement channels or between a single channel and the offset LO The latter is accomplished by using a reference channel 0 23 STABLE32 USER MANUAL e Archive File Records It is convenient to adopt the convention that while a gap in the data for all channels is a missing data point a gap in the data for an individual measurement channel represents the start of a new record Stable32 can process TSC archive data for a certain record for the last record for a span of MID dates or from a particular starting
173. fy the phase or frequency data as it is being read The data is scaled according to the following equation scaled value original value multiplier addend The Tag Scale and Tag Offset values modify the data timetags as they are being read A common use is to set the tag scale to 86 400 to convert MJD timetags into seconds e Options The Relative Max AF Absolute Max AF and LF Points to Skip values apply to the PSD Auto AF option of the Power function See the Power function section for more information about those parameters The Weight PSD Fit checkbox activates weighting of the semilog power law noise fit on a smoothed PSD plot The Smoothing Points Octave edit box controls the number of smoothed PSD points per octave of Fourier frequency The Many Tau checkbox determines whether the faster many tau method is used instead of an all tau Run stability analysis With the Many Tau option a selectable subset of the possible tau values is used to provide a quasi uniform distribution of points on the stability plot adequate to give the appearance of a complete set which can provide much faster calculating plotting and printing The Size edit box sets the approximate number of points used for the many tau analysis default 500 The two Reset pushbuttons restore the defaults for the PSD or many tau parameters e Notes 1 The display of data plots on the status bar applies only for XGA and higher screen resolutions 2 The Inpu
174. g box can be closed with the Cancel button or by closing the Edit dialog box 157 STABLE32 USER MANUAL 158 EDITING FUNCTIONS Replace Function e Purpose The Replace function is a Detailed Search sub function of the Edit function Use the Replace function to find and replace data phase or frequency data points that meet a particular criterion The Find function is also available to simply find certain phase or frequency data values Find What x m 8 5e 02 Eind Next Replace With o o Replace Next Replace All Iv Confirm Replacements Direction Up Close Note The of digits entered determines the search precision C Down n Help e Controls The Replace function uses a modeless dialog box that can remain open while the Edit function is active It contains the following controls Control Type Description Find What Combo Search type Edit Search value Replace With Edit Replacement value Direction Group Search direction controls Up Radiobutton Search upwards Down Radiobutton Search downwards Find Next Pushbutton Perform a Find operation Replace Next Pushbutton Perform a Replace operation for one point Replace All Pushbutton Perform a Replace operation for all points Confirm Checkbox Confirm each replacement Close Pushbutton Abort Replace function amp close dialog box Help Pushbutton Invoke the Replace help topic e Operation Select the search criterion with the two Find What
175. g times and is an important new general statistical tool 6 TOTAVAR is defined for phase data as 1 Y 2 Tot var 7 gt PAS i m AY FX em gt 27 N 2 2 where tT mt and the N phase values x measured at T t are extended by reflection about both endpoints to form a virtual sequence x from i 3 N to i 2N 2 of length 3N 4 The original data is in the center of x with i 1 to N and x x The reflected portions added at each end extend from j 1 to N 2 where x 2x1 xX1 and X N j 2XN Xn j TOTAVAR can also be defined for freguency data as Tot var 7 xu m Sp it jt y where the M N 1 fractional frequency values y measured at t t N phase values are extended by reflection at both ends to form a virtual array y The original data is in the center where y y for i 1 to M and the extended data for j 1 to M 1 is equal to y y and y y4 YMt 1 j The result is usually expressed as the square root Guu t the total Allan deviation TOTADEV When calculated using the doubly reflected method described above the expected value of TOTAVAR is the same as AVAR for white and flicker PM or white FM noise Bias corrections of the form 1 1 a t T where T is the record length need to be applied for flicker and random walk FM noise where a 0 481 and 0 750 respectively 65 STABLE32 USER MANUAL The number of equivalent X degrees of freedom for TOTAVAR can be estimated for w
176. ge Data File function The results of an Open operation will be displayed in a File Opened box if this feature is activated with the Show File Opened option of the Configure function e Filename Extensions The Open function supports DAT general data PHD phase data FRD frequency and all filename extensions Selecting PHD or FRD file types automatically selects the corresponding data type 115 STABLE32 USER MANUAL e Notes The data are read twice first to determine their size and layout and then to read the desired portion averaging and columns Commas are converted to spaces and the resulting whitespace spaces and tabs is used to divide the lines into columns The data are scanned by lines using an array of 8 le fields Non numeric input characters are ignored as are characters in excess of 8 fields Using a non unity averaging factor does not shorten the file reading process but will make the subsequent analysis faster Several configuration options can be set to alter the behavior of the file reading operation See the Configuration section of this User Manual for more information about these settings Configuration Item Description Show File Opened Show data plot and other information when file opened Status Plots Show mini data plots in status bar Max Data FileSize Set maximum data file size to read without averaging Non Numerics to Skip Set non numeric characters to skip at beginning of each
177. gram can be launched in several ways Like any Windows application it can be launched from the Start menu from the Run dialog by clicking on its program file Stable32 exe in Windows Explorer or via an icon on the desktop or taskbar By associating Stable32 with a filename extension Stable32 may also be launched by clicking on a data file or by dragging a data file to the Stable32 icon on the desktop The dat phd and frd filename extensions are associated with Stable32 during its installation e Data File Selection The data file to be opened may be entered in the Open Data File dialog box or selected from the list of the three most recently opened phase or frequency data files in the File menu Be sure to select the correct data type in the status bar or Open Data File dialog box The following options apply when a data file is opened e The Open Data File dialog box is invoked when the data filename and type is not known The data type may be defined with a phd or frd filename extension or a p or f command line option e The Multicolumn Data dialog box is invoked when multicolumn data is detected in the last numeric line of the data file e The Data File Opened dialog box is invoked unless it is disabled by the Show Data Opened configuration option or the o skip command line option e Tau Entry It is important that the correct tau value be entered for a data file This can be done by entering it in the Data File Opened or sta
178. h o1 EDF Empirical formulae for the Th ol EDF as used in Stable32 will be found in Reference 1 below e Th o1 Confidence Intervals A detailed discussion of the confidence intervals for Th ol is given in Reference 4 The Th ol confidence intervals are narrower and less skewed more symmetric than those based on chi square and Th ol therefore provides the highest confidence in estimating stability at large averaging factors Stable32 sets the Th ol error bars based on a chi square distribution and the Th o equivalent X degrees of freedom as given in Reference 1 e References The following references apply to the Th o1 statistic 1 D A Howe and T K Peppler Very Long Term Frequency Stability Estimation Using a Special Purpose Statistic Proceedings of the 2003 IEEE International Frequency Control Symposium pp 233 238 May 2003 2 T N Tasset and D A Howe A Practical Th ol Algorithm Unpublished private communication October 2003 3 TN Tasset Th oH Unpublished private communication July 2004 4 T N Tassert D A Howe and D B Percival Th ol Confidence Intervals Unpublished paper 2004 77 78 STABLE32 USER MANUAL TIME DOMAIN STABILITY MTIE e MTIE The maximum time interval error MTIE is a measure of the maximum time error of a clock over a particular time interval This statistic is very commonly used in the telecommunications industry It is calculated by moving an n point n t t
179. h ol m 212 4i 70 N NewTh ol m ZI Th ol m 7 N where n E 3 and denotes the floor function e Th oBR and Th oH The Th oBR Bias Removed algorithm of Reference 3 provides an improved method of automatic bias correction Stable32 uses this method in the Th ol Run function when automatic noise identification is selected 1 Y Avar m 9 3i 7 N n 17 Th ol m 212 4i t N Th oBR m To N Th ol m 7 N where n B and denotes the floor function Th oBR can be combined with the Allan variance to form the overlapping Allan and Th ol hybrid statistic Th oH that is available in Stable32 as the Th oH variance type k Avar m ry N for 1 lt m lt T Th oH m 7 N i A Th oBR m r N for E 0 75 lt m lt N I m even To where k is the largest available 7 20 T e Th ol Bias Reference 2 also includes an improved expression for the Th ol bias as a function of both noise type and averaging factor Bias AVAR Th ol a b m where m is the averaging factor and the constants a b and c are given in the table below Note that the effective tau for a Th ol estimation is t 0 75 m to where to is the measurement interval Noise Alpha a b c RW FM 2 2 70 1 53 0 85 F FM 1 1 87 1 05 0 79 W FM 0 1 00 0 00 0 00 FPM 1 0 14 0 82 0 30 W PM 2 0 09 0 74 0 40 76 TIME DOMAIN STABILITY This bias factor is applied to the Stable32 Th6ol results e T
180. he Drift dialog box by pressing Close Select the Statistics function Notice that the plot now shows only noise Close the Statistics box Choose the Scale function Change the data so it more closely resembles actual stability data by entering a Multiplier of 1 0e 11 and pressing OK If you wish examine the data again with the Edit function to see how it has changed Go to the Sigma function Accept the default Normal sigma type and Averaging Factor 1 Then press Calc to calculate the sigma value about 2 99e 10 Try the Show Details option and some other sigma types and averaging factors for this sample of white FM noise Go to the Run function Select the desired Variance Type and press Calc to produce a table of stability data Then press Plot to see it plotted or Print to send it to your printer Try the Options Lines and Notes functions if you wish to add a noise line or otherwise customize the stability plot S GraphiC Win c 146 sigma tkf oIx File Edit Drew Convert Help Dole 01 08 08 Time 16 46 50 FREQUENC Y STAB iL ITY File SIMPLEOOT a 8 e Line 1 W FM Somos 30226101 E i i Tau Sigma S 1 2 99e 01 o 2 2 08e 01 H 4 149e401 g 8 9 95e 00 2 16 7 85e 00 a 32 5 52e 00 CS 64 3 80e 00 o 128 2 85e 00 A ge Ree a eo g i a a He gt o 8 109 2 10 2 10 2 10 Averaging Time T Seconds dal fine s Sighha 30218786 01 Slop mel Go to the Conve
181. he basic t 1 data set 271 STABLE32 USER MANUAL Table IV Error Bars for n 1000 Point 1 Data Set with Avg Factor 10 Allan Dey Sigma Value Confidence Interval Y for Type ZPts Noise Type amp Ratio Remarks 95 CF Normal 9 965736e 02 CI 8 713870e 03 2 3 99 W FM 1 BI 0 870 1o CI 6 Overlapping 9 159953e 02 Max 6 t 1 014923e 01 7 119 07 981 W FM Max oy 1 1 035201e 01 8 114 45 x d 146 177 Min oy t 8 223942e 02 8 181 34 Modified 4 6 172376e 02 Max o 1 7 044412e 02 7 72 64 972 W FM 5 R n 0 384 Max 0 t 7 224944e 02 8 69 06 y df 94 620 Min o t 5 419961e 02 8 122 71 Table IV Notes 1 Theoretical B1 1 000 for W FM noise and 0 667 for F and W PM noise 2 Simple noise independent CI estimate oyx AN 1 001594e 02 3 This CI includes x a factor that depends on noise type Noise a k a W PM 2 0 99 F PM 1 0 99 W FM 0 0 87 F FM 1 0 77 RWFM 2 0 75 4 BW factor 27f t 10 Applies only to F PM noise 5 Theoretical R n for W FM noise 0 500 and 0 262 for F PM noise 6 Double sided 68 confidence interval p 0 158 and 0 842 7 Single sided 95 confidence interval p 0 950 8 Double sided 95 confidence interval p 0 025 and 0 975 272 OTHER INFORMATION Analysis Procedure e Analysis Procedure The Stable32 functions can be used freely as the circumstances dictate Nevertheless the following list shows a typical analysis procedure 1 Open a phas
182. he data set there is little error propagation in forming the summary statistics e Data Preprocessing Preprocessing of the measurement data is often necessary before performing the actual analysis which may require data averaging or removal of outliers frequency offset and drift Phase data may be converted to frequency data and vice versa Phase and frequency data can be combined for a longer averaging time Frequency offset may be removed from phase data by subtracting a line determined by the average of the first differences or by a least squares linear fit An offset may be removed from frequency data by normalizing it to have an average value of zero Frequency drift may be removed from phase data by a least squares or 3 point quadratic fit or by subtracting the average of the second 273 STABLE32 USER MANUAL differences Frequency drift may be removed from frequency data by subtracting a least squares linear fit by subtracting a line determined by the first differences or by calculating the drift from the difference between the two halves of the data The latter called the bisection drift is equivalent to the 3 point fit for phase data Other more specialized log and diffusion models may also be used The latter are particularly useful to describe the stabilization of a frequency source In general the objective is to remove as much of the deterministic behavior as possible obtaining random residuals for subsequent noise analysis
183. he database reference and measurement channels must be selected that were measured on the same system over the same time span Timetagged clock data is then written to a file where it may be used with Stable32 to perform an analysis e MMS Data The data output from a MMS in the form of time differences x are obtained by dividing the measured phase differences of the measurement and reference channels by their respective nominal frequencies and then subtracting them to remove the effect of the common offset reference x Ad meas Vmeas Abre Vref The x values have units of time in seconds The x t time fluctuations are related to the phase fluctuations by t x t 2nvo where vo is the carrier frequency in Hz Both and x t and Q t are commonly called phase to distinguish them from the independent time variable t These data are taken at a uniform measurement time ty The phase data may be sampled at a multiple t n to by using every nth point decimation During subsequent analysis the x t may be converted to y t values of dimensionless fractional frequency Af f The Stable32 Database function reads and stores timetags and phase x values in the phase timetags and data arrays The measurements are equally spaced at an averaging time tau that can be chosen within the database function as any integer multiple of the basic MMS measurement interval The timetags are formatted as Modified Julian Date MJD The MJD is b
184. he top row of the status bar displays either a prompt message about the current operation or shows the full filename of the active data plus the current date and MJD The active data type is selected with the Phase Data or Freq Data radio buttons or by clicking the L mouse button on their respective plots This row also shows the total of points in each data file The next row shows the file titles and the of analysis points The file title may be edited The bottom row shows the tau value and the analysis start and end points Those parameters may also be changed by entering the desired values into their corresponding edit boxes The Stable32 status bar optionally shows small plots of the phase and frequency data Those plots are activated by the Status Plots checkbox of the Configure function The active status bar plot is red and the inactive one is black which can be made the active data type by clicking with the L mouse button The active plot may be zoomed in centered on the position of the mouse cursor with the R mouse button and un zoomed out with the L mouse button The analysis limits change accordingly The status plots are available only with XGA 1024x768 or higher screen resolution and then only if the main window width is large enough The status bar also displays bitmaps for each data type to indicate 1 the data has changed and is unsaved 2 the data has corresponding timetags and 3 the analysis limits are restricted
185. his can be expressed as od Toren n Y la Ele 2 m To y N 3m 1 n l 6m i n 3m where the z m terms are the phase averages from the triply extended subsequence and the prefix denotes that the linear trend has been removed At the largest possible averaging factor m N 3 the outer summation consists of only one term but the inner summation has 6m terms thus providing a sizable number of estimates for the variance e References The following reference describes the TOTMVAR statistic D A Howe and F Vernotte Generalization of the Total Variance Approach to the Modified Allan Variance Proc 31 PTTI Meeting December 1999 pp 267 276 68 TIME DOMAIN STABILITY Hadamard Variance e Hadamard Variance The Hadamard variance is a 3 sample variance that is similar to the 2 sample Allan variance It examines the 2nd difference of the fractional frequencies the 3rd difference of the phase variations Because of this the Hadamard variance HVAR or Ho t converges for the Flicker Walk FM a 3 and Random Run FM a 4 power law noise types It is also unaffected by linear frequency drift For frequency data the non overlapping Hadamard variance is defined as M 5 7 2 Ho t A 2 2l Yu3 2Y n y gt where y i is the ith of M fractional frequency values at averaging time c For phase data the non overlapping Hadamard variance is defined as Ho 1 E 52 205 bs 3x 3x 7x
186. hite FM flicker FM and random walk FM noise by the expression b T t c where b 1 500 1 168 and 0 927 and c 0 0 222 and 0 358 respectively For white and flicker PM noise the edf for a total Allan deviation estimate is the same as that for the overlapping ADEV with the number of X degrees of freedom increased by 2 Stable32 supports the calculation of TOTADEV from phase or frequency data with the Total option under the Sigma and Run menus The calculation is always done from phase data by the doubly reflected method that does not require endpoint matching The Stable32 implementation follows the recipe described by D A Howe and C A Greenhall in Eq 3 of Reference 5 below e References The following references trace the development of the TOTVAR statistic 1 D A Howe An Extension of the Allan Variance with Increased Confidence at Long Term Proc 1995 IEEE Int Freq Cont Symp June 1995 pp 321 329 2 D A Howe and K J Lainson Simulation Study Using a New Type of Sample Variance Proc 1995 PTTI Meeting Dec 1995 pp 279 290 3 D A Howe and K J Lainson Effect of Drift on TOTALDEV Proc 1996 Intl Freq Cont Symp June 1996 pp 883 889 4 D A Howe Methods of Improving the Estinmation of Long term Frequency Variance Proc 1997 European Frequency and Time Forum March 1997 pp 91 99 5 D A Howe and C A Greenhall Total Variance a Progress Report on a New Frequency Stability Characterization Proc 1997
187. hout a end time having been entered the read operation will end when the last pair of measurement amp reference points is read In that case the actual number of points read will be less than indicated for the time span e Reference Timing Solutions Measurement Database Hardware and Software User Manual Timing Solutions Corp 4775 Walnut St Boulder CO 80303 136 FILE FUNCTIONS Database Details Database Details Additional information about the selected reference and measurement clock records can be obtained from the Database Details dialog box While this information is not necessary to use the database function it can be helpful for SQL queries to directly access the database The database entries associated with these items are shown in the table below Database Details x Item Clock Name Cesium Clock ID System ID Sys Name Frequency Channel Source ID Meas ID Begun By Ended By Reference Measurement Rubidium 1 2 1 1 Test Test 5000000 0000000000 5000000 0000000000 3 4 8 4 2 3 Details of selected reference and measurement clock records Details Item Clock ID System ID Frequency Channel Database Table s clock_names measurement list measurement systems meas system data measurement sources timer groups measurement list measurement sources Database Item Remarks clock_id clock_id system_id system_id system_id system_id frequency channel Uni
188. iable The spectral density of the phase deviations See Tau The square root or deviation of a variance often the 2 sample or Allan deviation oy 1 The change in frequency per tau interval Single sideband The one sided spectral density of the phase deviations rad Hz The one sided spectral density of the time deviations sec Hz The one sided spectral density of the fractional frequency deviations 1 Hz The interval between phase measurements or the averaging time used for a frequency measurement An analysis technique using an extended data set that provides better confidence at long averaging times A statistic for analyzing stability at large averaging factors extending out to 75 of the record length A bias removed version of Th ol A hybrid version of Th ol combining Th oBR with the Allan variance The time interval error of a clock Can be expressed as the rms time interval error TIE rms or the maximum time interval error MTIE OTHER INFORMATION Total Variance A 2 sample variance similar to the Allan variance with improved confidence at large averaging factors x t The instantaneous time deviation from a nominal time x t Q t 2nvo seconds where vo is the nominal frequency Hz This dependent time variable is often called phase to distinguish it from the independent time variable t y t The instantaneous fractional frequency deviation from a nominal frequency y t v t vo vo
189. ic Code 0200 284 APPENDICES fnt SWISS 000725050 a v 2 R cx TU dl c cO dd E CA 2 e E e Eo S w e E R e 8 E gt 2 ES 3 gt O D e QU HH eG oC O DB wea wy Sale due 4i PED due fH E 15 on Chee AB 5 B OOD OT T m xc TAL BH Oo o o 2 5 Qu owes M BA EE ae GE DNE Due LP M ai ES 0 AC a Ain gt x DB Nr To 2 C 3 0 UU cx x eb O lt am NE _ c o a og o 2 Ee 0 ux gt IN oe lt d o o o oOo A li L O IT 7 xwc 25zopopnu oimu Ccn no 0 0 Mm O o V OMA Eg lt m H A ce o X Kk O ks to 2 coe Se M gc Um Mc dne Swiss Font Numeric Code 0201 285 286 STABLE32 USER MANUAL w R 42 P BR 44H x un 45 u N Je 24 lt Il m 2 gt o eS x c o F LL n t U lt 8 Ny bp ap M V Go 80 el nt 8 35 0 52 J 2 44 OQ a A VD oca 0 lt E gt IR gt Sia S wm n Ales Tlo Qs ODO 135 153 R 105 Y 2 E 37 0 154 Po Qh io Xm Wh iss Qu Ds Zi Xo 30 Os TM ss Plos t 123 40 15 o Z w 24 4 158 91 08 25 42 25 92 Ol 26 lt 13 C Ji n s E S o 98 Mn O 4 ns D R lt I 76 N a Newsgrm Font Numeric Code 0202 APPENDICES WN amp NS O1 v A co gt e
190. ide left right or top of the page the top of the plot is to appear The default is the top The Convert menu s GEM command is used to display a GEM conversion dialog box to select the filename and page orientation of the GEM file to be produced The user is asked GEM 1 4 to select the page orientation The page orientation refers to which side left right or top of the page the top of the plot is CGM to appear The default is the top 41 STABLE32 USER MANUAL The Convert menu s PIC command is used to display a PIC conversion dialog box to select the filename and page orientation of the PIC file to be produced The user is asked to select the page orientation The page orientation refers to which side left right or top of the page the top of the plot is to appear The default is the top The Convert menu s HPGL and HPGL2 commands are used to display a HPGL conversion dialog box to select the filename and page orientation of the HPGL file to be produced The user is asked to select the page orientation and margin lengths to be used The page orientation refers to which side left right or top of the page the top of the plot is to appear The default is the top Convert cont The Convert menu s SCODL command is used to display a SCODL conversion dialog box to select the filename and page orientation of the AGFA SCODL file to be produced The user is asked to select the page orientation The page orientat
191. ints and octave band fits are controlled by the Pts and Fit boxes and the Info box controls the display of the FFT information Checking the Wide option causes the stability data to be plotted with wide lines This can be useful for producing plots with better visibility for presentations The Cursor option will activate the mouse during a plot to draw lines and display plot coordinates Use the Esc key to deactivate it before closing the plot Zero padding is used if necessary to raise the of time series data points to the next larger power of two The PSD results Fourier frequency and Log PSD are written to a data file with the default filename PSD dat See the Special Characters help topic for information about adding subscripts superscripts Greek letters etc to power spectrum plot titles and subtitles 188 ANALYSIS FUNCTIONS e PSD Windowing Data windowing is the process of applying a weighting function that falls off smoothly at the beginning and end to avoid spectral leakage in an FFT analysis Without windowing bias will be introduced that can severely restrict the dynamic range of the PSD result The Stable32 program offers a choice of four windowing types None Hanning Hamming and Multitaper The classic Hanning and Hamming windows can be applied for 1 to 3 times e PSD Averaging Without filtering or averaging the variances of the PSD results are always equal to their values regardless of the size of the time domain dat
192. ion All Stable32 files are by default stored in a single directory C Program Files Hamilton Technical Services Stable32 While any drive and directory can be used it is recommended that all these files be kept in that one place Stable32 will not start without access to its DLL files It is also important that the program be able to find the font and other GraphiC plotting support files While this condition is automatically satisfied by keeping all of the Stable32 files in a single directory the GPCWIN environment variable can also be used to accomplish that e GPCWIN The GPCWIN environment variable can be defined with the SET command to point to the directory where the GraphiC support files are located SET GPCWIN C Program Files Hamilton Technical Services Stable32 While normally unnecessary this can be used to share the same FNT files between several GraphiC applications See the help files for your particular operating system for information about how to use the SET command e Operation The default directory for all Stable32 operations is the one where it is installed and where the program is started That directory is where Stable32 looks for its support files and unless changed is where all output is written Thus regardless of where the current data is located the program will operate from its own directory This is particularly important when data is read from a floppy disk or read only media New Stable32 GraphiC plo
193. ion Enter the desired Avg Factor and press OK To abort press Cancel or OK with default averaging factor 1 e Phase Averaging Phase data averaging decimation which is done by simply eliminating the intermediate data points to form data at a longer tau which corresponds to frequency averaging Do not confuse this process with actual averaging of the phase data such as is done when computing the modified Allan variance e Frequency Averaging Frequency averaging is done by finding the mean value of the data points being averaged e Gaps Gaps 0s are ignored and the average will be a gap if all points in the group being averaged are gaps 165 STABLE32 USER MANUAL 166 EDITING FUNCTIONS Fill Function e Purpose Use the Fill function to fill gaps in the selected portion of phase or frequency data with interpolated values Leading and trailing gaps are removed the of data points is adjusted and the analysis limits are reset Gaps 2 A MNA Press OK to fill gaps in data with interpolated values e Controls The Fill dialog box contains the following controls Control Type Description Gaps Text Display gaps in data OK Pushbutton Perform the Fill function amp close dialog box Cancel Pushbutton Abort the Fill function amp close dialog box Help Pushbutton Invoke the Fill help topic e Operation Press OK To abort press Cancel or OK if gaps 0 e Caution The dat
194. ion refers to which side left right or top of the page the top of the plot is to appear The default is the top e Operations Copying to Clipboard GraphiC and Play use the clipboard to copy a bitmap of the client area of the window for use by other applications Use the Edit Copy Bitmap command to copy the bitmap to the clipboard Use the Edit Copy Metafile command to copy the metafile to the clipboard The clipboard utility may be used to view the clipboard Any application that will import a bitmap or metafile from the clipboard such as Word for Windows can paste the Play generated bitmap or metafile to its client area Converting TKF File GraphiC and Play can convert a TKF file to one of several different types of file by using the Convert pull down menu Simply pull down Convert and select the file type to convert the currently displayed TKF plot Drag and Drop Play uses the drag and drop feature of Windows to allow a TKF file to be dropped into the Play window to start the displaying of that TKF file Alternatively the user may associate TKF files with Play by defining a link between TKF files and Play Play supports the use of command line arguments and assumes the first argument to be a TKF file name to open and display Exiting GraphiC and Play may be terminated by selecting the File Exit menu or by entering an ALT X from the keyboard 42 Log File e Log File GENERAL A STABLE32 LOG file is automatically writt
195. ion on plot Read Config I Pushbutton Read config data from INI file Save Config N Pushbutton Save configuration data to INI file Plot Filename F Edit Enter plot filename X Axis Label Groupbox X axis label Label Static Text X axis label Log AF Y Axis Label Groupbox Y axis label Label Static Text Y axis label Window Z Axis label Groupbox Z Axis label Label Static Text Z Axis label Log Sigma Settings Groupbox Window settings Window Size W Edit Enter analysis window size Step Size Z Edit Enter analysis step size Windows Text Display analysis windows 233 STABLE32 USER MANUAL Variance Groupbox Variance choices AVAR A Radio Button Allan variance HVAR H Radio Button Hadamard variance Options Groupbox Plot options Date D Checkbox Show date on plot Box X Checkbox Draw box around plot Colors S Checkbox Show multicolor surface plot Grid G Listbox Select color surface plot grid Horiz View O Groupbox Horizontal viewpoint trackbar None Slider Set horizontal viewpoint Reverse 1 Checkbox Reverse horizontal orientation Vert View V Groupbox Vertical viewpoint trackbar None Slider Set vertical viewpoint None Progress Bar Show calculation progress Abort B Pushbutton Abort calculation Close C Pushbutton Close the Histogram dialog box Reset All R Pushbutton Reset all parameters to defaults Help P Pushbutton Invoke this help topic e Operation Enter desired plot Title SubTitle Message message Positio
196. iplier Edit Enter x axis scale multiplier X Divs Edit Enter x axis major scale divisions Start 3 Edit Enter starting point End 4 Edit Enter ending point Y Axis Group Y Axis parameters Label Edit Enter y axis label Offset Edit Enter y axis scale offset Multiplier Edit Enter y axis scale multiplier Data Max Text Display maximum data value Scale Max Edit Enter y axis scale maximum Data Min Text Display minimum data value Scale Min Edit Enter y axis scale minimum Y Divs Edit Enter y axis major scale divisions Ticks Edit Enter y axis minor scale ticks 203 STABLE32 USER MANUAL Options Group Plot options curve fits Type Combo Choose line options Date Checkbox Show date on plot Box 5 Checkbox Draw box around plot Fit 6 Checkbox Show fit parameters at bottom of plot Wide Checkbox Use wide lines for data plot Cursor 7 Checkbox Activate mouse cursor Plot File Edit Enter plot filename Read 1 Pushbutton Read plot configuration data Save 2 Pushbutton Save plot configuration data Reset All Pushbutton Reset all plot attributes to defaults OK Pushbutton Set plot attributes amp close dialog box Cancel Pushbutton Abort changes amp close dialog box Help Pushbutton Invoke the Plot Options help topic e Operation Enter the desired plot attributes and press OK to accept them or Cancel to abort Press Reset All to reset all attributes to their default values Both of the Stable32 phase and frequency
197. iting changes in phase and frequency data must be made with discretion so that the integrity of the data is not lost 155 STABLE32 USER MANUAL 156 EDITING FUNCTIONS Find Function e Purpose The Find function is a Detailed Search sub function of the Edit function Use the Find function to find phase or frequency data points that meet a particular criterion The Replace function is also available to find and replace phase or frequency data values Find What x y 8 5e 02 Eind Next Note The of digits entered Direction determines the search Up C Down precision Help e Controls The Find function uses a modeless dialog box that can remain open while the Edit function is active It contains the following controls Control Type Description Find What Combo Search type Edit Search value Direction Group Search direction controls Up Radiobutton Search upwards Down Radiobutton Search downwards Find Next Pushbutton Perform a Find operation Close Pushbutton Abort the Find function amp close dialog box Help Pushbutton Invoke the Find help topic e Operation Select the search criterion with the two Find What controls The numeric value also determines the search precision Set the search direction with the Up and Down buttons and press the Find Next button The result of a successful search is displayed in the Edit dialog box Additional search may be conducted with the Find Next button The Find dialo
198. itive manual analysis or batch operations Otherwise it is probably better to control the retrieving 50 GENERAL and storing of plot information manually with the individual Save and Read buttons of the Plot and Run function Options Lines and Notes dialog boxes The Use Smart Scales checkbox activates Y Axis data plot scales with units applied For example a phase plot with values in the 10 range will be shown as nanoseconds The Plot Labels checkbox and Label edit box are used to add organization and other such labels at the lower right corner of all plots e Data The Max Data File Size value default 999999 is not a program limitation but rather an option to deliberately bound the size of the data arrays This is useful to tailor the program to personal preferences or computer memory and speed limits The Max Data File Size value limits the number of data points that can be generated by the Noise function and controls the opening of the Large Data File dialog box for averaging a data file as it is read The Non Numerics to Skip value sets the number of nonnumeric characters that are skipped at the beginning of each line of phase or frequency data as it is read This value normally 0 can be used to help read data files that contain non numeric markers at the start of each line Data files are parsed for numeric characters one line at a time and a non numeric character terminates the reading of the current line This is desirabl
199. l and W Riley Uncertainty of Stability Variances Based on Finite Differences Proc 2003 PTTI Meeting December 2003 56 TIME DOMAIN STABILITY Allan Variance e Allan Variance The Allan or 2 sample variance AVAR is the most common time domain measure of frequency stability Its non overlapping version is defined as oO Dat where y i is the ith of M fractional frequency values averaged over the measurement interval Ti In terms of phase data the Allan variance may be calculated as 2 0 7 XN EX aa lt Bus where x 1 is the ith of the N M 1 phase values spaced by the measurement interval t The result is usually expressed as the square root o t the Allan deviation ADEV The Allan variance is the same as the ordinary variance for white FM noise but has the advantage for more divergent noise types such as flicker noise of converging to a value that is not dependent on the number of samples The confidence interval of an Allan deviation estimate is also dependent on the noise type but is often estimated as 0 t VN 57 58 STABLE32 USER MANUAL TIME DOMAIN STABILITY Overlapping Allan Variance e Overlapping Allan Variance The overlapping Allan variance is a version of the Allan variance 02 t AVAR that makes maximum use of a data set by forming all possible fully overlapping samples at each averaging time t It can be estimated from a set of M frequency measurements for averaging time t mt
200. le Plot TKF filename Null Position Message position 0 X Min X axis scale minimum value Null X Max X axis scale maximum value Null Y Min Y axis scale minimum value Null Y Max Y axis scale maximum value Null TablePos Table position 1 Wide Use wide plot line flag 0 X Label X axis tau label text Null Y Label Y axis sigma label text Null StabFile Stability data filename Null Date Date annotation flag 0 Box Draw box around plot flag 0 Table Draw sigma tau table on plot flag 1 ErrorBar Show error bars on stability plot flag 1 Fit Draw fit line flag 0 e SpectPlot The SpectPlot section of the STABLE32 INI file can contain the following parameters Keyword Description Default Title Plot title text Null Subtitle Plot subtitle text Null Message Message text Null Position Message position 0 Wide Use wide plot line flag 0 Y Tic y axis tics 5 Date Date annotation flag 0 Box Draw box around plot flag 0 Fit Draw fit line flag 0 Points Show PSD points on plot flag 1 PSD PSD type 0 WinType FFT windowing type 1 Win FFT windows 1 Mouse Mouse flag 0 Info Show PSD info on plot flag 0 Y Min Y axis scale minimum value Null Y Max Y axis scale maximum value Null Freq Carrier frequency Hz 0 e HistoPlot The HistoPlot section of the STABLE32 INI file can contain the following parameters Keyword Description Default Title Plot title text Null Subtitle Plot subtitle text Null Message Message text Null Position Message position 0 2
201. le can contain the following parameters the items are repeated for each note as indicated by the index i i 1 to 8 Keyword Description Default Size i Font point size 8 Border i Border flag 0 X Position i X axis position 0 0 Y Position i Y axis position 0 0 Text 1 Note text Null 296 APPENDICES e SigmaNotes The SigmaNotes section of the STABLE32 INI file can contain the following parameters the items are repeated for each note as indicated by the index i i 1 to 8 Keyword Description Default Size i Font point size 8 Border i Border flag 0 X Position i X axis position 0 0 Y Position i Y axis position 0 0 Text 1 Note text Null e Toolbuttons The Toolbuttons section of the STABLE32 INI file can contain the following flag parameters the order has no effect Keyword Description Default Open Show Open function toolbutton 0 Add Show Add function toolbutton 0 Read Show Read function toolbutton 0 Save Show Save function toolbutton 0 Conv Show Convert function toolbutton 0 Stats Show Statistics function toolbutton 0 Check Show Check function toolbutton 0 Run Show Run function toolbutton 0 Norm Show Normalize function toolbutton 0 Plot Show Plot function toolbutton 0 Drift Show Drift function toolbutton 0 Histo Show Histogram function toolbutton 0 Cal Show Calendar function toolbutton 0 Avg Show Average function toolbutton 0 Print Show Print function toolbutton 0 Noise Show Noise function toolbutton 0 Cl
202. line is controlled by the Zero checkbox and the Lag k checkbox selects the insertion of a lag k scatter plot Checking the Wide option causes the stability data to be plotted with wide lines This can be useful for producing plots with better visibility for presentations The Cursor option will activate the mouse during a plot to draw lines and display plot coordinates Use the Esc key to deactivate it before closing the plot e Noise Identification The Stable32 Autocorrelation function provides an estimate of the power law noise type white flicker random walk flicker walk or random run for the particular data type phase or frequency that is displayed as a message on the plot This estimate includes both the name of the closest power law noise type and the estimated alpha value based on the lag 1 autocorrelation value and is available for data sets of 30 and larger The estimated alpha value is particularly helpful for mixed noises because it indicates the approximate proportions of the two dominant noise types e g alpha 1 50 indicates an equal mixture of white and flicker PM noise e Lag Scatter Plot The Lag k checkbox inserts a scatter plot of the phase or frequency data plotted against itself with a lag of k The data at time t k is plotted on the y axis versus the value at time t on the x axis This plot is another way of showing the degree of correlation in the data and the slope of a linear fit to these points is closely related to
203. lized Phase uency Frequency t 1 1 892 103 11111 0 00000 2 809 20 11111 103 11111 3 823 34 11111 123 22222 4 798 9 11111 157 33333 5 671 117 88889 166 44444 6 644 144 88889 48 55555 7 883 94 11111 96 33333 8 903 114 11111 2 22222 9 677 111 88889 111 88889 10 0 0000 269 STABLE32 USER MANUAL Table II NBS Monograph 140 Annex 8 E Test Data Statistics Averaging Factor 1 2 Data Points 9 4 Maximum 903 893 0 Minimum 644 657 5 Average 788 8889 802 875 Median 809 830 5 Linear Slope 10 20000 2 55 Intercept 839 8889 809 25 Standard Deviation 1 100 9770 102 6039 Normal Allan Deviation 91 22945 115 8082 Overlapping Allan Dev 91 22945 85 95287 Modified Allan Dev 91 22945 74 78849 Time Deviation 52 67135 86 35831 Hadamard Deviation 70 80607 116 7980 Overlap Hadamard Dev 70 80607 85 61487 Total Hadamard Dev 70 80607 91 16396 Total Deviation 91 22945 93 90379 Total modified Dev 75 50203 75 83606 Time Total Deviation 43 59112 87 56794 Table II Notes 1 Sample not population standard deviation e 1000 Point Test Suite The larger frequency data test suite used here consists of 1000 pseudo random frequency data points It is produced by the following prime modulus linear congruential random number generator nj 16807 n Mod 2147483647 This expression produces a series of pseudo random integers ranging in value from 0 to 2147483646 the prime modulus 2 1 avoids a collapse to zero When started with the se
204. lot File C Program Files DevStudio MyProjects Sta Axis Y Axis Label Fourier Frequency f Hz PSD Type Le dBc Hz Phase Noise L f dBc Hz FFT Points 1024 Windowing Type Hamming y Windowings fi y PSD Points 512 Avg Factor 4 fi y PSD Std Dev 100 0 Fourier Interval Hz 9 765be 04 PSD Max Press Plot Scale Max Max Fourier Freq Hz 8000090 PSDMin fo Calc Scale Min PSD File C Program Files DevStu Smooth Max AF I PEKS Options v Date v Box Cursor v Eit v Pts v Wide 54 Press Plottor PSD plot Controls The Power dialog box contains the following controls Control Type Description Title 1 Combo Edit or select plot title SubTitle 2 Combo Edit or select plot subtitle Message 3 Combo Edit or select plot message Msg Position List Select message position Carrier Freg Edit Enter carrier frequency X Axis Group X axis parameters Label Text X axis label not editable FFT Points Text FFT data points Fourier Interval Text Spacing between frequency points Max Fourier Freq Text Highest frequency point Read Config Pushbutton Read plot configuration data Save Config Pushbutton Save plot configuration data Plot File Edit Enter file plot name Y Axis Group Y axis parameters PSD Type List Select PSD type Label Text X axis label not editable 187 STABLE32 USER MANUAL Windowing Type List Select FFT windowing type
205. lotting operation The SIGMA TAU stability data file is written immediately after the stability calculation before the Run Options box is available so the calculation may have to be repeated if the stability file name is changed Stability data and plots may also be sent to another directory by changing the Stability File and Plot Filename fields in the Run Options dialog box Checking the Wide option causes the stability data to be plotted with wide lines This can be useful for producing plots with better visibility for presentations The default table position is at the top right or bottom right of the stability plot depending on slope of the sigma tau results See the Special Characters help topic for information about adding subscripts superscripts Greek letters etc to stability plot titles subtitles and labels e Append Checking Append in the Run Plot Options dialog box causes the stability data from the next run to be appended to an existing stability file with the specified filename default SIGMA TAU This can be used with the Read function to easily produce a stability plot with multiple data sets Stable32 always initializes the Append flag to the off position thus assuring that the first stability file will be a new one After each run the Run Plot Options dialog box may be opened to change the Append flag thus allowing the results multiple runs to be combined New phase or frequency data may be opened the current data may be ma
206. lue Enter y axis sigma scale maximum 145 STABLE32 USER MANUAL Sigma Min Text Minimum sigma value Scale Min Edit Enter y axis sigma scale minimum Options Group Plot options Date Checkbox Show date on plot Box Checkbox Draw box around plot Bars 1 Checkbox Show error bars on plot Table 2 Checkbox Draw stability table on plot Fit 3 Checkbox Show fit parameters on plot Plot File Edit Enter plot filename Reset All Pushbutton Reset all plot attributes to defaults OK Pushbutton Set plot attributes amp close dialog box Cancel Pushbutton Abort changes amp close dialog box Help Pushbutton Invoke the Read Options help topic e Operation Enter the desired plot attributes and press OK to accept them or Cancel to abort Press Clear All to reset all attributes to their default values 146 READ FUNCTIONS Read Lines Function e Purpose Use the Read Lines function to add lines to a stability plot The possible line types are as follows Line Type Description Parameter None No line None Endpoints Line between certain endpoint values None Horizontal Horizontal line at certain sigma value None Vertical Vertical line at certain tau value None Noise Fit to certain power law noise model Sigma 1 Read Plot Lines E Line fi Up Type _ x Down Cancel Tau Sigma EE Start 3 00000e 02 y Start End 115200e 05 w End Clear All Noise Line Slope 05 W FM E E Bead
207. ly on the power law noise type Requiring manual noise selection avoids the problem of noise identification for biased data having the wrong sigma tau slope Dead time correction is problematic for data having multiple noise types In addition to introducing bias measurement dead time reduces the confidence in the results lowers the maximum allowable averaging factor and prevents proper frequency to phase conversion Moreover no information is available about the behavior of the device under test during the dead time It is recommended that these issues be avoided by making measurements with zero dead time 95 96 STABLE32 USER MANUAL References J A Barnes Tables of Bias Functions B1 and B2 for Variances Based on Finite Samples of Processes with Power Law Spectral Densities NBS Technical Note 375 January 1969 J A Barnes and D A Allan Variances Based on Data with Dead Time Between the Measurements NIST Technical Note 1318 1990 TIME DOMAIN STABILITY 3 Comered Hat e 3 Cornered Hat It is sometimes necessary to separate the noise contributions of the two sources that contribute to a variance measurement Methods exist for doing so by using the results of multiple measurements to estimate the variances of the individual sources Any frequency stability measurement includes noise contributions from both the device under test and the reference Ideally the reference noise would be low enough that its contribution to the m
208. lysis session is recorded in a log file Run Function Don t press Stop during an octave or decade run until at least one result is displayed The analysis point being processed is repeated if the run is stopped so the most efficient time to interrupt a run is immediately after a point is completed It may take a little while for the program to respond to the Stop button during a run with a large data set It may take a while for the progress bar to indicate anything when starting a run with a large data set The progress bar shows each point during a TOTMDEV TOTTDEV or MTIE octave or decade run and the overall progress during an all tau run During the latter the current averaging factor is displayed on the status bar 303 STABLE32 USER MANUAL 304 APPENDICES Appendix VI 5110Comm Communications Program e 5110Comm 5110Comm is a program to capture data from the Timing Solutions Corporation TSC now Symmetricom Model 5110A Time Interval Analyzer for analysis by Stable32 It may be launched from within Stable32 by clicking on its toolbutton or the TSC 5110A item in the Utilities menu TSC 5110A Communications Program lel ES come O Open 960081 N Filename c stable32 comm dat Close ES Press Startto Scale Factor 1 00000000008 09 Help read data into file via comm C List C PlotPhase 4 PlotFreq 1161 port MuR RCC IIAAM ult AA AL WERE LP J
209. many points as needed and using only the second half of the output e FW FM and RR FM Noise Generation The more divergent flicker walk FM a 3 and random run FM a 4 power law noise types may be generated by using the 1 f spectral property of a frequency to phase conversion For example to generate RR FM noise first generate a set of RW FM noise and save the resulting phase data Then read this RW FM phase data as frequency data and convert it to a new set of RR FM phase data e Sine Generation The Sine peak and Sine Period controls allow entry of the fractional frequency amplitude and period seconds of a sinusoidal component to be added to the simulated noise A finite amount of noise must still be included to avoid zero sigma These parameters are useful for simulating the effect of a periodic disturbance such as temperature or vibration The phasing is that of a positive sinusoid on the fractional frequency data No sinusoidal component is added unless both the peak value and period are non zero e Memory Usage Noise generation is a memory intensive process that requires about 48 bytes of peak memory usage per data point Large data sets can therefore involve relatively slow virtual hard drive swap memory e Caution The results from the Noise function overwrite the current data in the phase and frequency arrays e References N J Kasdin and T Walter Discrete Simulation of Power Law Noise Proceedings of the 1992 IEEE Fr
210. may be more prudent to simply analyze a gap free portion of the data e Phase Frequency Conversions Conversion from phase to frequency data is straightforward for data having gaps Because two phase points are needed to determine each frequency point as the difference between the phase values divided by their tau a single phase gap will cause two frequency gaps and a gap of N phase points causes N 1 frequency gaps Conversion from frequency to phase is more problematic because of the need to integrate the frequency data The average frequency value is used to calculate the phase during the gap which can cause a discontinuity in the phase record Analysis of phase data resulting from the conversion of frequency data having a large gap is not recommended e Drift Analysis The Stable32 drift analysis functions perform well for data having gaps It is important that missing data is represented by gaps to maintain a regular time sequence The Regularize function can be used to insert gaps into timetagged data that has missing points The Edit function highlights the first timetag value after a gap in blue The Insert feature of the Edit function can be used to manually insert a group of gaps 20 GENERAL e Variance Analysis The Stable32 variance analysis functions include provisions for handling gaps Some of these functions yield satisfactory results in all cases while others have speed limitations or provide unsatisfactory results for f
211. me Message Combo Enter or select plot message Default is Mean Removed value Msg Position List Select message location Default is top left Plot Filename Edit Enter plot filename Default is HISTO TKF X Axis Group X axis parameters Label Text X axis label not editable Y Axis Group Y axis parameters Label Text Y axis label not editable Options Group Plot options Date Checkbox Show date on plot Box Checkbox Draw box around plot Cursor Checkbox Activate mouse cursor for plot Fit Checkbox Draw normal curve fit on plot Fill Checkbox Fill histogram bars Normalize Checkbox Normalize data for zero mean If grayed normalization is required 197 STABLE32 USER MANUAL Mean Removed Text Value of average value removed from data Read Config Pushbutton Read plot configuration data from STABLE32 INI Save Config Pushbutton Save plot configuration data in STABLE32 INI Reset All Pushbutton Reset all plot attributes to defaults Close Pushbutton Close the Histogram dialog box Help Pushbutton Invoke the Histogram help topic e Operation Enter the desired Title Sub Title Message message Position and Options Check Normalize to remove the mean value from the data This may be required if the data has relatively small variations around a large average value Normalization does not permanently affect the data in memory If the Normalize checkbox is grayed normalization is required and will be done automatically and the mean value
212. mes for these files are PHASE TKF FREQ TKF SIGMA TKF DAVAR TKF SPECTRUM TKF AUTO TKF and HISTO TKF for phase data frequency data stability dynamic stability power spectrum and histogram plots respectively These filenames may be changed as an option within their respective Plot Options functions A name of NOTEK will suppress the writing of the TKF file e Stability Filenames A stability file is optionally written to the current disk directory at the end of each stability run This file contains a table of averaging time of analysis points and minimum nominal and maximum sigma information that can be printed or re plotted with the Read function The default stability filename is SIGMA TAU which may be changed in the Run Options dialog box This file is particularly useful to combine with other such files to create a composite stability plot for multiple runs using data over a wide range of averaging times Writing of the stability file is controlled by the Write Sigma File checkbox of the Configure function e Plot Data Filenames The Autocorrelation and Dynamic Stability functions write plot data files each time a plot is drawn The autocorrelation plot data file default name AUTO DAT comprises rows of lag and ACF value The dynamic stability plot data file fixed name XYZ DAT comprises rows of averaging factor window and sigma value 25 26 STABLE32 USER MANUAL GENERAL Timetags e Timetags The Stable32 progr
213. method for defining the time span for the data If Record is selected either enter the desired Record or check the Last record checkbox If Start MJD is selected as the time span method enter the Start MJD value in the corresponding edit box This will extract the data for the selected clock from that time to the end of the file If it is desired to also set the End MJD then check the End MJD checkbox and enter that value into its corresponding edit box Then press OK to extract the clock data or Cancel to abort the Read Archive function The Configure button brings up another dialog box that allows setting certain defaults for the Read Archive function 118 FILE FUNCTIONS Read Archive Configure e Purpose Use the Read Archive Configure dialog box to set defaults for the Read Archive function Read Archive Configure E Defaults Channels Meas Chan Ref Chan Enter defaults for Read Archive function e Controls The Read Archive Configure dialog box contains the following controls Control Type Description Defaults Group Read Archive default values Channels Edit Set the maximum of channels Meas Chan Edit Set the default measurement channel Ref Chan t Edit Set the default reference channel OK Pushbutton Perform the Read Archive Configure function amp close dialog box Cancel Pushbutton Abort the Read Archive Configure function amp close dialog box Help Pushbutton Invoke the Rea
214. mination of single or double sided confidence intervals for the modified Allan deviation for the estimated noise type and desired confidence factor e Time Variance The time variance is a measure of time stability based on the modified Allan variance e Hadamard Variance The non overlapping Hadamard variance uses 3 rather than 2 fractional frequency samples which allows it to converge for a 3 Flicker Walk FM and a 4 Random Run FM noises and causes it to be unaffected by linear frequency drift e Overlapping Hadamard Variance The overlapping Hadamard variance uses fully overlapping samples to calculate the Hadamard variance e Total Allan Variance The total variance uses a double reflection method to form a o t estimate with better confidence at long averaging times e Total Modified Variance The total modified variance also uses a double reflection method to form a mod o 1 estimate with better confidence at long averaging times e Total Time Variance The total time variance is a measure of time stability based on the total modified variance e TIErms The rms time interval error TIE rms is the rms value of the time deviations It can be calculated for phase data only 184 ANALYSIS FUNCTIONS e MTIE The maximum time interval error MTIE is maximum value of the time deviation over a moving window It can be calculated for phase data only e Th o1 Th ol is a special purpose statistic used to estimate
215. n p 1 Hadamard Variance Ho t The 3 sample Hadamard variance is used primarily as an alternative to the Allan variance for a frequency source having linear frequency drift or highly divergent a 4 or 5 noise It may be calculated by the non overlapping or overlapping method Total Hadamard Variance HO ota t The total Hadamard variance is similar to the Hadamard variance but uses a doubly reflected method that improves its statistical confidence at large averaging factors 104 FREQUENCY DOMAIN STABILITY e Sigma Tau Diagrams The following two diagrams show the relationship between the log o versus log t slopes for various power law noise processes for the normal and modified Allan variances Note that Mod o t is able to distinguish between white and flicker PM noise Sigma Tau Diagram li e i Sf Do Eo P do P Po Pod H a 1 11 2 a IO A NER NE Me 0 5 1 y rt ov E lg ON Flicker PM m ANA AAA AAA ee AA wa ait o t Mod Sigma Tau Diagram E white PM LN od Mod a t 2 H i i i i Sf w a 1 dsd up s io Ki ua M CU ME HN Oi log i AAA AA 4 Mod es ON Ficker PM er Dass mei node a Freg Det oy 105 STABLE32 USER MANUAL 106 FREQUENCY DOMAIN STABILITY Noise Spectra e Noise Spectra The random phase and frequency fluctuations of a frequency source can be modeled by power law spectral densities of the form S f h a f where
216. n Settings Options and Views Then press Plot to produce a dynamic stability plot or Close to close the dialog box The Window Size and Step Size set the width of the sliding analysis window and the of data points that it advances for each step Together these parameters determine the of analysis Windows and are constrained to be within acceptable limits A large of analysis windows will require a long calculation time which is shown in the Progress bar and can be stopped with the Abort button in which case the results obtained so far will be plotted The Horiz View trackbar slider sets the x and y axis left and right viewpoint of the plot the Vert View trackbar slider sets the y axis up and down viewpoint of the plot and the Reverse checkbox flips the horizontal plot orientation Changing these viewpoints can sometimes help to improve the visibility of the stability data Their default settings are in the middle of the sliders A dynamic stability analysis can be performed with either the overlapping Allan AVAR or overlapping Hadamard HVAR variance The latter is more appropriate when there is frequency drift in the data The resulting dynamic stability plot is saved as a tkf file with a filename entered in the Plot Filename edit box default DAVAR TKF The plot options provide choices to put the Date and other information at the top of the page draw a Box around the page and use multiple Colors for the 3D surface plot
217. n for frequency data e Auto Calc A drift analysis can be done automatically when the Drift function is invoked by setting the AutoCalc item in the Configure function 180 ANALYSIS FUNCTIONS Sigma Function e Purpose Use the Sigma function to calculate Allan or Hadamard variance statistics for the selected portion of the current phase or frequency data at a single averaging time The Run function is available for performing these calculations over a range of averaging times Variance Type Overlap Allan Calc Avg Factor Close Help dd Sigma 2 921983e 01 am Cee calculate selected Show Details e Controls The basic Sigma dialog box contains the following controls Control Type Description Variance Type Combo Choose desired variance type Avg Factor Edit Enter averaging factor Sigma Text Display Sigma result Show Details Checkbox Select detailed Sigma dialog box format Calc Pushbutton Calculate sigma Close Pushbutton Close Sigma dialog box amp restore previous data Stop Pushbutton Abort TOTMDEV TOTTDEV or MTIE calc Help Pushbutton Invoke the Sigma help topic Activating the Show Details option adds he following controls to the Sigma dialog box Control Type Description Var Params Group Variance parameters BW Factor Edit Enter bandwidth factor Tau Text Display tau Sigma Results Group Sigma values Std Dev Text Display standard deviation Noise Type Group Noise ID paramet
218. n the gap Filling is recommended before using the modified and time Allan variance functions especially for frequency data because these calculations are much faster for gapless data 16 GENERAL Stable32 has a Check function for locating and removing outliers from frequency data While the definition of an outlier is somewhat a matter of judgment it is important to find and remove such points in order to use the rest ofthe data Stable32 defines an outlier on the basis of its deviation from the median of the data The user may enter a deviation limit in terms of the median absolute deviation A 56 limit is the default This is a robust way to determine an outlier which is then replaced by a gap Automatic outlier removal is also provided which iteratively applies this method to remove all outliers It should be an adjunct to and not a substitute for visual inspection of the data A message controlled by the WarnZeroFreq configuration variable can be displayed during phase data entry to warn of equal adjacent phase values which will result in zero frequency points that are treated as gaps e Zeros Besides their use to denote gaps zeros can occur as actual data values This happens most often at the beginning and end of phase data and those zeros are not considered to be gaps All other embedded zeros are considered as gaps in phase data as are all zeros in frequency data To preserve such zeros as actual values change them to a v
219. n to generate a plot of the current phase or frequency data EZ GraphiC Win phase tkf Eile Edit Draw Convert Help Dar 02 77 30 ilme 700 30 Dolo Palms 1 PHAS E DATA phaac dat Fhe o cme dni 5 00 240 660 Data Point 201 STABLE32 USER MANUAL 202 ANALYSIS FUNCTIONS Plot Options Function e Purpose Use the Plot Options function to control the attributes of the data plot Phase Plot Options EI Title PHASE DATA gt OK SubTitle PHASE DAT gt Cancel Message gt Help Position Top Left gt Read1 Save 2 Reset All X Axis Y Axis Label Data Point gt I Keep 8 Label Phase Seconds gt Offset 0 000002 00 XDivs Offset 0 000002 00 Multiplier 1 000008 00 11 Multiplier 1 000006 00 Start 3 fi End4 1001 Data Max 4 35653e 00 Options Scale Max 4 500008 00 Type None No Lines DataMin 4 70788e 00 Iv Date V Box5 v Fte T Wide Cur Scale Min 55000000 PlotFile fe program files stable32 phase Y Div fio Ticks B e Controls The Plot Options dialog box contains the following controls Control Type Description Title Edit Enter plot title SubTitle Edit Enter plot subtitle Message Edit Enter plot message Position Combo Choose message position X Axis Group X Axis parameters Label Edit Enter x axis label Keep 8 Checkbox Keep X axis label for next plot Offset Edit Enter x axis scale offset Mult
220. ncExtension WriteSigmaFile AutoCalc AutoPlot Notepad MaxSize Select Phase or Freg data Phase selects phase data any other text selects freg Add a label to plots Label text for plots Increment the filename extension when data changes Write a file containing sigma data after a Run Automatically calculate sigmas when starting Run function Automatically draw plot when starting Plot function Use the specified text editor Maximum size of data arrays Default 0 ooooooo Phase 0 Null 0 0 0 0 NOTEPAD EXE 99999 291 Splash SigmaType RunType PhaseDriftType FreqDriftType NonNums Comma WarnZeroFreq SmartScale ACFNoiselD Left Top Right Bottom LastOpened OpenScale Header NoGreek ShowWelcome CheckDetails DriftDetails SigmaDetails WideEdit NormFreq XferTags ManyTau ManySize UseTags Weight Smooth PSDAvgSize PSDAvgMax PSDLFSkip PSDSmoothPPO PSDLineWeight e FregPlot The FreqPlot section of the STABLE32 INI file can contain the following parameters Keyword Title Subtitle Message X Label Y Label PlotFile Position 292 STABLE32 USER MANUAL Show startup splash screen Variance type for Sigma function Variance type for Run fiction Drift type for frequency data Drift type for frequency data non numeric characters to skip in lines of input data Use comma instead of decimal point in input data Warn about zero frequency points in input data Use
221. ncy Hz for various power law noise processes SSB Phase Noise Diagram 60 E Sf a 1 u A S f B a 2 pir ie A 40 Flidker hx 773 A cox al MK mE Iu EO EUN 0 ee E e a eee ee e ee dBc Hz MN teeb Ae VAN D NN NN Eo Fli k r P 140 ki E NL CE ce um 1 12200210 1445 160 0 4 5 108 FREQUENCY DOMAIN STABILITY Domain Conversions e Time and Frequency Domains The stability of a frequency source can be specified and measured in either the time or frequency domain Examples of these stability measures are the Allan variance o7 t in the time domain and the spectral density of the fractional frequency fluctuations S f in the frequency domain Conversions between these domains may be made by an analytical method based on a power law spectral model for the noise processes involved This method the one used by the Stable32 Domain function can be applied only when the dominant noise process decreases toward higher sideband frequencies Otherwise a more fundamental method based on numerical integration must be used The general time to frequency domain conversion is not unique because white and flicker phase noise have the same Allan variance t dependence When performing any of these conversions it is necessary to choose a reasonable range for o and t in the domain being converted to The main lobe of the o t and Mod o t responses occur at the Fourier frequency f 1 21 e Domains Conversions Domain
222. nd minimum data values and the scale factor per division Phase plots have units of seconds while frequency plots show dimensionless fractional frequency For plots the average fractional frequency and its standard error are shown on the lower line The current data point number is shown in the text box above the plot This number is useful for tagging purposes if a measurement condition such as supply voltage is changed During data capture all the controls in the 5110Comm dialog box are disabled except for the display selection window minimization and the Stop button If the 5110Comm dialog box is minimized its icon in the system tray displays the data point number to show the progress of the run It is OK to read data from the 5110Comm data file into Stable32 on the fly during a run In that way a preliminary analysis of the results can be performed while continuing to capture data Access to the help file during a run can be obtained by launching another instance of 5119Comm After a run the on screen portion of the listing phase plot and frequency plot can be examined And of course the data file can be read into Stable32 for a complete analysis The 5110Comm program uses a standard Windows initialization file 5110Comm ini to hold configuration information about the program This file retains the previous COM port data filename scale factor and display mode It can also be manually edited with a text editor su
223. nded All of the Stable32 dialog boxes may be closed with the Escape key Other standard Windows buttons and controls are used as appropriate for the particular function The use of default buttons is avoided so that the Enter key can be used to terminate edit control entries This causes the entry to be reformatted and checked for validity The only modeless dialog boxes are those for the Find and Replace functions e Data Arrays The basic Stable32 idiom is a pair of phase really time and frequency data arrays x 1 and yli respectively where the index i refers to data points equally spaced in time These usually contain equivalent data and conversions between them are provided The x values have units of time in seconds and the y values are dimensionless fractional frequency Af f The x t time fluctuations are related to the phase fluctuations by O t x t 2rvo where vo is the carrier frequency in Hz Both are commonly called phase to distinguish them from the independent time variable t The data sampling or measurement interval to has units of seconds It is called tau in many of the dialog boxes The analysis or averaging time c may be a multiple of to t mt where m is the averaging factor If units other than seconds are used for tau some of the results such as the FFT Fourier frequency scale will not be correct In addition there are corresponding phase and frequency timetag arrays These optional arrays are
224. nfidence of the resulting Allan deviation estimate Furthermore Chi squared statistics can be applied to calculate single and double sided confidence intervals at any desired confidence factor These calculations based on a determination of the number of degrees of freedom for the estimated noise type are the confidence intervals used by the Stable32 Variance function for the overlapping Allan deviation The same method is used by the Run function to show 1o error bars for its overlapping Allan deviation plot The error bars for the modified Allan and time variances are also determined by Chi squared statistics using the number of MVAR degrees of freedom for the particular noise type averaging factor and number of data points During the Run function noise type estimates are made at each averaging factor except the last where the noise type of the previous averaging factor is used 85 STABLE32 USER MANUAL e Noise Identification It is necessary to identify the spectral characteristics of the dominant noise process in order to set the confidence interval show the error bars and where appropriate apply a bias correction to the results of a time domain frequency stability analysis Stable32 uses two methods for power law noise identification based respectively on the lag 1 autocorrelation and the B1 bias factor The former method is preferred and is used when there are at least 30 analysis data points The lag 1 autocorrelation is an
225. nipulated or the run parameters may be changed between the runs that are combined e g to compare different data sets preprocessing steps or variances e Run Messages Messages describing all noise fits are available by exposing the run message drop down list 226 ANALYSIS FUNCTIONS Run Lines Function e Purpose Use the Run Lines function to add lines to a stability plot The possible line types are as follows Line Type Description Parameter None No line None Endpoints Line between certain endpoint values None Horizontal Horizontal line at certain sigma value None Vertical Vertical line at certain tau value None Noise Fit to certain power law noise model Sigma 1 Run Plot Lines x Line fi Y Up OK Down Cancel Tau Sigma mm Start 9 000006 02 Y stan JEE Print End fi 15200e 05 w End Clear Al Noise Line Slope 05 W FM E E Bead Save Sigma 1 9 53214e 09 Lines 1 e Controls The Run Line dialog box contains the following controls Some parameters do not apply to all line types Control Type Description Line Edit Enter of line to edit Up Pushbutton Increment line Down Pushbutton Decrement line Type Combo Select line type Tau Group X Axis line parameters Start Edit or Combo Enter x axis start of line End Edit or Combo Enter x axis end of line Sigma Group Y axis line parameters Start Edit Enter y axis start of line End Edi
226. noise types for the same averaging factor 2 This method of noise identification is reasonably effective in most cases The main limitations are 1 its inability to distinguish between white and flicker PM noise and 2 its limited precision at large averaging factors where there are few analysis points The former limitation can be overcome by supplementing the B1 ratio test with one based on R n the ratio of the modified Allan variance to the normal Allan variance That technique is applied to members of the modified family of variances MVAR TVAR and TOTMVAR The second limitation is avoided by using the previous noise type estimate at the longest averaging time of an analysis run One further limitation is that the R n ratio is not meaningful at a unity averaging factor A description of the power law noise identification method used in Stable32 can be found in Reference 2 e AVAR EDF The equivalent 4 of X degrees of freedom edf for the fully overlapping Allan variance AVAR is determined by the following approximation formulae for each power low noise type 86 TIME DOMAIN STABILITY Power Law AVAR edf where Noise Type N phase data points m averaging factor t t _ N 1 N 2m 2 N m F PM 1 2 E N 1 i 2m 1 N 1 2m oe 3 N 1 AN 2 4m 2m N Am 5 F FM AN 2 For m 1 23N 49 SN For m gt 1 4m N 3m TIUS N 2 N 1 3m N 1 4n i N 3 e MVAR EDF The
227. nstabilities JEEE Std 1139 1999 July 1999 MIL PRF 55310E Oscillators Crystal General Specification For March 2006 Classic Proc IEEE NASA Symp on the Definition and Measurement of Short Term Frequency Stability NASA SP 80 Nov 1964 Allan Variance D W Allan Statistics of Atomic Frequency Standards Proc IEEE Vol 54 pp 221 230 Feb 1966 Characterization of Frequency Stability NBS Technical Note 394 U S Department of Commerce National Bureau of Standards Oct 1970 J A Barnes et al Characterization of Frequency Stability JEEE Trans Instrum Meas Vol IM 20 No 2 pp 105 120 May 1971 C A Greenhall Does Allan Variance Determine the Spectrum Proc 1997 Intl Freq Cont Symp pp 358 365 June 1997 C A Greenhall Spectral Ambiguity of Allan Variance IEEE Trans Instrum Meas Vol IM 47 No 3 pp 623 627 June 1998 D A Howe Interpreting Oscillatory Frequency Stability Plots Proc 2000 IEEE Freq Contrl Symp pp 725 732 May 2002 Modified Allan Variance D W Allan and J A Barnes A Modified Allan Variance with Increased Oscillator Characterization Ability Proc 35th Symp on Freq Contrl pp 470 474 May 1981 P Lesage and T Ayi Characterization of Frequency Stability Analysis of the Modified Allan Variance and Properties of Its Estimate JEEE Trans Instrum Meas Vol IM 33 No 4 pp 332 336 Dec 1984 C A Greenhall A Shortcut for Computing the Modifi
228. nts is below the minimum A button to the right of the analysis limit bitmap restores the full analysis range A bitmap at the top center of the status bar indicates when the phase and frequency arrays contain equivalent data e Operation Click on the Phase or Freq button or plot to select the desired data type Enter the Tau value in seconds that applies to the current phase and frequency data Optionally enter values for the corresponding Start and End analysis point s if it is desired to restrict the analysis to a portion of the data Enter the title short filename of the phase or frequency data in the File edit box Right and left click on the Plot to zoom and un zoom the data display The Options Status Bar menu items may be used to select status bar controls from the keyboard e Limits The size of the phase and frequency data arrays is essentially unlimited and the maximum number of data points that can be processed is determined mainly by the computer memory and speed as set by the MaxSize configuration variable Only the top status bar message displays the full filename drive and path information The tau value must be positive and greater than zero The start and end analysis point s must be between 1 and the total of data points e Main Window The Stable32 main window may be resized and repositioned by the usual methods and these settings will be saved when the program is closed and reopened again A narrow main window
229. ock data also served as a useful cross check Known values of frequency offset and drift were inserted analyzed and removed Known values of power law noise were generated analyzed plotted and modeled 277 STABLE32 USER MANUAL 278 OTHER INFORMATION Acknowledgments e Credits Stable32 was written by W J Riley in C using the Win32 API and the Microsoft VisualC 5 0 compiler Two major 3rd party software components were used GraphiC Win 7 1 from Scientific Endeavors Corporation for the plotting functions and DataTable 3 0 from ProtoView Development Corporation for the data tables Most of the stability analysis functions use the FrequenC Library from Hamilton Technical Services NuMega BoundsChecker 5 03 Visual C Edition was used for debugging The help file was prepared with Help Writer s Assistant from Olson Software Limited and the installation program is InstallShield Express2 from InstallShield Software Corporation Extensive use was made of the mathematical algorithms in Numerical Recipes in C Many of these products as well as Windows from Microsoft Corporation are covered by copyrights and trademarks The Database function uses PostgreSQL an open source client server relational database program Its software tools and documentation are of exceptional quality and are highly recommended Information about PostgreSQL can be found at www postgresql org e History Stable32 began as a set of programs for the HP 85 computer
230. ogy Current Status and Future Considerations Proc 5th European Freq and Time Forum pp 1 9 March 1991 J Rutman and F L Walls Characterization of Frequency Stability in Precision Frequency Sources Proc IEEE Vol 79 July 1991 J A Barnes The Analysis of Frequency and Time Data Austron Inc Dec 1991 259 23 24 29 26 24 260 STABLE32 USER MANUAL C A Greenhall The Generalized Autocovariance A Tool for Clock Statistics Telecommunications and Mission Operations Progress Report Vol 42 137 Jet Propulsion Laboratory Pasadena CA May 1999 W J Riley The Basics of Frequency Stability Analysis Hamilton Technical Services C Audoin and B Guinot The Measurement of Time Cambridge University Press 2001 W J Riley The Calculation of Time Domain Frequency Stability Hamilton Technical Services W J Riley Techniques for Frequency Stability Analysis Tutorial at the 2003 Intl Freq Cont Symp May 2003 Standards and Specifications Report 580 Characterization of Frequency and Phase Noise International Radio Consultative Committee C C LR pp 142 150 1986 R L Sydnor Editor The Selection and Use of Precise Frequency Systems ITU R Handbook 1995 Guide to the Expression of Uncertainty in Measurement International Standards Organization 1995 ISBN 92 67 10188 9 IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology Random I
231. oise lines are supported Noise Alpha Slope Remarks W PM 2 1 0 Slope 1 5 for mod sigma F PM 1 1 0 W FM 0 0 5 F FM 1 0 0 RWFM 2 0 5 Aging 1 0 FWFM 3 1 0 Hadamard sigma only RRFM 4 1 5 Hadamard sigma only The power law noise lines have the selected slope and a sigma 1 intercept determined by the stability points weighted by the reciprocal of the range of their error bars The weighting can be eliminated by setting Weight 0 in the Preferences section of Stable32 ini Use of the noise line type is not usually appropriate for TIE rms and MTIE e Masks Masks can be added to a stability plot to show specification limits and the like They are defined in user written msk files per the format shown below To add a mask first select Mask from the list of line Types and then choose the desired mask file from the File list that appears in the Masks group box The mask and its label will then be included on the stability plot The label can be edited on the Run Notes function Mask files may be created with a text editor according to the following format 1 No line shall exceed 80 characters An optional first line beginning with as the first character can contain a comment such as information about the name origin amp purpose of the mask for documentation purposes only 228 ANALYSIS FUNCTIONS 3 A mandatory header line with four fields n x y 1 where int n mask data points double x label x posi
232. omation script script number 1 3 e Example To start the Stable32 program by loading a t 900 sec phase data file named CLOCK DAT enter and execute the following statement from the Windows command line STABLE32 P CLOCK DAT T 900 e Notes The tau value set with the T command line option applies to whichever type of data is loaded It takes precedence over any tau value set with the PhaseTau or FreqTau keyword items in the Inputs section of the STABLE32 INI configuration file Phase frequency and archive documents can be automatically opened by Stable32 by associating an extension with a corresponding action that includes the respective command line option For example to automatically opening a phd phase data file associate the phd extension with the phase action If a filename is entered on the command line without specifying the data type then Stable32 starts by invoking the Open Data File dialog box with that filename This feature may be used by associating an extension with the Stable32 program and clicking on any such file More than one association may be used The O SKIP option allows skipping display of the multicolumn and file opened dialog boxes when reading data with the F or P command It uses the default timetag 1 and data 29 columns for 2 column data and no scaling factor is applied Skipping is always done when a data file is opened with one of the three automation scripts 31 32 STABLE3
233. on Perform calculation to separate variances Close Pushbutton Close dialog box Help Pushbutton Invoke this help topic Plot Pushbutton Plot stability data Options Pushbutton Open Options dialog box Lines Pushbutton Open Lines dialog box Notes Pushbutton Open Notes dialog box Copy Pushbutton Copy stability results to Windows Clipboard Print Pushbutton Print stability results MM Indicator Indicates if min amp max sigma data read DF Indicator Indicates if degrees of freedom data read 247 STABLE32 USER MANUAL e Operation Enter stability data filenames using A B A C and B C edit boxes or Browse These stability files must contain 3 sets of data with the same sigma type and tau range in the standard Stable32 stability data file format as described for the Read function Only a placeholder value e g 1 is needed for the of analysis points and no entries are needed for the minimum and maximum sigma columns Then press Read to read the 3 sets of stability data which will be shown in the table and can be examined with Plot Options Lines and Notes buttons Then press Calc to separate the variances which can also be examined with Plot Options Lines and Notes features copied to the clipboard with the Copy button or printed with the Print button When done end the 3 Cornered Hat function with the Close button Error bars can be shown on the stability plots for a single unit They are determined by the maximum and minimum sigm
234. on to generate regular timetags for evenly spaced data Such timetags can be useful for examining and editing data especially if the starting time is known Timetags are generated for the entire data array regardless of the analysis limits Data Type Start 1 00000000e 00 Phase herement Net 4 licable KRESSA ER C Frequency Units Help Seconds Tau C Days Tau 86400 1 Press OKto generate timetag data C Other Enter Increment e Controls The Timetags dialog box contains the following controls Control Type Description Start Edit Enter starting timetag value Increment Edit Enter timetag increment if applicable Units Group Timetag units choices Seconds Radiobutton Use qt timetag units in seconds Days Radiobutton Use 1 86400 timetag units in days Other Radiobutton Use arbitrary timetag units amp increment Data Type Group Controls to select data type Phase Radiobutton Select phase data Frequency Radiobutton Select frequency data OK Pushbutton Perform Timetag function amp close dialog box Cancel Pushbutton Abort the Timetag function amp close dialog Help Pushbutton Invoke the Timetags help topic e Operation Select the applicable data type Phase or Frequency Enter the desired Start timetag value and units Seconds Days or Other If Other arbitrary units is chosen enter the desired timetag Increment Otherwise if Seconds or Days units are chosen the incremen
235. ontrols the display of the fit parameters at the bottom of the plot Fit Type Data Type Description None Both No curve fit Linear Frequency y atbt Quadratic Phase x a bt ct Log Freguency y a In bt 1 c Diffusion Frequency y a b ttc Average Both X x y y 205 STABLE32 USER MANUAL e Plot Messages Several standard messages such as the minimum maximum and average values the frequency drift and any offset removed or line fits are available by exposing the plot message drop down list e Plot Inserts Mini plots may be inserted at bottom left of phase data frequency data and stability plots These plots must have been generated previously and named p insert tkf f insert tkf and s insert tkf respectively For example a small plot of the frequency data can be inserted into a stability plot as shown in the sample below Dole OW UE Tienes VETE Deis Porta t thru SOB of SORT 7 Flac anDIE COT REQUENCY STABILITY GPS Block IIR AAFS S N 008 1072 Tou Sigmo 9 00e 02 9 99e 14 1 80e 03 1 02e 13 3 60e 03 1 03e 13 7 20e 03 9 36e 14 1 44804 8128 14 1 2 88e404 4 72e 14 5 76e 04 2 73e 14 1 15e 05 1 81e 14 2 30e 05 1 41e 14 4 61e405 1 28e 14 9 22e 05 1172 14 1 84e 06 143e 14 3 69e 06 1 5Je 14 7 37e 08 1 48e 14 Diffusion DrifiZDoy H D t o i B ET ation o0 Allan Devi 10 pping Overla 2 10 105 10 107 Averaging Time
236. ots in Domain function e Support Support for the Stable32 program is available from W J Riley Telephone Hamilton Technical Services 843 525 6495 650 Distant Island Drive Fax 843 525 0251 Beaufort SC 29907 USA E Mail stable32 g wriley com On line support including tutorial papers test data and updates is available from the Hamilton Technical Services web site at http www wriley com and http www stable32 com GENERAL Installation e Installation Stable32 is distributed with a standard Windows installation program called SETUP EXE which should start automatically when the CD ROM is inserted into the drive To install Stable32 manually use the Add Remove Programs applet in Control Panel under Start Settings or simply execute DASETUP from Start Run where D is the drive letter of your CD drive By default this will create a C Program Files Hamilton Technical Services VStable32 directory on your hard disk and will copy and decompress all the Stable32 files to it The installation program will also create a Stable32 program group containing an icon for Stable32 and will associate the dat frd and phd filename extensions with Stable32 Only about 15 MB of disk space is required Use the included uninstall program to remove the Stable32 program files any user generated files must be removed manually e Files The Stable32 installation comprises the following files which are all located in the STABLE32 directory Pl
237. ows Power Law HVAR edf coefficients Noise Type a0 al W FM 7 9 1 2 F FM 1 00 0 62 RW FM 31 30 17 28 FW FM 1 06 0 53 RR FM 1 30 0 54 e TOTMVAR EDF The edf for the total modified variance TOTMVAR is given by the formula b T t c where T is the length of the data record t is the averaging time and b amp c are coefficients that depend on the noise type as shown in the following table Power Law TOTMVAR edf Noise Type coefficients b c W PM 1 90 2 10 F PM 1 20 1 40 WFM 1 10 1 20 F FM 0 85 0 50 RW FM 0 75 0 31 e Th o1 EDF See the Th ol section of this User Manual for a discussion of the Th ol edf and confidence intervals e Analysis Points The in the Run stability table and the Analysis Pts in the detailed Sigma dialog box is the number of analysis points the of 2nd or 3rd differences summed in the sigma calculation This number is used in determining the confidence intervals Without gaps the s are equal to the following 88 TIME DOMAIN STABILITY Sigma Type Normal Allan M m 1 Overlapping Allan M 2m 1 N 2m Modified amp Time M 3m 2 N 3m 1 Total M m N m 1 Mod Time Total M 3m 2 N 3m 1 Hadamard M m 2 Overlapping Hadamard M 3m 1 N 3m where N phase data points M 1 M frequency data points m AF averaging factor For the normal Allan and Hadamard variances the rounding down associat
238. ox confirms the opening of a phase or frequency data file It displays the name and size of the file the of gaps and the maximum and minimum values of the data This dialog box also shows the first line of the selected file column s and a simple plot of the data Data File Opened EI Filename PHASE DAT DataType Phase Points 1001 Gaps 0 Maximum 4 3565286198918e 00 Minimum 4 7078794262138e 00 Timetag Column Data Column 1 None 0 0000000000000e 00 M Display Tau 0 1 000008 01 Scale Data From INI File Input Inputs Enter Tau 0 value for data Hel and press OK to continue Hep e Controls Besides displaying information about the data file that has just been opened the Data File Opened dialog box contains the following controls Control Type Description Tau Edit Enter Tau value for data OK Pushbutton Accept tau value and close dialog box Display Pushbutton Display data as text in Notepad Inputs Pushbutton Open Inputs dialog box Help Pushbutton Invoke the Data File Opened help topic e Operation Observe the properties of the data file that has been opened enter the correct Tau 0 value and then press OK to continue e Tau The Tau 0 value must be set to correspond to the basic measurement interval of the data in seconds to obtain correct analysis results It is preset to a value determined by the following order of precedence 1 a command line tau entry 2 a
239. pad or another ASCII text editor for that purpose Notepad or the substitute defined in the STABLE32 INI configuration file can be invoked from within Stable32 from the Utility Notepad menu or the Pad toolbutton If timetag information is available check the Show Timetags box to display it It is also helpful to check the Color Gaps and Color Outliers boxes to emphasize those points Several Timetag Formats are available including Modified Julian Date MJD Day of Year DOY Date and Exponential Exp The MJD format also serves to display any decimal numeric format The Go To group allows easy access to the data by point number while the Find group allows easy access to any gaps and outliers The Detailed Search group provides more detailed Find and Replace functions as described in the next sections of this User Manual The Edit After Highlighted Point group allows inserting or deleting a certain number of points The inserted points are 0 s gaps and this can be a convenient way to correct the data for missing points Data editing is accomplished by highlighting a data point with the left mouse button or moving to it with the up or down arrow keys A new value such as 0 for a gap can then be inserted with a numeric key or the existing value can be edited by pressing the F2 key which will activate the EDIT MODE annunciator Timetag values are not editable e Controls The Edit dialog box contains the following controls Control Ty
240. panels These are the SB and Carrier Freq for the frequency domain or Tau and Avg Factor for the time domain The BW and BW Factor applies only to white and flicker PM noise and may be entered later Then enter the PSD or Sigma power law noise parameters for any combination of RW FM F FM W FM F PM and W PM noise The corresponding parameters for the other domain are updated automatically as is the total noise for each domain Besides these domain conversions other common operations are changing the PSD Type to perform units conversions changing the SB Freq to obtain the phase noise versus sideband frequency and changing the Avg Factor to obtain sigma versus averaging time It all cases the overall display is automatically updated in a consistent manner To plot the PSD or sigma results enter the respective Start and End plot limits and press the respective Plot button The Domain dialog box may be cleared to its default values with the Clear All button and closed with the Close button e Recalculation Order Changing one of the Frequency group values updates the PSD items below it according to the corresponding sigma values Changing one of the Time group values updates the Sigma items below it according to the corresponding PSD values Changing a PSD or Sigma group value updates the corresponding item in the opposite domain Changing either the BW Hz or BW Factor updates the other value the BW factor depends on the tau value 240 ANALYS
241. parameter 239 STABLE32 USER MANUAL PSD FPM Edit Enter or read the flicker PM noise PSD parameter PSD WPM Edit Enter or read the white PM noise PSD parameter All Text Total PSD value Sigma Label Use to select sigma entries from keyboard Sigma RWFM Edit Enter or read the random walk FM noise sigma parameter Sigma FFM Edit Enter or read the flicker FM noise sigma parameter Sigma WFM Edit Enter or read the white FM noise sigma parameter Sigma FPM Edit Enter or read the flicker PM noise sigma parameter Sigma WPM Edit Enter or read the white PM noise sigma parameter All Text Total sigma value Clear All Pushbutton Restore all parameters to their default values Close Pushbutton End the Domain function amp close dialog box Copy 1 Pushbutton Copy conversion results to clipboard Help Pushbutton Invoke the Domain help topic PSD Plot Groupbox PSD plot parameters Start Freq Edit Enter PSD plot start frequency End Freq Edit Enter PSD plot end frequency Sigma Plot Groupbox Sigma plot parameters Start Tau Edit Enter sigma plot start tau End Tau Edit Enter sigma plot end tau Plot PSD Pushbutton Show PSD plot Plot Sigma Pushbutton Show sigma plot e Operation The Domain function is a flexible spreadsheet like tool that performs a variety of conversions as values are entered Begin by entering values for the domain being converted from Choose the desired PSD or Sigma Type and the associated basic parameters in the upper
242. pe Equations Group Equations for the drift fit Fit Parameters Group Results of drift fit a b and c Text Fit parameters e Operation Select the desired Drift Type and optionally check Remove Drift Then press OK to find and optionally remove the drift or Cancel to abort The Show Details checkbox changes the dialog box to a detailed format and the Help button invokes a Help screen A changed Drift Type clears the results e Detailed Drift Dialog Box The detailed Drift dialog box provides additional information about the drift analysis The Noise Model is the power law noise process corresponding to the selected drift type that provides white residuals The Equations box shows the equations for the noise fit while the Fit Parameters box shows the values of the all the fit parameters e Drift Analysis Methods Several drift methods are available for both phase or frequency data as described below The best method depends on the quality of the fit which can be judged by the randomness of the residuals Data Method Noise Model Phase Quadratic Fit W PM Phase Avg of 2nd Diffs RW FM Phase 3 Point Fit W amp RW FM Phase Linear Frequency Offset Phase Avg of Ist Diffs Frequency Offset Phase Endpoints Frequency Offset Freq Linear Fit W FM Freq Bisection Fit W amp RW FM Freq Log Fit Stabilization Freq Diffusion Fit Diffusion e Averaging Factor The detailed Drift dialog box also has an Avg Factor edit control when either the
243. pe e g L f depends mainly on the data type and noise specification The choice of calculation method e g periodogram and its options depend mainly on how to best satisfy the analysis objectives e g determining the noise type or detecting a discrete component Because most frequency stability spectral analyses are concerned with noise it is usually desirable to use a fairly large averaging factor to better determine the average noise level But a smaller averaging factor is better able to detect discrete components The auto AF periodogram method is generally a good compromise between frequency resolution and smoothing The less familiar multitaper method is often the best of all especially for determining the noise type power law slope PSD results at low Fourier frequencies have relatively low accuracy because little or no averaging is possible and can impair even weighted noise line fitting The number of low frequency PSD points omitted from the plot can be set by the PSDLFSkip read only configuration file Preferences item default 1 The value of the data size dependent maximum auto AF periodogram averaging factor can be set by the PSDAvgSize read only configuration file Preferences item default 64 and the absolute maximum averaging factor can be set with the PSDAvgMax read only configuration file Preferences item default 256 They should both be a power of 2 Thus the maximum AF is the smaller of N PSDAvgSize or PSDAvgMax where
244. pe Description Go To Group Go To controls Point Pushbutton Go to selected point Number Edit Enter point to go to Find Group Find controls Gap Pushbutton Find gap Prev Radiobutton Find previous occurrence Next Radiobutton Find next occurrence Outlier Pushbutton Find outlier 153 STABLE32 USER MANUAL Go To 1 00000000 0 00 00 a Point Number fi 2 00000000 8 5116010334397e 02 3 00000000 2 2047548258606e 01 Find 4 00000000 1 4707417985148e 01 E 5 00000000 3 4175630294613e 01 Gap C Prey Next 6 00000000 2 1457633784021e 01 Siame 7 00000000 5 5127998572089e 01 Jujar zerei 8 00000000 3 7986709938518e 01 9 00000000 2 9386363828828e 01 p Detailed Search 10 00000000 6 8407016576504e 01 End E 11 00000000 7 3555465081034e 01 p 12 00000000 8 8567199031108e 01 E S 13 00000000 75817416248199e 01 penita Ie 14 00000000 7 5255902203245e 01 m Del p 15 00000000 1 2292706697040e 00 16 00000000 11723102679510e 00 17 00000000 6 8921518932712e 01 M ColorGaps T Color Outliers 18 00000000 1 1606059406016e 00 vi Iv Show Timetags Timetag Format Press F2 to edit OK E MJD 00000000 00000000 C DOY YYYY DDD HH MM SS data in table C Exp 0 0000000000e 00 C Date YYMM DD HH MM SS Help Sigma Factor Edit Enter outlier criterion Detailed Search Group Detailed search amp replace controls Find Pushbutton Invoke Find func
245. played that prompts the user for the file name and page orientation The page orientation refers to which side left right or top of the page the top of the plot is to appear The default is the top The metafile file once generated may then be used by other applications such as desktop publishing packages Metafile The Convert menu s PostScript command is used to display a PostScript conversion dialog box to select the filename and type of PostScript file to be produced The user is asked to select either Encapsulated PostScript with or without a TIFF Postscript image embedded PostScript level 1 or 2 page orientation color separations and font The page orientation refers to which side left right or top of the page the top of the plot is to appear The default is the top Convert The Convert menu s TIFF command is used to display a TIFF conversion dialog box to select the filename and resolution of the TIFF file to be produced The user is asked to select one of four TIFF image resolutions and the page orientation The page orientation refers to which side left right or top of the page the top of the plot is to appear The default is the top TIFF The Convert menu s CGM command is used to display a CGM conversion dialog box to select the filename and page orientation of the CGM Computer Graphics Metafile file to be produced The user is asked to select the page orientation The page orientation refers to which s
246. que key Foreign key Unique key Primary key Foreign key Primary key 137 Source ID Meas ID Begun By Ended By 138 STABLE32 USER MANUAL measurement_sources measurement list measurements measurement list measurement list measurement list source id source id source id meas id begun by ended by Primary key Foreign key Primary key FILE FUNCTIONS Database Configure e Database Configure Configuration information for the database function is stored in the STABLE32 INI initialization file in standard Windows format comprising Section headings and Item string values These items may be edited directly with a text editor or preferably by using the Database Configure dialog box from within the Stable32 program which is invoked by pressing the Configure button The Database Configure dialog box is shown below Database Configure X Database Access Host IP Address 132 158 2 5 Database Name ftsc postgres 5 User Password Enter configuration parameters and press Cancel OKto accept Help Dialog Box ALT Control Control Control Key Type Description Database Access Group Box Database connection parameters Host IP Address I Edit Dot address or blank for localhost Database Name D Edit tsc postgres is standard MMS database name User U Edit tsc is standard MMS database user name Password W Edit tsc is standard MMS database password 139 STABLE32 USER MAN
247. quency data Exit Exit Stable32 program Edit Edit Edit phase or frequency data Convert Convert between phase and frequency data Normalize Normalize phase or frequency data for zero mean Average Combine data into a longer averaging time Fill Fill gaps in phase or frequency data Regularize Regularize data by using timetags to insert gaps Scale Scale phase or frequency data Part Remove all except part of phase or frequency data Clear Clear phase or frequency data Analysis Statistics Calculate basic statistics for phase or frequency data Check Check frequency data for outliers Drift Calculate drift for phase or frequency data Sigma Calculate Allan deviation for phase or frequency data Run Calculate stability statistics DAVAR Perform a dynamic stability analysis Power Plot power spectrum of phase or frequency data Histogram Plot histogram for phase or frequency data Autocorrelation Plot autocorrelation for phase or frequency data 3 Cornered Hat Use the 3 cornered hat method to separate variances Plot Phase Plot phase data Frequency Plot frequency data STABLE32 USER MANUAL Generate Noise Timetags Utility Calendar Domain Inputs Play TSC 5110A Stable ini Log Pad Autol Auto2 Auto3 Tabs Show Tabs Auto File Tabs Auto Change Tabs Auto Edit Tabs Auto Noise Tabs Save Current Data Rename Selected Tab Write Selected Tab Close Selected Tab Close
248. r Function Histogram Function Miscellaneous Functions 282 Calendar Noise Function Configure Filenames Autor 3 Cornered Hat Function APPENDICES Appendix II Special Characters e Special Characters The Stable32 GraphiC graphics functions make use of several special text characters The symbols and have special meanings Superscripts and subscripts may be entered into text strings as super and sub respectively Text color may be changed by entering N where N is the standard IBM color numbers shown below For example use 2 for green text to annotate a noise line The and symbols are not used by Stable32 To use the symbols and normally these characters should be preceded by For example use and to place and into the text Color Black Blue Green Cyan Red Magenta Brown White Dark Gray Light Blue 10 Light Green 11 Light Cyan 12 Light Red 13 Light Magenta 14 Yellow 15 Bright White O oo ao un KON Ola Stable32 uses four special characters to control the font and symbol set used for plot labels These control characters are inserted into the label text for plot labels with NUM LOCK on by pressing the ALT key and using the numeric keypad to enter one of the 4 digit numbers shown in the following table Font Code Character News 0200 E Swiss 020 Newsgrm 0202 Simplex 0203 E 283 STABLE32 USER MANUAL The GraphiC News and New
249. r overlapping method the latter provides better statistical confidence at the expense of somewhat longer computational time The total Hadamard variance TOTHVAR is a total version of the Hadamard variance e Modified and Total Variances The modified and total variances are not distinct variances but are considered to be techniques applied to the Allan and Hadamard variances e Th o Variances Th ol is a special purpose statistic that provides information equivalent to the Allan variance out to averaging factors equal to 75 of the record length Th oBR is a biased removed version of Th ol while Th oH is a hybrid statistic combining Th oBR with the Allan variance e Other Statistics Other statistics used for time domain frequency stability analysis include MTIE and TIE rms which are most commonly used in the telecom industry e Summary A summary of the Allan and Hadamard families of time domain stability measures can be found in the reference below which categorizes then according the following parameters Parameter Symbol Value Variance Remarks Order of phase d 2 Allan difference 3 Hadamard Allowable a gt 1 2d gt 3 Allan W PM thru RW power law FM noise noise exponent gt 5 Hadamard W PM thru RR FM noise Filter factor F m Unmodified m averaging 1 Modified factor t to Stride factor S 1 Non overlapped estimator Stride 1 S m Overlapped estimator e Reference C Greenhal
250. re needed to allow time for GraphiC plotting and printing The lines are simply comments e See Also See the WinBatch documentation for more information regarding these programs and commands See the Auto function for a limited means of stability analysis automation that is built into the Stable32 program 33 34 STABLE32 USER MANUAL GENERAL Copy Command e Copy Command Several of the Stable32 functions include a Copy button or menu item to copy information to the Windows clipboard where it can be viewed saved printed or pasted into another application The following table describes those functions and the information that can be copied Copy Command Properties Function Format Remarks Statistics Basic statistics Bitmap Screen dump OEM text Check Text Drift Text Sigma Text Power Metafile Histogram Metafile 3 Corn Hat Sigma tau table Text Data Plot Metafile Noise Noise parameters Text OEM text Calendar Bitmap All the data formats can be displayed with the Clipboard Viewer while the screen dump bitmaps can also be displayed with the Paint program The OEM text format should be used Be sure to use the Edit Metafile not Bitmap menu item for GraphiC plots OEM text OEM text OEM text OEM text 35 36 STABLE32 USER MANUAL GENERAL FrequenC FrequenC DLL The FrequenC dynamic link library DLL is a library of over 100 custom functions to support frequency stability analysis
251. requency data having large gaps The latter is most apparent at longer averaging times where the averaging factor is comparable to the size of the gap The speed limitations are caused by more complex gap checking and frequency data algorithms while the poor results are associated with the total variances for which conversion to phase data is required Filling can often help for the total variances Two general rules apply for the variance analysis of data having large gaps 1 use unconverted phase data and 2 check the results against the normal Allan deviation which has the simplest fastest gap handling ability The following table summarizes the gap handling limitations of the Stable32 variance functions See Reference 1 for more information Stable32 Gap Handling Limitations in Variance Functions Data Type Variance Remarks Phase Avoid freq to phase conversion Normal Allan Overlapping Allan Generally OK Modified Allan Avoid use with large gaps Fill gaps for faster calculation Time Avoid use with large gaps Frequency Hadamard Overlap Hadamard Avoid use with large gaps Total Avoid use with large gaps Modified Total Avoid use with large gaps Time Total Avoid use with large gaps Hadamard Total Avoid use with large gaps e Spectral Analysis The Stable32 spectral analysis functions fill gaps in the data before performing their calculations This can affect the low frequency portion of the spectrum 21
252. rt 1 End 513 Tau 0 00000e 00 Stat 1 End 512 Data tab operation is controlled by the Tabs main menu item that has several sub items as shown below rw Initially after the Stable32 program is launched no Tabs Options Help data tab row is displayed Clicking on the top Show Show Tabs Tabs item in the Tabs menu activates a blank tab row for both phase and frequency data switched in the v Auto File Tabs usual way That also activates all of the other Tab menu items The second group of four items Auto vod a File Tabs Auto Change Tabs Auto Edit Tabs and v Auto Edit Tabs Auto Noise Tabs select whether new data tabs are v Auto Noise Tabs automatically created when a new data file is read the current data file is changed or edited or a new noise Save Current Data file is generated These options can be selected in any combination The Save Current Data command Rename Selected Tab creates a new tab for the current data The Rename Selected Tab command renames the data file of the Write Selected Tab selected tab The Write Selected Tab command writes the data of the selected tab to disk The last group of Close Selected Tab two items contains the Close Selected Tab and Close Close All Tabs All Tabs commands to remove either the selected or all of the data tabs and free their memory Clicking on a tab selects it and reloads its
253. rt Scales Checkbox Use smart y axis scales for data plots Weight Sigma Checkbox Weight power law noise fits on stability plot Plot Fits Plot Label Group Select and enter settings for plot labels Label Plots Checkbox Check to label plots at bottom left Label Edit Enter text to appear as plot label e Data Page Controls The Data property sheet page contains the following controls 48 Control Type Data Reading Group Settings Max Data File Size Edit 4 Non Numerics Edit to Skip Use Comma as DP Checkbox GENERAL Description Settings for reading phase and frequency data Set maximum data file size to read without averaging Set non numeric characters to skip at beginning of each row of data Use comma instead of decimal point for input data Warn for Zero Checkbox Display warning if two adjacent phase data points are Freq Data equal Data Writing Group Settings for writing phase and frequency data Settings Write Header Checkbox Add header to data files Reset Pushbutton Restore default values max size amp non numerics Contour AEI General Toolbuttons Plots Data Ti Options General Toolbuttons Plots Data Inputs 6 Xx Tag Scale 8 6400000000000e 04 Tag Offset 0 00000000000008 00 Enter data input scaling values Tau sets data sampling interval sec Addend and multiplier modify data values For example use 1e 9 multiplierto convert data to nsec Tag
254. rt function and convert the frequency data into the corresponding phase data Notice that the status bar now shows a 513 point SAMPLE 004 phase data file Repeat some of the analysis and plotting functions with the phase data Try other Stable32 functions as desired Generate and analyze some simulated clock noise Try other plot options Try the domain conversions or generate and use timetags Use the context sensitive Help button as needed OTHER INFORMATION Test Suite e Test Suite The following tables summarize the values for several common frequency stability measures for both the classic NBS data set and a 1000 point portable test suite e NBS Data Set A classic suite of frequency stability test data is the set of nine 3 digit numbers from Annex 8 E of NBS Monograph 140 shown in Table I Those numbers were used as an early example of an Allan variance calculation This frequency data is also normalized to zero mean by subtracting the average value and then integrated to obtain phase values A listing of the properties of this data set is shown in Table II While nine data points are not sufficient to calculate large frequency averages they are nevertheless a very useful starting point to verify frequency stability calculations since a small data set can easily be entered and analyzed manually A small data set is also an advantage for detecting off by one errors Table I NBS Monograph 140 Annex 8 E Test Data Freq Norma
255. s Funct On se eerie E REPERTA I RENE PREIS 113 Open F tlctioh oe eee ree Fett rer eO erre de ES 115 iv Read Archive Function Read Archive Conti gure scat serere eer co e eI RISE RUE 119 A e 121 TABLE OF CONTENTS Database Configure READ FUNCTIONS RA e ERE 141 Read Plot EUA a 143 Read Options Function inerti nr nn srt 145 Read Lines Function e e ERR RHENO ee UDINE 147 Read Notes FUNCHOT eee RUBY ROUGE USERS 149 EDITING FUNCTIONS Print FUNCHOM EEE EA E eR ttd E PR IE 151 Edit Puticti n e RR AA LAAT Em aaa ea 153 A RR 157 Replace Fun tion 5 eiae e rrt rte tent rer Ee Hee te rt rettet s 159 Convert EUtlction ee REPRE aa AE aaa 161 Normalize Functt A MURAT LANKAL GM 163 Average Elo 3 net neret te iere ertet epist ee e 165 O 167 Scale Function Part E nctoti O nem etin eme n e tete RA 171 ANALYSIS FUNCTIONS Statistics O Mee RIED NR RR UNE co 173 Ch ck BUnction eee I Reti a enero erede kaptenit ae inane e tbe eoa et 175 Drift Function i e aee ii 177 Sigma Function Power Function Autocorrelation FOCO oerte e rere repe eon e ie 193 Histogram Function ii 197 Plot E nctioti 4 sc ERE PR IER POENI ERE REO UI ORE 199 A reote irte ee reden etse 201 Pl t Options F nction a 203 Plot Lines Function n NO 207 Plot Notes Function 209 Timetags Pum ti onic Saa 211 Noise PIO RARA 213 STABLE32 USER MANUAL Clear Functions muusikas 217 NN 219 Run Plo
256. s used to zoom in on a portion of the currently displayed TKF plot Once the user selects Zoom In a cross hair cursor is presented By clicking the left mouse button and moving the mouse a Zoom In box will appear Once the proper size Zoom In box is chosen clicking the right mouse button will start the drawing of the selected portion of the plot The zoomed portion of the plot can then be printed or converted Redraw or a space key will redisplay the original plot before it was zoomed The Draw menu s Zoom Out command is used to zoom out the currently displayed TKF plot Once the user selects Zoom Out a cross hair cursor is presented By clicking the left mouse button and moving the mouse a Zoom Out box will appear Once the proper size Zoom Out box is chosen clicking the right mouse button will start the drawing of the entire plot in the zoom box selected The zoomed out plot can then be printed or converted Redraw or a space key will redisplay the original plot before it was zoomed GENERAL The Convert menu s Bitmap command is used to generate a Windows Bitmap BMP file from the current plot The user may select the client area plot only entire Play window or entire screen to include in the bitmap The Bitmap file may then be used by other applications such as desktop publishing packages Bitmap The Convert menu s Metafile command is used to generate a Windows Metafile WMF file from the current plot A dialog box is dis
257. s x Title FREQUENCY STABILITY OK SubTitle SIGMA TAU v Cancel Message y Help Message Position Top Left y Read Config Save Config Beset All Table Position Top Right y Stability File SIGMA TAU Axis Y Axis Label Averaging Time EtE Secon Label Allen Deviation EsE y Et Tau Mex 6 400002 01 Sigma Max 14 81 700e 00 Scale Max fi 00000e 02 Tau Min 1 00000e 00 Scale Min fi 00000e 00 Scale Max 1 000008e 01 Sigma Min 7 30400e 01 Scale Min 1 000006 01 Options Iv Date M Box M Barsi M Table2 V F5 PlotFile D DEVSTUDIO MyProjects e Controls The Read Options dialog box contains the following controls Control Type Title Edit Sub Title Edit Message Edit Message Position Combo Table Position Combo Read Config Pushbutton Save Config Pushbutton Stability File Text X Axis Group Label Edit Tau Max Text Scale Max Edit Tau Min Text Scale Min Edit Y Axis Group Label Edit Sigma Max Text Scale Max Edit Description Enter plot title Enter plot subtitle Enter plot message Choose message position Choose table position Read options from INI file Save options in INI file Display name of stability file X Axis parameters Enter x axis label Maximum tau value Enter x axis tau scale maximum Minimum tau value Enter x axis tau scale minimum Y Axis parameters Enter y axis label Maximum sigma va
258. scale and offset modify tau value Use 86400 as tag scale to convert MJD timetags into seconds Bata input Sealing Matias 7 PSD Auto AF Parameters r PSD Smoothing Parameters A ae RESON MIS FF Weight Smoothed PSD Fit Tau 1 00000000000008 00 1 00000000000008 00 oaks s Addend f 0 0000000000000e 00 0 0000000000000e 00 Absolute Mex AF PoirisJOcisve Multiplier 1 00000000000008 00 1 00000000000008 00 LF Points To Skip P 1 00000000000008 00 0 0000000000000e 00 selel Restore PSD Defaults Peset v Many Tau Size 500 Restore Many Tau Size Reset Enter PSD Auto AF and Smoothing values All except LF Points must be a power of 2 See Help for more information Use Reset D button to restore defaults Select PSD smoothing and weighting as desired Select enter stability plot Many Tau option size as desired Use Resetto restore default size Page 6 Options Page 5 Inputs e Inputs Page Controls The Inputs property sheet page contains the following controls Control Type Description Scaling Values Group Data input and timetag scaling values for phase and frequency data Tau Edit Tau value in seconds Addend Edit Value to add to data points Multiplier Edit Factor to multiply data points by Tag Scale Edit Factor to multiply timetag values by Tag Offset Edit Value to add to timetags e Options Page Controls The Options property sheet page contains the following con
259. se The time variance TVAR o x measures the time fluctuations of a source or time distribution system All of these quantities are usually expressed as their square roots ADEV o t MDEV Mod o t and TDEV o t They are dimensionless except for the latter which has units of seconds The Allan variance can be calculated by either the non overlapping or overlapping method The latter provides better statistical confidence at the expense of a slight increase in computation time The results can be shown for a single t over a range of octave or decade t spacing or at every t for which there is sufficient data The total Allan and total modified Allan variances TOTAVAR and TOTMVAR are similar in purpose and expected value to the Allan and modified Allan variances respectively but use extended data sets to provide improved confidence at larger averaging factors at the expense of a significantly longer computational time e Hadamard Variances The Hadamard variance is a 3 sample variance that is similar to the 2 sample Allan variance It examines the 2nd difference of the fractional frequencies the 3rd difference of the phase variations Because of this the Hadamard variance HVAR or H0 t converges for the 55 STABLE32 USER MANUAL Flicker Walk FM a 3 and Random Run FM a 4 power law noise types It is also unaffected by linear frequency drift The Hadamard variance can also be calculated by either the non overlapping o
260. se ener nennen 103 187 Precision 15 157 159 Print FUN tin iet ec saben cas PESE PERENNE NE Sinead ERATES EPA GITE VEES RASEN e eas do 151 Quadratic 6 os ca E NS Gnade ot tut O OR 179 Read EUA Read Lines Function Read Notes Function References ie Rest D T R gularize FUNCION etse eremo re E MUR E re SUU ak pre e ed oak AS Remove Frequency Drift eire tere e ten katakana EEEE eR 177 REMOVE Gaps eere ER TEENS URN EE S IE d ree sveateds dacs ava ERN iaa Remove Outliers Replace Function Run Function A RUM EATS eirama di Run Notaria diia Run O PAS iii 310 Run Plot Foncea etes 223 A NON 129 A ede etre itte jah edes ete eI EN de ist ee E ree RC Hees 169 Second Differences dieere t e Ee D TVXERUIVON E CRI Saas NOUNS ETS 179 Separation of Variances sess enne nene enne nnne nein entente enne 97 Sigma PUNCH ON ese rs rre e i reae eh PA RE ORE S ES 181 Sigma Tau Diagrams sese eerte nennen enne teen trennen nennen eren treten rene enne 105 Special 01 21 10 16 535 DERE 283 Special Versions sc e dte a etre ee rece a n laama eaka ad Eee eee oer A dee ta He aa 45 Stable32 Statistics function RR Statistics Function Status Bar Student Version Support SYMMIMEC LI COMM se dass A AEAEE AATE T RRA 13 I ENIM 12 27 31 Test nu
261. separate the columns and each line may contain up to 1024 characters A single column is assumed to the phase or frequency data which is automatically loaded into the selected array Multicolumn data opens a special dialog box where the desired columns for the data and optional timetags can be selected The last line of the file that contains a numeric 0 9 character determines the number of columns and first 80 characters are displayed for easy reference Non numeric header and trailer lines at the top and bottom of the file are ignored including lines beginning with the UNIX style comment symbol Fields of numeric data in header rows may be read incorrectly and require subsequent editing but they will not interfere with the reading of later rows of actual data Slashes and colons as used in dates 04 23 97 and times 18 50 are converted to zeros 0 so that numeric data on the same row can be read Provisions are included for ignoring a selected of non numeric characters from the beginning of each row of phase or frequency data as it is read The NonNums configuration variable sets the of non numeric characters that are skipped at the beginning of each line of data This value normally 0 can be used to read data files that contain non numeric markers at the start of each line This value can be set in either the Configure dialog box or the STABLE32 INI configuration file Data files are parsed for numeric values one line at a
262. sgrm fonts are used for all plot titles sub titles and axis labels For example to insert the lower case Greek letter t into a stablity plot x axis label use the character sequence tE This will shift to the Greek math symbol set of the Newsgrm font changing the character t to a t and then return to the normal News font Lower case Greek letters are entered with the characters a through z in a fashion similar to the Windows Symbol set The News font is defined for codes between 33 and 199 while the Newsgrm font for 33 to 146 The News Swiss Newsgrm and Simplex fonts are shown in the tables on the following pages news fnt ls 2160 Clas Tilo eln Vus 152 y co 186 a s 316 De Uli fim Wiis 6 153 70 187 i 5 2 4 eo Ele V wv gl 1 Xu l 71 88 I 5 s Sto Flo WI ice hi ys s mAls 17 5 6 n Gle Klos i zZ i 55 i sw Us 7 His Y 15 Ji o 115 Xm E 91 9 55 8 5 Lo Zw kim Vin 115 00 92 w ls 9 Jia los l 42 59 f 76 ws 58 3 K o2 Mim 5 13 so m 0 194 42 so 76 Lis w MN 127 44 a 1 18 E 95 Y To I Milo Alim oliz C 5 2 Ofi79 i s B 4 61 78 Ns pm pio Wisc AE c Ce 57 45 le 2 Olos In g 130 lu ea Ali E os 46 e Pla Po alm riw lus 0 1 82 99 e 47 64 8 Q ss blus Si Alu 0 2 183 s Ole Ala Ro cle to Aliso Blur 250 4 ss Biss Siw d Um s l re d 185 News Font Numer
263. shbutton Perform conversion amp close box Cancel Pushbutton Abort conversion amp close dialog box Help Pushbutton Invoke the Convert help topic e Operation Select desired Conversion type and desired Normalize Frequency or Adjust Zero Frequency Transfer Timetags and Use Timetags for Tau options then press OK To abort press Cancel e Conversions Phase to frequency conversion is done by dividing the first differences of the phase points by the averaging time y x x j t The inverse frequency to phase conversion is done by piecewise integration using the averaging time as the integration interval x X y T Any gaps in the frequency data are filled to obtain phase continuity Two equal adjacent phase 161 STABLE32 USER MANUAL values will result in zero frequency which is treated as a gap unless the Adjust Zero Frequency option is used recommended see below e Zero Frequency The conversion of phase data having two equal adjacent values results in a fractional frequency value of zero While this is correct it will subsequently be treated as a gap in the frequency data That problem for which there is an optional warning during the reading of phase data can be avoided by using the Adjust Zero Frequency option during phase to frequency conversion which will adjust the frequency value to 1e 99 e Gaps Gaps in frequency data are filled in the converted phase data with values based on the average frequency e
264. sis Do not access the GraphiC menu items or resize the plot while it is drawing Problems have been reported on some systems if this is done See the Plot Options section for information about the cursor feature Launch PlayW and use it to make an unlimited number of copies of GraphiC plots as metafiles to the Windows clipboard xx 301 va 302 STABLE32 USER MANUAL Stability Analysis Repetitive Stable32 stability analysis procedures can be automated with WinBatch scripts This can save time assure consistency and allow the analysis to be done by less experienced personnel see batch Files below Time can be saved and errors avoided during a complex analysis by first setting up the data and plot filenames with the Files function Enter the tau value in the Data File Opened dialog box as a PhaseTau or FregTau Inputs item in the configuration file or automatically using timetag data without the Inputs values In the latter case the tau value can be scaled to seconds with the TagScale Inputs item The resulting tau value may have some small rounding error Observe the blue symbol at the top center of the status bar that indicates if the two data types are synchronized Large Data Sets The most important factor for analyzing large data sets with Stable32 like most Windows applications is RAM memory size not processor speed If possible average large data sets before beginning an analysis run Use the Stop button on
265. stics and Data Filtering Tutorial at 1993 IEEE Freq Contrl Symp June 1993 Computation and Algorithms W H Press B P Flannery S A Teukolsky and W T Vetterling Numerical Recipes in C Cambridge Univ Press Cambridge U K 1988 pp 216 217 W J Riley A Test Suite for the Calculation of Time Domain Frequency Stability Proc 1995 IEEE Freq Contrl Symp pp 360 366 June 1995 W J Riley Addendum to a Test Suite for the Calculation of Time Domain Frequency Stability Proc 1996 IEEE Freq Contrl Symp pp 880 881 June 1995 265 STABLE32 USER MANUAL 266 OTHER INFORMATION Example e Example 1 Double click on the Stable32 program group Start the Stable32 program by double clicking on its icon Go to the file open function by clicking on the Open toolbutton Select the frequency data type by clicking on the Frequency Radiobutton Open the SAMPLE DAT file by selecting it and pressing OK Observe the plot and statistics for this data file in the Data File Opened dialog box Close the Data File Opened dialog box by pressing OK eo A 9 Ot Re pO G2 Notice the frequency data file information shown in the status bar at the bottom right of the screen 9 Display the frequency data by clicking on the Edit toolbutton 10 Use the scrollbars to examine the frequency data The Edit function can display timetags gaps and outliers and can perform several search and replace functions which you can explore lat
266. t Seconds e N Rp S Y ma SE e Cursor Checking the cursor option activates crosshairs on the plot whose position is indicated at the right end of the GraphiC menu bar please ignore the strange characters This option also activates a line drawing feature The right mouse button starts a line and the right button ends it The line can be extended with another right button click or a new line started with the left button The lines can be deleted with the Del key Press the Esc key to deactivate the cursor function e Wide Lines Checking the Wide option causes the data to be plotted with wide lines with better visibility for presentations 206 ANALYSIS FUNCTIONS Plot Lines Function e Purpose Use the Plot Lines function to add lines to a data plot The possible line types are as follows Line Type Description Parameter None No line None Endpoints Line between certain endpoint values None Regression Linear frequency data or quadratic phase data regression line Frequency slope Average Horizontal line at average value Average Marker Vertical line at certain x axis value None Frequency Plot Lines x OK Line amp 1 Up Type ALME jm Down Cancel Lines 1 Cancel Axis Y Axis Help E 5 74890e 01 Start 1 00000e 00 sat e Print End fi 00000e 03 End 7 26495e 01 Copy Parameter Read Save Clear All e Controls The Plot Line dialog box contains the following con
267. t Encina 223 Run Options Function iie ten OH sida 225 R n Lings FUNCOM C H 227 Run Notes NA aia 231 Dynamic Stability FU 233 Re gularize Function 5 eg ER ERR SCR aA i 237 Domain FUnCt On in 239 MISCELLANEOUS FUNCTIONS Sto FUNCIONS A MEE 243 3 Cornered Hat Function esee entente nennen nnn 247 Calendar Function OTHER INFORMATION n i A a TARE 255 A EA A 259 locnm rc RE ETE TEN 267 MSU SUME 2 A AA TIE O AA SS EA EA 269 Analysis Procedure ete tiere tte emt ESATE PSAo hiv dre th terk ASIDE AAE R niid 273 Validat Oh ars NE 277 A cd 279 APPENDICES TStable32 FURCHONS vicios ica societat 281 II Sp cial Characters erret ene e enemies 283 TIL Editing Keys onec ROREM REIR HR SRR 289 TV Configuration File oti ntt inti ree ke PRI ets 291 V Hints and Notes niet ne RC ERI RR UR ION 301 VI 5110Comm Communications Program essere 305 INDEX vi GENERAL Stable32 e Introduction Stable32 is a 32 bit PC program for the analysis of frequency stability It allows the entry and editing of phase and frequency data the calculation of stability statistics and the plotting and printing of phase frequency and stability data Stable32 runs under Microsoft Windows 95 NT or higher and requires a 200 MHz Pentium class computer with a CD drive 32MB of RAM and a XGA color monitor A graphics printer is needed for text and graphics printouts
268. t Enter y axis end of line Slope Combo Noise type for fit Sigma 1 Text Noise line fit parameter Lines Text of lines entered 227 STABLE32 USER MANUAL Clear All Pushbutton Clear all lines Read Pushbutton Read line information from INI file Save Pushbutton Save line information in INI file Print Pushbutton Print line parameters OK Pushbutton Perform Run Line function amp close dialog box Cancel Pushbutton Abort Run Line function amp close dialog box Help Pushbutton Invoke the Run Lines help topic e Operation Enter the desired plot lines and press OK to accept them Print to print them or Cancel to abort Press Clear All to clear all lines or use the Read and Save buttons to retrieve and store line information A particular line can be chosen with either a Line entry or the Up Down buttons Up to 12 lines may be entered The line type is then selected from the Type list which varies according to the sigma type that is being run Most of the line types require a combination of Tau and Sigma Start and End values which may be either entered into an edit box or in the case of noise lines chosen from a list Noise lines also require a Slope choice that is appropriate for the particular sigma type and power law noise process The Sigma 1 value is shown for the noise fit The total of active Lines is also displayed All plot lines are cleared if the Run conditions are changed e Noise Lines The following power law n
269. t files PHASE TKF FREQ TKF SIGMA TKF SPECTRUM TKF and HISTO TKF will overwrite the previous ones if any If it is desired to keep one of those files it is important to rename it either from within the Filenames function or corresponding dialog box before plotting or manually from the command line after the plotting operation The same rule applies to the SIGMA TAU stability data file the PSD DAT power spectrum data file the AUTO DAT autocorrelation data file and the XYZ DAT dynamic stability data file Those files are written immediately after their respective calculations so to use a different name it must be changed before performing the calculation STABLE32 USER MANUAL GENERAL Program Model e Overview The Stable32 program is based on a simple main window with a number of modal dialog boxes to implement the functions These functions manipulate phase or frequency data arrays e Main Window The main window is empty except for menu and toolbar rows at the top and status bar rows at the bottom The menu and toolbar provide the command interface while the status bar displays information about the current phase and frequency data e Dialog Boxes Modal dialog boxes support all of the Stable32 functions These child windows use a consistent button naming convention The OK and Cancel buttons either accept or reject any changes that have been made while the Cale and Close buttons control functions that can be either repeated or e
270. t portion of the data Points Text Display the of points in the data file Avg Factor Edit Enter the averaging factor to be used to read the data file OK Pushbutton Accept selected option amp continue with Open Cancel Pushbutton Abort the Open operation Help Pushbutton Invoke the Large Data File help topic e Operation Choose one of the Average First or Last options and press OK or press Cancel to abort the Open operation With the Average option the minimum Avg Factor required to read the entire data file is displayed It may be increased if another larger averaging factor is desired The Avg Factor is always 1 for the First and Last options 123 STABLE32 USER MANUAL e Averaging Averaging of phase data is accomplished by simply eliminating the intermediate data points while averaging of frequency data uses the mean value of the points being averaged In either case the averaging factor is displayed as the default t value e Limits The maximum size data file that can be read is set by the Max Data File Size item in the Configure function The purpose of this setting is to automatically activate the data averaging dialog box when a large data file is read Set this parameter to a value appropriate to your computer s speed and RAM With the Average option there is essentially no limit to the size of the data file that can be read 124 FILE FUNCTIONS Data File Opened e Purpose The Data File Opened dialog b
271. t will be determined by the t value Press OK to generate the timetags or Cancel to abort the Timetags function 211 STABLE32 USER MANUAL e Caution Use caution when generating timetags for data that is not regular Do not confuse these artificially generated timetags with actual ones Such timetags can be useful to identify the position of data interruptions but gaps should be manually inserted into the data to provide regularity and the timetags should then be cleared The Regularize function cannot accomplish this with artificially generated timetags 212 ANALYSIS FUNCTIONS Noise Function e Purpose Use the Noise function to function to generate simulated power law clock noise Noise Parameters Alpha Noise OK Random Walk FM 0 00000e 00 2 parameter Cencel is Allan Flicker FM 0 000008 00 1 deviation at Copy Tau 1 sec White FM 0 00000e 00 0 Help Points Flicker PM 0 00000e 00 1 Num 51 3 White PM o 00000e 00 2 Tau 00000e 00 Fractional Frequency Parameters Offset 0 00000e 00 Drift per Tau Interval o 00000e 00 Sine peak o 00000e 00 Sine Period sec o 00000e 00 Fed Press OK to generate simulated power law clock noise e Controls The Noise dialog box contains the following controls Control Type Description Noise Params Group Power law noise parameters RW FM Edit Enter random walk FM noise coefficient o 1 Flicker FM Edit Enter fli
272. tain the x axis settings for future plots When using the default directory new Stable32 GraphiC plot files PHASE TKF FREQ TKF SPECTRUM TKF and HISTO TKF will overwrite the previous ones If it is desired to keep one of these files it is important to rename it either from within the corresponding dialog box before plotting or manually from the command line after the plotting operation Plot files may also be sent to another directory by changing the Plot Filename or Plot File field in the Plot Options dialog box When the SmartScale configuration option is on the default y axis phase 204 ANALYSIS FUNCTIONS data plot scales are whenever possible set to standard units like microseconds and nanoseconds and the frequency scales to pp10 XX notation Checking the Cursor option activates crosshairs on the plot whose position is indicated at the right end of the GraphiC menu bar please ignore the strange characters This option also activates a line drawing feature The right mouse button starts a line and the right button ends it The line can be extended with another right button click or a new line started with the left button The lines can be deleted with the Del key Press the Esc key to deactivate the cursor function Checking the Wide option causes the data to be plotted with wide lines This can be useful for producing plots with better visibility for presentations See Appendix II for information about adding subscripts superscripts
273. ted Enter the T Tau dead time ratio where tau is the measurement time and T is the time between measurements Dead time corrections are made using the B2 and B3 bias ratios which handle cases of single and multiple distributed measurement dead time respectively e Overlap amp Th o1 Hybrid The Overlap amp Th ol hybrid called Th oH provides stability data over the entire range of averaging times from the measurement interval to 75 of the record length Manually enter the type of power law noise that applies to the data to invoke the appropriate bias correction or use the Auto BR Bias Removed feature to automatically determine and remove the bias correction e All Tau The All Tau option is useful as a means of spectral analysis to identify periodic components in time domain stability data Without the Many Tau option it will calculate the stability at every possible tau value which can take a very long time With the Many Tau option which may be selected in the Configure Function a selectable subset of the possible tau values will be used to provide a quasi uniform distribution of points on the stability plot which can provide much faster calculating plotting and printing The default setting for the approximate number of points is 500 which may be set with the ManySize parameter in the Preferences section of the STABLE32 INI configuration file e Dead Time Bias correction for measurement dead time is available for the norm
274. the Allan variance at large averaging factors e Power Law Noise Type Estimates The power law noise type is estimated for each of the variance types by using either the lag 1 autocorrelation the B1 ratio the ratio of the standard variance to the Allan variance for zero dead time or R n the ratio of the modified to normal Allan variances The bandwidth factor BW 2nf to where f is the measuring system bandwidth in Hz applies to the R n calculation for flicker PM noise e Bias Correction Bias corrections are applied to the total variances and Th ol based on the estimated noise type e Confidence Intervals Single or double sided confidence intervals are determined using the of analysis points estimated noise type and the equivalent of X degrees of freedom for the particular variance type These are then used to calculate the corresponding maximum and optionally minimum sigma values e Auto Calc A sigma calculation can be done automatically when the Sigma function is invoked by setting the AutoCalc item in the Configure function 185 STABLE32 USER MANUAL 186 ANALYSIS FUNCTIONS Power Function Purpose Use the Power function to plot the power spectral density of the current phase or frequency data Tied PowRsPECTRUM H Plot SubTite 2 PHASEDAT mj Close Message 3 Help Message Position Toplet 2 Read Config Save Config Reset All Carrier Freg Hz 1 00000008 07 P
275. the printer to be setup without going to the Windows Control Panel The changes you make to the printer driver s setup will not be retained once Play is terminated File The File menu s Print command will print the currently displayed TKF plot to the currently selected printer device The printer may Print be setup using the Printer Setup command A dialog box is displayed while the printer output is being generated and allows the user to Abort printing before the output is started The File menu s Preferences command opens the preferences dialog box to allow the user to select preferences in printing The current options are printing an all white background even if the Preferences screen background is non white printing black lines in place of white lines on the screen and printing to fill the entire page instead of a 9 x 6 884 inch region The user may also select whether preference options will be saved upon exiting Play The File menu s Stop command will stop the plotting of the Stop current TKF plot An alt s from the keyboard can also be used to stop the current plot The File menu s Exit command will close the currently opened Exit TKF file and ask Windows to terminate the current instance of Play Windows Help will be terminated if left open when the user exits Play 39 4 0 STABLE32 USER MANUAL Copy Bitmap Copy Metafile Go To Plot The Edit menu s Copy Bitmap command will make a bitmap
276. time and a non numeric character normally terminates the reading of the current line While this is desirable to reject comments it will also prevent the reading of a line of actual data Thus if the data lines contain non numeric characters the NonNums feature will allow them to be read The MaxSize configuration variable sets the maximum number of data points that can be read without averaging An attempt to load a file that is either larger or too small lt 3 points will generate an error message A larger file can be processed with the Large Data File dialog box either by averaging it or by loading only the first or last portion A file that is smaller than 3 data points cannot be meaningfully processed and is not read 15 STABLE32 USER MANUAL Setting the Comma configuration variable with the Configure function or directly in the Preferences section of the STABLE32 INI file allows commas to be substituted for decimal points in data values e Header An optional header can be written at the top of phase and frequency data files as shown below by checking the Header option in the Configure function File C Data PHASE DAT Date 04 08 01 17 37 59 Type Phase Points 8192 Tau 1 000000e 000 This information can help to identify the data and can be shown by pressing the Display button in the Data File Opened dialog box when the file is subsequently read The header lines are ignored when the actual data is read and are
277. tion Replace Pushbutton Invoke Replace function Edit After Group Insertion and deletion controls Highlighted Pt Ins Pushbutton Insert gap s Del Pushbutton Delete point s Edit points to insert delete Color Gaps Checkbox Highlight gaps in blue Color Outliers Checkbox Highlight outliers in red Show Timetags Checkbox Show timetags along with data Timetag Format Group Timetag format choices MJD Radiobutton Show timetags in MJD format DOY Radiobutton Show timetags in DOY format Exp Radiobutton Show timetags in exponential format Date Radiobutton Show timetags in date format OK Pushbutton Accept editing changes amp close dialog box Cancel Pushbutton Abort editing changes amp close dialog box Help Pushbutton Invoke the Edit help topic 154 EDITING FUNCTIONS e Operation The Edit function can be used for several purposes The simplest use is to just display the current phase or frequency data Check the Show Timetags control to also display the corresponding timetag data and use the vertical scroll bars to scroll through the data The data point s are shown in the left column of the data display Use the Go To Point controls to move to a particular data point Check the Color Gaps and or Color Outliers to highlight those data points The outlier criterion can be set with the Sigma Factor entry box The Color Gaps option highlights timetag intervals that differ by more than 1 from the starting value and
278. tion Table III Notes 1 1000 9 957453e 01 1 371760e 03 4 897745e 01 4 798849e 01 6 490910e 06 4 865258e 01 6 104214e 06 1 517561e 04 5 577220e 03 9 737500e 01 4 570469e 01 5 571498e 06 2 884664e 01 2 922319e 01 2 922319e 01 2 922319e 01 1 687202e 01 2 943883e 01 2 943883e 01 2 943883e 01 2 922319e 01 2 418528e 01 1 396338e 01 1 Expected value 0 5 mr log fit oo nm 2 All slopes are per interval 3 Least sguares linear fit 4 Exact results will depend on iterative algorithm used Data not suited to 10 100 7 003371e 01 2 545924e 01 4 897745e 01 5 047888e 01 5 979804e 05 4 867547e 01 6 104214e 05 9 648320e 04 5 248477e 03 4 594973e 00 4 631172e 01 5 237080e 05 9 296352e 02 9 965736e 02 9 159953e 02 6 172376e 02 3 563623e 01 1 052754e 01 9 581083e 02 9 614787e 02 9 134743e 02 6 499161e 02 3 752293e 01 100 10 5 489368e 01 4 533354e 01 4 897745e 01 4 807261e 01 1 056376e 03 4 839644e 01 6 104214e 04 1 011791e 03 7 138988e 03 1 420429e 02 4 442759e 01 7 133666e 04 3 206656e 02 3 897804e 02 3 241343e 02 2 170921e 02 1 253382e 00 3 910861e 02 3 2376380 02 3 058103e 02 3 406530e 02 2 287774e 02 1 320847e 00 5 Sample not population standard deviation Expected value 1 V12 0 2886751 6 Expected value egual to standard deviation for white FM noise 7 Egual to normal Allan deviation for averaging factor 1 Calculated with listed averaging factors from t
279. tion in stability plot units double y label y position in stability plot units char 1 mask label string which must be enclosed in double quotes This label becomes a plot note and can be edited as a note before it appears on the plot The intent is for the label to automatically identify the mask on the plot 4 An arbitrary number of following lines containing x y data in stability plot units defining the mask These tau sigma points must be in exactly n rows of two space delimited columns Plot lines will connect these points on the plot so they need only define the corners of the mask on log log axes Otherwise the points can be dense enough to draw a general smooth curve The last line should be terminated with a CR LF 5 The mask filename shall have a msk extension and its name should relate in an obvious way to the mask label because it is the means for the user to select it 6 The mask file must reside in the same directory as the Stable32 exe executable file that launched the program Any number of such files can exist and are available for selection in the Run Plot Lines dialog Example of mask file test msk Test mask to use with PHASE DAT test data TDEV plot 3 10 5 5 Test Mask 1 5 105 100 5 T GraphiC Win sigma tkf 5 x Eile Edit Draw Convert Help Dale 11 04 05 Time 09 47 40 Dolo TIME STABILITY Filer PHASE OAT PHASE DAT 2 X uv ti e o o vi EIE o gt gsr o E Sigma ES
280. tion process and a Database configuration file item will be created The STABLE32 INI configuration file is rewritten each time the program closes 140 READ FUNCTIONS Read Function e Purpose Use the Read function to read print and plot stability data from disk This stability data may be a table of possibly edited stability results from one or more previous Run operations The main purpose of the Read function is to allow stability data from multiple runs with different basic averaging times to be combined onto a composite stability plot Stability File SIGMA TAU Sigma Type Norm al M 73 Min Sigma Sigma 3 158e 04 3 247e 04 3 336e 04 2 190e 04 2 279e 04 2 368e 04 1 569e 04 1 660e 04 1 752e 04 7 200e 03 1 128e 04 1 224e 04 1 319e 04 1 440e 04 6 159e 05 6 931e 05 7 703e 05 2 880e 04 5 256e 05 6 248e 05 7 241e 05 5 760e 04 2 776e 05 3 617e 05 4 458e 05 1152e 05 2 426e 05 3 762e 05 5 098e 05 Elo Select sigma type Then Read stability data file and Plot or Print e Controls The Open dialog box contains the following controls Control Type Description Stability File Text Stability data filename Sigma Type Combo Select sigma type Stability Data Table Display of stability data Read Pushbutton Read stability data from disk Close Pushbutton Close the Read dialog box Help Pushbutton Invoke the Open help topic Plot Pushbutton Plot the stability data Options Pushbutton Enter plot options Lines Pushbut
281. to add annotations to a stability plot Read Plot Notes xi Note 1 Up Point Size e Down Iv Border OK Text Cancel Note 1 a Help ig Clear All Pasition Notes 1 e Controls The Read Notes dialog box contains the following controls Control Type Description Note Edit Enter the of the note to edit Up Pushbutton Increment the note Down Pushbutton Decrement the note Point Size Edit Enter the point size for the note Text Edit Enter the text of the note Position Group Note position values x Edit Enter the x position of the note Y Edit Enter the y position of the note Notes Text notes entered Border Checkbox Draw a border around the note Read Pushbutton Read line information from INI file Save Pushbutton Save line information in INI file OK Pushbutton Accept the settings amp close dialog box Cancel Pushbutton Abort the changes amp close dialog box Help Pushbutton Invoke the Read Notes help topic Clear All Pushbutton Clear all notes e Operation Enter the desired plot annotations and press OK to accept them or Cancel to abort Press Clear All to clear all annotations 149 STABLE32 USER MANUAL 150 EDITING FUNCTIONS Print Function e Purpose Use the Print function to print a listing of all or a portion of the current phase or frequency data Data Type Phase Arle Data Range Star P Fines End 1001 T All Data
282. ton Enter plot lines Notes Pushbutton Enter plot annotations Print Pushbutton Print the stability data e Operation Choose the Sigma Type to be read and press the Read button Use the standard file open dialog box to open the stability file The stability filename and data will then be displayed Use the Plot or Print buttons to plot or print the stability data or the Close button to close the dialog box 141 STABLE32 USER MANUAL e Stability File Format The format of the stability files written after a Run operation and read by the Read function is slightly different from the screen display The screen columns are Tau Min Sigma Sigma and Max Sigma where is the number of analysis points Sigma is the nominal sigma value and the Min amp Max Sigma values are used to define the plot error bars The order of the stability file columns is Tau Sigma Min Sigma Max Sigma and DF The Min amp Max Sigma and DF number of X degrees of freedom columns are optional and if they are omitted the plot will show the Sigma values without error bars An example of a stability data file is shown below the column headings are not included in the file Tau Sigma Min Sigma Max Sigma DF 1 000e 01 999 2 922e 01 2 846e 01 3 005e 01 6 651e 02 2 000e 01 997 2 010e 01 1 953e 01 2 072e 01 5 693e 02 4 000e 01 993 1 448e 01 1 396e 01 1 506e 01 3 456e 02 8 000e 01 985 1 057e 01 1 006e 01 1 117e 01 1 818e 02 1 600e 02 969 6 19
283. trols Control Type Description Auto AF Params Group Parameters for Auto AF PSD calculation Relative Max AF Edit Relative maximum averaging factor Absolute Max AF Edit Absolute maximum averaging factor 49 STABLE32 USER MANUAL LF Pts To Skip Edit of low Fourier freq PSD points to skip Smooth Params Group Parameters for smoothing of PSD plot Weight Smoothed Checkbox Weight semilog power law smoothed PSD fit Smoothing PPO Edit points octave for smoothed PSD plot Stability Plot Group Parameters for stability plots Many Tau Checkbox Use many tau method for all tau plots Size Edit of many tau points Reset PSD Pushbutton Restore PSD default values Reset Many Tau Pushbutton Restore many tau default size e Operation Select the page and options desired and press OK to accept them or Cancel to abort Help invokes the Configure HTML help file page Most options take effect immediately while the Read Plot Information options will apply when the Stable32 program is restarted All of these options may also be changed by editing the STABLE32 INI configuration file e General The Write Sigma File checkbox controls the option to write the stability data to a file after a Run Use the Filenames function to set the stability data filename to a name other than its default SIGMA TAU before performing a Run The Autoinc Filename Ext checkbox controls the option to automatically increment the data filename after it changes Phas
284. trols Some parameters do not apply to all line types Control Type Description Line Edit Enter of line to edit Up Pushbutton Increment line Down Pushbutton Decrement line Type Combo Select line type X Axis Group X Axis line parameters Start Edit Enter x axis start of line End Edit Enter x axis end of line Y Axis Group Y axis line parameters Start Edit Enter y axis start of line End Edit Enter y axis end of line Parameter Text Display line parameter Lines Text of lines entered Read Pushbutton Read line information from INI file Save Pushbutton Save line information in INI file OK Pushbutton Accept changes close dialog box Cancel Pushbutton Abort changes close dialog box Help Pushbutton Invoke the Plot Lines help topic Print Pushbutton Print line parameters 207 STABLE32 USER MANUAL Copy Pushbutton Copy line information to clipboard Clear All Pushbutton Clear all lines e Operation Select the desired Line and Type The Enter the X Axis Start X Axis End Y Axis Start and Y Axis End values as applicable and press OK to accept them or Cancel to abort Press Clear All to clear all lines Copy to copy the line parameters to the clipboard or Print to print the line parameters 208 ANALYSIS FUNCTIONS Plot Notes Function e Purpose Use the Plot Annotations function to add annotations to a data plot Phase Plot Notes x Note amp 1 E Point Size e OK Een Iv Border
285. ts parameters may also be set with the Inputs function e See Also Configuration File Inputs Function 52 GENERAL Configuration File e Description The STABLE32 INI file holds all the configuration data for the Stable32 program The format of this file is that of a standard Windows INI file such as WIN INI The Section items define the sections of this file while the Keyword String items define the configuration information Each keyword is set equal to a string which may be either a Boolean value 0 or 1 or an unterminated string of characters which may contain spaces See Appendix IV for more information about the STABLE32 INI configuration file e Operation Ordinarily the reading and writing of STABLE32 INI is automatic and it is not necessary to edit it directly However manual editing is useful in batch file automation and can be done from within the Stable32 program using the Pad function The changes will take effect the next time the Stable32 program is started e Caution Stable32 may be run without a STABLE INI file but no toolbuttons will be displayed Use the Configure function to select the desired toolbuttons A STABLE INI file will be generated automatically when the program is closed 53 54 STABLE32 USER MANUAL TIME DOMAIN STABILITY Time Domain Stability e Time Domain Stability Stable32 implements the following measures of time domain frequency stability Statistic Name Symbol Description
286. tus bar by the t command line option by a Tau statement in a data file header by a PhaseTau or FreqTau statement in the Stable32 ini configuration file by the interval between the first two timetags or by using the default value of 1 0 seconds The precedence for setting the tau value is as follows 1 Manual entry 2 Command line 3 File header 4 INI Inputs 5 Timetag interval 6 Default e Reference W J Riley Launching and Opening Data Files in Stable32 Hamilton Technical Services web site 29 30 STABLE32 USER MANUAL GENERAL Command Line Options e Purpose Stable32 accepts several command line options These options allow phase frequency or archive data to be loaded a certain tau value to be set and an automation script to be executed when the program starts e Operation The command line options may be entered directly from the command line from the Windows Start Run prompt or from a batch file They are entered immediately after the STABLE32 command that starts the program The command line options begin with a minus and may be entered in upper or lower case Command Description P FILENAME Automatically load the phase data file FILENAME F FILENAME Automatically load the frequency data file FILENAME A FILENAME Automatically open the archive file FILENAME TTAU Automatically load the tau value TAU O SKIP Skip display of multicolumn amp file opened dialogs O AUTO Execute aut
287. uency Domain of Intersection Points of Slopes of Various Noise Processes 32th Freq Contrl Symp pp 514 519 June 1978 W F Egan An Efficient Algorithm to Compute Allan Variance from Spectral Density IEEE Trans Instrum Meas Vol 37 No 2 pp 240 244 June 1988 F Vernotte J Groslambert and JJ Gagnepain Practical Calculation Methods of Spectral Density of Instantaneous Normalized Frequency Deviation from Instantaneous Time Error Samples Proc 5th European Freq and Time Forum pp 449 455 March 1991 F Thomson S Asmar and K Oudrhiri Limitations on the Use of the Power Law Form of Sy f to Compute Allan Variance JEEE Trans UFFC Vol 52 No 9 pp 1468 1472 Sept 2005 W J Riley Stable32 Frequency Domain Functions Hamilton Technical Services Simulation S K Park and K W Miller Random Number Generators Good Ones are Hard to Find Comm ACM Vol 31 No 10 pp 1192 1201 Oct 1988 Kasdin and T Walter Discrete Simulation of Power Law Noise Proc 1992 IEEE Freq Contrl Symp pp 274 283 May 1992 T Walter Characterizing Frequency Stability A Continuous Power Law Model with Discrete Sampling IEEE Trans Instrum Meas Vol 43 No 1 pp 69 79 Feb 1994 Robust Statistics D B Percival Use of Robust Statistical Techniques in Time Scale Formation Preliminary Report U S Naval Observatory Contract No N70092 82 M 0579 1982 Gernot M R Winkler Introduction to Robust Stati
288. uency sources are shown in the following table Spectral Characteristics of Power Law Noise Processes Noise Type a B nu y n White PM 2 0 2 3 1 Flicker PM 1 1 2 2 0 White FM 0 2 1 1 1 Flicker FM 1 3 0 0 2 Random Walk FM 2 4 1 1 3 e Power Spectral Densities Four types of power spectral density PSD are commonly used to describe the stability of a frequency source PSD of Frequency Fluctuations S f The power spectral density PSD of the fractional frequency fluctuations y t in units of 1 Hz is given by S f h a f where f sideband frequency Hz PSD of Phase Fluctuations S f The PSD of the phase fluctuations in units of rad Hz is given by Sf Zrvoy gt S f where Vo carrier frequency Hz PSD of Time Fluctuations S f The PSD of the time fluctuations x t in units of sec Hz is given by S f h B f Sy f 2nff where B a 2 The time fluctuations are related to the phase fluctuations by x t t 2nv Both are commonly called phase to distinguish them from the independent time variable t Stable32 uses x t and y t arrays as its phase and frequency variables SSB Phase Noise f The SSB phase noise in units of dBc Hz is given by f 10 log S f These are the most common engineering units to specify phase noise 103 STABLE32 USER MANUAL e Variances Several types of variance are commonly used to describe the stability of a frequency source Standard Variance
289. ulate table of stability statistics 219 STABLE32 USER MANUAL Start AF 1 Edit Enter starting averaging factor for run Stop 2 Pushbutton Stop run Resume 3 Pushbutton Resume run Clear Pushbutton Abort run Close Pushbutton Close dialog box amp restore original data Help Pushbutton Invoke the Run help topic 1 Before run 2 During run 3 When stopped e Operation Select the desired Variance Type Alpha and if applicable Conf Factor Optionally check Remove Drift and 1 of 2 choose Decade 1 2 4 10 Octave 1 2 4 8 or All Tau tau increments no error bars are displayed for the All Tau option or enter a Start AF Enter the Dead Time ratio if it is not unity Then Press Calc to perform a stability run and Plot Copy or Print the results as desired To quit press Close The default Alpha selection is Auto which will automatically estimate the noise type If the noise type is known a priori then choose one of the specific alpha values In either case the alpha value for each averaging factor AF is used to determine each confidence interval A progress bar is displayed during a TOTMDEV TOTTDEV or All Tau analysis Those runs may be Stopped and then Resumed While stopped the current results may be printed plotted or copied To abort a stopped run press the Clear button e Stability Results Table The table of results from the stability run contains the following items Item Description AF Averaging fa
290. utliers to clipboard e Operation Observe the of Outliers that meet the default 50 criterion Enter the desired outlier criterion in the Sigma Factor box and press Cale to find the of outliers that meet this criterion Optionally check the Remove All Outliers checkbox and press OK to replace them with gaps or press Close to abort the Check function The detailed Check dialog box also presents a list of the outliers allows a choice of sorting by Position or Size absolute deviation from median and removing None All the Largest or the Selected outliers Pressing Print will print a list of the outliers and Copy will copy them to the clipboard e Outlier Recognition Stable32 uses the median absolute deviation MAD as its means of outlier recognition The MAD is a robust statistic based of the median of the data It is the median of the scaled absolute deviations of the data points from their median value defined as MAD Median y i m 0 6745 where m Median y i and the factor 0 6745 makes the MAD equal to the standard deviation for normally distributed data Each frequency data point y i is compared with the median value of the data set m plus or minus the desired multiple of the MAD e Limits The Check function does not work with phase data which must be converted to frequency data to apply the Check function e Auto Calc A check can be done automatically when the Check function is invoked by setting the A
291. utoCalc item in the Configure function e Caution Judgment is required when removing outliers Automatic outlier removal is convenient for quickly plotting and analyzing frequency data which may have to be removed to obtain meaningful results While it provides a degree of objectivity the analyst is still responsible for decisions regarding outlier removal It is particularly important to explain all phase discontinuities 176 ANALYSIS FUNCTIONS Drift Function e Purpose Use the Drift function to analyze phase or frequency data for frequency drift or find frequency offset in phase data It is common to remove the deterministic frequency drift from phase or frequency data before analyzing the noise with Allan variance statistics It is sometimes useful to remove only the frequency offset from phase data e Controls The basic Drift dialog box contains the following controls Control Type Description Drift Type Combo Select drift analysis type Slope Text Display slope value Remove Drift Checkbox Remove drift from data Calc Pushbutton Perform the Drift function Close Pushbutton Abort the Drift function amp close dialog box Help Pushbutton Invoke the Drift help topic Show Details Checkbox Show detailed Drift dialog box Activating Show Details adds the following controls to the Drift dialog box 177 STABLE32 USER MANUAL Control Type Description Noise Model Text Noise model for the drift ty
292. version will fail For example to use the operating system default path C My Documents the directory name must be shortened to mydocu 1 An alternative file format conversion method for bitmaps and metafiles is to use the Edit Copy GraphiC menu command This is the easiest way to transfer a plot into another open document The best format for including GraphiC tkf plots in a Microsoft Word document is as a Windows metafile wmf GraphiC tkf plots can be included in web documents as gif files by first converting them into bitmaps and then using the free conversion program BMPTOGIF available on the Hamilton Technical Services web site This is the best format for including GraphiC plots in an html document Better looking data plot scales can be obtained by scaling the y axis to ppl or standard units This will also eliminate duplicate scale markings and the colon that can appear in them This format is the default when the Smart Plot Scales configuration item is selected In the Y Axis Label edit control of the Plot Options dialog it is important to understand that brackets will create a superscript see Appendix II Problems have been reported while printing plots after reading data from read only network drives because the GraphiC functions are unable to write the temporary metafile needed for printing One solution to this problem is to copy the data file to a local drive for which you have write privileges before opening it for analy
293. window through the phase time error data and finding the difference between the maximum and minimum values range at each window position MTIE is the overall maximum of this time interval error over the entire data set MTIE 7 Max penn A Maxx Ming gichan where n 1 2 N 1 and N phase data points MTIE is a measure of the peak time deviation of a clock and is therefore very sensitive to a single extreme value transient or outlier The time required for an MTIE calculation increases geometrically with the averaging factor n and can become very long for large data sets although faster algorithms are available see Reference 4 below The relationship between MTIE and Allan variance statistics is not completely defined but has been the subject of recent theoretical work see References 2 and 3 below Because of the peak nature of the MTIE statistic it is necessary to express it in terms of a probability level B that a certain value is not exceeded For the case of white FM noise important for passive atomic clocks such as the most common rubidium and cesium frequency standards MTIE can be approximated by the relationship MTIE t B kp V ho t kg V2 0 t t where kg is a constant determined by the probability level B as given in the table below and h is the white FM power law noise coefficient 79 STABLE32 USER MANUAL e References The following references apply to the MTIE statistic 1 S
294. x t where vo is the nominal frequency 257 STABLE32 USER MANUAL 258 OTHER INFORMATION References References The following references are recommended to support the use of the Stable32 program for the analysis of frequency stability 10 11 12 13 14 15 16 17 18 19 20 21 22 General Special Issue on Frequency Stability Proc IEEE Vol 54 Feb 1966 J A Barnes Atomic Timekeeping and the Statistics of Precision Signal Generators IEEE Proceedings vol 54 pp 207 219 Feb 1966 Proc IEEE Vol 55 June 1967 G E P Box and G M Jenkins Time Series Analysis Forecasting and Control San Francisco Holden Day 1970 J A Barnes et al Characterization of Frequency Stability ZEEE Trans Instrum Meas Vol IM 20 No 2 pp 105 120 May 1971 B E Blair Editor Time and Frequency Theory and Fundamentals NBS Monograph 140 Annex 8 E p 181 May 1974 G Winkler A Brief Review of Frequency Stability Measures Proc 8th PTTI Meeting pp 489 527 Dec 1976 J Rutman Oscillator Specifications A Review of Classical and New Ideas Proc 31th Annu Symp on Freq Contrl pp 291 310 June 1977 J Vanier and M Tetu Time Domain Measurement of Frequency Stability Proc 10th PTTI Meeting pp 247 291 Nov 1978 P Lesage and C Audoin Characterization and Measurement of Time and Frequency Stability Radio Science Vol 14 No 4 pp 521 539 19
295. y data an inner averaging loop over m frequency values is necessary The result is usually expressed as the square root Ho t the Hadamard deviation HDEV The expected value of the overlapping statistic is the same as the normal one described above but the confidence interval of the estimation is better Even though all the additional overlapping differences are not statistically independent they nevertheless increase the number of degrees of freedom and thus improve the confidence in the estimation Analytical methods are available for calculating the number of degrees of freedom for an overlapping Allan variance estimation and that same theory can be used to establish reasonable single or double sided confidence intervals for an overlapping Hadamard variance estimate with a certain confidence factor based on Chi squared statistics df df and O max S xp df XX1 p df where x is the Chi square value for probability p and degrees of freedom df s is the sample variance o is the true variance and df is the of degrees of freedom not necessarily an integer The df is determined by the number of data points and the noise type The much smoother results it produces compared with the normal Hadamard statistic as shown in the plots below make it a more useful analytical tool 2 i 2 O min S 71 STABLE32 USER MANUAL Cole 03 13 99 Time 41 48 00 Dato Polnis 1 inu 1001 of 1001 Tou 1 000000Ge4 00 FREQUENCY STABILI
296. y where m is the averaging factor and ty is the basic measurement interval by the expression 2 Yum Xi gt 1 M 2m4 j m 1 2m M 2m 1 0 1 i j In terms of phase data the overlapping Allan variance can be estimated from a set of N M 1 time measurements as N 2m P E 2 Ojo Dope reet i l The result is usually expressed as the square root o t the Allan deviation ADEV The confidence interval of an overlapping Allan deviation estimate is better than that of a non overlapping Allan variance estimation because even though the additional overlapping differences are not all statistically independent they nevertheless increase the number of degrees of freedom and thus improve the confidence in the estimation Analytical methods are available for calculating the number of degrees of freedom for an overlapping Allan variance estimation and using that to establish single or double sided confidence intervals for the estimate with a certain confidence factor based on Chi squared statistics Sample variances are distributed according to the expression df s o where x is the Chi square s is the sample variance o is the true variance and df is the of degrees of freedom not necessarily an integer The df is determined by the of data points and the noise type The Stable32 program includes those procedures for the overlapping Allan variance function 59 60 STABLE32 USER MANUAL TIME DO
297. ype 0 Phase 1 Freq Stability analysis type Outlier sigma factor Extra delay time in msec Start data point End data point 0 last point Default CO OS OS OOOO OO OS Oo Oo Oo Oooo Script_ Normal Normal Null Quadratic Linear 299 STABLE32 USER MANUAL 300 APPENDICES Appendix V Hints and Notes Launching Stable32 Stable32 can be launched like any Windows application from the Start menu from the Run dialog or via an icon on the desktop By associating Stable32 with a filename extension such as dat Stable32 may also be launched by clicking on a data file or by dragging a data file to the Stable32 icon on the desktop Main Window The Stable32 main window has the best appearance and functionality with XGA 1024x768 or higher screen resolution and with the main window adjusted for nearly full width This allows the use of the mini data plots in the Stable32 status bar and all the toolbuttons If only a lower screen resolution is available use the Configure function to choose the desired toolbuttons and use the Stats function as an alternate way to observe the current data The position of the main window is saved between runs GraphiC Plots When performing a metafile file format conversion for a GraphiC plot within Stable32 make sure that the target path and filename comply with DOS filename conventions e g no more than 8 characters Otherwise the file creation process will produce an error and the con

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