Platinum TSS200 cable network tester
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1. 016 where N f is the complex conjugate of N f The energy in this cross correlation is Ern 02 a7 00 The expected energy in the cross correlation over time 0 lt t lt is given B Ban SOPIN f ISING df Err Th 18 Whitepaper Spread Spectrum Time Domain Reflectometry where Nr f is the Fourier transform of the subsection of n t used for the cross correlation for 0 lt t lt 7 Note that in general Nr f N f because the cross correlation may be over only a few bits of n t However the expected value for The expected noise power is _ ER _ En ISPYPING P af 19 which is true for any noise source n t including the Mil Std 1553 signal It is clear that 19 indicates that spectral overlap between the noise and STDR SSTDR signal results in unavoidable noise in the correlator output D SSTDR Modulation In order to perform a consistent cross correlation a reference signal must be available This brings us to the guestion of syn chronization If the reference signals modulation is off by 90 from the driving signals modulation the cross correlation of the received signal and the reference signal would be zero as the two signals would be orthogonal to each other Another cross correlation of the same signal could return a different result if the phase difference betwe2. WHITEPAPER SSTDR SPREAD SPECTRUM TIME DOMAIN REFLECTOMETRY USA IEEE SENSORS JOURNAL 5 6 DECEMBER 2005 1469 Analysis of Spread Spectrum Time Domain Reflectometry for Wire Fault Location Paul Smith Member IEEE Cynthia Furse Senior Member IEEE and Jacob Gunther Member IEEE Abstract Spread spectrum time domain reflectometry SSTDR and seguence time domain reflectometry have been demonstrated to be effective technologies for locating intermittent faults on air craft wires carrying typical signals in flight This paper examines the parameters that control the accuracy latency and signal to noise ratio for these methods Both test methods are shown to be effective for wires carrying ACpower signals and SSTDR is shown to be particularly effective at testing wires carrying digital sig nals such as Mil Std 1553 data Results are demonstrated for both controlled and uncontrolled impedance cables The low test signal levels and high noise immunity of these test methods make them well suited to test for intermittent wiring failures such as open cir cuits short circuits and arcs on cables in aircraft in flight Index Terms Aging wire detection arc detection seguence time domain reflectometry STDR spread spectrum time domain re flectometry SSTDR time domain reflectometry TDR wire fault detection I INTRODUCTION OR MANY years wiring has been treated as a system that could be
3. and type of cable 4 IV STDR SSTDR ANALYSIS The operation of STDR SSTDR depends on the fact that por tions of electrical signals are reflected at discontinuities in the characteristic impedance of the cable A spread spectrum signal shown in Fig 2 is injected onto the wires and as with TDR the reflected signal will be inverted for a short circuit and will be right side up for an open circuit 8 The observed reflected signal is correlated with a copy of the injected signal The shape of the correlation peaks is shown in Fig 3 In this figure the modulating frequency is the same as the chip rate Note that the sidelobes in the correlation peak are sinusoids of the same am plitude as the off peak autocorrelation of the ML code This is due to the selected modulation frequency and synchronization Use of a different modulation frequency or different synchro nization will yield a different correlation pattern that may have higher side lobes 4 Different PN sequences also have different peak shapes as shown in Fig 4 for ML and gold codes www T3innovation com SMITH et al ANALYSIS OF SPREAD SPECTRUM TIME DOMAIN REFLECTOMETRY 1 5 5 051 05 E via 1 5 gt 0 6 8 10 12 14 STDR signal SSTDR signal Fig 2 STDR and SSTDR signals The SSTDR signal is modulated with 1 0 1 0 8 4 E BS 02 4 L OF 4 Aa SE 02 4 get 04 2 06 6 4
4. clear that there is little advantage of STDR over SSTDR or vice versa However when the noise is not spectrally flat such as is the case with a Mil Std 1553 or other digital data signal the spectral overlap of the noise with the STDR SSTDR signal will change the relative benefits of STDR versus SSTDR www T3Innovation com 1476 Estimated Distance m IEEE SENSORS JOURNAL VOL 5 NO 6 DECEMBER 2005 Estimated Distance m b Fig 7 tested with S SSTDR 59 nz lt Time micro seconds Fig 8 ML code STDR signal at 1 V RMS with a signal length of 63 chips at 30 MHz operating in the presence of Mil Std 1553 at 10 V RMS Fig 8 shows a 1 V RMS STDR signal in the presence of 10 V RMS Mil Std 1553 Since the Mil Std 1553 signal is at 10 V RMS it is 20 dB above the STDR signal level The PN code length is 63 bits which will give a processing gain of 36 dB The chip rate in this figure is 30 MHz The processing gain for longer STDR sequences is higher so a lower power STDR signal can be used in an actual test system that will not interfere with the Mil Std 1553 signal Fig 9 shows a 1 V RMS SSTDR signal in the presence of 10 V RMS Mil Std 1553 The PN code length used to generate this SSTDR signal is 63 bits Even after the 36 dB processing gain the correlation peak shown in Fig 10 is not clear due to the high noise level after cor relation Consider however the clarity of th
5. controlled and uncontrolled impedance air craft cables with a variety of signals on the line were tested 4 Using curve fitting both methods had errors on the order of 3 cm for controlled impedance coax and 6 cm for uncon trolled bundled cable with or without 60 Hz signals for both open and short circuited cables However as expected SSTDR performs significantly better than STDR in the presence of the MilStd 1553 signal utilizing the uncontrolled impedance bun dled wire a worse case than normal since MilStd 1553 would www T3innovation com 1474 normally be implemented on controlled impedance twisted pair wire For an SNR of 24 dB STDR has an error of about 24 cm and SSTDR had less than 3 cm of error SSTDR still had less than 6 cm of error down to and SNR of 53 dB below the MilStd 1553 data signal Both methods could be used ef fectively since the required SNR for MilStd 1553 is 17 dB however the advantage of SSTDR for a high freguency noisy environment was clearly demonstrated V SIGNAL TO NOISE RATIO The SNR is defined as the signal power divided by the av erage noise power For a digital signal such as Mil Std 1553 this would be expressed as S _ Std 1553 Power N Background Noise Power 20 In the case of STDR SSTDR the STDR and SSTDR signals are the desired signals and other signals are noise Therefore considering the signal to noise power of the STDR and SSTDR signals in the presenc
6. down the cable at the same rate A Expected Correlator Output With Generalized Noise The correlator output can be analyzed in terms of the signal injected onto the cable various reflections of that signal and any unwanted signals noise received at the correlator input Let S n be a recursive linear sequence of period K consisting of 18 and 1 s Then let s t Sn pit n7 v t 0 so that s t is a recursive linear signal RLS of period consisting of 1s and 1 s Te is the minimum dura tion of a 1 or 1 otherwise known as a chip Note that 1 where lt lt otherwise 2 s t s t Ts 3 for any for a RLS of duration Ts The test system will send a signal s t onto the cable which will be reflected by some arbitrary number of impedance discon tinuities in the cable The reflected signals will return to the test system after some transmission delay Along with the reflected signals will be some noise that will depend on the nature of the cable being tested anomalies in the signal generation and extra neous noise The noise could be white noise or it could contain signals such as Mil Std 1553 Let x t be the received signal defined as x t mst 0 k 4 where is the amplitude of reflected signal 3 amp relative to s t Tk is the time delay before receiving reflection k and www T3Inn
7. m long The wires snake in and out within the bundle and although they are roughly parallel Whitepaper Spread Spectrum Time Domain Reflectometry 1471 throughout they definitely do not have even spacing throughout the bundle The response is not as smooth as that seen in Fig 5 due to the multiple small reflections that occur within the uncon trolled impedance bundle These multiple reflections as well as the variations in velocity of propagation that go with them will reduce the accuracy of the method somewhat for uncontrolled impedance cables as we shall see later When a peak detection algorithm to identify the approximate open circuit location is coupled with a curve fitting approach to determine its precise location the length of the wires can be calculated very accurately as shown in Fig 4 a and b for the controlled and uncontrolled impedance wires respectively The maximum error observed for controlled impedance cables is 3 cm and for the uncontrolled impedance wires is 6 cm The minimum measurable length for both systems is approximately 3 5 m as seen in these figures This is because the initial and final peaks overlap A more advanced curve fitting approach can be used to distinguish these overlapping peaks For the discussion that follows the ideal case will be assumed where the cable is lossless An additional assumption is that frequency dispersion is negligible in the cable That is that all frequencies travel
8. method is accurate to within a few centimeters for wires carrying 400 Hz aircraft signals as well as MilStd 1553 data bus signals Results are presented on both controlled and uncontrolled impedance cables up to 23 m long Early research on spread spectrum time domain reflectometry SSTDR 6 has considered fault location tests on high voltage power wires Sequence time domain reflectometry STDR 7 has been studied and used to test twisted pairs for use in commu nications More recently it has been demonstrated for location of intermittent faults such as those on aircraft wiring 18 These test methods could be used as part of a smart wiring system 2 and could provide continuous testing of wires on aircraft in flight with automatic reporting of fault locations to facilitate quick wiring repairs This could be done by integrating the elec tronics into either the circuit breaker or into connector savers throughout the system In order for this to be feasible the pro totype system that has been described here is being redesigned as custom ASIC which should cost on the order of 10 20 per unit in bulk This paper focuses on the analysis of SSTDR and STDR Parameters required for these methods to function as potential test methods on wires carrying 400 Hz ACor high speed digital data such as Mil Std 1553 are discussed This anal ysis is critical to determine the system tradeoffs between speed accuracy code length system complexi
9. noise type in cluding 400 Hz ac Mil Std 1553 and white noise www T3Innovation com SMITH et al ANALYSIS OF SPREAD SPECTRUM TIME DOMAIN REFLECTOMETRY B Scaling the Freguency of the STDR SSTDR Signal Let sy t 41 and Ts 1 where is con stant Using the scaling property of the Fourier transform and assuming gt 1 50 18 5 2 The signal of interest after correlation is the peak value in the autocorrelation of sy t which is Rs 0 and corresponds to the energy in s t given by 33 Ts 0 34 Examining correlator noise output we have Reyn t y t n t 35 and Era s 4 INg Pdf 36 ee gy ee If STDR is considered with the chip rate much greater than the Mil Std 1553 data rate of 1 MHz it can be assumed that S f is approximately constant in the region where the majority of the power of N f exists Then 1 S f w will also be approximately constant in that region if 7 gt 1 With these as sumptions 36 can be written as 1 SOPNOPY GER 67 and the average noise power is Er 2 1 mt Pp 38 Rayn T pe Pen 38 5 38 34 15 Nda Pn Eguation 39 states that in STDR mode doubling the chip rate of the PN code while leaving all other parameters the same will have no appreciable effect on the SNR for STDR tests if the major noise contribut
10. 00 Freguency MHz Mil Std 1553 SSTDR TDR Fig 12 Normalized PSD of a ML code STDR signal of length 63 chips at 30 MHz 1 V RMS ML code SSTDR signal of length 63 chips at 30 MHz 1 V RMS and Mil Std 1553 1 V RMS Signals are normalized with respect to the peak STDR power Normalized PSD dB Freguency MHz STDR w Noise XCorr Ideal STDR Fig 13 Normalized PSD of the cross correlator XCorr output for a pure ML code STDR ideal case signal of length 63 chips at 30 MHz 1 V RMS and a 1 V RMS ML code STDR signal in the presence of a 10 V RMS Mil Std 1553 signal the STDR and SSTDR signals with respect to the Mil Std 1553 signal can be examined The PSD of these three signals as used in the simulations is shown in Fig 12 normalized to the peak STDR power In Fig 12 it can be seen that the power in the Mil Std 1553 signal is centered about 0 Hz as is the power in the STDR signal The SSTDR signal however slopes down to a spectral null at 0 Hz dc If this is considered in light of 19 itis clear that there will be significantly more unwanted power in the cross correla tion of an STDR signal with Mil Std 1553 than there will be in the cross correlation of an SSTDR signal with Mil Std 1553 To compare SSTDR with STDR frequencies above the chip rate were not trimmed off prior to modulation which caused some aliasing in the SSTDR case Tests performed using ban dlimiting prior t
11. 2 0 2 4 6 Autocorrelation Offset Parameter n STDR autocorr SSTDRautocorr Fig 3 Autocorrelations of STDR and SSTDR signals from Fig 2 55 ect 5 lt T 30 20 10 0 10 20 30 Autocorrelation Offset Parameter n ML Code Auto Corr Gold Code Auto Corr Fig 4 Autocorrelations of ML and gold codes 1 0 8 0 6 5 SE 0 2 GE lt 0 6 20 0 20 40 60 80 100 120 Distance m STDR SSTDR Fig 5 Correlator output for STDR and SSTDR tests on 75 0 coax cable with an open circuit 23 m down the cable Note the peak at zero connection between the test system and cable multiple reflections and definitive shape of the correlation peaks The location of the peaks in the correlator output in conjunc tion with an estimate of the velocity of propagation indicates the distance to impedance discontinuities Fig 5 shows normal ized sample test data collected on 75 0 coax cable The cor relation peaks after 23 m are due to multiple reflections in the 23 m cable The response for noncontrolled impedance cable is not as clean which is to be expected because of the varia tion in impedance and subseguent small reflections as well as minor variation in velocity of propagation down the length of the cable Fig 6 a and b show the STDR and SSTDR corre lation responses measured on two 22 AWG wires in a loosely bundled set of 22 wires that is 9 9
12. MITH et al ANALYSIS OF SPREAD SPECTRUM TIME DOMAIN REFLECTOMETRY 1473 where S f is the Fourier transform of s t Since s t is of finite duration its power spectral density PSD is only nonzero if considered only over the integration time in which case 2 psp f 1 The total energy in the signal s t can be found in several ways as given by Rayleigh s theorem 11 Ta l PSD f df 12 Let n t be noise signal due to Mil Std 1553 operating on wires The Fourier transform of n t is given by N f N n t e PTS dt 13 Rayleigh s theorem gives energy of the signal n t as K Tn 00 T 14 and PSD defined over Tn as 2 PSD f 15 As n t is not a periodic function the cross correlation func tions listed below that deal with n will be linear cross corre lations If both s t and n t or their derivatives are used in cross correlation it will be operating on cycle of s t and be defined over 0 lt t lt Tn unless otherwise specified If only s t is shown in a cross correlation or autocorrelation it will be a circular cross correlation or autocorrelation and will be nonzero only for 0 lt t lt 73 Since Tn gt Ts Tn Ts Th and will be treated as if Tn Ts Tn The Fourier transform of the cross correlation of s t and n t is F Ren t Fist n 0
13. TDR 7 and modulated SSTDR 6 are detectable through cross correla tion even though they may be buried in noise The ability to pick out the signal is due to processing gain which for direct seguence spread spectrum DSSS can be expressed as pa _ 2 Te Re 2R where Wss is the bandwidth of the spread spectrum signal 7 is the duration of one entire STDR SSTDR sequence considering the entire sequence equal to one bit in communication system terms T is the duration of a PN code chip Re is the chip rate in chips per second and R is the symbol rate which in this case is the number of full seguences per second 16 Because of this processing gain it is reasonable to assume that a spread spectrum test system could operate correctly in a noisy environment with 400 Hz 115 V ACor digital data on the wires The test system could be designed such that it would not be damaged by or interfere with any of the signals already on the wires For the analysis that follows the digital data on the wires will be assumed to be Mil Std 1553 a standard aircraft communication data bus that specifies a 1 Mbit second datarate 2 25 20 RMS signal level normally operates on low loss Whitepaper Spread Spectrum Time Domain Reflectometry IEEE SENSORS JOURNAL VOL 5 NO 6 DECEMBER 2005 Digital 1 Controller PC Interface S SSTDR circuit diagram 3 dB 100 m 70 2 shielded twisted pair cable and allows for a SNR
14. autocorrelations is not egual even though the power in the signals used to generate them is egual In fact the power in the ML code autocorrelation is 56 the power in the gold code autocorrelation This extra power in the gold code autocorrelation is self induced noise power and it reduces the SNR for STDR SSTDR tests D STDR SSTDR Code Selection The optimal PN code depends on the nature of the application The PN code with the lowest side lobes in its autocorrelation is ML code It is therefore optimal for use when only one code will be used at a time The PN code with the next best autocorrelation properties is the Kasami code 11 It is the best PN code choice when simultaneous tests on one or more conductors can interfere with each other This is due to the high degree of orthogonality of signals in a Kasami set If however the number of simultaneous tests exceeds the number of codes in the Kasami set then codes with higher autocorrelation side lobes such as gold codes may be used One shot codes such as those similar to Barker codes may also be used for STDR SSTDR Many other PN codes are a poor choice for STDR SSTDR due to high autocorrelation side lobes or the lack of a single autocorrelation peak E STDR SSTDR Using ML Codes When the background noise is white noise the total noise power after correlation is identical for both the STDR and SSTDR cases because the noise is spectrally flat In this case it is
15. e correlation peak in Fig 11 In both cases the amplitude of the correlation peak Whitepaper Spread Spectrum Time Domain Reflectometry Actual versus distance estimated with a curve fit algorithm on a 75 0 cable and b a pair of two 22 AWG wires within a loose bundle of 22 wires 15 lt 10 AAA oe ARV VALAAN 5 j 4 e J 58 0 3 5 7 si N s sa 5 10 JYV E 15 L 1 lt 0 0 5 1 1 5 2 Time micro seconds Fig 9 ML code SSTDR signal at 1 V RMS with a signal length of 63 chips at 30 MHz operating in the presence of Mil Std 1553 at 10 V RMS 4 3 S 2 Ba 1 ve 5a 0 Bo 21 5 3 E 4 2 Time micro seconds Fig 10 Normalized cross correlation of a reference ML code STDR signal with the signal shown in Fig 8 is identical but the background noise levels are significantly different To gain insights into the dramatic difference in background noise levels shown in Figs 10 and 11 the spectral content of www T3Innovation com SMITH et al ANALYSIS OF SPREAD SPECTRUM TIME DOMAIN REFLECTOMETRY mi pirtin 0 2 0 0 2 0 4 0 6 0 8 Output V 1 0 5 0 Time micro seconds 0 5 1 Normalized Correlator Fig 11 Normalized cross correlation of a reference ML code SSTDR signal with the signal shown in Fig 9 RS 5 2 0 50 100 150 200 250 3
16. e of another signal Mil Std 1553 in this example gives XCorr STDR SSTDR Signal 21 N XCorr Mil Std 1553 Background Noise Gh after correlation where XCorr means cross correlated power The reflection terms represent reflec tions at various distances down the cable To detect each of these signals the correlator offset is set to time All other re flection terms are considered noise terms The received signal after cross correlation is Reg th Es 22 From 22 and 19 the SNR is 5 a E az E 23 N JE ISX AP df S f X f df Ts The integral in 23 needs to be carried out for every signal of interest that could be a noise source For spectrally narrow noise such as the 115 V 400 Hz on aircraft 23 simplifies to a 2 NI L BAX W a 2 vase Hz df V2 a 115 5 400 Hz 5 400 Hz 2 24 From this it can be seen that if S f has very little of its energy centered at 400 Hz the SNR will be large Whitepaper Spread Spectrum Time Domain Reflectometry IEEE SENSORS JOURNAL VOL 5 NO 6 DECEMBER 2005 For noise signals that are broad in freguency spectrum the integral in 23 is quite involved and is best handled numerically on a case by case basis The effects of changing certain parameters can be studied an alytically in such a way as t
17. en the modulating freguency and the PN code changed This would make the system very difficult to calibrate Because the choice has been made to use PN codes it makes sense to synchronize the modulating sinewave with the PN code 4 By generating the signals in a consistent way a ref erence signal can be generated which can be used consistently with the injected signal providing for a system that gives con sistent results under similar circumstances Sample aircraft cables tested with S SSTDR have significant loss at high frequency Noncontrolled impedance cables dis crete bundled wires over 60 m long have been tested with STDR and over 15 m long have been tested with SSTDR which has higher frequency content Another effect of realistic aircraft cable is the effect of vari ation in the velocity of propagation VOP Typical wires have VOP ranging from 0 66 to 0 76 times the speed of light 9 If the type of wire is known the correct velocity can be used to obtain the best possible calculation for the length of the wire If the type of wire is not known and average values are used addi tional errors of up to 10 could be observed Correlation peaks show higher dispersion if they are due to reflections farther down the cable as shown in Fig 2 This effect can be accounted for by changing the shape that is matched by the curve fitting algo rithm as it is applied to reflections from different lengths down the cable Results for both
18. er shows that SSTDR and STDR can be effective tools for locating defects on live cables and this was demonstrated for both controlled and uncontrolled impedance cables carrying 60 Hz similar to 400 Hz and 1 MHz Mil Std 1553 signals This discussion has shown that www T3innovation com 5 Innovation T3 Innovation 808 Calle Plano Camarillo CA 93012 Contact Us 805 233 3390 Www T3innovation com Made in USA
19. f the SSTDR signal can be adjusted to avoid mutual interference between the SSTDR and digital sig nals on the wires Tests with narrowband noise such as 400 Hz 115 V ac show a negligible effect on the correlator output com pared to wideband noise such as the digital signals discussed above VI CONCLUSION This paper has examined STDR and SSTDR using ML codes Equations were developed to enable system design by describing the interactions of the STDR SSTDR signal and various types of noise in the correlator output Simulations were performed for STDR and SSTDR tests for ML codes in the presence of a Mil Std 1553 background signal to study the effects of this type of noise on STDR SSTDR tests Equations were developed to describe the effects of scaling test system parameters including the number of chips in the PN sequence and the PN sequence chip rate used for STDR and SSTDR It was shown that doubling the PN code length doubles the SNR independent of the noise type and that doubling the chip rate and modulation frequency for SSTDR in the presence of Mil Std 1553 can have no appreciable effect on the SNR for STDR but can increase the SNR for SSTDR by 6 dB ML codes were identified as the best code to use for testing single wires at a time due to the higher self induced noise present with other code choices Kasami codes are the op timal codes to use when performing multiple interacting tests simultaneously The work covered in this pap
20. ineering Uni versity of Utah Salt Lake City UT 84112 USA and also with VP Technology LiveWire Test Labs Inc Salt Lake City UT 84117 USA e mail cfurse ece utah edu J Gunther is with the Department of Electrical and Computer Engineering Utah State University Logan UT 84322 4120 USA e mail jake ece usu edu Digital Object Identifier 10 1109 JSEN 2005 858964 often cannot be replicated or located During the few millisec onds it is active the intermittent fault is a significant impedance mismatch that can be detected rather than the tiny mismatch observed when it is inactive A wire testing method that could test the wires continually including while the plane is in flight would therefore have a tremendous advantage over conven tional static test methods Another important reason to test wires that are live and in flight is to enable arc fault circuit breaker technology 5 that is being developed to reduce the danger of fire due to intermittent short circuits Unlike traditional thermal circuit breakers these new circuit breakers trip on noise caused by arcs rather than re quiring large currents The problem is that locating the tiny fault after the breaker has tripped is extremely difficult perhaps im possible Locating the fault before the breaker trips could enable maintenance action This paper describes and analyzes one such method based on spread spectrum communication techniques that can do just that This
21. installed and expected to work for the life of an aircraft 1 As aircraft age far beyond their original expected life span this attitude is rapidly changing Aircraft wiring prob lems have recently been identified as the likely cause of several tragic mishaps 2 and hundreds of thousands of lost mission hours 3 Modern commercial aircraft typically have more than 100 km of wire 2 Much of this wire is routed behind panels or wrapped in special protective jackets and is not accessible even during heavy maintenance when most of the panels are removed Among most difficult wiring problems to resolve are those that involve intermittent faults 4 Vibration that causes wires with breached insulation to touch each other or the airframe pins splices or corroded connections to pull loose or wet arc faults where water drips on wires with breached insulation causing intermittent line loads Once on the ground these faults Manuscript received April 10 2004 revised September 14 2004 This work was supported in part by the Utah Center of Excellence for Smart Sensors and in part by the National Science Foundation under Contract 0097490 The associate editor coordinating the review of this paper and approving it for publication was Prof Michael Pishko P Smith is with VP Technology LiveWire Test Labs Inc Salt Lake City UT 84117 USA e mail psmith livewiretest com C Furse is with the Department of Electrical and Computer Eng
22. nce of noise with some additional random noise term that is zero mean Whitepaper Spread Spectrum Time Domain Reflectometry B Correlator Output in the Presence of White Noise The cross correlation of noise terms with s t can be dis cussed in terms of the nature of the noise terms If n is white Gaussian noise the cross correlation analysis can be described explicitly 11 From 6 the cross correlation of s t with n t has mean Fs E nk a 0 0 and variance i 8 where 2 is the noise power received at the input and E is the energy in the reference signal s t over one period Thus the effect of white noise in the system will be to add variation to the measurements proportional to the energy of the signal s t but it will not cause a consistent DC offset C Correlator Output in the Presence of Mil Std 1553 As with white noise the mean output of the correlator with Mil Std 1553 as the noise source n t is zero as shown in 6 The variance of the noise is a bit more involved to calculate since for Mil Std 1553 7 n t2 not proportional to O t 12 9 which is not the same as it is for white noise as shown in 8 The signal used for correlation s t will be integrated over a single period It can therefore be considered to be an energy signal 11 and its energy spectral density is given by Ges s t S 10 www T3innovation com S
23. o modulation did not show a significant differ ence in the SSTDR correlator output Fig 13 shows the PSD of the cross correlation shown in Fig 12 alongside the cross correlation of an STDR signal in the ideal case where there is no noise The background noise completely dwarfs the desired signal The frequency spectrum of the noise is broad due to the random sampling of the noise Whitepaper Spread Spectrum Time Domain Reflectometry 1477 sa 5 I N i 0 50 100 150 200 250 300 MHz XCorr Ideal SSTDR XCorr SSTDR w Noise Fig 14 Normalized PSD of the cross correlator XCorr output for a pure ML code SSTDR ideal case signal of length 63 chips at 30 MHz 1 V RMS and 1 RMS ML code SSTDR signal in the presence of a 10 V RMS Mil Std 1553 signal that naturally occurs in a single sample per iteration correlator design Fig 14 shows the PSD of the cross correlation shown in Fig 11 alongside the cross correlation of an SSTDR signal in the ideal case where there is no noise The background noise is significantly lower than the peak of the desired signal Again the freguency spectrum of the noise is broad due to the random sampling of the noise that naturally occurs in a single sample per iteration correlator design It is clear from these simulations that STDR and SSTDR can be used to find impedance changes in wiring It is also clear that the spectral content o
24. o provide excellent insight into fac tors other than signal and noise power that affect the SNR These analyzes are carried out below A Changing the Length of the STDR SSTDR Signal In order to approximate a signal with m times the number of chips as s t let us define a new signal sm t such that 5 f is proportional to S f and let the duration of sm t be mT T Letting the amplitude of s n be the same as s t sm t dt m s t dt mE 25 In the frequency domain Bon 1800084 f SmI VMSA 26 which is what would be expected if the duration of s t were increased by a factor of m by adding more chips to its sequence Letting Rs nlt 8m t x n t 27 gives ERs nn Siz which is the noise energy in the cross correlation of s t with n t over the time 0 lt t lt Th The expected value of the noise power over the interval 0 lt t lt is noise power over the interval 0 lt lt Tn given by DPIN df 08 Pr i mPn 29 which is valid because 7 gt The central peak of the autocorrelation is given by R 0 Es 30 The signal power is 0 mEs m E2 31 From 31 and 29 the SNR is 2772 2 62 Eguation 32 shows that doubling the length of the code while leaving all other parameters the same will double in crease by 3 dB the SNR This is true for any
25. of 17 5 dB 17 The block diagram of the STDR SSTDR block is shown in Fig 1 A sine wave generator operating at 30 100 MHz creates the master system clock Its output is converted to a square wave via shaper and the resulting square wave drives a pseudo noise digital sequence generator PN Gen To use SSTDR the sine wave is multiplied by the output of the PN generator generating a DSSS binary phase shift keyed BPSK signal To use STDR the output of the PN generator is not mixed with the sine wave The test signal is injected into the cable The total signal from the cable including any digital data or ACsignals on the cable and any reflections observable at the receiver is fed into a cor relator circuit along with a reference signal The received signal and the reference signal are multiplied and the result is fed to an integrator The output of the integrator is sampled with an analog to digital converter ADC A full correlation can be col lected by repeatedly adjusting the phase offset between the two signal branches and sampling the correlator output The loca tion of the various peaks in the full correlation indicates the lo cation of impedance discontinuities such as open circuits short circuits and arcs intermittent shorts Test data indicate that this test method can resolve faults in a noisy environment to within 1 10th to 1 100th the length of a PN code chip on the cable de pending on the noise level cable length
26. or is Mil Std 1553 Attention is now turned to changing the chip rate and modu lation freguency for SSTDR tests For SSTDR with a chip rate much greater than the Mil Std 1553 data rate of 1 MHz scaling the SSTDR chip rate and modulation freguency by a factor will change the slope near f 0 by a factor 1 1 So in the region where the Mil Std 1553 signal is significant 5 5 7 40 Is 40 With this approximation 1 18 NRING P Enn 80 Whitepaper Spread Spectrum Time Domain Reflectometry 1475 and the average noise power is 1 Pa 42 Rayn Pen 42 The SNR 42 and 34 is 1 p S 12 8 9 S N 7 43 apt Ran Equation 43 shows that in SSTDR mode doubling chip rate of the PN code and modulation freguency while leaving all other parameters the same will increase the SNR for SSTDR tests by 6 dB if the major noise contributor is Mil Std 1553 This is vastly superior to the STDR results C Self Induced Noise A certain amount of noise comes from the selection of a par ticular PN code This is considered noise because there is a de viation in the cross correlation of all PN codes from the ideal of a central peak with no side lobes Fig 7 shows the autocor relations of two identical power PN seguences one of which is using a ML code 10 and the other of which is using a gold code 10 Note that the power in the two
27. ovation com 1472 IEEE SENSORS JOURNAL VOL 5 6 DECEMBER 2005 E lt KAANAA e 0 1 l i i i i 0 20 40 60 80 Distance m a 0 4 T j 2 02 8 5 0 1 lt 0 1 2 0 2 o 03 i i E 0 20 40 60 80 9 Distance m Fig 6 a STDR and b SSTDR correlation response for an open circuit measured on two 22 AWG wires in a loosely bundled set of 22 wires that is 9 9 m long n t is a noise signal of duration 7 gt T that is statistically uncorrelated to s t The correlator output will be s t a t dt Ts s t azs t T dt E k f s t n t dt 5 As can be seen from 5 the correlator output will depend on the reflected signals and the noise and is therefore deter mined by both deterministic and nondeterministic signals The expected value E of the correlation must therefore be considered Ts E RssT s t 5 Ax8 t dt k Ts s t n t a s t x s t dt 6 0 k In the last step in 6 the fact that s t is zero mean and n t is asynchronous to s t was used The output of the correlator in the absence of noise is the sum of cross correlations of scaled and time shifted copies of s t and the original s t The expected output in the presence of noise is the same as the output in the abse
28. ty etc This ideal anal ysis provides information on the expected accuracy which is verified with tests of near ideal lossless controlled impedance coax The effect of realistic noncontrolled impedance cable is also evaluated and sources of error within a realistic system are discussed 1530 437X 20 00 2005 IEEE Whitepaper Spread Spectrum Time Domain Reflectometry www T3Innovation com 1470 Fig 1 CURRENT WIRE TEST TECHNOLOGY There are several test technologies that can be used to pin point the location of wiring faults Some of the most publicized methods are time domain reflectometry TDR 8 standing wave reflectometry SWR 12 freguency domain reflectom etry FDR 13 impedance spectroscopy 14 high voltage inert gas 15 resistance measurements and capacitance mea surements At the present time these test methods cannot re liably distinguish small faults such as intermittent failures on noncontrolled impedance cables without the use of high voltage In addition the signal levels reguired to reliably perform these tests may interfere with aircraft operation if applied while the aircraft is in use 4 Another test method is needed that can test in the noisy environment of aircraft wiring and that can be used to pinpoint the location of intermittent faults such as momentary open circuits short circuits and arcs III SPREAD SPECTRUM WIRE TESTING Spread spectrum signals both in baseband S
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