Lab1 System2.Order sol
Contents
1. Ci l Ajo dB So Hz Ag dB So Hz Ao dB So Hz simulated 20 7210 0 7210 20 7210 220 pF f heasured 20 7010 0 7500 20 7496 simulated 20 721 0 721 20 721 2200 PF f heasured 20 737 0 737 20 737 Table 5 1 2 Impact of Rp on Amplification Ao and fo pole fp constant R 100KQ Ry gt 10 KQ 100 KQ 1000 KQ Ci take val from above check CH 2 Overload Aol dB So Hz Ao dB fi o Hz Adl dB So Hz simulated 20 72100 0 7210 20 7210 220pF ineasured 20 77254 0 7200 20 717 5 2 Second Order System Table 5 2 1 Parameter s impact of on Amplification Ao cutoff frequency fo and stability D 20 Ao R2 10 KQ 100 KQ 1000 KQ D Ry ij Output level 20dB Output level 0dB Output level 10dB AdB fy KHz A fo dB Ao 4B fy KHz Af dB AdB fy KHz A fy dB imulated 0 7 23 6 01 R 50KQ simulated C12 220PF asured 0 7 20 5 88 imulated 0 7 23 3 09 R 70KQ simulate F Ci2 220pF casured 0 7 20 3 07 i 20 7 23 20 0 0 7 23 0 20 7 23 20 0 Ry 100K simulated C1 2 220pF EEEE 20 7 20 20 0 7 20 0 118 20 7 30 20 i 0 724 0 006 Ry 100K simulated 2 X X A a i measured 0 747 0 104 M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences Table 5 2 2 Stability observations in the time domain Voltage overshoot and osci2. A0 _ Ao a s gt 0 1 __ Ra TF 20 0 STF gt pa U s sl s b0 bi Ri R 1 ith s with b a wil S ma 1 Rp l RC c Mapping general to particular param A amplification at w 0 ron Ry 1 eae Mo Ri Ry Ci Wo cutoff frequency usedin s s o M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences Table 2 2 1 a with parameters Ao and o They are chosen such that both parameter affect one single aspect of the circuit only Ao is the DC amplification and wo the cutoff frequency as shown in Fig 2 1 1 2 below Any model electrical mechanical fluid etc with a single pole only to be considered can be described with this general model Table 2 1 1 b shows the transfer function of the circuit in Fig 2 1 1 1 b Table 2 1 1 c maps the particular parameters of b to the general model parameters of a Fig 2 1 1 2 First Order System a Magnitude and b Phase diagram The pole can be identified by its 45 b phase shift 180 135 90 Goal Find two particular parameters that effect one of the two general parameters only 1 Which device parameter in Fig 2 1 1 1 c affects DC amplification Ao and not pole o a era 2 Which device parameter in Fig 2 1 1 1 c affects pole o and not DC amplification Ao oy Sa 3 What is the DC amplification Ao as f R C7 Ao R 1 R 4 What is the cutoff frequency o as
3. case is D 1 2 How do you identify these cases in a Bode diagram Is D 0 more or less stable than D 1 or D0 21 M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences 7 Conclusions Draw your personal conclusions from this laboratory The general control loop model combined with the general 1 t and 2 order system models in the Laplace domain apply well to 1 and 2 order circuit behavior for both simulation and measurement The comparison of simulated and experimental results is respectable in face of the fact that very simlpy spice models were used Particularly the operational amplifiers were assumed to be near ideal having neither poles nor zeros infinite input and zero output impedance A better OpAmp macro should introduce at least two additional poles for every OpAmp 8 References 1 M Schubert Courses at Regensburg University of Applied Sciences Available http homepages fh regensburg de scm39115 gt Offered Education Courses and Laboratories 2 M Schubert 1 gt Document Linear Control Loop Theory 3 The Spice Page EECS Department of the University of California at Berkeley available http bwrc eecs berkeley edu Classes icbook SPICE 4 LTspice available http Awww linear com designtools software 5 M Schubert 1 gt LTSpice Input Files 6 Bode 100 User Manual available http www omicron lab com manuals pdf
4. f Rx C1 fo 1 27Rp1C1 M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences 2 1 2 Noise Transfer Function The noise transfer function NTF is generally defined as NTF Vom 2 5 err From noise source Ue we measure at the output U sw NTF Uerri Take the NTF from 2 or compute it from STF by translating Uer into an equivalent input signal Divide it by 1 s and multiply with STF s _ SRC s 30 NTF gt 0 2 6 s b 14 5R C Important e g for AX modulators 9 10 11 Low frequencies are suppressed proportional to s and therefore particularly for low frequencies 2 1 3 Stability There is a single pole in the negative s plane Itis Sp bi 1 Consequence Check the correct statement The system is X always stable stability depends on device parameters M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences 2 2 General and Particular Second Order System Models 2 2 1 Signal Transfer Function of a Second Order Electronic Circuit a Error b E Fig 2 2 1 a High level schematics b depicted for modeling c Realization with 1 R C 2 1 R2C2 b R Rp b2 R2 Rp2 and error source Uer Ao D are a set of parameters describing the general 2 order model They are chosen such that any of these parameters affects one aspect of the circuit only Ao is the DC amplific
5. html 7 Bode 100 Network Analyzer Suite available http www omicron lab com downloads html 8 M Schubert 1 gt Document BODE 00 Quickstart for Spectrum Analysis 9 J C Candy G C Temes 1 paper in Oversampling Delta Sigma Data Converters Theory Design and Simulation IEEE Press IEEE Order PC0274 1 ISBN 0 87942 285 8 1991 10 S R Norsworthy R Schreier G C Temes Delta Sigma Data Converters IEEE Press 1996 IEEE Order Number PC3954 ISBN 0 7803 1045 4 11 M Schubert 1 Document Delta Sigma Modulation is ae
6. 0 ca 700Hz and 1V peak peak to Uin Perform the 3 measurements to be noted in table 5 2 2 1 Dead beat limit case R S50KQ D 1 2 2 Butterworth case Rp 70KQ D 1 2 3 Phase Margin 45 case R 100KQ D 1 4 Try also Ry gt 100KQ and free oscillation Rp gt D 0 b Observe stage amplifications in the time domain Observe the amplification Ay2 of the input stage around OA2 as a function of R How can Ayz be modeled as function of Ao and Ay the amplification of the output stage around OA Hint The total amplification must be Ag Ay2 Ay while Ag Rp2 R2 and Ay R R Ayo and Av given gt Avy2 Avo Avi Analog Audio Signal Processing e Remove any sources connected to Uin e Connect the board s line in TRS plug to line out of the computer s sound card green e Connect the board s line out TRS plug to the speakers e Play music switch stability D by R amplification Ag amp bandwidth fo independently e Perceive the effect on the sound particularly for Rp for the different capacitances 19 M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences 5 Simulated and Experimental Results Summary 5 1 First Order System Table 5 1 1 Impact of C and R on Amplification Ao and fo pole fp D Use a simple resistor for the 1MQ measurements to avoid parasitic capacitive effects Ri gt 10KQ 100 KQ 1 MQ
7. 5 Respective LTspice 4 input files 5 are given on the web together with this documentation e During the hands on training concentrate on section 4 working with the Bode 100 network analyzer 6 7 8 Fill the measured fields of the tables in chapter 5 The organization of this laboratory is as follows Section 2 presents theoretical background according to 2 sections 3 and 4 offer simulation and experimental verification respectively Section 5 contains tables common to sections 3 and 4 In section 6 you can check your understanding of the fundamental goals of this laboratory Section 7 draws relevant conclusion M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences 2 Theory Typically the biasing voltage Ug is 40V In this case we use a mathematical trick Calculate with U U Us 2 1 After Solution U U Ug 2 2 2 1 General and Particular First Order System Models 2 1 1 Signal Transfer Function of a First Order Electronic Circuit a b Uin Vout Caption U Uy UBiasing Fig 2 1 1 1 a High level schematics b depicted for modeling c OpAmp realization with 1 R C b R Rp and error source U The signal transfer function STF is generally defined as STF a 2 3 Table 2 1 1 General and particular 1 order model taken from 2 2 4 a General 1 Order Model b Particular Model of Fig 2 1 1 1 b U
8. DC Factor kg VDD gnd gn U d 2 amp l Caption X 2 mm banana 4 mm banana BNC Fig 4 1 First Order System Configuration ji iii x ee O Preparing the Board Setup amp Calibration Disconnect TRS connector from the computer s sound card Speakers may be connected e Verify Vop 3 3V e Adjust the JN inputs of the OpAmp OA to Vg Vpp 2 e Set U OV using short circuit e Disconnect the output of OA2 from Uin i e Uerr2 is a break and connect Uin to Uinz e Set Robi Ri 100KQ Ci 220pF Preparing the Oscilloscope Let s Use Following Default Settings e Oscilloscope s CH1 shows the boards input voltage Vin e Oscilloscope s CH2 shows the boards input voltage Uou e Trigger channel CH1 14 M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences Preparing Bode 100 for Gain Phase mode mesurements e Bode Analyzer Suite Toolbar Configuration Device Configuration set switch right connecting Receiver 1 to CH1 Then shorten CH1 to OUTPUT externally with a BNC cable e Click the Gain Phase toolbar button F e Source Frequency 100Hz Level 0dB Attenuators 20dB Receiver Bandwidth 100Hz e Connect a Bode 100 s OUTPUT and CH1 and the board s Uin b CH2 to board s Uou Di e Click the Continuous Measurement gt or Single Measurement s button to measure Train in the Gain Phase mode the set
9. HOCHSCHULE REGENSBURG u UNIVERSITY OF APPLIED abor SCIENCES Laboratory 1 Analog Systems of 1 and 2 Order Prof Dr Martin J W Schubert Electronics Laboratory Regensburg University of Applied Sciences Regensburg M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences Abstract Electronic control loop circuits as typical e g for AX A D converters are compared to generalized first and second order models and verified by both simulation and measurement 1 Introduction Any system that can oscillate is of at least second order i e it has at least two memories The order of a model is the maximum of poles or zeros in its transfer function As higher order systems are difficult to treat by analytical calculus second order system considerations are popular They apply to higher order system models also when the first two poles are significantly lower than the rest of poles and zeros How to work through this laboratory 1 e There is no need to fully understand the theory in section 2 to benefit from this tutorial For theory it is enough to study the model summary in Fig subsection 2 3 An in depth mathematical derivation of the models is given in 2 e The Spice 3 simulations of section 3 are useful but no precondition for the hands on training They can be made with a personal computer running the free LTspice simulator Fill the simulated fields of the tables in chapter
10. R R DC amplification Ao a T System bandwidth 1 1 cutoff frequency Jo 27R C1 2m4 R C RpC gt Stability control n R R a parameter 2R VC Table 2 3 2 Controlling 2 order system stability for R R2 Rp2 100KQ and C C 2 15 Case D gt Rp f DevParam Ry KQ creep D gt 1 Rpi aper lt Rot abtim lt 50 ae aR R C dead beat aperiodic limit D 1 Reidotim b2 E 3 Butterworth J1 2 Rene Rp dblim V2 70 71 Phase margin 45 1 2 Ry Pm45 Rbi dblim 2 100 Ideal oscillator D 0 Ry gt eo M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences 3 Model Verification by Spice Simulation 3 1 Verifying the First Order Model with Spice Simulation is a valuable tool to proof and better understand the analytical calculus in the previous chapter Nowadays many derivatives of the UC Berkeley s Spice 3 simulator exist LTspice 4 is available free of charge and without simulation limitations The input file for the circuit in the figure above is available from the author Use it to proof the analytical results First of all summarize them Table 3 1 Impact of device parameters R R and C on Amplification A and pole fp DC ampl Ao cutoff frequ fo adjust Ap only by adjust fo only by Device parameter Rpi Ri 1 2nRp1C1 Ri Ci 3 1 1 Variation of R Fj LTspice IV System_1st_Order asc File Edit H
11. ation Wo the cutoff frequency and D adjusts the stability Goal Find three particular parameters that effect one of the three general parameters only 1 Which device parameter in Fig 2 2 1 c affects DC amplification Aj only Ro 2 Which device parameter in Fig 2 2 1 c affects stability Parameter D only Rpi 3 Which two parameter Fig 2 2 1 c affects the cutoff frequency wo only C C2 while C2 C keeps constant Ci Cio cr C2 C20 Cr Further questions important to understand the circuit 4 What is the DC amplification A of the amplifier stage with index 1 Rpi Ri 5 What is the DC amplification A of the amplifier stage with index 2 Ao Ai M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences 6 Compute phase and magnitude of STF2 s j p Hint It is easiest to compute STF general S j 2 7 STF generat S i a o ee 2p 05 B02 2590 s 2Ds 1 j 2Dj 1 1 2Dj 1 2D 2D Table 2 2 1 General and particular 2 order model taken from 2 2 8 a General 2 Order Model b Particular Model of Fig 2 1 2 Uou s QO STF general 7 Ag 7 Aoo 7 STES particular a 2 j s 2Ds 1 s 2Da s U nls s7 b as b a 0 s f 1 Rp s frequency normalized to A b R A amplification at 0 with L pi fs x 1 2 x b xx bx d attenuation time dimension 1 time p attenuation wave d
12. here oscillations in the step response no 11 M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences 3 2 Verifying the Second Order Model with Spice F Tspice IV System_2nd_Order asc DER Ele Edit Hierarchy Yiew Simulate Tools Window Help BsUPs 9 RLAR ROBBE LEM ASLEMS43 ZDVOOD C Him System_2nd_Order asc a4 System_2nd_Order raw eles 100KHz DEK Fig 3 2 LTspice simulation of the second order model here variation of Ru The input file for the circuit in the figure above is available from the author Use it to proof the analytical results First of all summarize them Table 3 2 Impact of device parameters R R2 c on DC ampl Ag D and cutoff frequ fo DC ampl Damping factor cutoff frequ adjust Ao adjust D adjust fo model Ao model D model fo only by onlyby only by Device R i 1 Parameter R RCR gt C R2 Roi Cr 12 M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences Observe the AC plot in the top part of Fig 3 2 colors inverted to save ink It is the system A s 1 s 2Ds 1 with s for varying values of D How can we measure f 0 21 for different values of D Hint look at the dashed curves the phase information of the plot Vary one after the other the parameters R2 Rp1 cr with C c Cio C2 c C29 in the spice model to proof table 3 2 qualitati
13. iences STF Proof the theory of tables 2 4 1 and 2 4 2 regarding Aj fo D dependencies Perform the 6 measurements to be noted in table 5 3 1 Consider proper settings of OUTPUT Level and Attenuator CH2 to avoid overloads Use a cursor to measure fo at 90 phase drop Try also R gt 100KQ and free oscillation Ry gt D 0 Conclusions Rz has impacton XAo Ofo OD R on OAo Ofo XD Ci20n OAo Xfo OD NTF Measuring the Noise Transfer Function e U 0V attach BNC short circuit or 50Q to Uin e R 10 100 or 1000KQ has no impact e Let CH2 connected to Uou as is e Feed Bodel00 s OUTPUT to U using injection transformer B WIT100 of Omicron Lab e Perform a frequency sweep Observe Low frequencies are suppressed with 40 dB dec Measuring the Errors in the Feedback Path e Feed Bodel00 s OUTPUT to U 3 using injection transformer B WIT100 of Omicron Lab Observe Amplification at low freq of the error Uers injected into the feedback path 0 dB Conclusions of the frequency domain measurements Errors at the system s input are amplified by the X STF Oo NTF Errors at the forward network s output are amplified by the STF X NTF Errors at the feedback network s output are amplified by the X STF Oo NTF Time Domain Measurements a Observe stability in the time domain Set R R R 2 100KQ Rp variable Remove Bode 100 s OUTPUT from the board s Uin Feed a rectangular waveform with frequency fo 1
14. ierarchy Yiew Simulate Tools Window Help Aad PF RIAR E Beet te Mm ASS LLH DVO System_1st_Order asc System_1st_Order raw System_1st_Order raw V vout T T a 100KHz System_1st_Order asc PULSE 0 1 1ms 1ps 1ps 10s 11s 1 ac dec 100 10 1Meg jtran 0 4ms 0 1us Step param R list 10K 50K 70K 100K 140K 300K 1000K Fig 3 1 1 LTspice simulation of the 1 order model Variation of R for the STF 10 M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences 3 1 2 Variation of R Fe4Tspice IV System_1st_Order_var_Rb1 asc DoR Ele Edt Hierarchy View gmdate Tools Widow Hep e jaca reo QQQRQ Boe E System_1st_Order_var_R1 asc System_1st_Order_var_Rbl asc AaB AS LLF3 ZDOVC Aa 100KHz System_1st_Order_var_Rb1 asc BEE Fig 3 1 2 LTspice simulation of the 1 order model Variation of Rp for the STF 3 1 3 Homework Fill Tables 5 1 1 and 5 1 2 To quantitatively proof table 3 1 fill the lines labeled with simulated in tables 5 1 1 and 5 1 2 Use AC mode for simulation Note that LTspice measurements are typically better done with constant device parameters i e without parameter list Use a cursor to measure A and f at 45 phase drop compared to phase at 0 NTF In the AC mode vary R by a list at U 0V U2 7 1V Agreement with Eq 2 6 yes Stability AC mode are t
15. imensionless Wo 3 _ O b 0 0 cutoff frequency usedin s s o De TORC Poles of the 2 order system w p2Vb 1 if D21 S12 D bo zN R Rp2 C o D ji D if D lt 1 5R C bl 1 209 2 2 2 Noise Transfer Function of the 2 Order System From noise source Ue we measure at the output U suw NTF Uerri To compute NTF from STF we translate Ue into an equivalent input signal by dividing it by 1 s and then multiply with the STF 2 2 STF S OTO S s gt 0 0 2 9 NIF CU ent 2 2 OM MO Sf OS O S OS OOk 5 From noise source U2 we measure at the output U su NTF3 Uerr2 To compute NTF from STF we translate U 2 into an equivalent input signal by dividing it by 7 s and then multiply with the STF STF s QQ SO s0 NTE U en L gt SG 2 10 OD O S OS tOO S O54 OO S Important e g for AX modulators Low frequencies are suppressed proportional to s M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences 2 2 3 Stability Investigation Considering the System s Poles From 2 8 we know p 22 5 2p 2 11 2 o QO RIR bets Knowing o and R e from 2 8 we can compute the aperiodic VRC Rp2 C2 2D C dead beat limit case using D 1 and derive the other cases from it see table below Table 2 2 3 Controlling stability with paramete
16. ll frequ Case Aperiodic dead Butterworth Phase Margin 45 beat limit case Uin 1V mV mV mV Usu voltage Simulated 0 0 40 5 4 05 163 16 3 Overshoot measured 0 0 50 5 180 18 Oscillation fi 2 frequency as fifo lt fo exact Im s 2a fyVl D 6 Check Your Knowledge Can you resolve acronyms STF and NFT What is their general definition as function of Vin Uerr Uou Can you apply these voltages if they are not given What are the STF STF and NTF NTF for the particular 1 and 2 order circuits of this laboratory Typically circuits are driven with a biasing voltage Ug to avoid a second power supply This DC offset is contradictory to the rules of LTI systems 2 What do we do to get mathematically rid of Ug 1 order system What two parameters characterize a very general 1 order STF with DC amplification and a single pole Which device parameters in our particular circuit have impact on only one of these general parameters Tendency of this impact e g lower x gt higher y Can this system become instable by parameter variations 2 order system What three parameters characterize a very general 2 order STF with DC amplification and two poles Which device parameters in our particular circuit have impact on only one of these general parameters Tendency of this impact e g lower x higher y What stability case is given for general parameter D 1 What
17. nnel and ground respectively Care about other students low volume Short test times please Ty s M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences 4 2 Second Order System Characterization camel y ol inane Cy FR nae Left Right Osti CH2 6 15V 4 LT317 V pp 2 7 5V Vout 1KQ Osc CH BODE100 amp max OUTPUT Ym 16nF CD74HC74M umm _1 Bit ADC Factor kg VDD gnd gn 7 U CE sO Sen 5 Caption 2 b 4 b BNC Fig 4 2 Second Order System Configuration oe a x i Board Setup amp Calibration Remove TRS connector coming from the computer s sound card e Verify that Vop 3 3V e Adjust the JN inputs of the OpAmps OA OA2 OA to ca Vg Vpp 2 e Remove bypass of OA2 Set Uer2 0V and Uer OV using short circuits e Set Ry Ri Rp2 R2 100KQ Cy C2 200pF Oscilloscope Default Settings e Oscilloscope s CH1 shows Um CH2 shows Uon trigger channel CH1 Bode100 Gain Phase mode Source Frequency 100Hz optimize Level and Attenuations Bode100 Frequency Sweep mode Use settings as described in subsection 4 1 5 Activate Trace 2 Measurement Gain Display Data Format Phase Check for Configuration Check for Calibration when CH1 is internally connected to OUTPUT 18 M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sc
18. o impact e Let CH2 connected to Usu as is e Feed Bodel00 s OUTPUT to U using injection transformer B WIT100 of Omicron Lab Perform a frequency sweep observe Low frequencies are suppressed with 20 dB dec Measuring the Errors in the Feedback Path Use the same measurement setup as above but measure Uou instead of Uou Then Uer is within the feedback path Observe Low frequencies are suppressed with 0 dB dec Conclusions of the frequency domain measurements Errors at the system s input are amplified by the X STF ONTF Errors at the forward network s output are amplified by the O STF X NTF Errors at the feedback network s output are amplified by the X STF ONTF Time Domain Measurements Observe stability in the time domain R a Ry 100KQ Uin 1Vpeak peak rectangular 4 KHz from the waveform generator e Observe Um and Usu at oscilloscope channels CH1 CH2 for C 220pF and 2 2nF Can you observe any voltage overshoot No 16 M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences Analog Audio Signal Processing Remove waveform generator Connect the board s line in TRS plug to line out of the computer s sound card green Connect the board s line out TRS plug to the speakers Play some music switch amplification Ao amp bandwidth fo independently Perceive the effects on the sound TRS Tip Ring Sleeve connected to left channel right cha
19. quency Sweep mode Click toolbar button Dy to switch to the Frequency Sweep mode Freq 100Hz 1MHz Log 201 Points Receiver Bandwidth 100Hz Level Attn optimized Activate Trace 2 Measurement Gain Display Data Format Phase Check Configuration and Calibration Everything ok Let s start the measurements 15 M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences STF Proof the theory of tables 2 2 1 and 2 4 regarding Ao and or fy dependencies Connect the Line out TRS plug to the speakers listen to one or two measurements to get a feeling for measurement duration and speed Perform the 8 measurements required to fill tables 5 1 1 and 5 1 2 Observe the Bode100 s overload indicator and oscilloscope channel CH2 Avoid overloads by setting OUTPUT Level and Attenuator CH2 properly e Agandfo for R 10KQ R 100KQ C 220pF 2 2nF gt note results in table 5 1 1 e Agandfo for R 100KQ R 100KQ C 220pF 2 2nF gt note results in table 5 1 1 e Agandfo for R 1000KQ R 100KQ C 220pF 2 2nF gt note results in table 5 1 1 e Agandfo for R 100KQ R 10KO C 220pF note results in table 5 1 2 e Agandfo for R 100KQ R 1MQ C 220pF note results in table 5 1 2 Conclusion R has impacton XAo X fo Rion XAo Ofo Con OAo Xfo NTF Measuring the Noise Transfer Function e U 0V attach BNC short circuit or 50Q to Uin e R 100KQ R 10 100 or 1000KQ has n
20. r D for R R2 Rp2 100KQ and C C2 2 12 Case D gt b o 1 gt Rs DevParam Ry KQ creep D gt 1 bi creep gt 200 Rot aper lt Rbl dblim lt 50 4 RiR dead beat aperiodic limit D 1 bi dblim 2 Ryl dblim b2 S 50 l 1 Butterworth O 70 71 D 41 2 bi gw v2 Ro pw Rot apiim 2 1 Phase margin 45 1 2 bi pase o Ry pmase Ror aptim 2 100 Ideal oscillator D 0 biose 9 R gt es Fill the last column in the table above such that it computes the value of Rp for R R Rp 100KQ and C C2 220pF Consequence The systemis O always stable X stability depends on device parameters a Pole Locus in the S o0 j plane aperiodic dead beat limit case val Butterworth Fig 2 2 3 a Locus of poles in the s plane and b respective step responses M Schubert 2 3 Model Summary OV Lab1 Analog Systems of 1 and 2 Order U in 1st order Fig 2 3 1 and 2 order system depending on switch S Regensburg University of Applied Sciences Verrt lt lt U out Table 2 3 1 Summary of 1 and 2 order models and parameters 2 14 Property Parameter 1 Order Model 2 Order Model Signal Transfer Ao Ay Function s s a o STF s s s 42Ds 1 Signal Transfer Ao Aoi Function using STF s S 09 s 2D s os Noise Transfer s 50 2 STF gt 0 s gt 0 Function NTF s RC RORG oe 3
21. tings of OUPUT Level and Attenuators In the Frequency Sweep mode things may happen too fast to observe Constant parameters below C 220pF Rpi 100KQO R Ray 100KQ Results in integral multiples of 10dB 1 Set Bode 100 s OUTPUT such that OA s output is max amp sinusoidal Level 0 dB 2 Adjust Attenuator CH1 such that CH1 is well loaded Attenuator CHI 20 dB 3 Adjust Attenuator CH2 such that CH2 is well loaded Attenuator CH2 20 dB Note your measurements Mag dB 38 mdB Phase 179 R 1MQ Results in integral multiples of 10dB 4 Set Bode 100 s OUTPUT such that OA s output is max amp sinusoidal Level 13 dB 5 Adjust Attenuator CH1 such that CH1 is well loaded Attenuator CHI 30 dB 6 Adjust Attenuator CH2 such that CH2 is well loaded Attenuator CH2 10 dB Note your measurements Mag dB 20 dB Phase 180 R 10KQ Results in integral multiples of 10dB 7 Set Bode 100 s OUTPUT such that OA s output is max amp sinusoidal Level 20 dB 8 Adjust Attenuator CH1 such that CH1 is well loaded Attenuator CHI 0 dB 9 Adjust Attenuator CH2 such that CH2 is well loaded Attenuator CH2 20 dB Note your measurements Mag dB 19 8 Phase 172 Keep in mind for the following measurements that Bode 100 s OUTPUT Level must be adjusted proportional 1 Ao R R Eventually peaking around fp must be respected too Bode 100 Fre
22. vely like in Fig 3 2 To quantitatively proof table 3 2 fill the lines labeled with simulated in tables 5 2 1 and 5 2 2 Use AC mode for simulation Note that LTspice measurements are typically better done with constant device parameters i e without parameter list Use a cursor to measure Ao fo A fo at 90 phase drop compared to phase at 0 NTF Settings AC mode Uin O0V Uer2 0V Uerrs 1V Does the result agree with Eq 2 9 yes What is the slope of Ujud f lt fo 40 dB dec NTF 3 Settings AC mode Uin O0V Uerr2 1V Uerrs 0V Does the result agree with Eq 2 10 yes What is the slope of Uouif lt fo 20 dB dec Stability Oscillations in the step response oscillate at p Im sp What is its model fp 2n with o vl D for DS1 creep case if D gt 1 A Proof that A f T Hint s j when o p Important consequence At f f here will always be a 90 phase shift Ao Ao Ap Ap STF2 i s aor ae ESS s 2Ds 1 j 2Dj 1 2Dj 2D 13 M Schubert Lab1 Analog Systems of 1 and 2 Order Regensburg University of Applied Sciences 4 Experimental Verification of 1 and 2 Order Model To get started with the BODE100 Vector Network Analyzer for this laboratory refer to 8 4 1 First Order System Characterization one _line_in blue l 6 15V ae LT317 V DD 27 5V Osci CH1 BODE100 4 me ma a Ug CP CD74HC74M tire __1 Bit A
Download Pdf Manuals
Related Search