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GX LII-2 – Lab Log: Bode Measurement Campaign on Resistive Dividers

by giux Electronics, Test equipment 28 min read

Before discussing the results of this new measurement campaign, I am linking the first article in the series here, where I described the starting point of the GX LII-2 project, the experimental test bench, and the first characterization tests. Since then, the measurement method, the setup, and especially the data processing have changed considerably.

Self-Built Injection Transformer: First Loop Gain Measurements and Calibration Test Bench

A measurement campaign more demanding than expected

This campaign proved quite demanding, mainly because the signals measured at the OUT and SENSE nodes are very small. Even under the most favorable conditions, peak-to-peak amplitudes are often only a few tens of millivolts, so careful setup becomes essential.

When a measurement is only intended to give a general idea of a circuit’s behavior, some compromises can be accepted; in this case, however, I am collecting data that I want to use to characterize the system properly. The final error results from the sum of many small contributions, so it becomes necessary to eliminate them, or at least reduce them, one at a time.

For this reason, during the acquisitions I chose to switch off practically all unnecessary electronics in the laboratory, including the LED lighting, and worked with a battery-powered lamp. I also paid close attention to the routing of power and signal cables and used high-permeability ferrite rings on the connections, with the aim of increasing the impedance to common-mode currents and further reducing interference introduced into the measurement system.

Despite these precautions, a residual low-frequency component remains visible, roughly in the 50–100 Hz range. Its origin still needs to be verified: it could be common-mode interference or a signal actually injected by some element of the setup.

Fortunately, the processing I use in GNU Octave does not derive magnitude and phase directly from the overall waveform amplitude, but instead extracts the component at the injection frequency by fitting. A 50 or 100 Hz disturbance is therefore not directly confused with the fundamental I am measuring, and its contribution to the final result is greatly reduced.

This does not make careful setup unnecessary; on the contrary, I still prefer to start with signals that are as clean as possible. Fitting is an additional safeguard against unwanted components, not a reason to neglect measurement quality.

GX LII-2 connected to the calibration bench for Bode measurements, with oscilloscope probes and a ferrite toroid on the power cables.
Setup used for the measurement campaign on resistive dividers. On the left is the calibration bench with selectable R/C networks; on the right is the GX LII-2 with the injection transformers. I added a high-permeability ferrite toroid with several cable passes on the power connections to increase the impedance to common-mode currents and reduce interference during acquisition.

Scope of this campaign

Seven resistive pairs, from 100 Ω to 100 kΩ, were characterized at 30 frequencies between 10 kHz and 700 kHz, performing both A and B acquisitions at every point. The injection branch uses Rinj = 18 Ω; CH1 measures VSENSE and CH2 measures VOUT. Vgen was not kept constant throughout the sweep, but adjusted point by point to maintain an adequate signal level while remaining in the linear region.

The LTspice trace used for comparison represents the ideal circuit built with the actual measured resistance values. I did not include capacitances, inductances, or other parasitic elements of the fixture and transformer in the model; the frequency-dependent structures that emerge experimentally are therefore not already incorporated into the simulated reference.

Measurement campaign data

Before moving on to the Bode plots, I report the data used for this campaign. The first table is the same one already presented in the first article of the series and contains the actual measured resistor values on the calibration bench. I include it again here for convenience because these values, rather than the nominal ones, are used as the reference in the subsequent processing and simulations.

Nominal seriesUpper R [Ω]Lower R [Ω]Rupper/Rlower
100R99.9499.701.002407
330R323.80324.400.998150
1k995.70999.000.996697
3.3k3260.003290.000.990881
10k9800.0010010.000.979021
33k32990.0032940.001.001518
100k99770.0099330.001.004430

For each resistive combination, I then collected in a second table the fundamental levels actually measured at the SENSE and OUT nodes, keeping the A and B acquisitions separate.

For each point, the table contains the nominal series value, the actual values of upper R and lower R, the measurement frequency, and the fundamental amplitudes obtained from the GNU Octave fit, expressed both as Vpk and Vpp.

The columns are therefore:

serie_nominale — divider identification
R_alto_ohm — actual upper-resistor value
R_basso_ohm — actual lower-resistor value
f_Hz — measurement frequency
VSENSE_A_Vpk, VSENSE_A_Vpp — fundamental at SENSE, measurement A
VOUT_A_Vpk, VOUT_A_Vpp — fundamental at OUT, measurement A
VSENSE_B_Vpk, VSENSE_B_Vpp — fundamental at SENSE, measurement B
VOUT_B_Vpk, VOUT_B_Vpp — fundamental at OUT, measurement B

Complete VSENSE and VOUT amplitude table
serie_nominale R_alto_ohm R_basso_ohm f_Hz VSENSE_A_Vpk VSENSE_A_Vpp VOUT_A_Vpk VOUT_A_Vpp VSENSE_B_Vpk VSENSE_B_Vpp VOUT_B_Vpk VOUT_B_Vpp
100R 99.94 99.7 10000 0.051966553 0.103933106 0.0515555058 0.103111012 0.0513025477 0.102605095 0.0522774051 0.10455481
100R 99.94 99.7 20000 0.0506356116 0.101271223 0.050048633 0.100097266 0.0499897897 0.0999795794 0.0507702399 0.10154048
100R 99.94 99.7 30000 0.0494554846 0.0989109692 0.0473021597 0.0946043194 0.0475143672 0.0950287344 0.0493570395 0.098714079
100R 99.94 99.7 50000 0.0509689175 0.101937835 0.0476714068 0.0953428137 0.0479383926 0.0958767851 0.0511129995 0.102225999
100R 99.94 99.7 80000 0.0527978907 0.105595781 0.0477935012 0.0955870024 0.0482230661 0.0964461323 0.0530146409 0.106029282
100R 99.94 99.7 100000 0.0559861529 0.111972306 0.0499663426 0.0999326852 0.0504354713 0.100870943 0.0562623129 0.112524626
100R 99.94 99.7 120000 0.049914423 0.099828846 0.0440890364 0.0881780729 0.0445418221 0.0890836442 0.0502048651 0.10040973
100R 99.94 99.7 140000 0.0588979736 0.117795947 0.0515834148 0.10316683 0.0521876548 0.10437531 0.0592600831 0.118520166
100R 99.94 99.7 160000 0.0502158428 0.100431686 0.0436936644 0.0873873288 0.044231718 0.0884634359 0.0504719501 0.1009439
100R 99.94 99.7 180000 0.0395268263 0.0790536526 0.0342196614 0.0684393229 0.0346156675 0.0692313351 0.0397271449 0.0794542898
100R 99.94 99.7 200000 0.0276955015 0.0553910031 0.0238474054 0.0476948108 0.0241639349 0.0483278698 0.0278573273 0.0557146546
100R 99.94 99.7 220000 0.025492782 0.0509855639 0.0218417041 0.0436834081 0.022136888 0.044273776 0.0256280189 0.0512560379
100R 99.94 99.7 240000 0.023608973 0.047217946 0.0201373159 0.0402746317 0.0204045315 0.040809063 0.0237110497 0.0474220993
100R 99.94 99.7 260000 0.0219702783 0.0439405566 0.018660442 0.037320884 0.0189113024 0.0378226047 0.0220626597 0.0441253194
100R 99.94 99.7 280000 0.0205535065 0.0411070129 0.0173633265 0.0347266531 0.017604651 0.035209302 0.0206294032 0.0412588063
100R 99.94 99.7 300000 0.0233136481 0.0466272962 0.0196198484 0.0392396968 0.0198870685 0.0397741369 0.0234079529 0.0468159059
100R 99.94 99.7 320000 0.0219787825 0.0439575649 0.0184149116 0.0368298232 0.0186666627 0.0373333253 0.0220673428 0.0441346855
100R 99.94 99.7 350000 0.0202453704 0.0404907407 0.0168379481 0.0336758962 0.0170927733 0.0341855466 0.0203137952 0.0406275905
100R 99.94 99.7 370000 0.0192402603 0.0384805206 0.0159190311 0.0318380622 0.0161690839 0.0323381679 0.0193039335 0.0386078669
100R 99.94 99.7 400000 0.01792498 0.03584996 0.0146925231 0.0293850462 0.0149334379 0.0298668758 0.0179723354 0.0359446707
100R 99.94 99.7 430000 0.0280098345 0.056019669 0.0227780537 0.0455561073 0.0231522252 0.0463044504 0.0281223406 0.0562446811
100R 99.94 99.7 450000 0.0268774008 0.0537548015 0.0217092236 0.0434184473 0.0220928692 0.0441857384 0.0269780335 0.053956067
100R 99.94 99.7 480000 0.0253584764 0.0507169527 0.0202896989 0.0405793978 0.0206599336 0.0413198673 0.025430841 0.050861682
100R 99.94 99.7 500000 0.0244414339 0.0488828678 0.0194292123 0.0388584247 0.0197967133 0.0395934267 0.0244920466 0.0489840932
100R 99.94 99.7 530000 0.0232105687 0.0464211374 0.0182452706 0.0364905411 0.0186006739 0.0372013478 0.0232410388 0.0464820775
100R 99.94 99.7 550000 0.0224518289 0.0449036579 0.0175321079 0.0350642159 0.0178801783 0.0357603565 0.0224793745 0.044958749
100R 99.94 99.7 580000 0.0214174038 0.0428348077 0.0165395117 0.0330790233 0.0168780749 0.0337561498 0.0214406191 0.0428812382
100R 99.94 99.7 600000 0.0207898229 0.0415796458 0.0159268442 0.0318536884 0.0162486214 0.0324972427 0.0208195107 0.0416390215
100R 99.94 99.7 650000 0.0194041859 0.0388083718 0.0145557463 0.0291114927 0.0148469906 0.0296939812 0.0194335371 0.0388670743
100R 99.94 99.7 700000 0.0182233133 0.0364466266 0.0133790917 0.0267581835 0.0136210037 0.0272420075 0.018252781 0.0365055619
330R 323.8 324.4 10000 0.0418762407 0.0837524813 0.0404807357 0.0809614715 0.0408110775 0.081622155 0.0415780428 0.0831560857
330R 323.8 324.4 20000 0.0405245034 0.0810490068 0.0395173709 0.0790347418 0.039659541 0.079319082 0.0404256591 0.0808513182
330R 323.8 324.4 30000 0.0395216434 0.0790432867 0.0372714988 0.0745429975 0.0374805726 0.0749611453 0.0392953406 0.0785906813
330R 323.8 324.4 50000 0.0475689374 0.0951378748 0.0434203772 0.0868407544 0.0436747197 0.0873494394 0.0474453475 0.094890695
330R 323.8 324.4 80000 0.0398270268 0.0796540536 0.0348495694 0.0696991389 0.0350817298 0.0701634596 0.0397021032 0.0794042063
330R 323.8 324.4 100000 0.0404123623 0.0808247246 0.0346212808 0.0692425616 0.0348511627 0.0697023254 0.0401954808 0.0803909616
330R 323.8 324.4 120000 0.0358552807 0.0717105614 0.0302927262 0.0605854523 0.0304927767 0.0609855535 0.0357407323 0.0714814647
330R 323.8 324.4 140000 0.0442760754 0.0885521509 0.0369614574 0.0739229148 0.037215346 0.0744306921 0.044110411 0.088220822
330R 323.8 324.4 160000 0.0399609389 0.0799218779 0.0330130076 0.0660260152 0.0332486297 0.0664972593 0.0398015503 0.0796031005
330R 323.8 324.4 180000 0.039738001 0.0794760021 0.0324884117 0.0649768235 0.0327498377 0.0654996754 0.0395442671 0.0790885343
330R 323.8 324.4 200000 0.0455223719 0.0910447438 0.0368274845 0.0736549691 0.0371411353 0.0742822706 0.0453226029 0.0906452058
330R 323.8 324.4 220000 0.0420486429 0.0840972857 0.0336606512 0.0673213023 0.0339643951 0.0679287903 0.0418159318 0.0836318635
330R 323.8 324.4 240000 0.0390313647 0.0780627295 0.0309337406 0.0618674812 0.0312481949 0.0624963898 0.0388237176 0.0776474352
330R 323.8 324.4 260000 0.0364372712 0.0728745423 0.0285492486 0.0570984972 0.0288856282 0.0577712565 0.0362600122 0.0725200244
330R 323.8 324.4 280000 0.0364523745 0.0729047491 0.0282381678 0.0564763357 0.0285783444 0.0571566889 0.0362505312 0.0725010623
330R 323.8 324.4 300000 0.0343707586 0.0687415171 0.0262738582 0.0525477163 0.0266403766 0.0532807531 0.0341594658 0.0683189316
330R 323.8 324.4 320000 0.0324912 0.0649824 0.0245549932 0.0491099863 0.0249120675 0.0498241351 0.0322754202 0.0645508405
330R 323.8 324.4 350000 0.0301105038 0.0602210076 0.0222940425 0.044588085 0.022641276 0.0452825521 0.029902042 0.0598040841
330R 323.8 324.4 370000 0.0287389113 0.0574778227 0.0209506433 0.0419012865 0.0212877587 0.0425755174 0.0285065202 0.0570130403
330R 323.8 324.4 400000 0.0336664974 0.0673329949 0.0240116039 0.0480232079 0.0244197594 0.0488395187 0.0334270942 0.0668541884
330R 323.8 324.4 430000 0.0317552866 0.0635105732 0.0220756141 0.0441512283 0.0224506134 0.0449012268 0.0314826379 0.0629652757
330R 323.8 324.4 450000 0.0306048337 0.0612096674 0.0209135917 0.0418271833 0.0212663088 0.0425326175 0.0303482018 0.0606964035
330R 323.8 324.4 480000 0.0290642991 0.0581285982 0.0193310001 0.0386620002 0.0196650451 0.0393300901 0.0288157051 0.0576314102
330R 323.8 324.4 500000 0.028138283 0.0562765659 0.0183697697 0.0367395395 0.0186787432 0.0373574864 0.0279013521 0.0558027042
330R 323.8 324.4 530000 0.0269123324 0.0538246647 0.0170420641 0.0340841281 0.0173353043 0.0346706085 0.0266674874 0.0533349749
330R 323.8 324.4 550000 0.0261751262 0.0523502523 0.016230725 0.03246145 0.0165145654 0.0330291307 0.0259257495 0.051851499
330R 323.8 324.4 580000 0.0251710155 0.0503420309 0.0150924964 0.0301849929 0.0153589463 0.0307178925 0.0249364459 0.0498728919
330R 323.8 324.4 600000 0.0245621209 0.0491242418 0.0143932561 0.0287865122 0.0146442177 0.0292884354 0.0243388419 0.0486776838
330R 323.8 324.4 650000 0.0232315329 0.0464630658 0.0128056079 0.0256112158 0.0130185019 0.0260370038 0.0230153581 0.0460307162
330R 323.8 324.4 700000 0.0221244983 0.0442489966 0.0114019007 0.0228038014 0.0115880516 0.0231761032 0.0219197229 0.0438394457
1k 995.7 999.0 10000 0.0419000115 0.0838000229 0.0413704171 0.0827408342 0.0408546883 0.0817093766 0.0423031459 0.0846062919
1k 995.7 999.0 20000 0.0416064301 0.0832128602 0.0393727837 0.0787455675 0.0392598552 0.0785197105 0.0416411308 0.0832822617
1k 995.7 999.0 30000 0.0401725698 0.0803451395 0.0375577629 0.0751155259 0.0372363507 0.0744727013 0.0403844152 0.0807688304
1k 995.7 999.0 50000 0.0491366155 0.098273231 0.0430924737 0.0861849473 0.043214237 0.086428474 0.0489707617 0.0979415234
1k 995.7 999.0 80000 0.0415190935 0.083038187 0.0342922514 0.0685845029 0.0345399632 0.0690799263 0.0412273992 0.0824547983
1k 995.7 999.0 100000 0.0474441692 0.0948883385 0.0381229801 0.0762459603 0.0385433833 0.0770867667 0.0470544747 0.0941089493
1k 995.7 999.0 120000 0.0423698339 0.0847396677 0.0331849344 0.0663698688 0.0336665609 0.0673331219 0.0419267216 0.0838534432
1k 995.7 999.0 140000 0.0467435674 0.0934871347 0.0358198767 0.0716397534 0.0363953637 0.0727907273 0.0462171741 0.0924343482
1k 995.7 999.0 160000 0.04240372 0.08480744 0.0317644534 0.0635289068 0.0323394671 0.0646789341 0.0418832226 0.0837664453
1k 995.7 999.0 180000 0.038807157 0.077614314 0.0283878891 0.0567757781 0.0289638678 0.0579277356 0.0383043644 0.0766087289
1k 995.7 999.0 200000 0.0456516132 0.0913032264 0.0325602689 0.0651205379 0.0332614726 0.0665229452 0.045029759 0.0900595179
1k 995.7 999.0 220000 0.0424032775 0.084806555 0.0294639015 0.0589278029 0.0301599497 0.0603198994 0.0418054754 0.0836109508
1k 995.7 999.0 240000 0.0396566377 0.0793132753 0.0267950583 0.0535901166 0.0274418236 0.0548836472 0.0390777643 0.0781555286
1k 995.7 999.0 260000 0.0372779516 0.0745559032 0.0244527186 0.0489054372 0.0250721884 0.0501443768 0.0367706016 0.0735412031
1k 995.7 999.0 280000 0.0377396316 0.0754792632 0.0239612467 0.0479224934 0.0245861714 0.0491723428 0.0372355043 0.0744710086
1k 995.7 999.0 300000 0.0358602622 0.0717205244 0.0219823937 0.0439647875 0.0225772303 0.0451544605 0.0353793867 0.0707587735
1k 995.7 999.0 320000 0.034235814 0.068471628 0.0201993642 0.0403987285 0.020779757 0.0415595139 0.0337401253 0.0674802505
1k 995.7 999.0 350000 0.0321670629 0.0643341259 0.0178649791 0.0357299582 0.0183900392 0.0367800784 0.031653779 0.0633075581
1k 995.7 999.0 370000 0.0413367899 0.0826735797 0.0219912357 0.0439824714 0.0226465411 0.0452930822 0.0407033803 0.0814067605
1k 995.7 999.0 400000 0.0392987816 0.0785975632 0.019447393 0.0388947861 0.0200808363 0.0401616725 0.0386832369 0.0773664739
1k 995.7 999.0 430000 0.0375980728 0.0751961455 0.0172173556 0.0344347113 0.0178311 0.0356622 0.0370153317 0.0740306635
1k 995.7 999.0 450000 0.0366140624 0.0732281248 0.0158617042 0.0317234085 0.0164388516 0.0328777032 0.036069803 0.072139606
1k 995.7 999.0 480000 0.0407425952 0.0814851903 0.0161313872 0.0322627743 0.0167427689 0.0334855378 0.0400698776 0.0801397552
1k 995.7 999.0 500000 0.0398542091 0.0797084183 0.0148147139 0.0296294279 0.0153884871 0.0307769743 0.0392340896 0.0784681792
1k 995.7 999.0 530000 0.0387438874 0.0774877749 0.0129558456 0.0259116912 0.0135289169 0.0270578337 0.0381438688 0.0762877377
1k 995.7 999.0 550000 0.0381216891 0.0762433783 0.011825677 0.023651354 0.0123964357 0.0247928714 0.0375138396 0.0750276792
1k 995.7 999.0 580000 0.0372568412 0.0745136824 0.010258084 0.0205161681 0.0107887561 0.0215775122 0.0366679401 0.0733358803
1k 995.7 999.0 600000 0.0367686803 0.0735373605 0.0092869489 0.0185738978 0.00980695812 0.0196139162 0.0361959572 0.0723919143
1k 995.7 999.0 650000 0.0357663497 0.0715326994 0.00713220303 0.0142644061 0.0076536363 0.0153072726 0.0351905321 0.0703810642
1k 995.7 999.0 700000 0.0350019455 0.0700038911 0.00542605664 0.0108521133 0.00588701601 0.011774032 0.0344289803 0.0688579606
3.3k 3260.0 3290.0 10000 0.0563444615 0.112688923 0.0537835744 0.107567149 0.0543001961 0.108600392 0.0558448659 0.111689732
3.3k 3260.0 3290.0 20000 0.0553259529 0.110651906 0.051950211 0.103900422 0.052342732 0.104685464 0.0549387142 0.109877428
3.3k 3260.0 3290.0 30000 0.0546120631 0.109224126 0.0485446575 0.0970893151 0.0490009918 0.0980019835 0.0541709037 0.108341807
3.3k 3260.0 3290.0 50000 0.0506495962 0.101299192 0.0418947731 0.0837895462 0.0424452799 0.0848905598 0.0502242746 0.100448549
3.3k 3260.0 3290.0 80000 0.049397655 0.09879531 0.037826069 0.075652138 0.038363353 0.076726706 0.0488447465 0.0976894929
3.3k 3260.0 3290.0 100000 0.0442456109 0.0884912217 0.032304996 0.0646099919 0.0328580245 0.065716049 0.0437281725 0.087456345
3.3k 3260.0 3290.0 120000 0.0447804549 0.0895609097 0.0311911163 0.0623822327 0.0318184152 0.0636368304 0.0442445148 0.0884890296
3.3k 3260.0 3290.0 140000 0.0452691797 0.0905383594 0.0299142201 0.0598284402 0.0305576078 0.0611152155 0.0447114366 0.0894228732
3.3k 3260.0 3290.0 160000 0.0416497187 0.0832994374 0.0259431074 0.0518862148 0.026568872 0.053137744 0.04103857 0.0820771401
3.3k 3260.0 3290.0 180000 0.0467149883 0.0934299767 0.027260538 0.054521076 0.0279683533 0.0559367067 0.046025326 0.092050652
3.3k 3260.0 3290.0 200000 0.0437987564 0.0875975128 0.0237631831 0.0475263662 0.0244717425 0.0489434851 0.0431243122 0.0862486244
3.3k 3260.0 3290.0 220000 0.0483232332 0.0966464665 0.0242452055 0.048490411 0.0250041611 0.0500083222 0.0475335675 0.095067135
3.3k 3260.0 3290.0 240000 0.0460295487 0.0920590973 0.0211443934 0.0422887868 0.0218972315 0.0437944629 0.0452585989 0.0905171977
3.3k 3260.0 3290.0 260000 0.0440969334 0.0881938667 0.0184582629 0.0369165259 0.0191519076 0.0383038153 0.0433352491 0.0866704982
3.3k 3260.0 3290.0 280000 0.0455507894 0.0911015789 0.0171633034 0.0343266067 0.0179230453 0.0358460905 0.0447110349 0.0894220699
3.3k 3260.0 3290.0 300000 0.0441520403 0.0883040806 0.0148944586 0.0297889172 0.0156380002 0.0312760004 0.0432995302 0.0865990603
3.3k 3260.0 3290.0 320000 0.0429796286 0.0859592572 0.0129161212 0.0258322424 0.0136094846 0.0272189691 0.042094382 0.084188764
3.3k 3260.0 3290.0 350000 0.0470963533 0.0941927066 0.011845466 0.023690932 0.0125740921 0.0251481842 0.0461154 0.0922308
3.3k 3260.0 3290.0 370000 0.0462521102 0.0925042204 0.0103880207 0.0207760415 0.0110682935 0.022136587 0.045270072 0.0905401439
3.3k 3260.0 3290.0 400000 0.0533450066 0.106690013 0.0104269217 0.0208538435 0.0111044291 0.0222088583 0.0521234278 0.104246856
3.3k 3260.0 3290.0 430000 0.0524672588 0.104934518 0.00974848624 0.0194969725 0.010216842 0.020433684 0.0512434046 0.102486809
3.3k 3260.0 3290.0 450000 0.0520325644 0.104065129 0.00986670852 0.019733417 0.0101668109 0.0203336218 0.050796664 0.101593328
3.3k 3260.0 3290.0 480000 0.064529127 0.129058254 0.013416825 0.0268336499 0.0134916187 0.0269832374 0.0629625605 0.125925121
3.3k 3260.0 3290.0 500000 0.0642402939 0.128480588 0.0144877011 0.0289754022 0.0144439191 0.0288878383 0.062681439 0.125362878
3.3k 3260.0 3290.0 530000 0.0639976762 0.127995352 0.0164557661 0.0329115321 0.0162589521 0.0325179042 0.0623851178 0.124770236
3.3k 3260.0 3290.0 550000 0.063933789 0.127867578 0.0178949807 0.0357899615 0.0176019053 0.0352038106 0.0622720339 0.124544068
3.3k 3260.0 3290.0 580000 0.0638969125 0.127793825 0.0201211815 0.040242363 0.0197376821 0.0394753643 0.0622146385 0.124429277
3.3k 3260.0 3290.0 600000 0.0639170617 0.127834123 0.0216071419 0.0432142839 0.021149547 0.042299094 0.0621992403 0.124398481
3.3k 3260.0 3290.0 650000 0.0642350564 0.128470113 0.0253322098 0.0506644196 0.0247670391 0.0495340782 0.0624211406 0.124842281
3.3k 3260.0 3290.0 700000 0.0647082209 0.129416442 0.0288847415 0.0577694829 0.0282953239 0.0565906479 0.0628688508 0.125737702
10k 9800.0 10010.0 10000 0.0560065648 0.11201313 0.0540902612 0.108180522 0.0546151768 0.109230354 0.0559409776 0.111881955
10k 9800.0 10010.0 20000 0.0560930412 0.112186082 0.0510769357 0.102153871 0.0516497413 0.103299483 0.056118614 0.112237228
10k 9800.0 10010.0 30000 0.0550935671 0.110187134 0.0480010452 0.0960020905 0.0484587011 0.0969174023 0.0550840234 0.110168047
10k 9800.0 10010.0 50000 0.0519931815 0.103986363 0.0405173724 0.0810347449 0.0410502169 0.0821004338 0.0519144809 0.103828962
10k 9800.0 10010.0 80000 0.0584588286 0.116917657 0.0393972875 0.0787945749 0.0397745907 0.0795491814 0.0583464223 0.116692845
10k 9800.0 10010.0 100000 0.0535980645 0.107196129 0.0325513318 0.0651026637 0.0328698676 0.0657397353 0.0533878473 0.106775695
10k 9800.0 10010.0 120000 0.0494621679 0.0989243358 0.0269030846 0.0538061691 0.0272024873 0.0544049746 0.0491746647 0.0983493294
10k 9800.0 10010.0 140000 0.0462241288 0.0924482576 0.0221533158 0.0443066317 0.0225063406 0.0450126812 0.045856447 0.0917128939
10k 9800.0 10010.0 160000 0.0484493121 0.0968986243 0.0203872439 0.0407744879 0.0208374955 0.0416749911 0.0479796523 0.0959593047
10k 9800.0 10010.0 180000 0.0461949655 0.092389931 0.0171151701 0.0342303402 0.0175896496 0.0351792993 0.0456793351 0.0913586702
10k 9800.0 10010.0 200000 0.0536118849 0.10722377 0.0177631172 0.0355262344 0.0183450743 0.0366901486 0.0529313208 0.105862642
10k 9800.0 10010.0 220000 0.0518817051 0.10376341 0.015913235 0.03182647 0.0165020489 0.0330040979 0.0511376308 0.102275262
10k 9800.0 10010.0 240000 0.0504963597 0.100992719 0.0150161012 0.0300322024 0.0155411568 0.0310823137 0.0497352735 0.099470547
10k 9800.0 10010.0 260000 0.0618428427 0.123685685 0.0186616919 0.0373233838 0.0192059023 0.0384118047 0.060837606 0.121675212
10k 9800.0 10010.0 280000 0.0607005397 0.121401079 0.0193185036 0.0386370072 0.0197497473 0.0394994946 0.0597050672 0.119410134
10k 9800.0 10010.0 300000 0.0598325439 0.119665088 0.0204853242 0.0409706485 0.0207678235 0.041535647 0.0587017007 0.117403401
10k 9800.0 10010.0 320000 0.0591282696 0.118256539 0.0219371109 0.0438742219 0.022260025 0.04452005 0.057991343 0.115982686
10k 9800.0 10010.0 350000 0.0621640959 0.124328192 0.025948693 0.0518973861 0.026062308 0.0521246159 0.0608983629 0.121796726
10k 9800.0 10010.0 370000 0.061731702 0.123463404 0.0276898577 0.0553797153 0.0277203374 0.0554406748 0.0604249363 0.120849873
10k 9800.0 10010.0 400000 0.0612083955 0.122416791 0.0302088707 0.0604177413 0.0302156609 0.0604313217 0.0598944315 0.119788863
10k 9800.0 10010.0 430000 0.0608473898 0.12169478 0.0325764421 0.0651528843 0.0325449059 0.0650898118 0.059499479 0.118998958
10k 9800.0 10010.0 450000 0.0606271306 0.121254261 0.0340660556 0.0681321112 0.0339872914 0.0679745827 0.0593030021 0.118606004
10k 9800.0 10010.0 480000 0.0604614127 0.120922825 0.0361898376 0.0723796751 0.0360631905 0.072126381 0.0590721443 0.118144289
10k 9800.0 10010.0 500000 0.0603343169 0.120668634 0.0374475683 0.0748951365 0.0373678671 0.0747357343 0.0589357027 0.117871405
10k 9800.0 10010.0 530000 0.0602250309 0.120450062 0.039214301 0.0784286019 0.0391496054 0.0782992108 0.0588121432 0.117624286
10k 9800.0 10010.0 550000 0.0601439703 0.120287941 0.0402775061 0.0805550122 0.0402384803 0.0804769607 0.0587392964 0.117478593
10k 9800.0 10010.0 580000 0.0600874571 0.120174914 0.0418283508 0.0836567016 0.0417568005 0.0835136009 0.0586671669 0.117334334
10k 9800.0 10010.0 600000 0.0600586855 0.120117371 0.0427919742 0.0855839483 0.0426875073 0.0853750147 0.0586313848 0.11726277
10k 9800.0 10010.0 650000 0.0600403136 0.120080627 0.0449047479 0.0898094958 0.04483048 0.08966096 0.0586021816 0.117204363
10k 9800.0 10010.0 700000 0.060060306 0.120120612 0.0466940994 0.0933881988 0.0466128992 0.0932257984 0.0585634925 0.117126985
33k 32990.0 32940.0 10000 0.0564700682 0.112940136 0.0538955676 0.107791135 0.0540478622 0.108095724 0.0566145228 0.113229046
33k 32990.0 32940.0 20000 0.0561244906 0.112248981 0.0512898349 0.10257967 0.0511634613 0.102326923 0.0566707173 0.113341435
33k 32990.0 32940.0 30000 0.056794017 0.113588034 0.0464400257 0.0928800514 0.0471493583 0.0942987166 0.0564361284 0.112872257
33k 32990.0 32940.0 50000 0.0548217827 0.109643565 0.0379357932 0.0758715864 0.0384440332 0.0768880664 0.054633742 0.109267484
33k 32990.0 32940.0 80000 0.0642051562 0.128410312 0.0358401784 0.0716803567 0.0366415971 0.0732831941 0.0636552759 0.127310552
33k 32990.0 32940.0 100000 0.0601368146 0.120273629 0.0306027933 0.0612055865 0.0315334747 0.0630669494 0.0594004866 0.118800973
33k 32990.0 32940.0 120000 0.0564066428 0.112813286 0.0276644747 0.0553289494 0.0286309904 0.0572619807 0.0556465443 0.111293089
33k 32990.0 32940.0 140000 0.0533780004 0.106756001 0.0264329181 0.0528658362 0.0273379914 0.0546759827 0.0524855255 0.104971051
33k 32990.0 32940.0 160000 0.0564251116 0.112850223 0.0291297245 0.0582594489 0.0300359254 0.0600718509 0.0553653089 0.110730618
33k 32990.0 32940.0 180000 0.0540845661 0.108169132 0.0295502535 0.0591005071 0.0303176412 0.0606352823 0.0530135804 0.106027161
33k 32990.0 32940.0 200000 0.0629221842 0.125844368 0.0365196761 0.0730393522 0.0372797955 0.0745595911 0.0616542917 0.123308583
33k 32990.0 32940.0 220000 0.0609609489 0.121921898 0.037479628 0.074959256 0.0381001151 0.0762002302 0.0596766539 0.119353308
33k 32990.0 32940.0 240000 0.0592908957 0.118581791 0.0384032597 0.0768065194 0.0389280146 0.0778560292 0.057966188 0.115932376
33k 32990.0 32940.0 260000 0.0578443283 0.115688657 0.0392414732 0.0784829464 0.0396884165 0.0793768331 0.0565435273 0.113087055
33k 32990.0 32940.0 280000 0.0566872364 0.113374473 0.040065193 0.0801303861 0.0404200299 0.0808400599 0.0553425981 0.110685196
33k 32990.0 32940.0 300000 0.0556446136 0.111289227 0.0407612463 0.0815224926 0.0410769916 0.0821539832 0.0543365997 0.108673199
33k 32990.0 32940.0 320000 0.0547688704 0.109537741 0.0413727779 0.0827455558 0.0416832226 0.0833664451 0.0534384732 0.106876946
33k 32990.0 32940.0 350000 0.0537016819 0.107403364 0.0422320003 0.0844640006 0.0423794802 0.0847589604 0.0523537079 0.104707416
33k 32990.0 32940.0 370000 0.0530865925 0.106173185 0.0427034894 0.0854069787 0.0428309278 0.0856618556 0.051747451 0.103494902
33k 32990.0 32940.0 400000 0.0522910699 0.10458214 0.043310668 0.086621336 0.0434041701 0.0868083402 0.0509518207 0.101903641
33k 32990.0 32940.0 430000 0.051641685 0.10328337 0.043805874 0.0876117481 0.0438858327 0.0877716654 0.0503089499 0.1006179
33k 32990.0 32940.0 450000 0.051281918 0.102563836 0.044118453 0.0882369061 0.0441694016 0.0883388033 0.0499450169 0.0998900337
33k 32990.0 32940.0 480000 0.0507768603 0.101553721 0.0444624995 0.088924999 0.0445344611 0.0890689221 0.0494603502 0.0989207005
33k 32990.0 32940.0 500000 0.0505014469 0.101002894 0.0446880897 0.0893761794 0.0447192479 0.0894384959 0.0491503786 0.0983007571
33k 32990.0 32940.0 530000 0.0501284544 0.100256909 0.0449800968 0.0899601937 0.0450043162 0.0900086324 0.048793299 0.097586598
33k 32990.0 32940.0 550000 0.0499145867 0.0998291734 0.0451367807 0.0902735615 0.0451784707 0.0903569414 0.0485841954 0.0971683908
33k 32990.0 32940.0 580000 0.0496203475 0.099240695 0.045357792 0.0907155841 0.0453818356 0.0907636713 0.0482945546 0.0965891092
33k 32990.0 32940.0 600000 0.0494367552 0.0988735105 0.045470945 0.0909418901 0.0455118214 0.0910236429 0.0480985525 0.0961971051
33k 32990.0 32940.0 650000 0.0489236885 0.0978473771 0.0455777228 0.0911554457 0.0458424966 0.0916849932 0.0477937854 0.0955875708
33k 32990.0 32940.0 700000 0.0486419402 0.0972838804 0.0458013757 0.0916027514 0.046068772 0.0921375441 0.0475141527 0.0950283054
100k 99770.0 99330.0 10000 0.0571721826 0.114344365 0.0534815128 0.106963026 0.0538124287 0.107624857 0.0567739285 0.113547857
100k 99770.0 99330.0 20000 0.0576079529 0.115215906 0.0502431532 0.100486306 0.0506649291 0.101329858 0.0571411458 0.114282292
100k 99770.0 99330.0 30000 0.0580552393 0.116110479 0.0459858713 0.0919717426 0.0471287324 0.0942574647 0.0570311225 0.114062245
100k 99770.0 99330.0 50000 0.0553106926 0.110621385 0.0404957812 0.0809915624 0.0420178293 0.0840356586 0.0542690973 0.108538195
100k 99770.0 99330.0 80000 0.0628412903 0.125682581 0.0465354584 0.0930709168 0.0486899395 0.0973798791 0.0612606274 0.122521255
100k 99770.0 99330.0 100000 0.0579908584 0.115981717 0.0443161912 0.0886323825 0.0463343215 0.0926686429 0.0563815927 0.112763185
100k 99770.0 99330.0 120000 0.0539421595 0.107884319 0.042684211 0.085368422 0.0444326287 0.0888652573 0.0524562691 0.104912538
100k 99770.0 99330.0 140000 0.0507440136 0.101488027 0.0414620732 0.0829241464 0.0429218026 0.0858436051 0.0493514342 0.0987028684
100k 99770.0 99330.0 160000 0.0535756907 0.107151381 0.0450504175 0.090100835 0.0464400381 0.0928800762 0.0521105852 0.10422117
100k 99770.0 99330.0 180000 0.0513640654 0.102728131 0.0442725063 0.0885450125 0.0454495517 0.0908991035 0.0499752305 0.099950461
100k 99770.0 99330.0 200000 0.0495972447 0.0991944894 0.0436299367 0.0872598734 0.0446862832 0.0893725663 0.0482815782 0.0965631565
100k 99770.0 99330.0 220000 0.0481761292 0.0963522584 0.0431364343 0.0862728685 0.0440389433 0.0880778866 0.0469106835 0.093821367
100k 99770.0 99330.0 240000 0.0470344092 0.0940688184 0.0427528918 0.0855057836 0.0435385725 0.0870771451 0.0458568371 0.0917136743
100k 99770.0 99330.0 260000 0.0460932281 0.0921864562 0.0424246754 0.0848493509 0.0431455998 0.0862911997 0.044974505 0.0899490099
100k 99770.0 99330.0 280000 0.0453060951 0.0906121902 0.0421499726 0.0842999451 0.0428506847 0.0857013694 0.0442664454 0.0885328908
100k 99770.0 99330.0 300000 0.0446389237 0.0892778474 0.0419255079 0.0838510158 0.0425536247 0.0851072494 0.0436346285 0.087269257
100k 99770.0 99330.0 320000 0.0440823226 0.0881646453 0.0417414707 0.0834829414 0.0422883496 0.0845766991 0.043066774 0.086133548
100k 99770.0 99330.0 350000 0.0434035796 0.0868071591 0.0415122459 0.0830244918 0.0420165714 0.0840331427 0.0424218897 0.0848437795
100k 99770.0 99330.0 370000 0.0430226541 0.0860453082 0.0413775655 0.082755131 0.0418596698 0.0837193396 0.0420710154 0.0841420308
100k 99770.0 99330.0 400000 0.0425706039 0.0851412078 0.0412510243 0.0825020485 0.0416648624 0.0833297249 0.0416165582 0.0832331165
100k 99770.0 99330.0 430000 0.0421943333 0.0843886666 0.0411111629 0.0822223258 0.0415005142 0.0830010283 0.0412343008 0.0824686016
100k 99770.0 99330.0 450000 0.0419631174 0.0839262348 0.041033667 0.0820673341 0.0414411592 0.0828823184 0.0410665955 0.0821331911
100k 99770.0 99330.0 480000 0.0416844694 0.0833689388 0.0409321175 0.0818642349 0.0412915994 0.0825831987 0.0407770529 0.0815541057
100k 99770.0 99330.0 500000 0.0414775753 0.0829551505 0.0408298084 0.0816596168 0.0412236229 0.0824472459 0.0406181385 0.0812362769
100k 99770.0 99330.0 530000 0.0412923944 0.0825847889 0.0407651122 0.0815302244 0.0411435959 0.0822871919 0.0404263602 0.0808527205
100k 99770.0 99330.0 550000 0.0411682686 0.0823365372 0.0407303907 0.0814607814 0.0410677477 0.0821354955 0.0402786219 0.0805572439
100k 99770.0 99330.0 580000 0.0409995129 0.0819990258 0.0406687235 0.081337447 0.0410186531 0.0820373062 0.0401272992 0.0802545984
100k 99770.0 99330.0 600000 0.0409006468 0.0818012935 0.0406152431 0.0812304862 0.0409521301 0.0819042601 0.0400212311 0.0800424621
100k 99770.0 99330.0 650000 0.0406832475 0.0813664949 0.0405266134 0.0810532268 0.0408309307 0.0816618614 0.0397767143 0.0795534286
100k 99770.0 99330.0 700000 0.040503018 0.081006036 0.0404403495 0.0808806989 0.0407561994 0.0815123989 0.0396175851 0.0792351702
VGEN values used for the measurements
f100Ω330Ω1k3.3k10k33k100k
10k0.70.50.50.70.70.70.7
20k0.70.50.50.70.70.70.7
30k0.70.50.50.70.70.70.7
50k0.80.70.70.70.70.70.7
80k1.00.70.70.80.90.90.9
100k1.20.80.90.80.90.90.9
120k1.20.80.90.90.90.90.9
140k1.61.11.11.00.90.90.9
160k1.51.11.11.01.01.01.0
180k1.31.21.11.21.01.01.0
200k1.01.51.41.21.21.21.0
220k1.01.51.41.41.21.21.0
240k1.01.51.41.41.21.21.0
260k1.01.51.41.41.51.21.0
280k1.01.61.51.51.51.21.0
300k1.21.61.51.51.51.21.0
320k1.21.61.51.51.51.21.0
350k1.21.61.51.71.61.21.0
370k1.21.62.01.71.61.21.0
400k1.22.02.02.01.61.21.0
430k2.02.02.02.01.61.21.0
450k2.02.02.02.01.61.21.0
480k2.02.02.32.51.61.21.0
500k2.02.02.32.51.61.21.0
530k2.02.02.32.51.61.21.0
550k2.02.02.32.51.61.21.0
580k2.02.02.32.51.61.21.0
600k2.02.02.32.51.61.21.0
650k2.02.02.32.51.61.21.0
700k2.02.02.32.51.61.21.0

Looking for information about DUT impedance

One of the goals of this campaign is to determine whether, in addition to the Bode plot itself, the signals already acquired can provide indirect information about DUT impedance.

During each measurement I know Vgen and simultaneously measure VOUT and VSENSE, both in amplitude and phase. These data describe not only the DUT transfer function, but also how the generated signal is actually transferred through the transformer and the injection branch.

The idea is therefore to begin looking for systematic relationships between Vgen, the voltage actually present on the injection branch, frequency, and divider impedance. I do not necessarily expect a single quantity to determine DUT impedance by itself, but a sufficiently broad characterization could provide useful parameters to combine later with the other measurement data.

At the same time, this type of analysis can help me better understand the behavior of the GX LII-2 itself: how much of the voltage produced by the generator actually reaches the injection branch, how this ratio changes with frequency, and how strongly it depends on the load connected to the secondary.

I built a first intuitive table to see whether useful information could be obtained from the ratio between Vgen and the signal actually present across Rinj (18 Ω). The differential voltage VOUT​−VSENSE​ is calculated vectorially, taking phase into account, rather than as a simple difference between the two measured amplitudes:

|Vd| = √( VOUT2 + VSENSE2 − 2 VOUT VSENSE cos φ )

This is important because, when OUT and SENSE are nearly in phase opposition, the differential voltage can be close to the sum of the two amplitudes, rather than to their simple numerical difference.

Resulting table
Nominal series Frequency [kHz] VGEN [Vpp] |VOUT−VSENSE| A [mVpp] |VOUT−VSENSE| B [mVpp] A/B average [mVpp]
100R 10 0.7 207.014 207.152 207.083
20 0.7 201.340 201.492 201.416
30 0.7 193.441 193.684 193.562
50 0.8 197.156 197.979 197.568
80 1 201.042 202.355 201.698
100 1.2 211.765 213.278 212.521
120 1.2 187.894 189.404 188.649
140 1.6 220.838 222.802 221.820
160 1.5 187.721 189.335 188.528
180 1.3 147.420 148.633 148.027
200 1 103.036 104.009 103.522
220 1 94.624 95.499 95.062
240 1 87.451 88.203 87.827
260 1 81.223 81.922 81.572
280 1 75.797 76.444 76.120
300 1.2 85.824 86.563 86.194
320 1.2 80.746 81.443 81.095
350 1.2 74.128 74.790 74.459
370 1.2 70.281 70.924 70.603
400 1.2 65.197 65.790 65.494
430 2 101.514 102.516 102.015
450 2 97.111 98.110 97.611
480 2 91.233 92.152 91.693
500 2 87.678 88.549 88.114
530 2 82.848 83.656 83.252
550 2 79.904 80.690 80.297
580 2 75.851 76.612 76.231
600 2 73.370 74.111 73.741
650 2 67.857 68.537 68.197
700 2 63.143 63.718 63.431
330R 10 0.5 164.710 164.770 164.740
20 0.5 160.060 160.101 160.080
30 0.5 153.486 153.436 153.461
50 0.7 181.783 182.065 181.924
80 0.7 149.203 149.436 149.320
100 0.8 149.937 149.981 149.959
120 0.8 132.198 132.384 132.291
140 1.1 162.373 162.567 162.470
160 1.1 145.866 146.036 145.951
180 1.2 144.379 144.533 144.456
200 1.5 164.620 164.872 164.746
220 1.5 151.351 151.515 151.433
240 1.5 139.870 140.106 139.988
260 1.5 129.919 130.259 130.089
280 1.6 129.329 129.629 129.479
300 1.6 121.242 121.576 121.409
320 1.6 114.050 114.354 114.202
350 1.6 104.773 105.071 104.922
370 1.6 99.346 99.575 99.461
400 2 115.318 115.680 115.499
430 2 107.629 107.855 107.742
450 2 103.007 103.219 103.113
480 2 96.765 96.954 96.859
500 2 92.993 93.154 93.073
530 2 87.889 88.001 87.945
550 2 84.794 84.877 84.836
580 2 80.513 80.589 80.551
600 2 77.899 77.965 77.932
650 2 72.067 72.068 72.067
700 2 67.050 67.015 67.033
1k 10 0.5 166.523 166.282 166.403
20 0.5 161.920 161.659 161.790
30 0.5 155.282 155.083 155.183
50 0.7 184.184 184.163 184.173
80 0.7 151.463 151.427 151.445
100 0.9 170.978 171.114 171.046
120 0.9 151.001 151.137 151.069
140 1.1 165.034 165.189 165.111
160 1.1 148.272 148.425 148.348
180 1.1 134.345 134.526 134.435
200 1.4 156.385 156.575 156.480
220 1.4 143.708 143.929 143.818
240 1.4 132.886 133.039 132.963
260 1.4 123.452 123.685 123.569
280 1.5 123.397 123.642 123.519
300 1.5 115.684 115.908 115.796
320 1.5 108.870 109.029 108.949
350 1.5 100.063 100.067 100.065
370 2 126.650 126.661 126.655
400 2 117.472 117.466 117.469
430 2 109.589 109.597 109.593
450 2 104.888 104.891 104.890
480 2.3 113.626 113.416 113.521
500 2.3 109.175 108.979 109.077
530 2.3 103.149 102.972 103.061
550 2.3 99.564 99.356 99.460
580 2.3 94.551 94.272 94.412
600 2.3 91.493 91.218 91.356
650 2.3 84.669 84.372 84.521
700 2.3 78.797 78.372 78.584
3.3k 10 0.7 220.218 220.177 220.197
20 0.7 214.297 214.365 214.331
30 0.7 206.002 206.084 206.043
50 0.7 184.872 185.150 185.011
80 0.8 174.362 174.364 174.363
100 0.8 153.071 153.160 153.116
120 0.9 151.937 152.126 152.031
140 1 150.366 150.529 150.448
160 1 135.173 135.181 135.177
180 1.2 147.901 147.896 147.898
200 1.2 135.015 135.029 135.022
220 1.4 144.910 144.768 144.839
240 1.4 133.981 133.848 133.915
260 1.4 124.548 124.301 124.425
280 1.5 124.551 124.259 124.405
300 1.5 116.828 116.478 116.653
320 1.5 110.006 109.499 109.753
350 1.7 114.554 113.943 114.248
370 1.7 108.660 108.026 108.343
400 2 118.846 117.918 118.382
430 2 110.943 109.906 110.425
450 2 106.232 105.090 105.661
480 2.5 125.020 123.461 124.240
500 2.5 120.205 118.562 119.384
530 2.5 113.739 111.935 112.837
550 2.5 109.775 107.906 108.840
580 2.5 104.338 102.349 103.344
600 2.5 101.008 99.009 100.008
650 2.5 93.618 91.396 92.507
700 2.5 87.262 84.834 86.048
10k 10 0.7 220.075 220.970 220.523
20 0.7 214.071 215.387 214.729
30 0.7 205.932 206.882 206.407
50 0.7 184.918 185.831 185.375
80 0.9 195.706 196.229 195.967
100 0.9 172.153 172.327 172.240
120 0.9 152.245 152.174 152.209
140 0.9 135.681 135.492 135.587
160 1 135.443 135.152 135.297
180 1 122.825 122.430 122.627
200 1.2 135.454 134.839 135.147
220 1.2 124.553 123.828 124.190
240 1.2 115.192 114.369 114.781
260 1.5 134.034 132.869 133.452
280 1.5 125.182 123.938 124.560
300 1.5 117.447 116.079 116.763
320 1.5 110.584 109.144 109.864
350 1.6 108.473 106.788 107.630
370 1.6 102.973 101.181 102.077
400 1.6 95.652 93.760 94.706
430 1.6 89.361 87.347 88.354
450 1.6 85.577 83.532 84.555
480 1.6 80.525 78.372 79.448
500 1.6 77.445 75.219 76.332
530 1.6 73.301 70.977 72.139
550 1.6 70.778 68.405 69.591
580 1.6 67.295 64.857 66.076
600 1.6 65.167 62.686 63.927
650 1.6 60.445 57.856 59.151
700 1.6 56.390 53.691 55.040
33k 10 0.7 220.656 221.314 220.985
20 0.7 214.720 215.601 215.161
30 0.7 206.437 207.161 206.799
50 0.7 185.298 185.830 185.564
80 0.9 196.256 196.148 196.202
100 0.9 172.621 172.176 172.399
120 0.9 152.547 151.961 152.254
140 0.9 136.018 135.240 135.629
160 1 135.843 134.825 135.334
180 1 123.196 122.054 122.625
200 1.2 135.906 134.430 135.168
220 1.2 125.001 123.406 124.203
240 1.2 115.612 113.953 114.782
260 1.2 107.475 105.773 106.624
280 1.2 100.424 98.684 99.554
300 1.2 94.213 92.454 93.334
320 1.2 88.736 86.809 87.773
350 1.2 81.569 79.614 80.591
370 1.2 77.407 75.431 76.419
400 1.2 71.889 69.886 70.887
430 1.2 67.112 65.076 66.094
450 1.2 64.275 62.235 63.255
480 1.2 60.459 58.370 59.414
500 1.2 58.160 56.021 57.090
530 1.2 55.018 52.857 53.938
550 1.2 53.124 50.947 52.036
580 1.2 50.519 48.306 49.413
600 1.2 48.899 46.672 47.786
650 1.2 45.335 43.119 44.227
700 1.2 42.293 40.023 41.158
100k 10 0.7 221.300 221.158 221.229
20 0.7 215.557 215.343 215.450
30 0.7 207.176 206.882 207.029
50 0.7 185.927 185.434 185.681
80 0.9 196.727 195.979 196.353
100 0.9 172.971 172.040 172.506
120 0.9 152.816 151.933 152.375
140 0.9 136.145 135.172 135.658
160 1 135.981 134.870 135.426
180 1 123.246 122.124 122.685
200 1 112.520 111.406 111.963
220 1 103.425 102.305 102.865
240 1 95.663 94.516 95.089
260 1 88.908 87.806 88.357
280 1 83.047 81.931 82.489
300 1 77.892 76.759 77.326
320 1 73.270 72.176 72.723
350 1 67.349 66.247 66.798
370 1 63.860 62.803 63.332
400 1 59.296 58.190 58.743
430 1 55.344 54.258 54.801
450 1 52.973 51.896 52.435
480 1 49.821 48.705 49.263
500 1 47.895 46.783 47.339
530 1 45.289 44.187 44.738
550 1 43.718 42.610 43.164
580 1 41.547 40.420 40.984
600 1 40.216 39.082 39.649
650 1 37.265 36.115 36.690
700 1 34.718 33.557 34.138

A normalized parameter for comparing different impedances

To make the different series easier to compare, I then normalized the differential voltage measured across Rinj to the generator amplitude. I therefore defined, separately for acquisitions A and B:

KA(f,R) = |VOUT − VSENSE|A VGEN

and

KB(f,R) = |VOUT − VSENSE|B VGEN

I then also calculated the average value:

Kavg(f,R) = KA + KB 2

The average is calculated in the linear domain, not in dB. In this way, K directly represents the fraction of the voltage set on the generator that appears as the actual differential voltage across the injection branch.

To make the comparison easier to read, instead of including the entire numerical matrix in the body of the article I chose to plot KA​, KB​ and Kavg as functions of frequency for all seven resistive pairs. The complete data remain available as a downloadable CSV file.

  • Rapporto tra tensione differenziale misurata sul ramo di iniezione e Vgen per la configurazione A, riportato per tutte le sette coppie resistive.
    Rapporto tra tensione differenziale misurata sul ramo di iniezione e Vgen per la configurazione A, riportato per tutte le sette coppie resistive.

The three graphs show a fairly clear pattern. At lower frequencies, the curves for the different resistance values are more widely separated, while they progressively converge as frequency increases. The dependence on DUT impedance therefore appears stronger in the lower part of the band, whereas at higher frequencies the injection-transfer behavior becomes much more similar among the different resistive configurations.

It is also interesting to note that KA​ and KB​ show very similar trends and that their average retains the same overall structure. This makes K_avg​ a particularly useful quantity for continuing the analysis, because it reduces the weight of differences associated with A/B orientation and allows the common behavior of the system to be examined more directly.

For the moment, I do not consider this ratio a direct measurement of DUT impedance. The goal is to determine whether there is a sufficiently regular relationship between Vgen, the actual injected voltage, frequency, and load impedance that could later be used as additional information when characterizing both the DUT and the GX LII-2 itself.

It should also be remembered that the curves shown here were not obtained with Vgen held constant throughout the sweep: the generator amplitude was changed as a function of frequency to maintain an adequate signal level. Frequency and Vgen are therefore not yet experimentally separated variables in this analysis of K.

It is important to distinguish this analysis from the tests performed in recent days on the influence of Vgen on the Bode plot. In those tests I experimentally verified that, as long as the system remains in its linear region, using a fixed Vgen or varying it to improve the signal level does not significantly change the final magnitude and phase result.

The parameter K introduced here is a different quantity: it directly describes the ratio between the differential voltage across the injection branch and the voltage set on the generator. Its possible independence from Vgen has not yet been experimentally verified.

The available measurements show a clear dependence on frequency and some separation among the different impedances, but at this stage I cannot yet assume that:

K = K(f, R)

rather than, more generally,

K = K(f, R, VGEN)

Separating these dependencies will therefore require a dedicated test, keeping frequency and divider constant while varying only Vgen. This does not call into question the previous verification that the Bode plot is independent of Vgen: it concerns only the new parameter K and its possible use as additional information about the behavior of the injection circuit and, potentially, DUT impedance.

It is therefore perfectly possible to have, at the same time:

H = H(f, R)

independent of VGEN, but:

K = K(f, R, VGEN)

Overall results of the resistive campaign

With the campaign on the seven resistive dividers completed, I can finally compare all configurations from 100 Ω to 100 kΩ in the same way.

The following graphs show, for each divider, the magnitude and phase obtained in the two A and B configurations, the result of their combination, and the reference obtained from the LTspice simulation.

An important result is already evident from a first visual inspection: the final measurement obtained from the A/B combination is much more robust than the individual A and B measurements. The latter can diverge substantially as frequency and impedance increase, while the combined result remains generally close to the behavior predicted by the simulation.

This does not, of course, mean that the system is now fully characterized. This campaign concerns only resistive impedances and does not yet allow the same conclusions to be extended to DUTs whose impedance at the injection point has a significant reactive component. This is one of the reasons why the calibration bench also includes a capacitive section, which I will use in a later phase.

For the conditions explored so far, however, the results are beginning to show that the A/B method can keep the final measurement sufficiently stable even when the two acquisitions, considered separately, become strongly dependent on secondary-winding orientation.

Magnitude

In the first gallery I collected the magnitude plots for all seven resistive pairs, ordered from 100 Ω to 100 kΩ. This makes it possible to follow directly how the separation between A and B evolves with impedance and frequency and, above all, to compare it with the behavior of the compensated final measurement.

  • Grafico Bode del modulo del partitore 100 ohm con misure A e B, media A/B e riferimento LTspice.
    Modulo della funzione di trasferimento per il partitore resistivo 100 Ω–100 Ω. Le misure A e B si separano progressivamente con la frequenza, mentre la combinazione A/B rimane molto vicina al riferimento LTspice.

Phase

The second gallery shows the phase plots in the same order. Here too, the main point is to compare the evolution of configurations A and B with the result obtained after combining them.

  • GX LII-2 – Bode fase partitore 100 Ω–100 Ω
    Fase misurata sul partitore 100 Ω–100 Ω. L’inversione A/B produce deviazioni opposte, mentre la fase mediata rimane prossima al comportamento previsto dalla simulazione.

Acquisition diagnostics

To complete the results, I also include the plots produced by the Octave script for coherent waveform-deformation diagnostics. These plots do not directly enter the Bode calculation, but provide an additional check on acquisition quality and on the possible presence of compression or systematic waveform deformation.

  • Grafico diagnostico della deformazione coerente dei segnali VSENSE e VOUT per il partitore 100 ohm.
    Diagnostica della deformazione coerente delle acquisizioni A e B per il partitore 100 Ω–100 Ω. Il controllo è utilizzato come indicatore complementare della qualità delle acquisizioni.

To avoid judging the effectiveness of A/B compensation only by visual inspection, I also summarized the deviation of the final measurement from the LTspice model over the entire acquired bandwidth. For each divider, the table reports the mean absolute error and the maximum deviation observed across the 30 measurement points.

Dividermean |ΔM| [dB]max |ΔM| [dB]mean |Δφ| [°]max |Δφ| [°]
100 Ω0.0650.1040.4520.963
330 Ω0.0640.1010.4500.754
1 kΩ0.1590.3970.7571.163
3.3 kΩ0.1060.2940.6451.684
10 kΩ0.0920.2020.2620.737
33 kΩ0.1470.2330.3000.924
100 kΩ0.2150.3540.4381.615

Across all seven series, the mean absolute magnitude error remains between about 0.064 and 0.215 dB, while the phase error remains between about 0.26° and 0.76°. The maximum deviations observed over the entire campaign also remain below about 0.40 dB in magnitude and 1.7° in phase. These figures therefore provide a quantitative measure of what is already evident in the plots: the deviations of the individual A and B measurements can be very large, but the residual after combining them remains much smaller.

Revisiting the 33 kΩ case

These results also lead me to revisit a point made in the first article in the series, when characterization was still at an early stage.

For the 33 kΩ divider I wrote:

Here too, reversing the secondary highlights an asymmetric component, but the A/B average no longer matches the response predicted by the simulation. A component of the error therefore remains in both secondary orientations and cannot be eliminated by reversal.

I then continued by observing that:

The tests indicate that there are at least two different contributions: one associated with transformer asymmetry, which changes sign when the secondary is reversed and can therefore be greatly reduced by combining A and B, and a second contribution common to both measurements, which becomes important under certain impedance conditions.

That description accurately reflected what emerged from the first available acquisitions. The complete resistive campaign now makes it possible, however, to put that initial interpretation into better perspective.

The large deviation of the A/B average observed at the time with the 33 kΩ divider does not reappear with the same magnitude in the new measurements. On the contrary, the current plots show that even when the individual A and B configurations begin to diverge strongly, their combination generally remains much closer to the LTspice reference.

This does not mean that every error common to the two configurations has disappeared. A residual after A/B compensation is still present and, as I will examine more closely shortly, has its own dependence on frequency and impedance. What has changed compared with the first observations is mainly its magnitude, which is considerably smaller than those initial 33 kΩ tests suggested.

I cannot retrospectively determine which single factor produced the deviation observed at that stage. The initial measurements were mainly exploratory, and the experimental setup was not yet being managed with the level of care achieved during this campaign.

During the tests it became clear just how sensitive these measurements are to bench conditions. The signals at OUT and SENSE can be only a few tens of millivolts and, under these conditions, ambient noise, common-mode currents, cable routing, connection quality, and other elements of the measurement chain can become comparable with the useful signal.

For the current campaign I therefore tried to reduce these error sources systematically, paying greater attention to wiring and grounding, eliminating unnecessary interference sources from the bench, using ferrites on the connections, and relying on Octave’s fundamental-component fit to extract magnitude and phase.

The problem encountered with the intermittent BNC connector was also a very concrete example of how an apparently minor defect can cause significant changes in acquisitions of this type.

I therefore do not regard the initial 33 kΩ result simply as a “bad measurement.” It was instead a useful step in the characterization because it showed how important it is to check the entire experimental chain before attributing a structure observed in the data to the DUT or the transformer.

In light of the current campaign, I can therefore say that, at least for the resistive loads explored, the A/B system is performing better than those early measurements suggested.

A residual of the combined measurement relative to the reference nevertheless remains, and its structure deserves closer examination.

A/B compensation and residual measurement error

The plots obtained for the seven resistive pairs clearly show a behavior already observed in the first tests: as frequency increases, the measurements made in the A and B configurations can move far away from the LTspice reference. The deviations, however, occur predominantly in opposite directions.

For this reason I do not interpret this component as an error common to both measurements, but as an error dependent on transformer orientation, essentially antisymmetric with respect to A/B reversal.

A very simple model, which I do not consider exact but which describes qualitatively what I observe quite well, is:

HA ≃ HDUT · E
HB ≃ HDUT E

where E schematically represents the error component that changes reciprocally when the secondary terminals are reversed.

In this ideal model, combining the two measurements gives:

HAB ≃ √(HA HB) ≃ HDUT

In my case the combination is performed in the logarithmic domain for magnitude and after alignment of the phase branches; the meaning is nevertheless equivalent to a geometric mean of the linear quantities.

A particularly clear example can already be seen in the 100 Ω series: at 700 kHz measurement A reaches about −2.60 dB, while B is about +2.51 dB; after A/B combination the result returns to about −0.044 dB, with a phase of about 179.45°.

The A/B average is therefore not simply reducing random noise: the results are highly consistent with cancellation of a component that is nearly reciprocal with respect to transformer reversal.

What remains after this compensation is the quantity that, at least for now, I want to define as the common residual of the measurement relative to the reference. This residual cannot automatically be attributed to either the transformer or the DUT. If I represent it schematically as an overall factor in the measurement chain, I can imagine something like:

Eresidual ≃ Etransformer · Eprobes · Echannels · Ewiring · Efixture · …

This expression is deliberately qualitative: its main purpose is to emphasize that the observed residual belongs to the entire DUT + measurement-system chain, and not necessarily to a single element.

The first practical conclusion from the resistive campaign is nevertheless positive. Under the conditions characterized so far, A/B compensation keeps the residual small enough for me to consider the GX LII-2 already usable, at least as a first approximation, for DUTs in which the impedance seen from the injection point is predominantly resistive and falls within the explored range.

This conclusion cannot yet be extended to impedances with a significant reactive component. This is precisely one of the reasons why the calibration bench also includes a capacitive section: I will have to verify whether the same cancellation capability is retained when the impedance becomes complex.

Another interesting aspect is that the residual of the A/B measurement does not appear to behave like a simple calibration constant. The plots show dependencies on both frequency and impedance. In some regions, especially at lower impedances and below about 100 kHz, small non-monotonic structures are also visible. At present I cannot determine whether these are actual resonances: they could result from interactions among the transformer, parasitic capacitances and inductances, Rinj, wiring and, more generally, the measurement fixture, as well as the probes and acquisition chain.

In the future I would therefore like to study the residual not only as an error to be corrected, but also as a possible observable quantity capable of providing information about both the DUT and the behavior of the measurement system itself. I will not try to build such a model yet: this first campaign is intentionally exploratory.

For the moment, the practical result is simpler: the individual A and B measurements can become strongly orientation-dependent, while their combination remains much more stable and close to the simulated reference.

Global FFT analysis of the A/B acquisitions

As a final check on the resistive campaign, I also used the acquisitions already available for a broader spectral analysis. The goal was not to produce a separate FFT for every CSV: with dozens of frequencies and two A/B configurations for each divider, this would have produced hundreds of spectra that were difficult to compare. I therefore chose to build a GNU Octave script that automatically summarized the spectral content of the entire campaign for each divider, while still keeping configurations A and B separate.

For each CSV, the script knows the test frequency from the same association file used for Bode processing. Both channels are analyzed, with CH1 = VSENSE and CH2 = VOUT; the final summary retains the channel on which a given component reached its highest amplitude.

The important point is that the fundamental is not removed simply by zeroing the nearest FFT bin. Instead, for each acquisition a time-domain fit is performed

x(t) = A sin(2πf0t) + B cos(2πf0t) + C

and the FFT is then performed on the residual

r(t) = x(t) − xfit(t)

In this way, both the DC component and the fundamental at the exact frequency set for that measurement are removed, greatly reducing the risk that the fundamental and its spectral leakage dominate the residual spectrum. The harmonics 2f0​, 3f0​, etc. are intentionally left in place and can therefore be identified by the analysis.

Before the FFT, a Hann window is applied and its coherent gain is compensated; a single-sided spectrum expressed in Vpk is then obtained. To compare all acquisitions directly, the script also selects the most common Increment value and a common number of samples so that the spectra share the same frequency grid. In the typical case of these acquisitions, with Δt = 4 ns and 300000 samples, this gives 250 MS/s, a duration of about 1.2 ms, a resolution of about 833.3 Hz per bin, and a Nyquist frequency of 125 MHz.

The next step is perhaps the most distinctive aspect of this analysis. The spectra from the different acquisitions are not averaged. Instead, for each bin the maximum amplitude encountered over the entire campaign is retained:

SA(f) = maxi |XA,i(f)|

SB(f) = maxi |XB,i(f)|

This produces two maximum envelopes, one for A and one for B. These plots do not represent the system’s “average spectrum”; rather, they answer the question: which spectral lines managed to become most prominent at least once during the entire campaign?

The 20 strongest local maxima are then selected from the envelopes for A and B. For each maximum, the CSV files retain frequency, amplitude in Vpk and dBVpk, channel, the test frequency of the CSV that produced it, source filename, and classification. This keeps the graph compact while still allowing every peak to be traced back to the measurement from which it originated.

Some maxima in the first few kilohertz also appear in the lowest part of the spectrum. With the approximately 1.2 ms record duration used in these acquisitions, any 50 or 100 Hz components cannot be resolved as separate spectral lines: they appear mainly as slow variations within the record and can contribute to leakage in the first bins. For this reason, I do not currently assign a specific origin to the structures observed in this region.

A significant fraction of the peaks consists of harmonics

Analyzing the files fft_top_A.csv and fft_top_B.csv for all seven resistive dividers — 100 Ω, 330 Ω, 1 kΩ, 3.3 kΩ, 10 kΩ, 33 kΩ, and 100 kΩ — makes this characteristic particularly clear.

Considering all 280 peaks selected by the script, that is, 20 for each A/B configuration of the seven dividers, 100 are low-order harmonics identified directly from their relationship to the test frequency. Specifically:

81 second harmonics, 18 third harmonics, and one fourth harmonic.

This is therefore more than one third of the entire set of selected maxima, rather than a handful of isolated coincidences.

Some relationships appear repeatedly across different dividers and orientations. For example, 40 kHz in the 20 kHz test, 60 kHz in the 30 kHz test, 100 kHz in the 50 kHz test, 160 kHz in the 80 kHz test, and 200 kHz in the 100 kHz test are all 2f0​ components.

Similarly, 3f0​ components appear, such as 30 kHz in the 10 kHz test and 90 kHz in the 30 kHz test. The campaign also contains one component classified as a fourth harmonic, i.e. 4f0​.

This provides a useful internal check of the entire procedure. After intentionally removing the fundamental, the script recovers a large number of the components expected to remain when the waveform is not perfectly sinusoidal. The fundamental is subtracted by time-domain fitting, while 2f0​, 3f0​, and higher harmonics are deliberately left in the residual.

The observed harmonics are therefore not simply an artifact of using maximum envelopes: many of the selected lines retain a precise and repeatable relationship with the excitation frequency.

It should also be remembered that only the 20 strongest local maxima are shown for each A or B campaign. The absence of a particular harmonic from the ranking therefore does not mean that it is absent from the spectrum; it only means that, in the global envelope for that series, at least twenty structures reached a greater amplitude. The script also retains the complete aggregated spectrum, bin by bin.

Components that do not follow the test frequency

Alongside the harmonics, however, a second group of signals appears with completely different characteristics.

The line at 62.5 MHz is particularly evident: it appears among the selected maxima in both A and B for all seven dividers analyzed.

Across the entire campaign, its maximum amplitude lies approximately between 0.34 and 0.98 mVpk, corresponding to about −69.5 to −60.2 dBVpk.

A structure around 105.7 MHz is also extremely recurrent and can be observed across all the different impedances and in both A and B configurations. In this case it is more accurate to describe it as a group of spectral lines, because the script often selects several closely spaced maxima in the same region. The selected peak amplitudes are typically around −72 to −66 dBVpk.

A component close to 125 MHz appears in many, though not all, of the A/B rankings. The value is generally that of the bin immediately below 125 MHz, which is entirely consistent with the discrete nature of the FFT grid.

For two of these structures, the relationship with the sampling rate is particularly clear:

62.5 MHz = fs 4

and

125 MHz = fs 2 = fN

With fs​ = 250 MS/s, the second frequency therefore coincides with the Nyquist frequency.

The feature I find most interesting is not simply the absolute frequency values, but their recurrence across seven different impedances, two transformer orientations, and many excitation frequencies.

Unlike the low-order harmonics, these lines do not shift with f0​.

For this reason, I currently consider it plausible that at least some of these components belong to the acquisition chain rather than to the resistive DUT or the intentionally injected signal. Possible contributors include clocks, ADC operation, sampling architecture, internal digital processing, aliases, or other elements of the instrumentation.

The region around 105.7 MHz does not show an equally simple relationship with fs​, so the data currently available do not allow a specific origin to be assigned to it.

This intentionally remains an experimental hypothesis, not a definitive identification of the source.

Caution when interpreting the automatic classification

There is one final important detail in interpreting the CSV files.

The script checks whether the frequency of each maximum is compatible with an integer multiple of the test frequency of the CSV from which that maximum originates. This criterion works very well for low-order harmonics such as 2f0​, 3f0​, or 4f0​, but it can produce purely mathematical coincidences when the frequency ratio becomes very large.

I therefore do not regard these labels as proof that a component is harmonic in origin. To distinguish physically meaningful harmonics of the test signal from recurrent spectral lines, the harmonic order, the test frequency of the source file, and above all whether the line frequency follows f0​ or remains essentially fixed as the measurement changes must all be considered together.

This is precisely what makes the many 2f0​, 3f0​, and 4f0​ components much more significant: in those cases, the line frequency actually follows the excitation frequency.

What this analysis says about acquisition quality

This processing therefore adds another level to the characterization.

On one hand, it separates the intentional fundamental and reveals numerous harmonics consistent with the test signal, providing an independent check on the non-sinusoidal content of the acquisitions.

On the other hand, as the amplitude decreases further, components begin to emerge that do not follow the excitation frequency and instead appear to belong to the instrumentation or, more generally, to the acquisition chain.

The observed high-frequency lines range from a few hundred microvolts up to about 1 mVpk. The fact that structures of this amplitude are distinguishable and recurrent across all seven resistive campaigns does not, of course, demonstrate the absolute accuracy of the bench, but it does indicate that acquisition stability, signal-to-noise ratio, and numerical processing are sufficient to reveal phenomena much smaller than the fundamental used for the Bode measurement.

This is also an interesting methodological result: after working to reduce noise, connection problems, and common-mode interference, the acquisitions are consistent enough not only to derive magnitude and phase, but also to observe the residual spectral structure of the measurement.

The files produced by the script also retain both the peak rankings and the full aggregated envelope bin by bin; the PNG files are therefore only a compact representation of data that remain available for numerical analysis.

FFT analysis gallery

The following plots collect the results of the global FFT analysis for all seven resistive pairs, from 100 Ω to 100 kΩ. For each divider, the upper panel shows the 20 highest-amplitude residual components identified in campaign A, while the lower panel shows the corresponding result for campaign B. The intentional fundamental was removed before the FFT, so the plots contain harmonics, spurs, and other residual components that emerged from the full set of acquisitions.

  • Analisi FFT delle 20 componenti residue più forti nelle acquisizioni A e B del partitore resistivo da 100 ohm del GX LII-2.
    Analisi FFT globale del partitore da 100 Ω. Sono riportate le 20 componenti residue di maggiore ampiezza emerse nelle campagne A e B dopo la sottrazione della fondamentale intenzionale.

The Octave script and guide can be downloaded below; unfortunately, the ZIP archive containing all the CSV files is too large to upload here.

fft_partitore_e_guidaDownload

Conclusions

With this spectral analysis, I consider the first systematic GX LII-2 characterization campaign on resistive dividers complete.

The measurements made it possible to verify the robustness of A/B compensation, quantify the residual relative to the simulation, begin studying the relationship between Vgen and the actual injected voltage, and finally use the same acquisitions to examine residual spectral content beyond the fundamental.

The global FFT revealed a particularly interesting distinction: on one hand, numerous low-order harmonics appear that directly follow the test frequency; on the other, recurrent high-frequency lines emerge that are largely independent of the resistive DUT and f0​, potentially providing a signature of the acquisition chain.

I do not consider these results a definitive calibration of the instrument, but rather a first experimental characterization broad enough to begin distinguishing what belongs to the measurement, what depends on the injection system, and what may belong to the instrumentation used to observe it.

In the next few days I will perform measurements with the capacitive bench.

#A/B compensation #Bode measurements #calibration bench #common-mode noise #DUT impedance #FFT analysis #frequency response #GNU Octave #GX LII-2 #harmonic analysis #injection transfer #injection transformer #Loop Gain #LTspice #measurement residual #oscilloscope measurements #resistive dividers #spectral analysis

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