DIY capacitance measurement using simple RC bridge based technique - Page 1
Forum section: electronics / general

author: trobbins
author_rank: Frequent Contributor
timestamp: February 15, 2022, 03:51:52 am
content: This general topic has come up before in 2 threads (https://www.eevblog.com/forum/metrology/is-precision-capacitor-measurement-with-a-dvm-and-signal-gen-possible/andhttps://www.eevblog.com/forum/metrology/capacitance-measurement-with-limited-gear/) and Henrik_V has pointed to a test method described by Mariscotti in the 2010 journal Measurement.I've looked through theMariscotti paperand aim to set up a practical measurement rig with instrumentation I have available.I can effectively eliminate frequency measurement error with a HP3325A digital synthesised sinewave using a GPSDO frequency reference (https://www.eevblog.com/forum/projects/budget-gpsdo-a-work-in-progress/), and may be able to use the HP's output directly without the need for a buffer opamp.Although Mariscotti used a FET input buffer to achieve a total effective parasitic bridge and buffer input capacitance of 1.0pF, I hope to see if an opamp or IA can approach a low pF input given that I have some vintage parts that indicate device input capacitance of circa 2pF. I have a bench 6.5 digit out of cal DMM with confirmed 600kHz bandwidth so that should allow suitably low measurement accuracy for relative measurement of capacitances in a decade box, as well as absolute accuracy down to circa 0.1%. Apart from random capacitor measurements, my main incentive is to tweak a decade capacitor box to hopefully within 0.1% across the step ranges.Has anyone used this measurement technique ? I was a bit quizzical about how the paper identified an effective parasitic jig capacitance of 1.0pF, but then went on to describe an example capacitor measurement of 101.209pF (including the stray capacitance) and suggesting a 0.001pF uncertainty.I also want to compare measurements using the above technique with a soundcard and REW software impedance measurement technique I often use for inductive parts. The REW technique has a base impedance accuracy related to a calibration resistor, where I can use a 0.05% HOLCO H8 Y. The advantage of the REW technique is the speed of measurement, and that capacitance values can be calculated and displayed at any frequency within the measurement sweep range, and I'd like to independently show that measurement accuracy could be repeatably down towards 0.1%.Ciao, Tim

author: David Hess
author_rank: Super Contributor
timestamp: February 16, 2022, 09:19:14 am
content: Quote from: trobbins on February 15, 2022, 03:51:52 amThe drain of the JFET input buffer is bootstrapped to reduce the effects of the gate-to-drain capacitance. The gate-to-source capacitance is bootstrapped by the source follower configuration.For an operational follower, the supply connections could be bootstrapped from the output to reduce the effective input capacitance.

author: trobbins
author_rank: Frequent Contributor
timestamp: February 16, 2022, 09:41:39 am
content: Yes, I was thinking of ways to mitigate practical issues, and one way could be to float the buffer and even use a handheld 4-digit DMM, to avoid ground loop concerns - especially if I use a HP3325A for signal input.Another aspect is that I may not have an immediate need for accuracy better than 0.1% for capacitors below 1nF, so suppressing parasitic buffer input capacitance may be a lesser aim. So my initial efforts are likely to just go any simpler practical path. I have been able to recommend that the alternative measurement technique (soundcard and REW software) provide a 4-digit parameter calculation result, to align better with a 4-5 digit result from a DMM, as up to now the REW software was only displaying impedance parameter results to 3-digits.

author: Kleinstein
author_rank: Super Contributor
timestamp: February 16, 2022, 10:08:42 am
content: The JFET used in the buffer amplifier is not that special and not that critical. One may have to find/selct one with a suitable threshold so that the DC level if acceptable.Measuring such small capacitors with high accuracy is anyway tricky, as it does not need much to get a few pF of parasitic capacitance in parallel to the DUT. An accurate small capacitance kind of needs to be shielded, like the low value capacitance standards.One can measure small capacitors (down to the sub pF range) resonable well with a transimpedance amplifier at the receiving side and than a relatively large voltage at the DUT. Ideally one would use a phase sensitive detection (could be in software) to reduce the noise and detect errors from phase shifts.The test frequency may be relatively low, to be well below the bandwidth limit of the amplifier.

author: trobbins
author_rank: Frequent Contributor
timestamp: February 16, 2022, 10:50:54 am
content: Mariscotti in his paper used a regression technique to show he had 1.0pF of effective parasitic capacitance at the input to his buffer amp. As he indicated, few labs would have adequate instrumentation to make a 1pf measurement, hence the regression technique was deemed practical enough.

author: trobbins
author_rank: Frequent Contributor
timestamp: February 19, 2022, 09:17:38 am
content: I now have a Cambridge Decade Capacitor with 4 decades from 0.1nF to 1uF. Each decade comprises 4 capacitors (1, 2, 3, 6) except the first decade with five capacitors (1, 2, 3, 4, 6) and a 10x0.1nF span. The capacitors are british TMC polystyrene with 3% tolerance marking for 0.1nF span, 2% for 1nF span, and +/-1% for 10 and 100nF spans - all with a 350Vdc wkg rating, and the larger caps have what looks like sorting batch labels applied. It appears that TMC caps were marked with PYE from perhaps 1960 onwards (when PYE took over), so this box is likely late 1950's.With a simple Aneng 8009 all the dialed capacitor values appear to be within 1%, and with a step consistency that indicates a better tolerance could be achievable. All capacitors exceed 2000Megohm leakage at 250Vdc, and the switches and unit look like it has had an easy life, so at the moment it will make a good capacitor decade box to try and determine what measurement accuracy can be reached, and if it is practical to trim where needed.

author: KT88
author_rank: Frequent Contributor
timestamp: February 19, 2022, 12:39:03 pm
content: On weakness of Mariscottis circuit is the single-ended bridge excitation. It exposes the output to a high common mode voltage.A differential approach would reduce the effect of input parasitics of the output buffer significantly...The reference for the voltage measurement would have to change from GND to the excitation side of the half bridge.

author: trobbins
author_rank: Frequent Contributor
timestamp: February 19, 2022, 09:54:07 pm
content: The excitation side generates an AC voltage symmetric with ground. At bridge balance, the input voltage to the buffer is an AC voltage symmetric with ground.

author: KT88
author_rank: Frequent Contributor
timestamp: February 21, 2022, 10:55:02 am
content: QuoteThis is exactly the problem with this circuit: The high impedance node of the halfbridge sees a large amplitude which also excites mainly parasitic capacitances.On top of that changes the amplitude against ambient (parasitics) by inverting the exitation. Without tight control of the mechanical dimensions an uncertainty of several pF must be expected - bye bye ppms...It would be ideal if the output (center) of the halfbridge would not carry an AC voltage and only the low impedance nodes are "hot"...A differential excitation would at least reduce the output voltage but not by a lot unfortunately, due to the phase shift.

author: trobbins
author_rank: Frequent Contributor
timestamp: February 21, 2022, 11:59:57 am
content: Perhaps one step back first. My aim is a diy measurement, with an aspirational accuracy approaching 0.1% tolerance (ie. 1000ppm, not circa 10ppm). My target parts are all vintage polystyrene, with a likely significantly large tempco in the range of circa 100-160ppm/degC, so I have to be mindful of ambient temp getting outside of my typical 20-25degC span. And I only have three measurement techniques to call upon: an Aneng 8009 handheld; a soundcard and software with calibration to a 0.05% resistor; and Mariscotti's technique with some 0.1% tolerance bridge arm resistors (I only have a small number of ad hoc values to hand of Welwyn RC55's that are used and may be subject to abuse). So I need to be aware that I can't shoot for the stars wrt absolute accuracy and tolerances.I have just undertaken a sweep of measurements using those three measurement techniques, and they all certainly correlate to each other. The soundcard/software and Mariscotti techniques align to about a consistent 0.5% difference (1-9nF and 10-90nF decades so far), whilst the Aneng meter is consistent within a range and about +2%, +0.9% and +0.4% for three increasing decade ranges.My initial view is that the soundcard/software provides the highest confidence, as soundcard sample rate frequency is 0.0011% low (compared to <1ppb GPSDO synthesised frequency), and calibration is to a 0.05% resistor, and measurement value can be aligned to a frequency where phase shift is 90deg.Apart from the techniques, I also aim to characterise the 4-decade capacitor box, which has a circa 65pF intrinsic stray capacitance which is likely due to the 4 switch mechanisms (each switch mechanism uses multiple contacts and associated wiring as each decade only uses 4 capacitor parts), and where the stray level appears to change with switch setting by up to about 20pF (ie. certainly noticeable on the 100p-1000p decade), so I will likely need to make a lookup table.The Mariscotti technique provides about 0.02% tolerance in frequency, mainly due to the toggling and frequency step size available to get equal voltage readings on my 6.5 digit picotest. However so far I have used a 10k 0.1% bridge resistor which I haven't attempted to cross-check with the other 0.1% parts I have to provide some confidence it is still ok. I also have some doubt about making measurements that are not in a frequency range where phase is known to be 90deg.I do have the ability to suppress stray capacitance to ground on the meter side (by using a 4 digit handheld meter), and on the excitation side (by using a laptop and battery powered soundcard), so will try those next when I do a measurement sweep of the 100p-1000p decade.

author: Kleinstein
author_rank: Super Contributor
timestamp: February 21, 2022, 12:18:04 pm
content: With small capacitors it helps when the half bridge is highly assymmetric. So a rather low voltage at the resistor and a high voltage at the capacitor. Impedance ratio effects how important the input capacitance is. With a small resistor to ground the input capacitance sees less voltage.

author: KT88
author_rank: Frequent Contributor
timestamp: February 21, 2022, 01:37:31 pm
content: That won't change anything as the parasitics are still in parallel with the DUT (CUT).Depending on the size (geometrical not electrical) of the DUT parasitic capacitances would span from a few hundred fF to more than 100pF. For a decade capacitor of 1nF or less it would be more guessing that measuring...Some improvement could be provided by guarding the DUT and Rref with the according drive signal.

author: trobbins
author_rank: Frequent Contributor
timestamp: February 22, 2022, 04:25:57 am
content: Some progress on measurement comparison details:For the Mariscotti method, I used four different 0.1% bridge resistors (two 1k62, one 1k74 and the 10k) and observed a 0.00 to 0.05% variation in measured capacitance for the 10nF setting, indicating that the 0.1% tolerance reference resistors are likely all still within 0.1% tolerance.The Mariscotti method measured levels are about +0.41 to +0.46% more than the REW measured levels for the 10nF setting. That relative % difference was observed for the 5-9nF, 10n-90nF and 100n-900nF decades, with the difference increasing to about 0.9% as capacitor setting reduced to 1nF, and continued to increase as capacitor setting reduced from 1000p to 100p (lowest decade).The Mariscotti method was checked for some stray capacitance paths. A mains powered excitation source (PC and soundcard) was compared with a non-mains source (laptop and battery powered soundcard), and the difference in measured capacitance was only 1pF for the 700pF setting. The method was also checked with a mains powered DMM for voltage measurement, and when a battery powered Aneng 8009 meter was used, and no discernible change in measured capacitance was observed for the 100nF setting (a lower capacitor setting could not be used as the Aneng meter has a nominal 1kHz bandwidth). My next move is likely to do some measurements on discrete capacitor parts of below 100pF, where stray capacitance opportunities from the physically large metal decade box are avoided.I also need to compare the soundcard/REW method when different calibration reference resistor values are used, as the existing calibration has only used a 10 ohm 0.05% resistor.

author: KT88
author_rank: Frequent Contributor
timestamp: February 22, 2022, 10:17:41 am
content: Hi Tim, thanks for sharing your results! If you have time it would be interesting if you could post a photo of your setup.As the method only gives the impedance and not the capacitace+ESR, it should be possible to get the ESR by using a 2x or 1/2x resistor and repeat the measurement. The ESR should show a 1/2x or 2x voltage drop thus a slight shift in impedance. That way ESR and capacitance could be calculated...CheersAndreas

author: Kleinstein
author_rank: Super Contributor
timestamp: February 22, 2022, 11:14:03 am
content: Getting the ESR is tricky when only looking at the AC amplitude. It can work by looking at different frequencies and especially the case of rather high frequency. Anyway here it is about small capacitors and there the concepts of ESR is not so suitable - that is more something for large electrolytic ones.The full impedance analysis is more something for the method using the soundcard (REW) or an VNA or a dedicated RLC bridge.

author: trobbins
author_rank: Frequent Contributor
timestamp: February 22, 2022, 11:22:22 am
content: Hi Andreas, I certainly looked for ESR (impedance minima) in the soundcard/REW plot, but even for the largest 900nF decade capacitance (which is actually 100n//100n//200n//200n//200n//200n) the impedance doesn't fall beyond about 2 ohm by 96kHz, so not enough measurement system bandwidth to see an actual impedance minima or bathtub characteristic. REW does some modelling of equivalent parameters (shown as 51 milliohm) but I just reported a bug for that particular parameter so that reported parameter may change soon with a software update.The ESR of these polystyrenes may well be down below 0.1 ohm per 100n or 200n part, and similar to a good metalised polypropylene. Wrt the Mariscotti technique, I am limited by the low tolerance resistor values I have, although I do have a few 10 ohm 0.05%, however with a 100nF cap the frequency is up around 160kHz so I need to be mindful of excitation voltage level and resistor dissipation - I'll see how that goes tomorrow.Apart from keeping cables short and separated, and using a wooden bench with a bit of clearance to other items and myself, the Mariscotti jig switching is done with a reasonably sizeable vintage DPDT mains power switch, and voltages read with my body away from the jig. Stray capacitance to body is noticeable in a slight change in measured voltage level when I'm near the large decade box or holding the toggle switch, so I'll just use a fixed capacitor next to see have well the measurement performs with a range of Soshin +/-2% 500V dipped silver mica's I have that go down to 10pF.

author: Kleinstein
author_rank: Super Contributor
timestamp: February 22, 2022, 11:56:06 am
content: One can also use the simple RC bridge in the assymmetric case, so not adjust the frequency to get the same voltage (and this way eliminate the DMM linearty as a error source), but use different voltages.This would be a bit more like the measurement with the soundcard are done. Ideally the measurement with the soundcard sould also have a high input impedance buffer for the measurement.For small capacitors the relevant case would be especially a relatively small resistor to ground and the DUT from the signal source. So the amplier input impedance and parasitic capacitance to ground would be in parallel to the ref. resistor with relatively low impedance. Many of the modern RLC bridges work a bit similar, with a TIA to measurent the current instead of the simple resistor to ground.

author: kleiner Rainer
author_rank: Regular Contributor
timestamp: February 22, 2022, 11:57:23 am
content: Hi Tim,maybe measuring small capacitances at higher frequencies could help.Recommended reading:https://www.g3ynh.info/zdocs/bridges/index.htmlhttps://www.g3ynh.info/zdocs/bridges/appendix/YZ_scalar.pdfThe second link explains how to measure impedances only with voltage measurements at several points in the network without measuring phase. Maybe an independent method to check your method.Greetings,Rainer

author: trobbins
author_rank: Frequent Contributor
timestamp: February 23, 2022, 12:53:51 pm
content: I've been able to confirm that my simple Mariscotti test setup provides reasonable measurement of low pF value +/-2% silver mica caps: 10+10 measures as 20.6pF; 33 measures as 35.4pF; 100 measures as 102.2pF; and 330 measures as 330.6pF. I am just using my typical bench instrumentation of a mains powered soundcard and PC run software to act as sinewave signal generator, and a mains powered Picotest DMM for voltage measurement. Photo of layout below.For 100p and 330p measurements I used a 49k9 0.1% bridge resistor. For 20 and 33pF I had to use 143k9 (47k+47k+49k9) as the soundcard has a 96kHz upper limit, and I didn't want to get the HP3325A out. The setup certainly gets more sensitive to nearby earthy objects as the bridge arm resistance gets higher.The Aneng 8009 has accuracy issues, and provides a zero result under about 15pF. The soundcard based impedance setup also has a harder time with accuracy as capacitances get low - a link to that measurement technique ishttps://www.roomeqwizard.com/help/help_en-GB/html/impedancemeasurement.html.So without resorting to a FET input buffer, it looks like the Mariscotti technique is useful for me, but I would need a capacitor standard or two to have high confidence with the accuracy I was achieving.

author: KT88
author_rank: Frequent Contributor
timestamp: February 23, 2022, 06:12:54 pm
content: Interesting results...The intriguing part of this method is indeed it's simplicity: only two AC voltages have to be tuned to have the exactly same amplitude - no need for a linear or otherwise accurate meter - well, some short term stability and decent noise specs are still required...The downsides are the high impedance node at a pretty high voltage and the changing voltages against ambient wher inverting the polarity of the excitation.I put a small simulation together with an improved circuit. Comments welcome.Active_Mariscotti_CapMeter.asc(1.92 kB - downloaded 60 times.)CheersAndreas

author: trobbins
author_rank: Frequent Contributor
timestamp: February 24, 2022, 12:40:04 am
content: I am using a Picotest M3510A for Vac measurement - I got it in a damaged state as it had some faulty voltage ranges and no resistance or capacitance or diode readings. I recovered the voltage ranges without a schematic but haven't yet recovered the other ranges as that is a bit more complicated - so unfortunately no capacitance measurement from that device. Its Vac input impedance is not specified but I just measured it as 1 Megohm shunted by nearly 2pF (if my quick maths is correct).I have some AD521 instrument amp modules and will get one of those operating with battery power to use as an alternative buffer, to see if measurement values are repeatable on low value caps. Otherwise I don't think I have any exotic fet input opamps, just some CA3130 and 3140's.

author: Kleinstein
author_rank: Super Contributor
timestamp: February 24, 2022, 08:47:52 am
content: An input resistance for the AC range of about 1 M ohms is standard for the higher resolution meters. Handheld ones may use the same 10 M "divider" as for DC. 2 pF would be exceptionally low, it usually is more (e.g. 20 pF like a scope input), already from the parasitics inside.The OP circuit the KT88 showed is a bit like some RCL meters work. The slightly tricky part is to make sure the OP is not oscillating. So I would look for an OP with a good phase reserve. FET OPs are quite common (e.g. TL072, TLC272, MCP600x). The faster ones may have slightly lower input capacitance. In the TIA type circuit the input capacitance of the OP is not that important - though it contributes to the tendency to oscillate and in this respect the faster OPs are more critical. One could still consider the measurement circuit a black box and maybe allow some extra FB capacitance and than calibrate it to a reference resistor as a DUT.

author: trobbins
author_rank: Frequent Contributor
timestamp: February 24, 2022, 09:33:30 am
content: Yeh I reckon I mucked up a decimal point with the 2pF, and forgot to allow for another meter input capacitance, so need to redo all of that.

author: KT88
author_rank: Frequent Contributor
timestamp: February 24, 2022, 11:58:15 am
content: QuoteThese amps are by far too slow for an active excitation - to keep the center node quiet (virtual GND) at higher frequencies, much faster amps are required - the chosen ADA4891 has GBWP of 220MHz and is a cheap low noise video amp as a bonus...The idea behind the active circuit is to provide low impedance outputs that would work with any meter.

author: mawyatt
author_rank: Super Contributor
timestamp: February 24, 2022, 02:52:08 pm
content: Quote from: KT88 on February 24, 2022, 11:58:15 amMaintaining a quality virtual ground depends heavily on the OP-AMP GBW Product. Since the OP-AMP input is a very high impedance to start with, and must be "driven" to a virtual ground by means of available negative feedback which rolls off with frequency due to the OP-AMP Open Loop Gain roll off. This is exactly why in ~1980 we developed a custom summing node type OP-AMP which had a very low input impedance on the - input, and high on the + input, and very high bandwidth but low power consumption (our RTSA used over 30). The idea was to start with a low - input impedance, then drive it down further with negative feedback since the application required high precision weighted summation of various high frequency signals with little interaction (causes intermodulation). The first version of the summing node were implemented with discrete bipolar transistors and then custom CMOS chip, later this technique became known as Current Mode Feedback Amplifiers.Maybe using a CMFB amplifier instead of the conventional OP-AMP would extend the operation range, but you will still need an equal range measuring device.Anyway, just a thoughtBest,Edit: Just sketched up what I recall the early discrete rendition of the summing node looked like.

author: Kleinstein
author_rank: Super Contributor
timestamp: February 24, 2022, 03:44:34 pm
content: The GBW of the OP-amp should be considerably higher than the frequency used, but one is free to operate at a relatively low frequency (e.g. 100-1000 Hz range). With a fast OP-amp the ciruit as shown can easily get unstable, e.g. due to the input capacitance of the OP. There is no abolutute need to have the same voltage at the resistor as at the capacitor and a smaller resistor eases the demand on the bandwidth.It is anyway easier to use an extra measurement with a accurate resistor at the DUT position as the reference point and not with the precision resistor in the feedback position. This allows to also have some capacitance in the feedback and this way get stability also with a fast OP-amp.To some degree the residual voltage due to the limited GBW can be included in the model - if needed the voltage at the "virtual ground point can also be measured.

author: mawyatt
author_rank: Super Contributor
timestamp: February 24, 2022, 05:10:02 pm
content: A little analysis will show that the OP-AMP minimum GBW Product requirement is:GBW Product > F*(Q-2), where F is frequency of operation and Q is the Virtual Ground Quality Factor (Input Signal Magnitude/Virtual Ground) virtual ground of the input.Example: A selected frequency of 10KHz and effective virtual ground Quality Factor selected is 10,000 (Vin =10VPP, Virtual Ground = 1mVPP):GBW Product > 10K(10,000 -2) ~1GHzUsing the mentioned TL072 which has a GBWP of ~3MHz results in measurement frequency of < 300Hz, TLC272 < 200Hz and the ADA4891 <22KHz.CAUTION, these results are VERY OPTIMISTIC since the GBWP is aSmall Signal parameter, and theactual Large SignalGBWP is much less, usually less than 1/5 the specifiedSmall SignalGBWP.So what does this mean in reality?? That the expected results of a Quality Virtual Ground need to be resolved with an OP-AMP that has aPower or Large SignalGBWP of at least the numbers presented and since many OP-AMPs don't specify this parameter, one needs to increase the small signal GBWP requirement by at least an additional 5X, safer would be 10X!! This is why we developed the summing node way back in 1980Best,

author: KT88
author_rank: Frequent Contributor
timestamp: February 24, 2022, 10:31:56 pm
content: Given that the Mariscotti approach aims for simplicity with no need for sophisticated gear one must accept that it has it's limitations. Pushing it beyond about a few kHz will result in rapidly increasing uncertainties. Mitigation of some of the effects is possible but fairly limted.If a good (DIY) testfixture can be used it would be at least pretty reliable for binning of capacitors without the need of an Agilent 4278A for example...This comes in handy for DIY loudspeaker building, Sallen-Key filters and more at a budget.If one is interested in what could matter at higher frequencies look up 'Haddad Resistor'... you will be staring into a deep rabbit hole.

author: trobbins
author_rank: Frequent Contributor
timestamp: February 25, 2022, 11:30:22 am
content: I was able to recalculate what I did the other day, as well as alternately measure the Picotest DMM VAC input impedance, and it seems to be circa 12pF // with 1 Megohm for the 1V and 10V ranges that I use for the Mariscotti testing.I then tweaked a pcb assembly I had to act as a low-capacitance input buffer - it comprises a series 10k into an LM310 unity-gain buffer (circa 1.5pF input spec, with at least 100kHz bandwidth flat) feeding directly in to an AD521 set for unity gain, and all powered from an isolated dc/dc (AD 940) - that then went to the Picotest DMM. The remainder of the test setup was as before. Compared to previous Mariscotti setup (direct in to DMM), measurement of a 330pF silver mica was within 1.5pF (test frequency was 48kHz), and measurement on decade box was within 1.0pF for 300p to 700p settings (test frequency up to 43kHz).I may do some comparisons on lower values to 20pF, but that pretty much brings me to an end for this activity (unless I luck upon a capacitance standard). Thanks gang for the comments - much appreciated.

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: February 25, 2022, 01:59:54 pm
content: It seems like an OK method but I don't understand the reluctance to find a good reference cap. With one or two good reference caps, it's so easy to build a conventional bridge, why wouldn't you? The conventional bridge will also give you dissipation factor, though a polystyrene or polypropylene will be essentially zero.http://www.conradhoffman.com/cap_bridge.pdf

author: trobbins
author_rank: Frequent Contributor
timestamp: February 25, 2022, 05:08:46 pm
content: No reluctance - I just don't have one or two reference caps.

author: TimFox
author_rank: Super Contributor
timestamp: February 25, 2022, 05:51:04 pm
content: Another method I have used to measure arbitrary impedances in the audio range is to use a lock-in amplifier with differential input.For example, I have done careful measurements of the actual primary impedance of an audio transformer with a loaded secondary.My PAR 129A is rated from 0.5 Hz to 100 kHz. Each input (A or B) is rated for 100 Megohms in parallel with 20 pF.Setting up the lock-in correctly allows measurement of (A), (A-B) and (-B) voltages, in-phase and quadrature components, with respect to the (Reference) input.The DC outputs for each phase component can be read neatly on two 3.5 or 4.5 digit voltmeters.The configuration puts a male BNC to double binding post adapter on (A) and (B) inputs.The excitation voltage from a clean audio generator goes to the (Reference) and from there to the hot side of (A).A calibration resistor (I use RNC90 metal-foil resistors that have good tolerance and relatively low capacitance) goes from the hot side of (A) to the hot side of (B), and the DUT goes across the (B) binding posts.This allows a measurement of the jig impedance (input capacitance and resistance of B plus capacitance of BNC adapter) with DUT disconnected.Inserting the complex voltages into a spreadsheet, along with the calibration resistance and unloaded voltage, gave me the impedance as a function of frequency over the useful range of the PAR 129A.Note that in the drawing attached, (A-B) and the calibration resistance gives the current into the (B) node, which flows into the parallel combination of the DUT and the input impedance of (B), including the BNC adapter.

author: trobbins
author_rank: Frequent Contributor
timestamp: February 25, 2022, 10:50:36 pm
content: That technique looks exactly like what the REW software does with a soundcard.https://www.roomeqwizard.com/help/help_en-GB/html/impedancemeasurement.htmlREW automated the calibration process by doing three sweeps for open, short and a reference resistor, and then throws in some automated modelling of the impedance response to simplify results for capacitor or inductor parts. I was checking that performance the other day for when different values of reference resistor were being used, as I typically just used a 10R 0.05% Holco - there certainly was an improvement when using higher valued reference values to measure higher valued DUT resistances, but no significant change for calculated DUT capacitor accuracy.I also use that impedance measurement technique for audio transformer assessments (https://www.dalmura.com.au/static/Williamson%20output%20transformer%20measurements.pdf) as it is a valuable tool to have around now compared to a decade or two ago.The input resistance of each channel on my soundcard is 1 Megohm, although I haven't attempted to try and determine its shunt capacitance, although I likely could ball-park it as I had to modify a 100:1 scope probe to flatten its frequency compensation by removing an internal shunt capacitor in the probe bnc end compensation box.

author: Kleinstein
author_rank: Super Contributor
timestamp: February 25, 2022, 11:27:18 pm
content: With a small capacitor it may be better to swap the position of the resistor and the capacitor. The input impedance is than more relative to the resistor and not relative to the DUT. Of cause the math is slightly different - so the SW would need to support it and the cal measurements are no longer that easy - would need a 2nd resistor for calibration.

author: KT88
author_rank: Frequent Contributor
timestamp: February 26, 2022, 12:43:39 am
content: Not sure what you mean... The original circuit uses a switch to revert the polarity of the halfbridge to compare both voltage drops. At the same voltage across both impedances you have no difference between both switch positions at the output anymore. That's also why it requires equal amplitudes across both impedances (mentioning impedance because also the resistor has some reactance). The comparison at one voltage level mitigates (almost) every effect of non-linearity of the (AC-) meter as well as loading by the input impedance of the meter and cable parastics so it doesn't affect the result. That way we see some remarkable results although Tim didn't use a professional test fixure with shielded leads...

author: trobbins
author_rank: Frequent Contributor
timestamp: February 26, 2022, 04:10:22 am
content: I concur with KT88 on the ability of the DPDT toggle to balance the impedance of each bridge arm. I just finished off repeat measurements of 20p, 33p and 100p silver mica's with the LM310/AD521 buffer and measured +0.5pF, -1.3pF, and -1.4pF respectively in comparison to no buffer, with frequency changing from 52kHz to 11kHz respectively. So in those sample measurements there appears to be some variation, which is likely related to voltage measurement parasitic capacitance and/or resistive loading differences, and the pursuit of lowering such parasitics may be a tangible benefit for measurement of cap under 1nF.One aspect of any such measurement setup is to not use shielded cable for all parts of the circuit. When I used just the DMM (photo in post #18) I purposefully used only short unscreened test leads to the DMM, and didn't try to screen the DPDT switch - preferring to use distance to anything as my friend. Even with the LM310 buffer I used simple wire connections to the bridge so as to avoid screen coupling parasitics. The excitation source (soundcard sits in a metal tray) was moved close to the DPDT switch for photo convenience, and a screened cable is used from the soundcard up until just short of the switch. A non-metallic board to fix the switch and cables in place may well improve repeatability, but perhaps of benefit only for capacitors that are in the pF range and not in a decade box.

author: KT88
author_rank: Frequent Contributor
timestamp: February 26, 2022, 02:11:29 pm
content: One source of uncertainty/inaccuracy is the parasitic capacitances 'see' different voltages across them depending on the switch postion. I tried to addreess that witrh my active Mariscotti circuit.There is also an improvement possible by intrducing shielding against the excitation nodes of the bridge. The switch must be positioned directly at the driver and gnd while the shields are connected as close as possible to the reference resistor and the DUT. Both impedances must be completely covered by the shield. This setup would possibly remove the need for a high impedance buffer if the meter is in AC mode. Reason: all impedance ratios stay the same independantly of the switch position.

author: trobbins
author_rank: Frequent Contributor
timestamp: February 27, 2022, 03:14:47 am
content: As an indicator of some parasitic uncertainty, I did a few more tests.I modified the excitation signal connection to the end terminals of the toggle switch by using screened cable up to the switch terminals, with cables coming in from the other side of the switch from the R-C bridge parts. I didn't 'go the whole hog' and add a small metal foil screen around each hot signal terminal - that could be an incremental improvement, but so also could be to use a DPDT with physically larger terminal spacings, and identifying a lower capacitive input buffer or further separating that buffer from the bridge parts.The 20pF SM capacitance measurement decreased 0.26pF, the 33pF increased 0.07pF, and the 100pF and 330pF values didn't change. Certainly the layout/placement of the RC parts can subtly change a measurement, but that was seen as down below circa 0.01pF.I then put a metal shroud (two aluminium baking trays which I sometimes use to screen my soundcard) around the RC parts/switch and buffer enclosure, with a connection to buffer ground, and could discern a 0.09pF reduction in the 20pF part.All good fun for someone who wants to pursue low pF level measurements.

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: February 27, 2022, 04:12:16 pm
content: I keep looking at this circuit and wondering if there's anything to be gained by winding a balanced transformer to give the input some symmetry. It's not hard to do and extremely accurate ratios can be had if you bifilar wind. It's the trick behind many bridges and impedance comparators.

author: Kleinstein
author_rank: Super Contributor
timestamp: February 27, 2022, 07:01:54 pm
content: The transformer would help with a capacitor vs capacitor bridge, but it would not help that much with a C vs R half-bridge, as the 2 sides are out of phase. So the center would still not be near zero.It could more help to have something like a 1:10 transformer and than do a small cap to larger cap step.

author: trobbins
author_rank: Frequent Contributor
timestamp: November 29, 2024, 07:49:24 am
content: Just to round out this technique, I was able to compare the capacitance measurement of a vintage GR239E variable air condenser at 100% dial. The GR calibration capacitance on the base of this device was 1025pF.The Mariscotti method measured 1033pF +/-1pF. The soundcard with REW software calculated 1035pF at 1kHz. A MCP BR2822 measured 1029.5pF at 100Hz.And I just used an ESI 250DA impedance bridge to give 1032.5pF with series D=0.033 at 1kHz, and an 11pF D=0.036 reading for no connection to the DUT terminals.I used a soundcard and REW software in spectrum mode to easily null the bridge at its 1kHz generator signal, rather than the magic eye (which wasn't working). I had to use the 250DA internal generator, as it doesn't provide an isolated external generator input via its screened coupling transformer, so I couldn't use the soundcard's generator output as an option (I think the later 250DE has that capability).I'll now go through the cal procedure for the 250DA to see if there is any off-normal setup that would show a D of 0.033 for an air vane capacitor.