DIY capacitance measurement using simple RC bridge based technique

[trobbins]

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/ and https://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 the Mariscotti paper and 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

[David Hess]

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.

The 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.

[trobbins]

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.

[Kleinstein]

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.

[trobbins]

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.

[trobbins]

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.

[KT88]

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.

[trobbins]

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.

[KT88]

The excitation side generates an AC voltage symmetric with ground

This 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.

[trobbins]

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.

[Kleinstein]

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.

[KT88]

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.

[trobbins]

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.

[KT88]

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...
Cheers
Andreas

[Kleinstein]

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.

[trobbins]

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.

[Kleinstein]

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.

[kleiner Rainer]

Hi Tim,

maybe measuring small capacitances at higher frequencies could help.

Recommended reading:

https://www.g3ynh.info/zdocs/bridges/index.html

https://www.g3ynh.info/zdocs/bridges/appendix/YZ_scalar.pdf

The 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

[trobbins]

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 is https://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.

[KT88]

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 27 times.)

Cheers
Andreas

[trobbins]

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.

[Kleinstein]

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.

[trobbins]

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.

[KT88]

FET OPs are quite common (e.g. TL072, TLC272, MCP600x)

These 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.

[mawyatt]

FET OPs are quite common (e.g. TL072, TLC272, MCP600x)

These 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.

Maintaining 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 thought 

Best,

Edit: Just sketched up what I recall the early discrete rendition of the summing node looked like.