DIY capacitance measurement using simple RC bridge based technique

[Kleinstein]

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.

[mawyatt]

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) ~1GHz

Using 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 a Small Signal parameter, and the actual Large Signal GBWP is much less, usually less than 1/5 the specified Small Signal GBWP.

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 a Power or Large Signal GBWP 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 1980

Best,

[KT88]

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  .

[trobbins]

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.

[Conrad Hoffman]

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

[trobbins]

No reluctance - I just don't have one or two reference caps.

[TimFox]

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.

                           

[trobbins]

That technique looks exactly like what the REW software does with a soundcard. https://www.roomeqwizard.com/help/help_en-GB/html/impedancemeasurement.html

REW 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.

[Kleinstein]

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.

[KT88]

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...

[trobbins]

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.

[KT88]

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.

[trobbins]

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.

[Conrad Hoffman]

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.

[Kleinstein]

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.