Simple Measurement of a Small Capacitance

Just to get it clear (in my head), when you say "... which can have value modification with frequencies ...", do you mean that the capacitance is frequency-dependent?

Yes, unfortunately and as you noticed at high frequencies. Capacitance measurements are used in humidity sensors but at low frequency. Here it is something different, thus the problem!

I wonder if there maybe a confusion in where you are applying the term "frequency". As I mentioned earlier a test signal with a frequency of 1 kHz will put the impedance of a 4 pF capacitor at 40 Mega-ohms. Possibly you could test the capacitance every millisecond (1 kHz) with a 10 MHz test signal. This would then put your capacitor impedance at a more practical 4 Kilo-Ohms. This will limit errors from leakage resistance but you will still have parasitic capacitance and inductance problems.

The "frequency" is the one of the capacitance changes. It is NOT the frequency of any supply, in order to measure at 1 kHz the voltage/current used for the measurement have to be at least 20x higher in frequency and if possible even higher.

I expected some suggestions about schematics or usable components. Till now only one was made. I thought myself about possibilities and I wanted to confront my thoughts with some high skilled specialists. I am still waiting some more input.

Actually, the value associated with the capacitor is fixed. However, the reactance of the capacitor changes as a function of frequency. A 4pF capacitor will always be a 4pF capacitor. To say the value changes with frequency is probably what is throwing people off.

"... the value associated with the capacitor is fixed..." - if that were the case, the problem would be relatively easy. Which is why I asked my first question.

I am very sorry to be obliged to answer that if YOU cannot imagine a variable capacitance this does not mean that such cases do not exist. It is a TRULY variable capacitance which I have to measure in order to determine the amplitude of the variation cause.

I gave the example of the humidity sensors where the capacitance does change its value according to the variations of the dielectric constant depending on the humidity degree. In my case it is a variation due to the position changes of the electrodes.

You see a capacitor ONLY as an electric component but in fact the capacitance variation effect is used in many other applications. In the range 100...200 pF there is no problem but in the range of 4 pF it is a real problem even if the parasitic capacitances mentioned by RED FRED are maintained at a minimum. The other problem is the dynamic of changes (up to 1kHz), as mentioned in the 20 Hz range no problem really.

The reason I asked the question is that what I need is a simple solution since cost will be an important factor and I hopped and still have the hope that among such a high skilled group I will have the chance to get a GOOD idea. I forgot to mention in previous messages that resolution is as well an important factor beside repeatability.

Doesn't sound like you're interested in guesses, but I'm posting anyway. Sorry if it doesn't help.

http://www.smartec.nl/pdf/apputi06.pdf

Good Answer

Thank you it seems to be very interesting I shall contact them for details. I will let you know what I got for further information. As Red fred noticed this is not a very trivial problem. You deserved a GA !

I had a look quite thorough via Google but I did not formulate the right way since this did not come up.

Measuring a capacitor this small will always run into complications of the test leads parasitic capacitance dominating the capacitance. I am a little baffled though with the combination of values you show here. I do not believe the range of your capacitances. You will never get to 0 pF and less than 0.1 pF with any macroscopic components that I know of. At 1 kHz your largest capacitance (4 pF) will have an impedance of nearly 40 E6 Ohms. So at this low of a frequency the capacitor leakage resistance may dominate any losses. Now I do see such tiny trimmer capacitors used in RF filter networks. Frequently the trimmer capacitor is configured in parallel with a larger fixed capacitor.

I gave the range of course it does not go to zero. But it will vary about 30 to 50 % around the 4 pF. Parasitic capacitances are almost no present due toe the fact that the device has to be very near to the variable capacitance.

Capacitors charge/discharge at a given rate based on time constant. They follow a curve based on the natural log. Below is a snapshot of one of my 'cheat sheets':

By modifying a sample-and-hold circuit, using a constant current source through a given resistor value, and measuring the voltage across the capacitor, you can derive a very accurate and repeatable measurement of the capacitance. Using a known constant current source would remove a huge amount of uncertainty due to parasitics.

Hope this helps...

MRH620

A technique not apparently discussed in Kramarat's reference (which deserves a GA) is the Wien Bridge technique, which may be of interest...

It is of course it has the advantage to have a voltage output which is easier to process.

I shall have a look more in the depth because it is important to have a limited non-linearity.

Thank you

Nick Name

I still am baffled, what is it exactly OP desires to measure. Small cap. is not such a thing, rather a possible means to measure something else in a specific, but not yet specified environment.

A random example. In paper production moisture in the fast moving sheet can be measured capacitively due the high epsilon of water relative to paper fibers. High concentration of fibre dust is a fundamental distraction for the sensor. Periodic, automatic cleaning is essential to make it to work at all.

I used a lot of capacitance measurements for acceleration sensors and similar devices. See photo below of mass and flexure layout. The surface of the moving mass with a fixed metallised electrode in the housing is the capacitance, used two sided here.

Very often these have moving metallic plates of 0.1 to 1 cm2 at distances of 100µm so will have a capacitance of 1 to 10 pF without input of acceleration (that will change the distance).

The simplest configuration to measure this is a Schmitt-Trigger CMOS inverter AC14 or HC14,

don't use ACT series.

One of these inverters, the output connected via a very stable resistor R to the input will give a stable RC oscillator that is oscillating with the input capacitance and the feedback R.

Connect your unknown Capacitor from input to ground. So it is in parallel to the input capacitance. Now you will measure the sum of input plus your capacitance plus some stray capacitance depending on layout.

Try to stabilise the unwanted capacitances. We got resolutions down to 0.1fF!

A further possibility is to operate a second one with a known very good (quartz dielectric) reference capacitor.

If these are connected to each other via a Flipflop and divider you will get a train of pulses first from one RC then from the second RC - easy to readout.

RHABE

Thank you, it is an important input for me. Up to which mechanical frequency have you used the system ? The frequency range can be for some applications quite low but for other it must be high enough in order to get the peaks. Thus the question.

"The op-amp needs sufficient loop gain so that R_F / A_VOL < X_C coax." And "cheap 5MHz op-amp" ...

Oops! Actually, to use the example's values, this means the op-amp needs an f_T well above 5MHz, or the coax capacitance must be well below 300pF, or R_F must be lower than 22M, for good accuracy at the higher measurement frequencies.

Thank you it is a solution which is for me due to its simplicity quite interesting, as the solution RHABE suggested, I shall have to think it over and see how I can use one of them.

Since the whole circuit will be about 6..8 mm (1/4..1/3 ") from the capacitance the parasitic C will be quite small even in comparison with the Cx value.

I see that I was not optimistic but realistic expecting GOOD suggestions from the team.

Thanks to all for participation and interest, the discussion is not closed if anybody has another suggestion I will be delighted but this does not reduce the value of the input till now.

Thanks again

Nick

Of course, but it will take some time since it is a new project and the finances are not yet very clear.

I shall start with a paper analysis and if possible with a circuit simulation and try to make some optimizations before I start any think real.

Small caps can also be measured with the "substitution method " (General Radio's terminology). If you have a bridge that can measure 100 pf with a resolution of .1 pf (or even .01 pf), you can balance out a stable 100 pf device, then parallel it with the unknown device of 1 to 10 pf. Balance the bridge again, and subtract the two values to get the unknown value.

And make it up to 1000 times per second! Wow! This is in fact NOT the solution I can use since I will never be so fast.

What I need is a signal - voltage or current - proportional to the capacitance value which I can process and use for further actions.

Why not?

FET switches are pretty fast.

We did switching in the above mentioned accelerometer circuitry typically in the range of 10KHz to 10MHz.

But this is not directly suited to your problem as this circuit is measuring (C1-C2)/(C1+C2) and this is proportional to (delta-x)/x if the metallic plate moves in parallel and no stray capacitance is working.

This gives a pulse width modulated waveform that was used as analog voltage after low pass filtering as the intended bandwidth of the devices varied between some KHz and some Hz.

Counting individual time intervals is possible but will need an exceedingly fast counter or digital divide by n that has some unwanted delay time..

Measurement at the very low frequency you are suggesting will give some much bigger difficulties.

So may be you think about some modulation.

RHABE

Regards.

Good answer mathematically delt with.

I am not a mathematition type engineer but somewhat a practical technologist.

In simple words to measure small resistance, capacitors or inductors [passive components] a 4wire measurement network is required to cancell measuring cables' effects.

Looking at this drawing four years later, I'm surprised I didn't add a 90-degree phase shift in the reference side. Normally I do this with an integrator op-amp stage (-90º works as well as +90º, simply giving an inverted output from the multiplier). I see the 90º angle signaled in the drawing.

Also, in answer to a question about the use of a '4053 spdt switch in place of a multiplier, we're talking here about synchronous detection, or rectification. This can be done by creating a new inverted form of the signal, and switching back and forth between the signal and its -180º version, at the same frequency and phase as the signal (e.g., driven from the oscillator source). You simply average the switch's output to get the answer, e.g. with the RC shown in my drawing. Any signals not synchronous and in phase, will average to zero. (The '4053 switch approach also rectifies signals at all the odd harmonics of the reference, whereas the multiplier does not.)

Those values and those frequencies can be measured with a General Radio 1615 (1620 for a system with oscillator and detector). It is a transformer ratio arm bridge built in the early '60s, but they are available on the used market. It was the most accurate C-measuring device for many years. Details at:

http://www.ietlabs.com/pdf/Datasheets/1620.pdf

Hi,

Your post is not very clear. I have an old vacuum tube L-C meter with a 3pF full scale range. It is a Tektronics model 130. The test frequency is 100-200kHz. Are you saying that you have to measure the capacitor at low frequencies? I also have a digital capacitance meter that was $15 kit. Are you trying to design you own?

-S

My post is clear at least for me: the about 4pF capacitance changes continuously its value over time with frequencies (of the changes) from zero to 1 kHz. Its value is a measure for the changes cause.

Great! Now I've got it clear (I think). Please confirm:

1. The instantaneous value of the capacitance is independent of the frequency of the applied electrical signal.
2. The value of the capacitance changes with a frequency of up to 1kHz.
3. You want to measure the capacitance, sampling at up to 1kHz (or rather tracking the value with a response time such that you can follow the variation at up to 1kHz).

I don't think I'm alone in confusing the use of the word "frequency". When using the terms "capacitance" and "frequency" in the same sentence I believe it's natural to assume that the frequency refers to an electrical AC signal.

We can move on (I hope).

Do you have a (practical) limit to the frequency of the electrical signal you can use to 'excite' the capacitor?

1-YES changes are due to an external effect. 2-YES frequency can be zero to several hundred Hz but a surge can reach an frequency of 1 kHz (as a component in case of a Fourier transform). 3-YES again the output signal can be (after a good filtering) passed to an ADC converter and further processed for non-linearity and temperature influences. There are solutions available of the shelf but for frequencies in the range of 10 to max 25 Hz. If one does not want to get impulsive loads recognized those are sufficient. In some applications even under Hz dynamics are enough. My thought was that due to rather high frequency it would be better to have an analog circuit and at the end make the transfer to digital. The logical succession was : oscillator / circuit to obtain a voltage whose amplitude is proportional to capacitance changes / filter /analog correction for offset / digital / correction of influences as non-linearity and temperature on gain and offset / further use. As for the frequencies I though about 20 kHz for the oscillator and 2..3 kHz low-pass filter second order if possible. I came on CR4 in order to verify my way of thinking since although I deal with instrumentation and data processing am not very familiar with all circuits. The suggestion I got is in same direction but simpler. If you want I can later show what I thought before coming. I write "later" because i do not want to influence the way other think it would penalize results! As I already wrote since price and dimensions will be important I consider the discussion still as OPEN and will be very thankful for any input. Resolution (the question arose) has to be around 1/1000. Uncertainty is not so stringent and the device being calibrated more important is the repeatability. Thanks to all Nick

Ah, I also misunderstood, thinking you were referring to a capacitance measurement frequency, not its rate of variation.

You can use the simple HP scheme I outlined above, although with a say 25kHz measurement frequency, and set the multiplier's filter at say 500us, and sample the resulting DC-to-1kHz voltage at say 5ksps, and thereby see any rapid variations in capacitance. How much resolution do you need? You may want to use a multi-pole filter to eliminate 25kHz ripple.