Simple method of measuring small capacitances.

22.05.2020 18:17

I stumbled upon this article on Analog Devices' website while looking for something else. It looks like instructions for a student lab session. What I found interesting about it is that it describes a way of measuring small capacitances (around 1 pF) with only a sine-wave generator and an oscilloscope. I don't remember seeing this method before and it seems useful in other situations as well, so I thought I might write a short note about it. I tried it out and indeed it gives reasonable results.

Image by Analog Devices, Inc.

I won't go into details - see original article for a complete explanation and a step-by-step guide. In short, what you're doing is using a standard 10x oscilloscope probe and an unknown, small capacitance (Crow in the schematic above) as an AC voltage divider. From the attenuation of the divider and estimated values of other components it's possible to derive the unknown. Since the capacitance of the probe is usually only around 10 pF, this works reasonably well when the unknown is similarly small. The tricky part is calibrating this measurement, by estimating stray capacitances of wires and more accurately characterizing the resistance and capacitance of the probe. This is done by measuring both gain of the divider and its 3 dB corner frequency.

Note that the article is talking about using some kind of an instrument that has a network analyzer mode and can directly show a gain vs. frequency plot. This is not necessary and it's perfectly possible to do this measurement with a separate signal generator and a digital oscilloscope. For measuring capacitances of around 1 pF using a 10 pF/10 MΩ probe a signal generator capable of about 100 kHz sine-wave is sufficient. Determining when the amplitude of the signal displayed on the scope falls by 3 dB probably isn't very accurate, but for a rough measurement it seems to suffice.

The measurement depends on the probe having a DC resistance to ground as well as capacitance. I found that on my TDS 2002B scope you need to set the channel to DC coupled, otherwise there is no DC path to ground from the probe tip. It seems obvious in retrospect, but it did confuse me for a moment why I wasn't getting good results.

I also found that my measured signal was being overwhelmed by the 50 Hz mains noise. The solution was to use external synchronization on the oscilloscope and then use the averaging function. This cancels out the noise and gives much better measurements of the signal amplitude at the frequency that the signal generator is set to. You just need to be careful with the attenuator setting so that noise + signal amplitude still falls inside the scope's ADC range.

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