Measuring capacitance with an oscilloscope

Using Arduino General Electronics
1

I want some advice from the real electronics experts here. :slight_smile:

I saw this interesting video by Martin Lorton about measuring capacitance:

I decided to reproduce his test results myself.

I used his test circuit:

Feeding in a 1 kHz signal (square wave) at 1V peak to peak, we see this:

Zooming in on one cycle, we find the point where the voltage reaches 63.2% (that is, 632 mV).

We are choosing 63.2% because this is:

1 - e-1 = 0.63212

Switching to the "time" cursor we measure how long it takes to charge to this point:

From the Wikipedia article, we read:

The RC time constant, the time constant (in seconds) of an RC circuit, is equal to the product of the circuit resistance(in ohms) and the circuit capacitance (in farads), i.e. T = R * C.

Thus C is equal to T / R

I measured 47 uS as the time, so thus the capacitance was:

C = 0.000047 / 1000

In other words, 47 nF, which is in fact the capacitor I used. So far so good, the theory agrees with practice. And I've learnt a bit more about capacitors.

Now the interesting thing is if we increase the frequency. Say, to 3 kHz. The original waveform (the 1 kHz one) is saved in the background in white.

Now it looks like the capacitor barely has time to discharge before recharging again.

And if we increase to 8 kHz:

Now the capacitor is not fully discharging nor fully charging.

I presume the frequency at which this starts to happen has a name. Is it the "cut-off frequency"?

2

in most texts yes

3

The pictured waveforms are close to the cutoff frequency, within a tolerance level that I find visually satisfying. But look at the peak to peak voltages : 600mV and 1010mV for the output and input channels. Take the ratio :

600/1010 = .594

When you adjust the frequency so that the VOLTAGE ratio is .707, that is the 3db cutoff frequency.
At the 3db cutoff frequency, the POWER ratio is 1/2 and the voltage ratio is .707 . The cutoff frequency is less than 8khz by an amount that fits within my tolerance for variation.

4

The ratio of peak voltages being 1/sqrt(2) only applies to sinusoidal waveforms, the peak voltage
of a composite waveform has no simple relationship to the energy of the signal, for that
you need the RMS voltage or current.

The cut-off frequency is where 50% of the energy/power is rejected, and RMS values scale
as square-root of power.

A composite waveform consists of several frequencies simultaneously so that the attentuation
will in general be different for the different components, so the notion of a cut-off frequency
isn't really appropriate for the waveform as a whole, just for sinusoidal signals.

5

OK, thanks for that. Measuring with a sine wave I see:

1 kHz

3 kHz

5 kHz

10 kHz

20 kHz