Author Topic: Fun way to measure input capacitance of scope  (Read 148 times)

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Offline kronos

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Fun way to measure input capacitance of scope
« on: July 14, 2021, 05:53:59 pm »
I have been playing with the pros and cons of connecting a coaxial cable to the scope instead of the probe. I have also been checking the transmission line stuff. And I wondered how much the input capacitance of my scope really is (it is specified as 13 pF).
Yes, you can measure it in many ways. For example, connecting it via a resistor to a sharp square wave generator and looking to its rise time. I liked however the idea of measuring it with a nanoVNA. You can connect it (or any capacitor) to the VNA input (after calibrating), and it can measure it in the Smith Chart, sure. I have found however that this measurement is sometimes not very reliable.

So I have seen that connecting to the VNA a coaxial cable of known characteristics (impedance, velocity factor, length) and then connecting this coax to the scope (which is what you do when you use a direct coax connection instead of a probe, but without terminating it with a 50 ohm load) can help. At least I got correct measurements.

The method is based upon the response at the input of that coax when terminated by a capacitor (in this case, the input of the scope, as the 1 M ohm resistor is infinite in practice). It behaves as a notch filter, like in the figure.

So when you measure its reflection coefficient with the VNA (frequency range from 50 MHz to 200 MHz for example, depending on your cable length), you get this Smith chart:

Notice that you can measure the frequency at which it crosses the (-1,0) point (or zero impedance). This is the frequency of the notch in the frequency response.

It is easier and more precise to measure the phase with the VNA:

The searched frequency is the one where the phase reaches -180 degrees, and you see clearly the jump from -180 to 180.

In any case, it turns out that this frequency fulfills the following equation:

So you have just measured the frequency, and you know all other parameters except for the capacitance C. You can then clear it from the equation.

A small change in value of the capacitor makes a great change in the frequency of the notch, and this is very precisely measured by the phase plot of the VNA. So this method helps with very small capacitors, in pF range.

I have measured the input capacitance of my Rigol scope to be 12 pF with one vertical amplifier and 14 pF with the other. The specified value is 13 pF, so it seems to be OK.
« Last Edit: July 14, 2021, 06:17:27 pm by kronos »

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