# How to precisely measure small charges?

I have a phenomenon which creates (small) displacements of charges (that I cannot quantify for now, this is the main problem, let's say that the charge surface density will be the same as when you rub an inflated balloon against your hair), and I want to measure it. My idea is to use a small capacitor (0.1 pF) which will store the displaced charges, linked to a precise oscilloscope. I need the oscilloscope to be interfaced with my pc hence someone advised me to get one on picotech.com. I guess I most of all need a very sensitive oscillo, which will be able to measure very small voltages. And I guess I need the smallest capacitance possible because of V = q/C.

What do you think of this approach ? I'm sure there are effects that I didn't take into account (I'm a mathematician, beginner in electronics), and could someone advise me which oscilloscope I could buy, please ? My budget is up to 400 euros. Thank you !

• I think the input capacitance of your oscilloscope will swamp a 0.1pF capacitor. You must give us an estimate of how much charge you want to observe. At the end of the day, 400 euros is probably not going to get high-end test equipment. – Elliot Alderson Aug 9 '19 at 21:10
• @ElliotAlderson let's say that the charge surface density will be the same as when you rub an inflated balloon against your hair, which then can stick to the ceiling – Alfred Aug 9 '19 at 21:21
• That's not helpful. I've never measured the charge from that experiment. How many coulombs are you talking about? Why are you talking about "charge surface density" instead of absolute amounts of charge? I think you need to give us much more information. – Elliot Alderson Aug 9 '19 at 21:24
• In that case, you need something more along the lines of an electrometer. This topic is also discussed on EEVblog, here and here. – Dave Tweed Aug 9 '19 at 21:28
• Dave Tweed has it. Search for an "electrometer amplifier" to use as a sensitive front end to a rather ordinary scope. – Brian Drummond Aug 9 '19 at 21:59

If you use a transimpedance charge amplifier, the input capacitance of the amplifier is to a virtual ground so it only has an effect (to first order) on noise.

simulate this circuit – Schematic created using CircuitLab

R1 provides a DC path for the bias current and should be very high value

Ignoring R1, output voltage change for input charge q is -q/C1

The op-amp could be an electrometer type, but if you have no idea of the charge magnitude you might want to start with a $2.50 (or 0.25) one before you use a$25 one.

Maybe try 100pF or 1nF and 10M (time constant 1ms/10ms) assuming that fits with the timing of your charge impulse.

A decent fA bias current op-amp can probably provide a useful output with signals of 100uV or less, which represents a charge of 0.01pC with 100pF. You can add an amplification stage afterward if you want a bit more voltage- wide-bandwidth scopes tend to be pretty noisy even at x1.

I suspect you have quite a bit of charge based on your ballpark description and you may have to have more capacitance and/or series resistance to avoid damaging voltages- anothe reason to start with a cheaper socketed op-amp.