# How to build a charge amplifier with fC resolution and low bandwidth?

#### Sim

Nov 16, 2022
1
Hello, I am quite new to electrical engineering, I only had a few lectures at my uni, so I only know the bare basics.
My goal is to measure a charge on a single particle that flies through a faraday cage. The time the particle stays in the cage is from 0.1 to 1 sec, and its charge is in the range of fC.
I used TINA from TI to build a circuit that should work, but when I physically built the circuit, I found that it did not work as intended.
Can someone wiser than I am, help me or just comment if the circuit makes sense?

Below is the first circuit that I designed. In this configuration, I can clearly measure 10pC.
The problem comes when I want to go one order lower into fC range.
The gain on the first op-amp is maxed out because when I increase R1 the bias current will saturate the op-amp, and if I lowered the C2 the induced charge would leak, and I am not able to preserve the shape of the input signal.
This makes the gain on the first op-amp 2x10^7.
My solution to this was to introduce the second op-amp in voltage multiplier configuration that will increase the gain by approx 3 orders of magnitude. So far, so good.

Now comes the problem.
The bias current from the first op-amp lifts the baseline of the inverting input to the second op-amp by a few hundred millivolts. This causes problems in the amplification because the noninverting input is at ground potential. Therefore, I am limited in the amplification of the second stage because this offset adds to the gain and oversaturates the second amplifier quite easily.

My idea, which did not work, was to add a third op-amp as a voltage follower of inverting input into U2, that filters the signal. This, in my head, would negate the problems with the lifted base voltage since I would supply the same base voltage to the noninverting input of U2, and the signal only would pass and be amplified. Which would give me those two orders of magnitude that I desperately need.

I have condensers next to each power rail (they are deleted in this figure to make it more readable).
According to TINA, this approach should work, but in reality, I am not able to achieve it. The green is the input signal, and red is the output; where at the start, you can see the tendency to oversaturation, but it is counteracted by the voltage follower U3, and after the voltage stabilizes, I inject 100fC into the circuit with on the output is converted into 40mV which I can measure.

Sadly this works only in the TINA. In reality, I get oversaturated signal which does not decay, so it seems like that voltage follower does not work.
Can anybody help me or tell me what good practices are in building such circuitry?

#### dragon

Oct 31, 2022
248
Are u putting 3 transistors in series to get more amplification?
The problem is maybe the first transistor isnt sensitive enough for the gate to open with such a small current.

You need an amplifier which has no on threshold, it just activates on any amount of signal. I think you need to do this when amplifying hall voltages,.because its microscopic how much volts you get.

EDIT... i know you are using op amps, but op amps are made from transistors and they might not be sensitive enough for the low signal. maybe 10^7 is a correct amplification factor, i was thinking it would be less but thats probably because i've always been using high voltages for my base voltages lately.

Last edited:

#### Alec_t

Jul 7, 2015
3,600
The bias current from the first op-amp lifts the baseline of the inverting input to the second op-amp by a few hundred millivolts.
Can't you cancel this out by off-setting the input of the second opamp appropriately?

Feb 19, 2021
784
There are OpAmps with much lower Ibias than you are using :

Of course you have to pay great attention to PCB leakage paths, humidity, air contaminants..

See following , section on C leakage.

And this on soakage :

Regards, Dana.

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