# charge amplifier frequency reponse

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#### Skyland

##### Junior Member level 3
I have designed a charge amplifier to convert the charge from the force sensor into voltage. The force of the sensor is dynamic from 0 to 100N which is modelled as a voltage source V3 with a sine wave oscillating from 0 to 1KHz. C2 is the sensor static capacitance. The current source B1 is differentiating the voltage from V3. The system need to be able to respond between 0.1 to 1KHz. The problem is as shown in the AC simulation result the circuit on the right hand side does not give a low pass filtered response with a cut off frequency of 1KHz. I have made the circuit on the left hand side with a current source just to confirm that the charge amplifier is designed properly and the response is is as expected so the problem seem to be coming from the charge source. What could be the problem?

#### FvM

##### Super Moderator
Staff member
The problem is as shown in the AC simulation result the circuit on the right hand side does not give a low pass filtered response with a cut off frequency of 1KHz.
No, the first order low-pass is compensated by the differentiate (ddt) operation.

#### Skyland

##### Junior Member level 3
No, the first order low-pass is compensated by the differentiate (ddt) operation.
Any suggestions of how this could be solved and still keeping the force sensor into play?

Skyland

### Skyland

Points: 2

#### Skyland

##### Junior Member level 3
Change 1K Rfb to 10M or more is mandatory for a charge Amp

Chopper stabilized will give lowest input DC offset.

Simple example here https://www.mmf.de/instrumentation.htm

The frequency response is fine with the circuit on the left hand side, I am not sure how increasing Rfb would change the response of the circuit with the sensor source?

#### SunnySkyguy

The gain is an impedance ratio of Rf/Rin and the piezo sensor is very high impedance with a motional capacitance.

So like matching a 10:1 scope probe R ratio effects flat frequency response if Rsensor is known. Otherwise make it big so that charge is amplified, but not DC offset from input bias current or input offset voltage.

Skyland

### Skyland

Points: 2

#### Skyland

##### Junior Member level 3
The gain is an impedance ratio of Rf/Rin and the piezo sensor is very high impedance with a motional capacitance.

So like matching a 10:1 scope probe R ratio effects flat frequency response if Rsensor is known. Otherwise make it big so that charge is amplified, but not DC offset from input bias current or input offset voltage.

isn't the gain 1/Cf?

I have changed Rf and the response is still not a high pass with a cut off of 1KHz

#### SunnySkyguy

Anthing with high gain @ 1kHz in a charge Amp will not be affected by the Rf when sufficiently large. The RC time constant defines the HP break point; the LP breakpoint is defined by the device GBW and anything up in the 1MHz area is internal feed forward stuff, which can be neglected.

Your Response for acceleration should be flat to near DC depending RC time constant.
The upper range depends on GBW product and choice of amp.

As you might guess your choice is sub-optimal.
Velocity is the integral and position the 2nd integral of the output.

Check your source simulation , if you choose acceleration force then dq/dt is the input and thus the gain dV(f)/dq(f) should be flat over the region of interest.
Each sensor has a charge size Q . review https://www.colorado.edu/physics/ph...ctureNotes/nagle_phys1120_sp06_lectures22.pdf

1/2pi*Rf*Cf will determine the high pass break point.

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