Charge amplifier

A charge amplifier is an electronic current integrator that produces a voltage output proportional to the integrated value of the input current. This is effectively a measurement of the electrical input charge; hence the naming of the device.

The amplifier offsets the input charge using a feedback reference capacitor, and produces an output voltage inversely proportional to the value of the reference capacitor but proportional to the total input charge flowing during the specified time period; hence the circuit acts as a charge-to-voltage converter. The gain of the circuit depends on the values of the feedback capacitor and the feed-in resistor.

Charge amplifiers are usually constructed using an operational amplifier or other high gain semiconductor circuit with a negative feedback capacitor. The input current is offset by a negative feedback current flowing in the capacitor, which is generated by an increase in output voltage of the amplifier. The output voltage is therefore dependent on the value of input current it has to offset and the inverse of the value of the feedback capacitor. The greater the capacitor value, the less output voltage has to be generated to produce a particular feedback current flow.

The input impedance of the circuit is almost zero because of the Miller effect. Hence all the stray capacitances (the cable capacitance, the amplifier input capacitance, etc.) are virtually grounded and they have no influence on the output signal.

An "ideal circuit" for analysing charge amplifier operation is shown below:

The circuit operates by passing a current that charges or discharges the capacitor C_f during the time under consideration, which strives to retain the virtual ground condition at the input by off-setting the effect of the input current. Referring to the above diagram, if the op-amp is assumed to be ideal, nodes v₁ and v₂ are held equal, and so v₂ is a virtual ground. The input voltage passes a current ${\displaystyle {\frac {v_{in}}{R_{1}}}}$ through the resistor producing a compensating current flow through the series capacitor to maintain the virtual ground. This charges or discharges the capacitor over time. Because the resistor and capacitor are connected to a virtual ground, the input current does not vary with capacitor charge and a linear integration of output is achieved.

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Wikipedia