Charge amplifier

Design

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.

Ideal circuit

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 v i n 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.

The circuit can be analyzed by applying Kirchhoff's current law at the node v₂, keeping ideal op-amp behaviour in mind.

I B = 0 in an ideal op-amp, so:

Furthermore, the capacitor has a voltage-current relationship governed by the equation:

Substituting the appropriate variables:

v 2 = v 1 = 0 in an ideal op-amp, resulting in:

Integrating both sides with respect to time:

If the initial value of v_o is assumed to be 0 V, this results in a DC error of:

Practical circuit

The ideal circuit is not a practical integrator design for a number of reasons. Practical op-amps have a finite open-loop gain, an input offset voltage and input bias currents ( I B ). This can cause several issues for the ideal design; most importantly, if v in = 0 , both the output offset voltage and the input bias current I B can cause current to pass through the capacitor, causing the output voltage to drift over time until the op-amp saturates. Similarly, if v in were a signal centered about zero volts (i.e. without a DC component), no drift would be expected in an ideal circuit, but may occur in a real circuit. To negate the effect of the input bias current, it is necessary to set:

R on = R 1 | | R f .

The error voltage then becomes:

The input bias current thus causes the same voltage drops at both the positive and negative terminals. A practical circuit is shown below.

Also, in a DC steady state, the capacitor acts as an open circuit. The DC gain of the ideal circuit is therefore infinite (or in practice, the open-loop gain of a non-ideal op-amp). To counter this, a large resistor R F is inserted in parallel with the feedback capacitor, as shown in the figure above. This limits the DC gain of the circuit to a finite value, and hence changes the output drift into a finite, preferably small, DC error. Referring to the above diagram:

where V I O S is the input offset voltage and I B I is the input bias current on the inverting terminal. R f ∥ R 1 indicates two resistance values in parallel.

In practice, the gain of the circuit is expressed in charge input required to obtain a voltage output, such as picocoulomb per volt.

Applications

Common applications include amplification of signals from such as piezoelectric sensors and photodiodes, in which the charge output from the transducer is converted into a voltage.

Charge amplifiers are also used extensively in instruments measuring ionizing radiation, such as the proportional counter or the scintillation counter, where the energy of each pulse of detected radiation due to an ionising event must be measured. Integrating the charge pulses from the detector gives a translation of input pulse energy to a peak voltage output, which can then be measured for each pulse. Normally this then goes to discrimination circuits or a multi channel analyzer.

Charge amplifiers are also used in the readout circuitry of CCD imagers and flat-panel X-ray detector arrays. The amplifier is able to convert the very small charge stored within an in-pixel capacitor to a voltage level that can be easily processed.

Advantages of charge amplifiers include:

Other uses