Physics and Engineering of Radiation Detection

8.1. Preamplification 469

be achieved if no current flows into the preamplifier’s input. This implies that the
amplifier’s input impedance should be very large (Ra≈∞).

Ra

Cf

Cd
Vout

Figure 8.1.3: Basic principle of a charge sen-

sitive preamplifier. The charge accumulated

on the detector capacitanceCdis allowed to

integrated on a feedback capacitorCf.The

voltage at the output is then proportional to

the input charge.

Fig.8.1.4 shows a detector, whose output is connected to theinvertinginput of a
charge integrating preamplifier. Without the feedback capacitor, this circuit would
act as an inverting voltage sensitive preamplifier with the output voltage of

Vout=−AVd. (8.1.11)

HereVdis the input voltage andAis the preamplifier gain. Typical operational
amplifiers have very large gains (A1). If we now connect a feedback capacitor
to the circuit, the input voltage would be given by the sum of voltage across this
capacitorVfand the output voltage, i.e.,

Vd = Vf+Vout

= Vf−AVd

⇒Vf =(A+1)Vd. (8.1.12)

This of course is valid only if the preamplifier has infinite impedance, which is
generally true to a good approximation. UsingQ=CV,wecanwritetheabove
relation in terms of accumulated charges on input and feedback capacitances.

Qf

Cf

=(A+1)

Qin

Cin

⇒Cin =(A+1)Cf

Qin

Qf

≈ (A+1)Cf (sinceQin=Qf) (8.1.13)

HereQinandCinare the charge and capacitance at the input of the amplifier re-
spectively. This equation shows that the input capacitance is a function of feedback
capacitance and gain of the amplifier.Cinis sometimes referred to as thedynamic
capacitance of the preamplifier. Note thatCinis not detector’s capacitance, which
we will include in the equations later. A quantity that is often quoted is thecharge
gain, which is obtained by taking the ratio of the output voltage to the correspond-
ing input charge. Unlike the conventional open loop gainA, this gain is not a