Physics and Engineering of Radiation Detection

470 Chapter 8. Signal Processing

dimensionless quantity. Charge gainAQcan be computed from

AQ =

Vout

Qin

=

AVin

CinVin

=

A

Cin

=

A

A+1

1

Cf

≈

1

Cf

(sinceA1). (8.1.14)

This shows that the charge gain can be increased by choosingCfof lower capacity.

Vout

Vf

Cf

Cd VdVin

+

−

=

Figure 8.1.4: Schematic of a simple charge

sensitive preamplifier. The detector is shown

as a capacitive load and is connected to the

inverting input of the preamplifier. Without

the feedback capacitor, the circuit will work

as an inverting voltage sensitive preamplifier

since the input impedance of the preamplifier

is very large.

Another quantity of interest is thecharge transfer efficiencyηinof the preampli-
fier. It characterizes the efficiency of transfer of charge ondetector’s capacitanceto
the feedback capacitance. Only in ideal case it is possible to have a 100% charge
transfer efficiency but it can be approached up to a good approximation by choosing
appropriate capacitances.ηinis defined as

ηin=

Qf

Qt

, (8.1.15)

whereQtis the total charge on detector and dynamic capacitance. If we represent
detector capacitance byCd,thenQt=Qd+Qin. Using this and the fact that
Qf=Qin=CinVin, we can write the charge transfer efficiency as

ηin =

Qin

Qin+Qd

=

1

1+Qd/Qin

=

1

1+CdVd/CinVin

=

1

1+Cd/Cin

. (8.1.16)

Here we have made use of the fact that the voltage across the detector capacitance is
equal to the voltage at amplifier’s input stage, i.e.,Vd=Vin. This is a true statement
as can be verified by inspecting Fig.8.1.4. It is apparent from this expression that a