Physics and Engineering of Radiation Detection

392 Chapter 6. Scintillation Detectors and Photodetectors

effective resistance seen by the output signal will actually be

1

Rl,eff

=

1

Rl

+

1

Ra

,

orRl,amp =

RlRa

Rl+Ra

. (6.5.22)

Rn−1

Vout Rl Rn

Ra

Cs

Anode

+HV

C

Amplifier

Figure 6.5.20: Typical output circuit of a PMT with amplifier

having internal resistanceRa. The effective resistance seen by the

output signal depends onRlas well asRa.

The productRl,effCsis generally referred to as the time constant of the output
circuit, though it is also not uncommon to seeRlCsbeing referred to as the time
constant instead. The capacitanceCsrepresents the combined capacitance of the
tube and the stray capacitance of the cables and is generally very small. SinceCs
depends on the mechanical structure of the tube and the cables therefore it can
not be varied much. On the other hand, one is at liberty to choose a value of the
load resistanceRlaccording to the requirements. Now, there are two competing
requirements for this choice. One is the cutoff frequency, which should be as large
as possible. This would require the load resistance to be as small as possible. The
other requirement stems from the fact that the load resistance is used to convert
the output current into voltage and hence, for reliable measurement of the output
voltage, its value should be as large as possible. But we saw making it large has the
downside of making theRl,efflarge and cutoff frequency small. Another problem
is that the largerRlis the higher is the potential drop across it, which would make
the potential drop between the last dynode and the anode small. The consequence
of this would be the buildup of space charge at the last dynode and poor collection
of charges leading to nonlinearity in the response, certainly not a very desirable
effect. It is apparent that these conditions can not be met at the same time and
one must choose an optimized solution based on the requirements of the particular
application.