Physics and Engineering of Radiation Detection

8.3. Pulse Shaping 485

Cd Ri

Rd Ci

Integrator

CR−RC

Shaper

CR−RC

Shaper

Differentiator

(a) In Out

(b)

Figure 8.3.6: (a) A simple CR-

RC shaper and (b) its response to

two different input pulses: a step

input and a more realistic pream-

plifier output. A perfect step input

does not produce any undershoot

while a significant undershoot can

be expected when the output of a

practical preamplifier is fed into the

shaper. This undershoot can result

in underestimation of the height of

a subsequent pulse.

The choice of time constant of a CR-RC shaper depends on the particular require-
ments of the detection system. The measurement resolution and high rate capability
are two competing factors that must be considered to find an optimized solution.
Good resolution demands that the time constant be large enough to ensure complete
integration of the detector signal. For example for scintillation detectors the time
constant is chosen to be at least three times the decay constant of the scintillator.
However such a long pulse duration might be problematic in high rate situations
particularly due to the pulse undershoot problem mentioned above. In such a case
the time constant is shortened at the expense of resolution.
Whatever time constant we choose, there is always a possibility for a pulse to
arrive before the previous one has reached the baseline. If a large number of pulses
arrive during the undershoot times the measured pulse amplitudes will be far less
than the actual amplitudes. It may lead, for example to significant broadening of
the measured energy distributions and consequently the system resolution will be
seriously affected. Fortunately this problem can be solved by the so called pole-zero
cancellation circuitry.

B.1 Pole-ZeroCancellation.....................

As we saw above, the output of a realistic preamplifier can not be approximated by
a step input pulse. In fact the exponentially decaying pulse from the preamplifier
output looks very similar to the step input response of a CR filter. This implies
that the response of a CR-RC shaper to such a pulse can be studied by assuming
a CR-CR-RC circuit with a step input pulse. To study such a circuit we should
take a look at itstransfer function, which is simply a mathematical representation
of its behavior under different conditions. For computational purposes the transfer
function is mostly transformed into a complex space with a continuous or a discrete
domain (Laplace domain for continuous function orZdomain for discrete function).