Physics and Engineering of Radiation Detection

488 Chapter 8. Signal Processing

of circuit 8.3.8.

Solution:

Examination of transfer function 8.3.8 of circuit 8.3.8 reveals that if we choose

Rpz=τp/Cd, it will transform the numerator (RpzCds+1) into (τps+1).

This will cancel out the identical term in the denominator thus eliminating

the undershoot from the output. The transfer function in this case will become

H(s)=

τpτds

τp(τds+1)+τd

1

(τis+1)

. (8.3.9)

It should be noted that even a small drift inCdwill make the undershoot

reappear and the pole will not be totally eliminated. Modern systems em-

ploy additional circuitry to adjust for such changes automatically to keep the

undershoot at minimum.

B.2 BaselineShiftMinimization..................

In many applications it is desired that the electronic circuitry following the amplifiers
is AC-coupled. This might induce baseline shifts in the signal with varying count
rate. In order to actively minimize such base line shifts a baseline restorer circuitry is
introduced. One such circuit is shown in figure 8.3.9 Here the addition of another CR
differentiator after the RC integrator produces a bipolar pulse instead of a unipolar
one. Although such a circuit minimizes the baseline shifts but the longer duration of
its bipolar output makes it unsuitable for high rate applications. Its signal to noise
ratio is also worse than the simple CR-RC shaper.

Cd1 Cd2

Rd1 Rd2

Ri

Ci

Differentiator Integrator Differentiator

Figure 8.3.9: CR-RC-CR shaper. The output of this shaper is a bipolar

pulse which minimizes the baseline shifts.

8.3.C Semi-GaussianPulseShaping..................

The simple CR-RC pulse shapers we visited earlier work well for applications where
high resolution is not required and signal-to-noise ratio is not a very important
consideration. For systems where improvement in signal-to-noise ratio is of prime
importance, the simple RC integration circuitry must be replaced with a complicated
active integrator. Such networks can improve not only the signal-to-noise ratio but
are also capable of decreasing the width of the output pulse. Fig. 8.3.10 shows a
typical 2-stage active integrator circuit.