Abstract :
The emphasis of this paper, in which a systematic approach to nuclear pulse shaping is presented, is on the power, versatility, and practicability of lumped-element transfer functions and their associated networks. The approach consists of first determining a suitable theoretical, but realizable, lumped-element transfer function for the problem at hand -- pulse height analysis is the example used in this paper -- and of then synthesizing this transfer function in a way that minimizes the sensitivity of the final output-pulse shape to network element variations. Finally, the network is built and tested using elements having tolerances determined by a sensitivity analysis of the chosen circuits. The unipolar transfer functions and networks discussed in this paper have better signal-to-noise ratios than any other published lumped-element transfer functions or networks. One unipolar pulse function has a signal-to-noise ratio that is only 0.5% worse than that of the delayline-produced triangular pulse. Since the bipolar pulses discussed in this paper are more symmetrical about the base line than those of any other published lumped-element network, spectral peaks at high count rates obtained with these networks will be more symmetrical than those obtained with any other lumped-element network. Furthermore, these symmetrical pulses will produce smaller countrate-dependent base-line shifts than will less-symmetrical equal-area pulses. Although the networks that are discussed in this paper are extremely useful for pulse height analysis, the systematic approach that is presented is more important because of its obvious extensions to other pulse shaping problems in nuclear physics.
