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Gated-Integrator Pulse Shaping With germanium detectors, the time required to collect all of the charge from a gamma-ray interaction in the detector depends on the location of the interaction in the detector. The charge collection time can vary from 100 to 200 ns in a small detector, and by as much as 200 to 700 ns in a large germanium detector. As a result, the preamplifier output pulses have rise times varying over that same time range. In conventional pulse-shaping amplifiers (e.g., semi-Gaussian pulse shaping), these variations in rise time can affect the amplitude of the amplifier output pulse and cause degradation of the energy resolution. The longer rise times on the preamplifier output pulse cause a lower amplitude on the amplifier output pulse. This effect is called the "ballistic deficit." For shaping time constants in the range from 6 to 10 µs, the effect is negligible, because the peaking time of the amplifier output pulse is very long compared with the longest charge collection time in the germanium detector. However, when high counting rates are anticipated, much shorter shaping time constants must be used. The contribution of ballistic deficit to resolution degradation increases rapidly as the shaping time constant is reduced below 2 µs. Consequently, ballistic deficit becomes the dominant limitation on energy resolution at high counting rates using conventional, semi-Gaussian, or triangular pulse-shaping amplifiers. The gated-integrator amplifier solves the ballistic deficit problem by integrating the signal until all the charge is collected from the detector. Figures 16 and 17 illustrate the principle. For simplicity, the prefilter has been depicted as a delay-line shaping amplifier. The width of the prefilter pulse determines the shaping time for the entire gated-integrator amplifier. For illustration purposes, two extreme rise timecases are drawn for the preamplifier pulse: zero rise time (solid line) and a long rise time (dashed line). At the output of the prefilter, the zero rise time pulse produces a rectangular pulse shape, while the longer rise time pulse generates a trapezoid. The duration of the trapezoid is longer than the rectangular pulse by an amount equal to the preamplifier pulse rise time. The gated-integrator portion of the amplifier serves two functions. It reduces the high-frequency noise contribution, and it eliminates the ballistic deficit. Before the prefilter pulse arrives, switch S1 is open and switch S2 is closed, causing the gated-integrator output to be at ground potential. At the instant the prefilter pulse arrives, switch S1 closes and switch S2 opens, and the prefilter signal is integrated on capacitor CI. The integration period is set to last as long as the longest prefilter pulse duration. Consequently, all pulses generate the same output pulse amplitude from the gated integrator, independent of their rise time at the preamplifier output. At the end of the integration period, S1 opens and S2 closes to return the output pulse to baseline quickly. Because the filter characteristics are switched at certain points in time, the gated integrator is called a time-variant filter. In contrast, the amplifiers previously discussed have time-invariant filters. The signal-to-noise ratio of the gated integrator approaches the performance of a time-invariant filter with a true triangular pulse shape. This makes it virtually the ideal filter for the short shaping times required for high counting rates. Because it is difficult to implement a delay-line prefilter with a quality that is adequate for germanium detectors, practical gated integrator amplifiers typically utilize active RC networks in the prefilter. This results in the pulse shapes shown in Fig. 18. The deviation from a rectangular prefilter shape and the extra integration time required to accommodate the longest charge collection times causes a minor loss of signal-to-noise ratio compared with an ideal triangular pulse shape. However, the signal-to-noise ratio is less important than elimination of ballistic deficit for optimum energy resolution at the short shaping times required for high counting rates. Gated-integrator amplifiers permit operation at ultra-high counting rates with germanium detectors without a substantial sacrifice of energy resolution (Fig. 19).
Figure 16. A Simplified Representative of the Gated-Integrator Amplifier.
Figure 17. Pulse Shapes in the Simplified Gated-Integrator Amplifier: (a) at the Preamplifier Output, (b) at the Prefilter Output, and (c) at the Gated-Integrator Output. See the corresponding points in Figure 16.
Figure 18. Pulse Shapes in the Model 973 Gated-Integrator Amplifier for a 5-µs Integration Time.
Figure 19. The 1.33-MeV
Gamma-Ray Peak from a 60Co Source, Acquired with (a) a
Model 672 Amplifier with a Triangular Pulse Shape and 0.5-µs Time Constant, and (b) the Model 973 Amplifier with
a 2.5-µs Integration Time. Maximum
amplifier throughput is 73,000 counts/s for both cases. |
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