The existence of an optimum triggering fraction for leading-edge timing with scintillation detectors stimulated the design of a circuit that would always trigger at the optimum fraction of the pulse height for any pulse height.^4,5 This circuit is now known as a Constant-Fraction Discriminator (CFD). An additional benefit of the constant-fraction discriminator is that it essentially eliminates amplitude-dependent time walk for signals having consistent rise times. The net result is optimum time resolution over a wide dynamic range of pulse heights.

The pulse shaping employed in a constant-fraction timing discriminator is shown in Fig. 3. The input signal is split into two parts. One part is attenuated to a fraction f of the original amplitude, and the other part is delayed and inverted. These two signals are subsequently added to form the constant-fraction timing signal. The delay is chosen to make the optimum fraction point on the leading edge of the delayed pulse line up with the peak amplitude of the attenuated pulse. Consequently, adding the two signals yields a bipolar signal with a zero-crossing that corresponds to the original point of optimum fraction on the delayed signal. The constant-fraction discriminator incorporates a timing discriminator that triggers on the zero-crossing, thus providing a time marker at the optimum fraction of pulse height. Since the time of zero-crossing is independent of pulse amplitude, the constant-fraction discriminator delivers virtually zero walk. (In practice, a minuscule amount of walk is still experienced for pulse amplitudes below 200 mV, because the zero-crossing comparator requires a finite amount of charge to move its output from the "0" to the "1" state.)

A functional representation of the circuits in a constant-fraction discriminator is shown in Fig. 4. As previously discussed, the input signal is delayed and inverted, and a fraction of the undelayed signal is subtracted from it. A bipolar pulse is generated, and its zero-crossing is detected and used to produce an output logic pulse. A leading-edge arming discriminator provides energy selection and prevents the sensitive zero-crossing comparator from triggering on any noise inherent in the baseline preceding the pulse. The attenuation factor f is the fraction of the pulse height at which timing is desired. Walk and jitter are minimized by proper adjustment of the zero-crossing reference, and by selection of the correct attenuation factor and delay. As shown in Fig. 2(b), the timing resolution from a constant-fraction discriminator is better than that from a leading-edge timing discriminator, even for a narrow range of pulse heights. Also, the time resolution with a CFD is remarkably insensitive to the choice of triggering fraction. In the scintillation detector application, a fraction somewhere between 0.2 and 0.4 is a reasonable choice. For further examples of actual performance, see the data sheets on Constant Fraction Discriminators.

⁴D. A. Gedcke and W. J. McDonald, Nucl. Instr. and Meth. 55(2): 377 (1967).
⁵D. A. Gedcke and W. J. McDonald, Nucl. Instr. and Meth. 58(2): 253 (1968).

Figure 3.  Formation of the Constant-Fraction Signal.
 

Figure 4.  Functional Representation of a Constant-Fraction Discriminator.