# Constant Fraction Discriminator

A constant fraction discriminator (CFD) is a special discriminator for processing electrical pulses from radiation detectors, for example . It is used to generate exact time stamps from wide pulses with changing signal amplitudes but with a constant rise time.

A meaningful, but unusual German term for this device is proportional discriminator .

## application

1. Comparison of threshold value triggering (left) and constant fraction triggering (right).

Typical input signals for CFDs are pulses from plastic scintillation counters , such as those used to measure the lifespan of positrons . Here one is faced with the problem of using broad, so temporally "smeared" signals to trigger and stop "stopwatches" in order to measure time spans that are much shorter than the pulse widths.

The scintillator pulses have rise times that are well above the desired time resolution, but are always the same regardless of the pulse height. The simple threshold discriminator cannot be used here for timing purposes, since the triggering time depends on the total pulse height (so-called time walk effect, Fig. 1 left). However, constant rise times and pulse shapes mean that a triggering when a fixed, always the same fraction of the total pulse height is reached (Fig. 1 right) results in a triggering time that is independent of the total pulse height.

## Working principle

The (in this example, usually positive) input signal is processed separately in two parallel paths. In one path, it is delayed by a fixed amount of time that is less than the rise time of the signal. In the other path, the signal is inverted (ie converted from positive to negative) and multiplied by a factor ( ). The two signals treated in this way are added again. The first zero crossing of the sum signal with a positive first derivative, i.e. from negative to positive, is used as the trigger time. ${\ displaystyle c}$${\ displaystyle 0