A constant fraction discriminator (CFD) is an electronic signal processing device, designed to mimic the mathematical operation of finding a

maximum In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given r ...

of a pulse by finding the zero of its

slope In mathematics, the slope or gradient of a line is a number that describes both the ''direction'' and the ''steepness'' of the line. Slope is often denoted by the letter ''m''; there is no clear answer to the question why the letter ''m'' is use ...

. Some signals do not have a sharp maximum, but short rise times

t_r

. Typical input signals for CFDs are pulses from plastic scintillation counters, such as those used for lifetime measurement in positron annihilation experiments. The scintillator pulses have identical rise times that are much longer than the desired temporal resolution. This forbids simple threshold triggering, which causes a dependence of the trigger time on the signal's peak height, an effect called ''time walk'' (see diagram). Identical rise times and peak shapes permit triggering not on a fixed threshold but on a ''constant fraction'' of the total peak height, yielding trigger times independent from peak heights.

From another point of view

time-to-digital converter In electronic instrumentation and signal processing, a time-to-digital converter (TDC) is a device for recognizing events and providing a digital representation of the time they occurred. For example, a TDC might output the time of arrival for ea ...

assigns timestamps. The

needs fast rising edges with normed height. The plastic scintillation counter delivers fast rising edge with varying heights. Theoretically, the signal could be split into two parts. One part would be delayed and the other low pass filtered, inverted and then used in a variable-gain

amplifier An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost t ...

to amplify the original signal to the desired height. Practically, it is difficult to achieve a high dynamic range for the variable-gain amplifier, and

analog computer An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (''analog signals'') to model the problem being solved. In ...

s have problems with the inverse value.

Principle of operation

The incoming signal is split into three components. One component is delayed by a time

t_d

, with

0\ll t_d\le t_r

it may be multiplied by a small factor to put emphasis on the leading edge of the pulse and connected to the noninverting input of a

comparator In electronics, a comparator is a device that compares two voltages or currents and outputs a digital signal indicating which is larger. It has two analog input terminals V_+ and V_- and one binary digital output V_\text. The output is ideally : ...

. One component is connected to the inverting input of this comparator. One component is connected to the noninverting input of another comparator. A threshold value is connected to the inverting input of the other comparator. The output of both comparators is fed through an

AND gate The AND gate is a basic digital logic gate that implements logical conjunction (∧) from mathematical logic AND gate behaves according to the truth table. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If not al ...

. A discriminator without that constant fraction would just be a comparator. Therefore the word

discriminator In distributed computing, a discriminator is a typed tag field present in OMG IDL discriminated union type and value definitions that determines which union member is selected in the current union instance. Unlike in some conventional programm ...

is used for something different (namely for an FM- demodulator). Often the

logic levels Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

are shifted from -15 V < low < 0 < high < 15 V delivered by the comparator to 0 V < low < 1.5 V < high < 3.3 V needed by CMOS logic.

Applications

If the discriminator triggers a sampler with a following comparator this is called a single channel analyzer (SCA). If an

Analog-to-digital converter In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide ...

is used, this is called a multi channel analyzer (MCA).

References

* Beuzekom, M. (2006). "Identifying fast hadrons with silicon detectors"
Appendix A
University of Groningen Faculty of Mathematics and Natural Sciences Dissertation {{DEFAULTSORT:Constant Fraction Discriminator Signal processing Measuring instruments