Detecting a signal pulse is usually basic electronics, but you start to find more complications when you need to time the signal’s arrival in the picoseconds domain. These include the time-walk effect: if your circuit compares the input with a set threshold, a stronger signal will cross the threshold faster than a weaker signal arriving at the same time, so stronger signals seem to arrive faster. A constant-fraction discriminator solves this by triggering at a constant fraction of the signal pulse, and [Michael Wiebusch] recently presented a hacker-friendly implementation of the design (open-access paper).
A constant-fraction discriminator splits the input signal into two components, inverts one component and attenuates it, and delays the other component by a predetermined amount. The sum of these components always crosses zero at a fixed fraction of the original pulse. Instead of checking for a voltage threshold, the processing circuitry detects this zero-crossing. Unfortunately, these circuits tend to require very fast (read “expensive”) operational amplifiers.
This is where [Michael]’s design shines: it uses only a few cheap integrated circuits and transistors, some resistors and capacitors, a length of coaxial line as a delay, and absolutely no op-amps. This circuit has remarkable precision, with a timing standard deviation of 60 picoseconds. The only downside is that the circuit has to be designed to work with a particular signal pulse length, but the basic design should be widely adaptable for different pulses.
[Michael] designed this circuit for a gamma-ray spectrometer, of which we’ve seen a few examples before. In a spectrometer, the discriminator would process signals from photomultiplier tubes or scintillators, such as we’ve covered before.
Proper component matching and layout for consistent timing and impedance matching to avoid reflections in delay line. A clean source would work better, maybe some analog clamping or RC differentiators?
The paper does describe 50 ohm matching.
That’s pretty clever and neat. And a bit of genius to use commodity LVDS receivers for the detectors.
One real-world application that isn’t mentioned in the paper is positron emission tomography (PET) imaging: Here, a positron annihilation event is detected by the coincidence of the two 511 keV gamma rays that are emitted — this tells you the event happened somewhere along the line between the two detectors that registered the event. In PET scanners, many thousands of detectors are used, so many millions of such possible pairs of detectors (and lines of response) exist.
While simply the detection of the two gammas is sufficient to say the event occurred, you want to get the time window as small as possible to ensure that the two detection events came from the same positron decay, and not two separate events that happen to be in the same detection window (producing a false positive).
Narrow time windows decreases the false positive rate, and also allows you to increase the activity of the source, to decease image acquisition time and improve counting statistics (=signal to noise ratio).
What’s really cool is when you can get sub-nanosecond time discrimination: Now you can tell where along that detection line the event happened, which adds additional information to the image reconstruction process, further improving image quality. In practice, centimeter-scale (30-60 ps) localization of the event along the line of response is possible, dramatically improving the image quality over previous systems that could discriminate only to nanoseconds.