Jitter, walk and drift are the three major factors limiting time resolution. These characteristics are most readily described by reference to a simple leading-edge timing discriminator, as illustrated in Fig. 1.

A leading-edge timing discriminator incorporates a simple voltage comparator with its threshold set to the desired voltage (Fig. 1). When the leading edge of the analog pulse crosses this threshold the comparator generates a logic pulse. The logic pulse ends when the trailing edge of the analog pulse crosses the threshold in the opposite direction. The initial transition of the logic pulse is used to mark the arrival time of the analog pulse, and this time corresponds to the threshold crossing on the leading edge of the analog pulse.

In the absence of noise and amplitude variations, the leading-edge discriminator would mark the arrival time of each analog pulse with precision and consistency. However, many systems include a non-negligible level of electronic noise, and this noise causes an uncertainty or jitter in the time at which the analog pulse crosses the discriminator threshold. If e_n is the voltage amplitude of the noise superimposed on the analog pulse, and dV/dt is the slope of the signal when its leading edge crosses the discriminator threshold, the contribution of the noise to the timing jitter is

Timing jitter = e_n / (dV/dt).           (10)

If the noise cannot be reduced, the minimum timing jitter is obtained by setting the discriminator threshold for the point of maximum slope on the analog pulse. If a low pass filter is applied to reduce the noise by slowing down the pulse rise time, the slope in equation (10) normally decreases more rapidly than the noise diminishes, and the net result is an increase in timing jitter. Therefore, it is best to preserve the fastest possible rise time from the signal source. For further guidance on choosing the appropriate rise time for the preamplifier and amplifier that precede the timing discriminator, see the introduction on Preamplifiers and Amplifiers. Electronic noise makes a significant contribution to timing jitter with silicon charged-particle detectors, fast photodiodes, Si(Li) detectors, and germanium detectors, and to a somewhat lesser extent with microchannel plates, microchannel plate PMTs, and channeltrons.

With scintillation detectors (scintillators mounted on photomultiplier tubes) the noise contribution is usually negligible, but there is a another important contribution to timing jitter: statistical fluctuations in the arrival time of the pulse at the detector output. The optimum solution for this application is discussed below. Germanium detectors also bring a special problem to the timing task, because the rise times of the pulses from these detectors vary over a wide range, and this variation is a dominant source of timing jitter. The special solution for timing with germanium detectors is described later in this section.

"Walk" is the systematic dependence of the time marker on the amplitude of the input pulse. Fig. 1 shows two pulses which have exactly the same shape, but one has twice the amplitude of the other. The higher amplitude pulse crosses the discriminator threshold earlier than the smaller pulse. This is the source of "walk" or time slewing. With a leading-edge timing discriminator, smaller pulses produce an output from the discriminator later than larger pulses do. When observed on an oscilloscope, the timing discriminator output pulses appear to "walk" back and forth on the time axis in response to the variations in the input pulse amplitudes. Obviously, "walk" can seriously degrade the time resolution when a wide range of pulse amplitudes must be processed. The constant-fraction discriminator, ARC timing, and other zero-crossing techniques are highly recommended for eliminating or minimizing "walk".

Drift is the long-term error introduced by component aging and by temperature variations in the discriminator circuits. This is a significant contributor to the timing error only when the temperature changes noticeably during long measurement periods.

Figure 1.  Jitter and Walk in Leading-Edge Time Derivation.