ORTEC Logo

Home | Applications | Contact Us
Products | Service | Training
  Timing with TACs

When a timing application demands picosecond precision, a time-to-amplitude converter is a prime candidate. A TAC can achieve such exceptional precision because it uses an analog technique to convert small time intervals to pulse amplitudes. Figure 1 illustrates the principle. (Although the actual circuitry in a TAC employs sophisticated transistor switches, the devices in Fig. 1 have been represented as toggle switches for a simpler description.)

A Functional Diagram of a Time-to-Amplitude Converter.
Figure 1.  A Functional Diagram of a Time-to-Amplitude Converter.

Before a time measurement starts, all the switches in Fig. 1 are closed. The arrival of the leading edge of the "start" signal opens the "start" switch, and the converter capacitor begins to charge at a rate set by the constant-current source. The leading edge of the "stop" signal opens the "stop" switch and prevents any further charging of the capacitor. Because the charging current I is constant, the voltage developed on the capacitor is given by

where t is the time interval between start and stop pulses and C is the capacitance of the converter capacitor. Consequently, the voltage is proportional to the time interval. This voltage pulse is passed through the buffer amplifier to the linear gate. A short time after the stop pulse arrives, the linear gate switch opens to pass the voltage pulse through the output amplifier to the TAC output. After a few microseconds, all the switches return to the closed condition. This terminates the output pulse and discharges the capacitor to ground potential in preparation for the next pair of start and stop events. The result is a rectangular output pulse with a width of a few microseconds and an amplitude that is proportional to the time interval between the start and stop pulses. This pulse is typically fed to an ADC or a multichannel analyzer for pulse-height measurement.

As the conversion and measurement process is repeated for additional pairs of start and stop pulses, a time spectrum grows in the multichannel analyzer memory. The shape of this spectrum will depend on the time correlations between the start and stop events. For strongly correlated events, as experienced in gamma-gamma coincidence experiments, the spectrum is usually a well-defined peak with a shape that is nearly Gaussian. In fluorescence lifetime measurements, the time peak has a sharp rise at "zero" time followed by an exponential decay. In the case of totally uncorrelated start and stop events, the shape of the spectrum is determined by the Interval Distribution, which describes the probability of the length of time intervals between randomly arriving events.1 If nstart is the number of valid start pulses accepted by the TAC and MCA during the measurement of the time spectrum, and rstop is the average counting rate of the random, uncorrelated stop pulses, the number of counts recorded between times t and t + dt in the time spectrum will be

If rstop is very small compared to the reciprocal of the TAC time range, the spectrum from the uncorrelated events will appear to be a flat background.

Typically, the start and stop inputs of time-to-amplitude converters are designed to accept the fast logic signals from timing discriminators. Each timing discriminator, in turn, derives its signal from the amplified output of some type of detector or transducer. On the shortest time ranges, time-to-amplitude converters can deliver exceptionally fine time resolution (~10 ps). Under such circumstances, the controlling factors for time resolution are normally the timing jitter and walk contributed by the sources of the start and stop signals.

1Ron Jenkins, R. W. Gould, Dale Gedcke, Quantitative X-Ray Spectrometry, Marcel Dekker, New York, 1981, First Edition, Chapter 4.