The rate of events arriving at the detector is r_i, and r_o is the rate of analyzed events at the output of the ADC. T_W is the width of the amplifier pulse at the noise discriminator threshold (Fig. 6). T_P is the time from the start of the amplifier pulse to the point at which the ADC detects peak amplitude and closes the linear gate. U [T_M – (T_W –T_P)] is a unit step function that changes value from 0 to 1 when T_M is greater than (T_W –T_P). For successive-approximation ADCs, T_M is the fixed conversion time of the ADC and includes the time required to transfer the data to the subsequent memory. With a Wilkinson ADC, the value of T_M is given by Eq. 1. At high counting rates, it is desirable to have an ADC conversion time that is less than the time taken for the amplifier pulse to return to the baseline after peak amplitude.

Correction for the dead-time losses implied by Eq. 2 can be accomplished by several methods. Those ORTEC ADCs, MCAs, and MCBs incorporating live-time clocks typically utilize the Gedcke-Hale livetimer.* In that case, the livetimer subtracts time during the time interval T_P in order to compensate for pile-up losses. The live-time clock is turned off from the time of peak detection until the pulse returns to baseline (T_W – T_P), or until the ADC dead-time interval T_M is over, whichever interval is longer.

For ADCs without live-time clocks, the scheme in Fig. 7 can be used to correct for dead-time losses. A pulser with a 93-Ω output impedance, a fast rise time, and an adjustable, exponential decay time injects reference pulses into the amplifier input in parallel with the preamplifier output. First, the amplifier pole-zero cancellation is adjusted on the signals from the preamplifier with the pulser turned off. The amplifier pole-zero adjustment is left in that position for the remainder of the operation. Second, the pulser is turned on, and its decay time is adjusted to achieve perfect pole-zero cancellation on the pulse at the amplifier output. Third, the pulser amplitude is adjusted to place the pulser peak near the high-energy end of the spectrum, where it will not interfere with radiation peaks that must be analyzed. During the measurement time, the ADC will accumulate pulser events in the spectrum, along with real events from the detector. The pulses from the pulser experience the same dead-time effects as do the real events from the detector. If the counter is turned on and off at the same time as the ADC, the number in the counter represents the number of pulses presented to the amplifier by the pulser. The counts in each channel of the spectrum must be multiplied by the ratio of the number in the counter to the number of counts in the spectrum's pulser peak to correct for the dead-time losses.

For pulsed-reset preamplifiers, the exponential-decay-time pulser must be replaced with a low-frequency (<100 Hz) square wave generator, whose output is fed to the preamplifier test input. The rise and fall times of the square wave must be similar to the detector charge collection time.

*Ron Jenkins, R.W. Gould, and Dale Gedcke, Quantitative X-Ray Spectrometry, (New York and Basel: Marcel Dekker, Inc.,)1981, pp. 209-287, First Edition.

Figure 6. The Sources of Dead Time with an Amplifier and ADC.

Figure 7. Dead-Time Correction by Pulse Injection.