Pole-Zero Cancellation

Pole-Zero Cancellation

In the simple CR-RC circuit described in Fig. 9, there is a noticeable undershoot as the amplifier pulse attempts to return to the baseline. This is a result of the long exponential decay on the preamplifier output pulse. At medium to high counting rates, a substantial fraction of the amplifier output pulses will ride on the undershoot from a previous pulse. The apparent pulse amplitudes measured for these pulses will be too low, which leads to a broadening of the peaks recorded in the energy spectrum. Most spectroscopy amplifiers incorporate a pole-zero cancellation circuit to eliminate this undershoot. The benefit of pole-zero cancellation is improved peak shapes and resolution in the energy spectrum at high counting rates.

Figure 12 illustrates the pole-zero cancellation network, and its effect. In Fig. 12(a), the preamplifier signal on the left is applied to the input of the normal CR differentiator circuit in the amplifier. The output pulse from the differentiator exhibits the undesirable undershoot. The following equation applies:

Undershoot Amplitude = Differentiator Time Constant
Pulse Amplitude Decay Time Constant of Preamp Pulse

For a given preamplifier decay time constant, longer amplifier shaping time constants yield larger undershoots.

In Fig. 12(b), the resistor R_pz is added in parallel with capacitor C_D, and adjusted to cancel the undershoot. The result is an output pulse exhibiting a simple exponential decay to baseline with the desired differentiator time constant. This circuit is termed a "pole-zero cancellation network" because it uses a zero to cancel a pole in the mathematical representation by complex variables. Virtually all spectroscopy amplifiers incorporate this feature, with the pole-zero cancellation adjustment accessible through the front panel. Exact adjustment is critical for good spectrum fidelity at high counting rates. Some of the more sophisticated amplifiers simplify this task with an automatic PZ-adjusting circuit.

Figure 12. The Benefit of Pole-Zero Cancellation.