Pole-Zero Analysis of Distributed Radio-Frequency Acceleration Systems

It is shown that the frequency-dependent input impedance of a lossless distributed network may be represented by the frequencies of the input impedance poles and zeros. Then, given the network reactance at a single frequency other than that of a pole or zero, one may apply Foster's reactance theorem to determine the input impedance at any frequency.1 Using the frequency-dependent impedance representation, one may calculate the response of the system to any periodic driving function.