A New Approach to the Problem of Cascade Synthesis

Several familiar procedures in the synthesis of driving-point and transfer impedances yield a network in the form of a cascade of two-terminal-pair networks, each of which is responsible for a set of zeros of the even part of the prescribed impedance. In each of these procedures, the computation of the typical component network begins with the determination of the equivalent tee-circuit; and then a remainder function (from which other component networks are to be found) is determined by subtracting the tee's branch impedances (or admittances) from previously determined functions. In general an equivalent circuit of some other configuration must be determined from the tee-circuit, to achieve physical realizability. These computational procedures are rather laborious, and the subtractions may cause serious degradations of numerical accuracy. In this paper, a more direct approach is suggested. It leads to the same ultimate networks in a more logical way, and obviates much of the computational tedium. The general approach is developed here primarily in terms of RC transfer impedances, but applications to LC networks are also included.