On the Approximation Problem in Network Synthesis

A procedure is presented for the synthesis of a network to yield a prescribed magnitude versus frequency characteristic. The given characteristic is replaced by a sequence of straight line segments of arbitrary slope. Each line segment is associated with a zero-pole pair properly placed on the real p axis, where p is the complex frequency variable. In this manner a real, rational network function is obtained whose magnitude variation approximates the given one. Methods for predicting the realizability of the approximating function are discussed in the application to the design of two terminal and two-terminal pair networks. To illustrate the methods outlined in the paper, a complete procedure is given for the design of attenuation equalizers using constant-resistance ladder sections.