Determining the Zeros and Poles of Linear Circuit Networks Using Function Approximation

A numerical method for determining the significant singularities corresponding to the network function of a linear circuit is presented. This method is based upon function approximation of both the magnitude and phase of frequency response data. A linear network function of the form of a ratio of two polynomials in the Laplacian variable s is assumed. The frequency response data are approximated using the nonlinear least-squares algorithm of Levenberg and Marquardt. The polynomials are then factored into roots and those singularities having a negligible effect are removed. ZAP, a computer program implementing this method, has proven to be a valuable design aid for performing pole-zero analysis in the design of linear integrated circuits.