Pole-zero analysis of microwave filters using contour integration method exploiting right-half plane

Abstract

This paper presents the pole-zero analysis of microwave filters using contour integration method exploiting right-half plane (RHP). The poles and zeros can be determined with only S21 by exploiting contour integration method on the RHP along with certain S matrix properties. The contour integration in the argument principle is evaluated numerically via the finite-difference method. To locate the poles or zeros, the contour divide and conquer approach is utilized, whereby the contour is divided into smaller sections in stages until the contour enclosing the pole or zero is sufficiently small. The procedures to determine the poles and zeros separately are described in detail with the aid of pseudocodes. To demonstrate the effectiveness of the proposed method, it is applied to determine and analyze the poles and zeros of various microwave filters.