Comparison of Vector Fitting and Contour Integration Methods for Pole-Zero Analysis of Microwave Filters

This paper presents the comparison of vector fitting and contour integration methods for pole-zero analysis of microwave filters. Two cases of microwave filters are considered, which include an all-pole classical coupled line filter and a linear phase filter with complex zeros. The poles and zeros obtained using vector fitting method with different chosen number of poles and fitting bandwidth are analyzed. It is found that the poles and zeros may be inconsistent depending on the chosen number of poles and bandwidth. Furthermore, the method may introduce spurious complex zeros that do not satisfy the S parameters unitary conditions, while the poles also do not maintain periodicity between frequency bands for transmission line structures. On the other hand, the poles and zeros obtained using contour integration method are consistent and certain. They also satisfy the unitary conditions and periodicity for transmission line structures.