The focus of this thesis is on developing theories and techniques to extract lossy microwave filter parameters from data. In the literature, the Cauchy methods have been used to extract filters’ characteristic polynomials from measured scattering parameters. These methods are described and some examples are constructed to test their performance. The results suggest that the Cauchy method does not work well when the Q factors representing the loss of filters are not even. Based on some prototype filters and the relationship between Q factors and the loss, we conduct preliminary studies on alternative representations of the characteristic polynomials. The parameters in these new models are extracted using the Levenberg–Marquardt algorithm to accurately estimate characteristic polynomials and the loss information.

In this thesis the general Chebyshev filter synthesis procedure to generate transfer and reflection polynomials and coupling matrices were described. Key concepts such as coupled resonators, non-resonant nodes have been included. This is followed by microwave duplexer synthesis. Next, a technique to design dual band filter has been described including ways to achieve desired return loss and rejection levels at specific bands by manipulating the stopbands and transmission zeros. The concept of dual band filter synthesis has been applied on the synthesis of microwave duplexer to propose a method to synthesize dual band duplexers. Finally a numerical procedure using Cauchy method has been described to estimate the filter and duplexer polynomials from measured responses. The concepts in this thesis can be used to make microwave filters and duplexers more compact, efficient and cost effective.