Bandpass network function realization in Richards domain and its application to UWB patch antenna matching

In the literature, it is well known that complex Richards-Plane is a transformed domain of Laplace-Plane which is obtained under a tangent hyperbolic mapping. Network functions generated in terms of Richards frequency are periodic in actual frequencies with periodicity π. Once a lowpass prototype network function is designed in Richards domain it is this periodic feature that makes the corresponding periodic bandpass network function to appear at certain bands repetitively in the frequency axis. Designer can choose the interested band among these repetitive bands depending on the application requirements. In the work, a matching network built with microstrip commensurate transmission lines is designed for a microstip patch antenna which is designed to operate in 3.2448-3.744 GHz band, potentially to be used in UWB applications. SRFT (Simplified Real Frequency Technique) is used in the design and very good agreement found between the theoretical design and simulations done in MWO (AWR).