A high precision cascade synthesis technique for real frequency matching involving Brune and Darlington Type-C sections

In this work, we introduce a high precision cascade synthesis technique for lossless matching networks involving Brune and Darlington Type-C sections. In the present manuscript, we generalized our previously introduced high precision LC-ladder synthesis algorithm to include the extraction of finite real frequency and right half plane (RHP) transmission zeros of an impedance function as Brune and Darlington Type-C sections respectively. In the modified synthesis algorithm, after each finite frequency and RHP transmission zero extraction, remaining immittance function is corrected using a parametric approach. It is shown that proposed high precision algorithm can synthesize immittance functions of up to 40 reactive elements with accumulated relative error in the order of 10^-1. The modified high precision synthesis package is developed in MatLab environment and it is integrated with the real frequency techniques to design high complexity matching networks over broad bands. An illustrative example is presented to exhibit the usage of the proposed high precision synthesis algorithm.