Optimum Design of Multi-Section Asymmetrical Transdirectional Couplers with Port Impedance Matching up to S Band Frequency

Abstract

The method of least squares is developed for the optimum design of multi-section asymmetrical transdirectional (ATRD) couplers with arbitrary port impedance matching. Firstly, transmission matrix of a section of coupler is obtained, then the transmission matrix of whole multi-section coupler is determined, from which the scattering matrix of device is obtained. An error function is then constructed by scattering parameters. According to design specifications, error function depends on physical parameters of coupler (such as widths, spacings and lengths of transmission line sections and capacitor values), of which minimum point gives optimum values of it’s dimensions and capacitors. Optimum design is carried out for a specified frequency response and bandwidth. Error minimization is implemented by the combination of genetic algorithm (GA) and conjugate gradient method (CGM). The design is verified by full-wave simulation software, fabrication and measurement. Several 3 dB, 6 dB and 10 dB couplers are designed with different bandwidths and port impedances. Compared to the proposed design method, design of asymmetrical multi-section couplers by full-wave simulation softwares is by trial and error and at best random and almost impossible because of extremely high CPU time due to the large number of parameters of coupler geometrical structure.