Comments on "A Symmetrical Four-Port Microstrip Coupler for Crossover Application

In the paper of Chen and Yeo (2007), the authors demonstrate a four-port coupler for crossover application. In their eigenmode model analysis, the entire circuit is decomposed into tapers and two rings with four external arms. In formulation, the eigenadmittance of the inner substructure is taken account as the load of that of the outer one. A cascade of P short sections is then used to approximate the taper and incorporated into the model of the composite structure by successively applying the input admittance formula of a loaded transmission line. Finally, one prototype circuit solution obtained by an optimization process is demonstrated. In this paper, the transmission line theory is applied to the circuit analysis. It is found that the circuit structure is so versatile for the crossover application that infinite numbers of solutions can be simply obtained by solving two simultaneous equations. In addition, the tapers for input/output matching can be saved, leading not only to circuit area reduction, but also to formulation simplification. A microstrip coupler is fabricated and measured for confirmation.