Optimum Design of Broadband Branch-Line Couplers with Arbitrary Power Division and Impedance Transformation

In this paper a numerical method is presented for the design and optimization of a broadband branch-line coupler for arbitrary power division between its output ports over a specified frequency band together with impedance matching of the source to the load impedances. First, the reflected and transmitted wave amplitudes at the four ports of the coupler are expressed in terms of its reflection and transmission coefficients, which are themselves written in terms of the scattering parameters and finally transmission matrix parameters in the even- and odd-mode analysis. Then an error function is constructed for the specified power division ratios in the desired frequency bandwidth including dispersion models. The minimization of error function determines the widths, spacings and lengths of the strip conductors. The frequency responses obtained from the computer programs and fabrication and measurement of two couplers indicate the effectiveness of the proposed method.