In this paper a new method for the design and optimization of microstrip parallel coupled-line bandpass filters is presented which allows for the specification of frequency bandwidths and arbitrary source and load impedance transformation. The even- and odd-mode theory and the relationships between impedance, transmission and scattering matrices and their properties are used to construct a positive definite error function using the insertion losses at discrete frequencies in the pass, transition and stop bands. The dispersion relations for the coupled line are also taken into account. The minimization of the error function determines the widths, gap spacings and lengths of the coupled-line filter, for the optimum design and realization of filter specifications. The proposed filter design and optimization method is coded by computer programs and the results of simulation, fabrication and testing of sample filters together with comparisons with available full-wave analysis softwares, indicate the efficacy of the proposed method. Filter design with up to 50% bandwidth and the design of shorter lengths of coupled line sections are achievable by the proposed method in part due to the incorporation of impedance matching.

In this paper the method of least squares is employed to design an axially symmetric contradirectional multisection coupled - line coupler together with the impedance matching of real generator and load impedances. An error function is constructed for the required coupling (C) based on the squared magnitude of the ratio of the coupler voltage to that at the incident port. Another algorithm based on the reflected and transmitted wave amplitudes is developed by the method of least squares for the design of a coupled - line coupler with impedance matching of different input and output complex impedances and arbitrary coupling and length. The error functions are minimized to determine the coupler geometry, namely the normalized strip conductor widths (u=w/h) and separation (g=s/h) and the coupler length, where h is the substrate thickness. A procedure is presented to provide the initial values of u and g. The computer implementation of the proposed method shows that a proper coupler design is possible for any given coupler length. This is particularly interesting where space limitations impose contraints on the coupler length. The results are favorably compared with available computer simulation softwares.