Optimization-Based Design of Multi-Band Branch-Line Coupler With Arbitrary and Band-Distinct Power Division Ratios and Phase Differences

This paper presents a novel optimization-based procedure for designing a multi-band branch-line coupler with arbitrary output power division ratios and phase differences that are distinct at each of arbitrarily-allocated design frequencies. The procedure aims to find the optimal parameters of the design that result in the best possible performance while maintaining the deviation from the desired specifications within a predefined tolerance level. This procedure uses the analytical S-parameters of the proposed coupler which are derived using even-odd mode analysis. A tri-band (1.5/2.4/4.2 GHz) and a quad-band (1.5/2.4/3.5/4.2 GHz) microstrip prototypes are developed using the proposed procedure to have band-distinct power division ratios and phase differences. For validation, both prototypes are simulated, fabricated, and measured. At all operating frequencies, the measured deviations from the desired power division ratios and phase differences are within 1 dB and 10$^\circ$, respectively. Also, the measured matching and isolation are $< $ −11 dB at all design frequencies. The achieved measurement results and the agreement between measured results and theoretical expectations demonstrate the applicability of the proposed design procedure in practice. The proposed coupler is a candidate for use in analogue multi-band multi-beam antenna arrays, and the proposed design procedure can be applied in designing other multi-band microwave devices.