A New Design Approach for Dual-Band Quadrature Hybrids With Practically Unlimited Band Ratio, Enhanced Power Division, and Arbitrary Port Impedance

This paper introduces a novel design methodology for a dual-band branch-line coupler (DBBLC) that, for the first time, facilitates practically unlimited band ratio, enhanced flexibility in power division, and arbitrary port termination impedance concurrently. This approach ensures precise power distribution, matching, and isolation requirements by utilizing a generalized coupler core paired with an L-section impedance-matching network. This paper details an innovative and comprehensive analytical strategy for DBBLC design, which overcomes the limitations noted in prior research by deriving a generalized formula for the power division ratio (k) and simplifying the design equations to decrease complexity. This method enables the simultaneous realization of varied power division ratios, frequency ratios (r), and port impedances ( $Z_{p}$ ), thus offering remarkable design versatility. The effectiveness of this new analytical design methodology is corroborated through several design examples. Moreover, two prototype models operating at 1 GHz/2.5 GHz ( $r=2.5, k=0$ dB) and 1 GHz/2 GHz ( $r=2, k=4.77$ dB) frequencies, constructed on Rogers' RO4003C substrate, exhibit >22 dB return loss, <0.64 dB amplitude imbalance as well as <1° phase imbalance of the transmission parameters and >25 dB isolation at all the targeted frequencies. Therefore, the development and validation of this new DBBLC structure, as demonstrated by the strong correlation between our simulated and experimental findings, not only surpasses the capabilities of existing models, but also broadens the applicability of dual-band couplers in modern wireless communication systems.