A Design Approach for Asymmetric Coupled Line Tandem Couplers With Arbitrary Terminal Real Impedances and Arbitrary Power Dividing Ratio

A novel design methodology for asymmetric coupled line tandem couplers with arbitrary terminal real impedances and arbitrary power dividing ratio is proposed in this article. By reasonably equating the quarter-wavelength asymmetric coupled line section with multiple single quarter-wavelength transmission lines in the vicinity of the central frequency point, an equivalent branch line model of the asymmetric coupled line tandem coupler is established and analyzed. Relationships between four terminal real impedances, four image impedances, and the power dividing ratio ${r}_{p}$ , for satisfying conditions of the perfect isolation, perfect match of ports, and power dividing requirement simultaneously, are deduced. The simplified analysis method and design formulas for symmetric coupled line tandem couplers are also presented and verified from the simulation level. Based on the extraction of unit length resistance, inductance, conductance, and capacitance parameters from full-wave simulation S-parameters of coupled lines, procedures for quickly and accurately obtaining the initial structural parameters values are provided in detail, significantly reducing the burden of subsequent optimizations. Two tandem couplers, respectively, with power coupling degrees (dB) of 2 dB ( $r_{p}\approx 0.5849$ ) and 3 dB ( $r_{p}$ = 1) were designed and fabricated. Both couplers are very compact ( $0.0073\lambda _{g}^{2}$ for 3 dB), maintain good orthogonality between the through and coupled ports, achieve the broadband property without introducing additional circuits or components, and strictly meet the expected coupling degree. The great consistency between the simulated and measured results powerfully proves the rationality of the proposed analysis theory, as well as the validity of our design methodology.