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

The introduction of asymmetric coupled lines (ACLs) features directional couplers with advantages such as great design flexibility, broadband, impedance transformation, and compact structure. This letter innovatively proposes a generalized design methodology for ACL couplers with arbitrary terminal real impedance and power division ratio (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r_{p}$ </tex-math></inline-formula>). Using the decoupled branch-line model of ACLs, design equations between terminal real impedances, image impedances, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r_{p}$ </tex-math></inline-formula> are provided, unifying the analysis of branch-line hybrids and coupled line couplers. For verification, three coupled line couplers with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r_{p}$ </tex-math></inline-formula> of 10 dB, 20 dB, and 30 dB, and fractional bandwidths of 48%, 38.5%, and 41.5%, respectively, were implemented.