Novel Generic Asymmetric and Symmetric Equivalent Circuits of 90° Coupled Transmission-Line Sections Applicable to Marchand Baluns

Three different equivalent circuits (asymmetric, symmetric, and mixed) of the 90° coupled transmission-line sections are proposed for Marchand baluns, including the accurate modeling of the effect of the connecting segment. The asymmetric one consists of one set of coupled transmission-line sections and two identical uncoupled transmission-line sections. Due to the asymmetry and a four-port circuit configuration, it seems to be difficult to derive the design formulas for the asymmetric equivalent circuit, thus leading to their indirect derivation by adding two identical transmission-line sections with effectively “negative” electrical lengths to the original 90° coupled transmission-line sections. The symmetric one may be obtained by combining the even- and odd-mode equivalent circuits, while the mixed equivalent circuit is combining the asymmetric and the symmetric ones. As a proof-of-concept, a symmetric and an asymmetric equivalent circuits along with a Marchand balun with a connecting section were implemented at 2 GHz, demonstrating a very good agreement between the simulated and the experimental values.