A Broadband and Equivalent-Circuit Model for Millimeter-Wave On-Chip M:N Six-Port Transformers and Baluns

Abstract

A new equivalent-circuit model and parameter-extraction method for six-port M:N on-chip transformers and baluns are presented in this paper. All of the elements in the proposed model are extracted directly by $S$ -parameters based on full-wave electromagnetic (EM) simulations. Series branches in the model are used to capture the characteristics of the primary and secondary windings. The shunt impedance networks on the terminals represent the substrate loss. The magnetic coupling effects of windings are denoted by six mutual inductances. The electrical coupling effects are represented by mutual capacitances. In this paper, we have developed a parameter-extraction methodology for mutual inductances of six-port transformers. The proposed model and parameters extraction methodology are verified with a number of six-port transformers with different turn ratio by measurements and full-wave EM simulations. The proposed model shows good agreement with measured data over a wide frequency band.