Second-Order Equivalent Circuits for the Design of Doubly-Tuned Transformer Matching Networks

The doubly-tuned magnetic transformer, comprising coupled inductors shunted by capacitors, is today widely in use as interstage network and for impedance matching in silicon millimeter waves amplifiers. It provides several advantages, compared with simple LC resonators, but the design is made complex by the high order of the network, featuring multiple resonances, and by the large number of components to be selected. In this paper, a novel approach for the analysis and design of such a network is proposed. It is shown that the response can be very well approximated, in the neighborhood of each resonance frequency, by a second-order parallel or series RLC equivalent circuit. This yields simple equations for the impedance, the bandwidth, and the power loss, giving intuition into the network behavior, and greatly simplifying the design. Based on the results of the analysis, guidelines for the network optimization are proposed, targeting minimum power loss and a flat broadband response. Design examples of practical interest are presented: the component values estimated by hand calculation are in very good agreement with those provided by a numerical circuit optimizer.