Globally Optimal Matching Networks With Lossy Passives and Efficiency Bounds

Impedance transformation is one of the central concepts in high-frequency circuits and systems and is used ubiquitously for optimal power matching, noise matching, and high-efficiency power delivery to the antenna by power amplifiers. The matching network can be generally expressed as a path on the Smith chart and given the load and source impedances, there are theoretically infinite ways to achieve the transformation. When losses are included, each path will encounter a different loss, and currently, no comprehensive theory exist for finding the most optimal matching network. Furthermore, the networks will also provide different bandwidths of operation. Due to the matching network losses, it is often not optimal to force conjugate matching for maximizing end-to-end power transfer efficiency. In this paper, we provide a method toward finding 1) the globally most efficient path between two arbitrary impedances with lossy passives; 2) given the source and the load impedances, the optimal (typically non-conjugate) impedance to match and the highest efficiency path to reach the impedance; and 3) upper bounds on achievable efficiencies under the various scenarios. This paper also proposes ways to combine this method with nonlinear load-pull simulations for optimal combiner and matching network for integrated power amplifiers. This analysis creates interesting ways to maximize efficiency and bandwidths simultaneously and the paper also discusses this joint optimization. To the best of our knowledge, this is the first comprehensive analysis of globally optimal impedance transformation networks between arbitrary impedances with lossy passives.