Methods for finding globally maximum-efficiency impedance matching networks with lossy passives

Impedance transformation using on-chip passive elements is ubiquitously used in RF and mm-Wave circuits and systems for optimal power matching, interstage and noise matching, and high-efficiency power delivery to the antenna by power amplifiers. While conjugate matching gives optimal efficiency for lossless passives, the results are markedly different when constituent passives have finite quality factors. Given the load and source impedances, there may be infinite ways to achieve the transformation, albeit each incurring different loss. In this paper, we investigate the methods to deduce the global maximum efficiency of power transfer between two arbitrary impedances with lossy passives. This paper also proposes methods to combine this with nonlinear load-pull simulations for optimal efficiency combiner and matching network for integrated PAs. To the best of the authors' knowledge, this is the first comprehensive analysis of globally optimal impedance transformation networks between arbitrary impedances with lossy passives.