Analysis of high efficiency multistage matching networks with volume constraint

Matching networks have useful applications in transforming voltages and impedances in resonant inverters and dc-dc converters. Stacking multiple stages of matching networks can, in some cases, increase the efficiency because each stage is responsible for smaller transformation, but it also reduces the available inductor volume for each stage which can increase the loss. We present optimization of matching networks with volume constraints to determine the optimum number of stages and other design choices for various transformation ratios, volumes and impedances. Scaling models of inductor performance with size are presented and their effect on the efficiency of single-stage and multistage matching networks is analyzed. The analytical results are verified by an experiment using 1- and 2-stage matching networks with a total volume constraint and a voltage transformation ratio of 4. Simple design rules for designing matching networks are presented for voltage transformation ratios lower than 20.