Power transfer theory on linear passive two-port systems

Abstract

This paper theoretically revisits linear passive two-port systems from the viewpoint of power transfer. Instead of using the conventional S21 magnitude, we propose generalizing the kQ product as a figure of merit for two-port performance evaluation. We explore three examples of power transfer schemes, i.e. inductive, capacitive, and resistive channels. Starting from their voltage-current equations, the kQ formula is analytically derived for each scheme. The resultant formulas look different in appearance but are all physically consistent with ωM/R, which stems from the original definition of kQ product in a primitive transformer. After comprehensively learning from the three examples, we finally extend the theory to a black-box model that represents any kind of power transfer channel. In terms of general two-port Z-parameters, useful mathematical expressions are deduced for the optimum load, input impedance, and maximum power transfer efficiency. We also supplement the theory with helpful graphics that explain how the generalized kQ behaves as a function of the circuit parameters.