Angular expression of maximum power transfer efficiency in reciprocal two-port systems

This paper presents a novel formula of maximum power transfer efficiency for general reciprocal two-port systems. Considering an arbitrary scheme of wireless power transfer system excited by a power source with finite available power. Then we define the efficiency as load-to-source power ratio. Next we translate it into the immittance matrix domain employing the network port parameters. To maximize the efficiency, we impose the simultaneous conjugate conditions upon the source and load impedances. We finally reach an elegant expression of maximum efficiency by heuristically introducing a new angular quantity. Its tangent square plays the role of power efficiency index, while its double-angle tangent works as a general extension of conventional k-Q product. One can use the angle as a lucid design pilotage even before learning a word of resonance or mutual coupling. This theory enables wireless system engineers to widely explore the feasibility over various kinds of power transfer regimes rather than just magnetic coupling between two coils.