Abstract
This paper offers a new theory on impedance matching circuits in regard to maximum power transfer efficiency. We start by reviewing the theory for wireless couplers employing kQ as a figure of merit. Next, we explore how to formulate maximum power transfer efficiency for matching circuits. From the result, we propose a general formula featuring Poincare length stemming from hyperbolic geometry. We then use this to formulate the performance of inductive- and capacitive-wireless couplers. We finally reach an outcome stating that the quality factor should be common to input and output ports to minimize the Poincare length. We also find that the Poincare length decreases when the coupling coefficient increases.
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