This paper presents a feedback-loop technique for analyzing and designing RF power links for transcutaneous bionic systems, i.e., between an external RF coil and an internal RF coil implanted inside the body. The feedback techniques shed geometric insight into link design and minimize algebraic manipulations. We demonstrate that when the loop transmission of the link's feedback loop is -1, the link is critically coupled, i.e., the magnitude of the voltage transfer function across the link is maximal. We also derive an optimal loading condition that maximizes the energy efficiency of the link and use it as a basis for our link design. We present an example of a bionic implant system designed for load power consumptions in the 1-10-mW range, a low-power regime not significantly explored in prior designs. Such low power levels add to the challenge of link efficiency, because the overhead associated with switching losses in power amplifiers at the link input and with rectifiers at the link output significantly degrade link efficiency. We describe a novel integrated Class-E power amplifier design that uses a simple control strategy to minimize such losses. At 10-mW load power consumption, we measure overall link efficiencies of 74% and 54% at 1- and 10-mm coil separations, respectively, in good agreement with our theoretical predictions of the link's efficiency. At 1-mW load power consumption, we measure link efficiencies of 67% and 51% at 1- and 10-mm coil separations, respectively, also in good accord with our theoretical predictions. In both cases, the link's rectified output dc voltage varied by less than 16% over link distances that ranged from 2 to 10 mm.