This paper formulates a class-E synchronous RF rectifier from a new viewpoint. The key point is to introduce a matrix and convolute the DC terms into RF matrices. The explicit expression of input impedance is demonstrated in plane geometry. We find out their input impedance exhibits a geodesic arc in hyperbolic geometry under ZVS operation, where the theoretical RF-DC conversion efficiency results in 100%. We verify the developed theory both numerically (circuit simulation) and experimentally (6.78MHz, 100W). We confirm that the input impedance becomes a geodesic arc for a wide range of DC load resistance. The presented theory is quite elegant since it is based on a matrix-based formulation and plane-geometrical expression.

This paper presents a comprehensive design approach to load-independent radio frequency (RF) power amplifiers. We project the zero-voltage-switching (ZVS) and zero-voltage-derivative-switching (ZVDS) load impedances onto a Smith chart, and find that their loci exhibit geodesic arcs. We exploit a two-port reactive network to convert the geodesic locus into another geodesic. This is named geodesic-to-geodesic (G2G) impedance conversion, and the power amplifier that employs G2G conversion is called class-G2G amplifier. We comprehensively explore the possible circuit topologies, and find that there are twenty G2G networks to create class-G2G amplifiers. We also find out that the class-G2G amplifier behaves like a transformer or a gyrator converting from dc to RF. The G2G design theory is verified via a circuit simulation. We also verified the theory through an experiment employing a prototype 100 W amplifier at 6.78 MHz. We conclude that the presented design approach is quite comprehensive and useful for the future development of high-efficiency RF power amplifiers.