The dynamic characteristics of the class E power amplifier with frequency modulation are derived. Such an analysis is essential for designing amplitude and frequency modulated amplifier systems such as an EER scheme. Conventionally, an analytical expression for the frequency response of a frequency modulated class E amplifier has not been derived yet. This omission is rectified here by modeling the circuit with both a low-frequency model and a high-frequency model. Further, a time domain waveform is derived from the frequency domain transfer function for some typical time varying drive signals. The analytical results for the frequency response of a 1-MHz class E amplifier are shown to match PSpice simulations and measured values well.

Design equations for satisfying off-nominal operating conditions of the class E amplifier with a nonlinear shunt capacitance for a grading coefficient of 0.5 and the duty cycle D=0.5 are derived. By exploiting the off-nominal class E operation, various amplifier parameters such as input voltage, operating frequency, output power, and load resistance can be set as design specifications. As a result of the analysis in this paper, the following extension of the usability of the class E amplifier was achieved. With rising up the dc supply voltage, the shunt capacitance which achieves the off-nominal operation can be increased. This means that a transistor with higher output capacitance can be used for ZVS operation. This also means that maximum operating frequency which achieves ZVS can be increased. An example of a design procedure of the class E amplifier is given. The theoretical results were verified with an experiment.

This paper presents an analysis-based design method for designing the class-Φ22 wireless power transfer (WPT) system, taking its subsystems as a whole into account. By using the proposed design method, it is possible to derive accurate design values which can make sure the class-E Zero-Voltage-Switching/Zero-Derivative-Switching (ZVS/ZDS) to obtain without applying any tuning processes. Additionally, it is possible to take the effects of the switch on resistance, diode forward voltage drop, and equivalent series resistances (ESRs) of all passive elements on the system operations into account. Furthermore, design curves for a wide range of parameters are developed and organized as basic data for various applications. The validities of the proposed design procedure and derived design curves are confirmed by LTspice simulation and circuit experiment. In the experimental measurements, the class-Φ22 WPT system achieves 78.8% power-transmission efficiency at 6.78MHz operating frequency and 7.96W output power. Additionally, the results obtained from the LTspice simulation and laboratory experiment show quantitative agreements with the analytical predictions, which indicates the accuracy and validity of the proposed analytical method and design curves given in this paper.