Generalized Average Model of the Class-E2 DC-DC Resonant converter

Abstract

In this paper, the generalized average model of the Class-E$^2$ DC-DC resonant converter has been introduced. The standard average model is not interesting in resonant converters due to their large waveform oscillations. In addition, steady-state approaches restrain the converter to hysteresis control. The resonant tank voltage, reconstructed by the fundamental component, as performed in LLC converters by extended describing function, is not suitable for the Class-E$^2$ topology because the inverter/rectifier interface voltage requires, at least, the third-order harmonic usage. This work relies on the generalized average method to perform the large-signal and small-signal models of the Class-E$^2$ converter. This paper shows how to systematically deal with the following modeling issues: negative index from the convolution summation, complex numbers from the Fourier coefficients and high number of state-space variables. The theoretical approach is confirmed by measurement in an assembled 800 kHz Class-E$^2$ converter based on voltage-controlled oscillator.

Keywords

• circuit modeling
• dc-dc power converters
• resonant converters