A mathematical model is derived for the parallel resonant converter (PRC) in which a simple comparator circuit applied to the inductor current is used to establish stable oscillations at the resonant frequency in cases of high Q. Second order differential equations are solved to construct a piecewise phase-plane trajectory explaining the generation of a stable limit cycle and predicting its amplitude and period. The self-oscillating mechanism is explored in other resonant converters and verified by simulation. In all cases, switching between the two circuit configurations of the converter is produced by the change of the input inductor current sign. Measurements in a 100 W PRC prototype oscillating around 500 kHz are in good agreement with the theoretical predictions.

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A general approach for the analysis and design of self-oscillating resonant converters is presented in this paper, for a particular class of circuits in which the change of input voltage polarity is caused by the zero-crossings of the input inductor current. The key features of the method are an analytical description in the time-domain of a spiral that eventually converges into an ellipse, and a frequency–domain analysis that explains the behavior of the ellipse as a limit cycle. On a theoretical basis, this class of circuits behaves as loss-free resistors (LFR) because in steady-state the input inductor current is in phase with the first harmonic of the input voltage. The proposed analytical procedure predicts accurately the amplitude and frequency of the limit cycle and justifies the stability of its generation. This accuracy is reflected in the close agreement between the theoretical expressions and the corresponding simulated and measured waveforms. Third and fourth order resonant converters are designed following simple guidelines derived from the theoretical analysis.

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