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.