Frequency-domain simulation of power electronics circuits by using describing functions in a modified nodal approach

A new approach for AC analysis of switching-mode power converters is presented. It is based on the use of two concepts: the bifrequency transfer function, which relates the input and output spectrums of the power electronics circuit, and the describing function. In order to calculate the input-to-output or control-to-output frequency response, small sinusoidal perturbations in either the line voltage or the control variable are considered. The fundamental component of the output variable at the perturbation's frequency is determined by using the zeroth order term of the Fourier transform of the impulse response, allowing then for the deduction of the line and control describing functions. No additional approximations (as neglecting higher order terms, etc) are required. The method is applied for the simulation of a switched-capacitor-based DC-to-DC converter.