Cyclic mode RMS: derivation, framework and application to LLC resonant converters

This paper presents a general method to estimate the root mean square (RMS) of currents and voltages within a switching converter using matrix manipulation of its state-variable representation without having to generate waveforms prior to RMS evaluation. The method uses cyclic-mode analysis of the state-variable model and the multi-dimensional shooting method to determine the steady-state operating conditions of a converter, and then applies the new technique to estimate the RMS of the states. Although applied to resonant converters in the paper, the work has general applicability; it is not restricted to a particular converter topology and can be applied to arbitrary-order state-space models. This generality distinguishes the proposed method from previously reported lower-order or converter-specific treatments. The viability and accuracy of the method is verified for an LLC converter through comparison with SPICE simulation, first-harmonic approximation and experimental measurements.