Performance analysis of envelope modelling applied to resonant converters

Resonant converters are often studied using their envelope models, i.e. the transfer functions that relate the envelope of the output quantities to those of the input ones. Transfer functions can accurately represent only the input-output relation of linear systems and hence any method used to develop the envelope model cannot be accurate if the resonant converter processes the envelopes in a non-linear way. This paper works out a general criterion that recognizes whether the envelope processing is linear or not, the type of the eventual non-linearity and its amount. The criterion is expressed in terms of conditions that have to be fulfilled by the input-output Bode diagram of the converter. These conditions are of general validity and do not depend on the converter topology; their applicability is not limited to resonant converters, but it can be extended to any system. The conditions have been derived by reviewing the procedure that leads to the Modulated Variables Laplace Transform method for the development of the envelope models. The theoretical results are verified at first by simulations and then by experimental tests carried out on two different resonant topologies of a prototypal converter that works as wireless battery charger.