A generalized method for calculating the RMS values of switching power converters

In this paper an analytical method is presented which allows the exact calculation of the RMS value of the state space variables of a switching power converter, whose starting point is the unified state-space representation of the switched networks and the end result is a complete form of equations that include both the DC and RMS values. The method proposed in this paper bridges the gap which exists between the state-space technique and the small signal approximation that departs from the steady state. Ripple values are negligible, compared to the steady state values themselves. A new extended circuit model is proposed whose fixed topology contains all the elements of any DC-to-DC converter, regardless of its detailed configuration, and by which different converters can be characterized in the form of a table conveniently stored in a computer data bank to provide a useful tool for computer aided design and optimization. Finally, examples are given for buck, boost, and buck-boost regulator topologies.