On the periodic behavior of PWM DC-DC converters

In this paper, we present a method to compute the periodic behavior of PWM dc-dc converters. The method is based on Fourier series and can be seen as a generalization of the state space averaging techniques that are well-known in the field of dc-dc converters. The method of this paper can be used to compute the periodic behavior of a dc-dc converter up to any degree of accuracy. This can be done in open loop as well as in closed loop situations. In an open loop situation the method only requires the solving a set of linear equations in the Fourier coefficients. It is shown that the periodic behavior in an open loop situation always is stable. In a closed loop situation the method requires the solving of a set of equations consisting of the previously mentioned set of linear equations in the Fourier coefficients, combined with an additional nonlinear equation in the relative pulse width (duty ratio). In both situations the method of this paper can be implemented in an efficient way. The method is illustrated by means of known examples taken from the literature and is shown to be useful in establishing whether or not a periodic behavior in a closed loop situation is stable.