Analytical closed‐form solution for transient analysis of boost DC‐DC converters

Abstract

PurposeThe purpose of this paper is to suggest a new analytical methodology for transient analysis of DC‐DC power converters. The closed‐form solution obtained following this methodology is suitable both for design of passive elements of the converter and for the development of control techniques.Design/methodology/approachThe methodology is based on a mixed use of Laplace transform and z‐transform. The expressions of variables of the set of equations, characteristic of a DC‐DC converter, are first evaluated in the Laplace domain for the generic switching interval. The solutions obtained are then z‐transformed in order that they match in each contiguous time interval, to form the complete transient response.FindingsThe new solution methodology allows the analytical determination of time constants of DC‐DC converters, also in presence of large duty‐cycle variations. Moreover, it is possible to evaluate easily the influence of passive elements on converter's behaviour, without several numerical simulations.Originality/valueThe analytical solution of linear systems is well known both in transient and in steady‐state conditions. However, when there is an infinite number of poles in the Laplace transform of the input signals, such as the case of switching power converters, the inversion in a closed form of the Laplace transform of the solution can be cumbersome. The methodology presented tries to overcome this problem by using an approach based on the z‐transform. Operating in this way, a closed‐form solution can be obtained both in transient and in steady‐state conditions, for all the main topologies of switching power converters. The procedure has been explained in detail for the sample case of boost DC‐DC converters.