Analytical closed-form solution for transient analysis of boost DC-DC converters
Purpose - The 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/approach - The 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. Findings - The 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/value - The 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.
transforms transient response electric power switching circuits direct current