Exact and approximated analysis of voltage-commutated dc-to-dc converters

Due to the voltage-commutation, it is necessary to take an additional subinterval into account during analysis. The difference equation of sample values is set up starting from piecewise linear differential equations. For pulse-width modulated control a dynamic model follows, linearized around the steady state working point. In the case of dc choppers the useful signal is the low-frequency mean value. The difference equation of the mean value behaviour can be obtained via a discrete relation between mean and sample value. If sufficient smoothing is provided a continuous equivalent differential equation can be derived. Via series expansions, an analytical approximation model is obtained, which simply can be interpreted as continuous equivalent circuit. Then a further analysis follows with the well known methods of dc networks.