Exact and approximated analysis of voltage-commutated DC-TO-DC converters

Due to the voltage-commutation, one has 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. One obtains via series expansions an analytical approximation model, which simply can be interpreted as continuous equivalent circuit. Then a further analysis follows with the well known methods of dc networks.