The Periodical solution of networks containing piecewise linear or controlled components

In this thesis, a new method is presented to find the periodic steady-state soluations of nonlinear networks which yield periodic steady-state responses when excited by periodic inputs. Instead of the nonlinear compenents in the network, the presented method is based upon the treatment of their equivalent representations which are obtaind by piecewise linear approximation and composed of linear RLC components, constant voltage and current sources and periodically operating switches. During the application of the method, first, the regions in their piecewise linear characteristics and the approximate durations for which the elements stay in these regions under steady-state conditions are determined. For this, transient analysis is applied. Later, using these data and applying the steady-state analysis, the time durations which are found approximately are corrected iteratively with in a desiredVI accuracy, and finally the steady-state solution of the network is obtained. In the analysis, instead of numerical integration and optimization techniques explicite exact formulas are used, therefore the results are attained in a short time. To perform these computations a computer program named PGEDAN is prepared and it is applied on several examples exposing the properties of the method. KEY WORDS: Nonlinear networks, piecewise linear networks, networks containing periodically operated switches, steady-state analysis, exact analysis.