Algebraic Representation of DC-DC Converters and Symbolic Method of their Analysis

The algebraic representation of idealized DC-DC PWM converters covering various structures and their connection is given. The algebra is constructed on the basis of hyper-complex numbers - hypernions and allows the analysis of the structures of the converters by using of a symbolical method. The possibility of the calculation of a discontinuous current and soft switching is also considered. Such an abstract description of various schemas allows reducing their variety to several basic structures and formalizes a problem of the synthesis of the converters with the desired parameters. The numerical solution of the algebraic expressions is easily carried out with the help of the standard mathematical programs MATHCAD or MATLAB.