Polynomial Decomposition in Active Network Synthesis

This paper deals with the use of polynomial decomposition as a basis for the synthesis of active RC networks. The first part briefly reviews the formation and important properties of the Horowitz decomposition. Next, the relationships between the decompositions of two polynomials are presented in the form of three basic theorems. Significant in the development of these theorems is the use made of the theory of positive real functions. The active network function is treated as the even or the odd part of a positive real impedance, and hence the wealth of information available on positive real functions is brought to bear on the problem of active synthesis. The tie between active and passive synthesis is then illustrated by means of a method of active driving point synthesis, which closely parallels the synthesis of lossless terminated passive networks.