Abstract :
An important problem in network design is the synthesis of driving-point impedance functions. As is well known, O. Brune was the first to state the necessary and sufficient conditions for physical realizability. Unfortunately, the synthesis technique which he proposed leads in general to perfectly coupled transformers. This is true also in the ease of the contributions made later by S. Darlington. Perfect transformers were eliminated by R. Bott and R. J. Duffin. However, their solution is, in general, expensive in terms of the number of elements that are required. Since the publication of their letter, many attempts have been made to find a solution that would lead to networks containing a number of elements closer to the minimum specified by Brune. An advance in this direction has been made by F. Miyata for a restricted class of positive real functions. He bas centered attention on the even part of the impedance function. The following paper exploits this point of view and amplifies some of the ideas given by Miyata. In addition, several new ideas are described relative to methods of decomposing the even part of the impedance function in such a way as to obtain a network without perfect transformers.
