Passive Multiterminal Networks Without Transformers

This is the authors' abstract. We don't add key points for this paper.

It is known that any scalar function f(p) of the complex frequency variable that is the admittance function of a passive finite network is in fact the admittance function of a network that can be realized without transformers. This paper shows that an m times m matrix-valued function Y(p), m ges 2, given that it is an admittance matrix, is the admittance of a network that contains no transformers if and only if it enjoys two further properties: 1) for each real p > 0 Y(p) is the admittance of a passive resistive network specific to p; and 2) a property defined as the null space property. It is shown that property 1) severely limits the class of m-terminal networks, m > 1, that can be realized without transformers. The author concludes that, for passive systems, transformers are here to stay.