Passive Multiterminal Networks Without Transformers

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.