We show that Q always has as many zero eigenvalues as the minimal value of N of the different phases and they do not have any influence on either the stability properties or the order of the transfer functions. We give explicit formulas for computing the not necessarily zero eigenvalues of Q on the basis of a matrix of smaller dimension than Q. The method is elaborated for SC circuits designed by bilinear SC resistor replacements. It is pointed out that the SC circuit can easy be asymptotically unstable in the sense of Lyapunov even in the case when the reference filter is stable. It will be proven that the stability is always an oscillation of zero average value and its magnitude can be computed only on the basis of the prototype network. Finally the results are illustrated by an example.
ASJC Scopus subject areas
- Electrical and Electronic Engineering