Rigorous determination of the stability of linear n-node circuits from network determinants and the appropriate role of the stability factor K of their reduced two-ports

The generally accepted method of ascertaining the stability of microwave circuits, i.e. reducing the complicated N-node networks to Two-Ports between input and output, and requiring that K>1 and |Δ_s|<1 at all frequencies, is not rigorous and can fail in actual designs. Failure is not contingent on any particular symmetry of the circuits. Moreover, the conditions under which the criteria fail are outside the confines of the calculations of K and the additional condition. The failure is shown to stem from the fact that no definitive determination can be made on the stability of entire networks from the location of the zeroes of their reduced Two-Port determinants. In this paper, we offer a rigorous and practical method for determining the stability of any N-node network composed of elementary elements