Using degree theory to determine the minimum number of unstable operating points that a nonlinear circuit must possess
M.M. Green, Alan N. Willson · 2003
It has been shown previously that any structurally stable operating point (i.e., an operating point that does not disappear when the component values are perturbed slightly) of a nonlinear circuit must have an index of either +1 or -1. It is shown here that any operating point that has an index of -1 must be unstable. A simple relationship is derived between the number of operating points with index -1 and with index +1, thereby proving that if a circuit is known to possess n structurally stable operating points (n has been shown previously to be odd), then (n-1)/2 of these operating points must be unstable and hence unobservable for the physical circuit. A special case of this result proves that an bistable circuit must possess at least three operating points.>