Linear Time Varying G-C Networks: Stable and Unstable

This paper studies the stability of linear time varying conductance-capacitance networks. Several sets of sufficient conditions for their stability are given. In particular, instability can occur only if both the G matrix and the C matrix are time varying. In the limit of very large pump frequencies, the stability of periodic piecewise constant networks is determined by a simple relation. The design of unstable G-C networks is explained and illustrated by two examples. In the second example the
q
vector (whose components are sums of charges on condensers in certain cut sets) has components that behave like sine waves modulated by increasing exponentials.