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 vector (whose components are sums of charges on condensers in certain cut sets) has components that behave like sine waves modulated by increasing exponentials.