Stability of Simple Lumped-Distributed Networks With Negative Capacitors

A majority of non-Foster antenna matching circuits and non-Foster metamaterials are based on a simple parallel combination of positive and negative capacitor. It is known that these networks are stable if the overall “mesh” capacitance is positive. Here, we show that this widely accepted criterion fails if a transmission line of any finite length (different from zero) is inserted between an ideal positive capacitor and an ideal negative capacitor. Such a network is always unstable, which appears to be a serious drawback. However, we also show that a realistic, band-limited negative capacitor can be designed in a way that assures stable operation.