Influence of transmission line on stability of networks containing ideal negative capacitors

Majority of non-Foster-based metamaterials or antenna matching circuits are based on simple networks that contain parallel or series combination of positive and negative capacitor. It is well-known that these networks are stable, if the overall capacitance is positive. It is shown that this stability criterion becomes fundamentally different if a segment of a transmission line is inserted between the ideal positive capacitor and ideal negative capacitor. In parallel and series networks, the presence of a transmission line segment of any finite length (different from zero) causes instability. This counter-intuitive behavior is caused by the unstable system pole located at the positive real axis of a complex plane. However, it appears possible to remove that pole by a proper design of a practical negative capacitor and, therefore, assure stable operation.