Stability of embedded non-Foster metamaterials with potentially unstable circuit parameters

Recent advances have motivated renewed interest in the development of wideband metamaterials using non-Foster circuits. In contrast to passive metamaterials, the presence of active circuits in non-Foster metamaterials requires consideration of stability issues. Stability arguments for non-Foster metamaterials are often predicated on analysis of lumped-element representations of individual unit cells comprising the metamaterial. The present work considers the use of such potentially unstable non-Foster unit cells to form a stable system in the limit, under certain embedding constraints. Stability of an embedded active metamaterial is first considered. Then, non-Foster elements are introduced into a lumped-element transmission line model of a unit cell. Combining the two analyses, conditions are presented for stable systems in the limit, with straightforward extension to multidimensional non-Foster metamaterials.