How to Accurately Predict Instability in non-Foster and Time-varying Circuits?

There is a clear trend towards including active components such as non-Foster elements and time-varying elements in electromagnetic systems, especially those based on metamaterials and metasurfaces. These systems, like all active systems, can become unstable under certain circumstances. In this contribution, the advantages and disadvantages of common linear stability prediction methods are compared: port-based methods, transfer-function-based methods, and feedback-theory-based methods. It is shown that the number of methods that can reliably predict physical behavior is very limited, especially for systems based on time-varying elements. Finally, some new ideas of the development of a generalized method, that could be used for systems based on non-Foster elements as well as for systems based on time-varying elements, are discussed.

I. Introduction

Classical metamaterials and metasurfaces are based on an array of passive unit cells consisting of resonators, transmission lines, small antennas, scatterers, or lumped elements. Due to background physics, these systems are reciprocal and subject to unavoidable limitations on the maximum operating bandwidth [1]. In recent years, therefore, there has been a clear trend towards incorporating active elements into the above electromagnetic systems to increase their versatility. Most popular approaches include non-Foster (NF) elements [1]–[8] and time-varying (TV) elements [9]–[14].