General Stability Theory of Non-Foster and Time-varying Elements
Abstract
The goal of this three-year research effort is to develop a theoretical framework to predict the stability-bandwidth constraints of both non-Foster networks and time-varying networks. If successful, the proposed project will produce a design tool for stability bandwidth optimized non-Foster/ time-varying metamaterials/metasurface systems. In recent years, there has been a clear trend toward using non-Foster and time-varying active elements in artificial electromagnetic structures to increase their versatility. Non-Foster elements are linear electronic circuits that mimic the inverse dispersion of hypothetical negative capacitors and negative inductors, thus violating the well-known Foster s reactance theorem. Their use can lead to broadband antenna matching structures and metamaterial/metasurface-based systems. Unfortunately, it is well known that ensuring stable operation of non-Foster systems is an extremely difficult task. Despite intensive worldwide research efforts, there is still no reliable stability prediction method that ensures an optimal trade-off between operating bandwidth and stability robustness. On the other hand, time-varying reactive elements behave like parametric mixers/transducers. In addition to the well-known applications in parametric amplifiers, time-varying elements have recently been proposed for introducing non-reciprocity, temporal cloaking, and serrodyne frequency conversion in metamaterials/metasurfaces-based devices, just to name a few. Interestingly, studies of these new applications almost completely ignore the issue of stability, even though it is well known that time-varying networks can be unstable. As in the case of non-Foster systems, there is no general theory of the stability of time-varying systems. In this project, it will be shown that non-Foster networks, generalized non-Foster networks (networks containing negative resistors in addition to negative capacitors and negative inductors), and time-varying networks share the same physical background. Based on this, a unified theoretical framework for stability analysis and prediction of non-Foster networks, generalized non-Foster networks, and time-varying networks as well as their arbitrary combination, will be developed. The theory will be based on a rigorous solution of differential equations describing non-Foster/time-varying systems in either the time domain or the Laplace domain as well as associated equivalent circuits. The goal should be a system of equations (or inequalities) that tells the designer in what range of external impedances stable operation is guaranteed for the prescribed bandwidth. The results obtained by developed theory will be compared with numerical and experimental results of representative non-Foster and time-varying systems from the literature. Finally, it will be attempted to use the developed stability theory for the design of novel stability-robust non-Foster/time-varying unit cell for future active metasurfaces.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 20, 2023
- Source ID
- FA86552217055
Entities
People
- Silvio Hrabar
Organizations
- Air Force Office of Scientific Research
- Faculty of Electrical Engineering and Computing, University of Zagreb
- United States Air Force