Stability assessment of non-Foster circuits based on time-domain method

• Published in: IET microwaves, antennas & propagation antennas & propagation, 2015-12, Vol.9 (15), p.1769-1777
• Main Authors: Elfrgani, Aseim M, Moussounda, Renaud, Rojas, Roberto G
• Format: Article
• Language: English
• Subjects: antenna applications; Assessments; circuit stability; circuit stability analysis; Circuits; Instability; inverters; invertors; Lyapunov exponents; Lyapunov methods; maximal Lyapunov exponent; Microwave antennas; microwave applications; microwave circuits; MLE; negative impedance converters; negative impedance convertors; non‐Foster circuit; Positive feedback; potential instability; Stability; Stability analysis; time series; time series signals; time‐domain analysis; time‐domain method
• ISSN: 1751-8725; 1751-8733; 1751-8733
• DOI: 10.1049/iet-map.2014.0671

Non-Foster circuits are attractive for microwave and antenna applications since they are not restricted by the gain-bandwidth product. A persistent problem with these circuits is the potential instability (mainly unwanted oscillations) due to the presence of positive feedback. The stability properties of these circuits are discussed with a time-domain technique that computes the largest (maximal) Lyapunov exponent (MLE) for time-series signals within the circuit's structure as well as at its output to determine with confidence the circuit's stability. In case of instability, the circuit is stabilised with different controllers. A circuit or system is considered stable when the MLEs obtained from signals at multiple nodes are negative. Moreover, the effect of small DC bias variations on stability is also studied. The proposed stability analysis approach has been successfully applied to two known topologies: namely, negative impedance converters and inverters.