Kapitza-Inspired Stabilization of Non-Foster Circuits via Time Modulations

Abstract: With his formal analysis in 1951, the physicist Pyotr Kapitza demonstrated that an inverted pendulum with an externally vibrating base can be stable in its upper position, thus overcoming the force of gravity. Kapitza's work is an example that an originally unstable system can become stable after a minor perturbation of its properties or initial conditions is applied. Inspired by his ideas, we show how non-Foster circuits can be stabilized with the application of external \textit{electrical vibration}, i.e., time modulations. Non-Foster circuits are highly appreciated in the engineering community since their bandwidth characteristics are not limited by passive-circuits bounds. Unfortunately, non-Foster circuits are usually unstable and they must be stabilized prior to operation. Here, we focus on the study of non-Foster $L(t)C$ circuits with time-varying inductors and time-invariant negative capacitors. We find an intrinsic connection between Kapitza's inverted pendulum and non-Foster $L(t)C$ resonators. Moreover, we show how positive time-varying modulations of $L(t)>0$ can overcome and stabilize non-Foster negative capacitances $C<0$. These findings open up an alternative manner of stabilizing electric circuits with the use of time modulations, and lay the groundwork for application of, what we coin \textit{Vibrational Electromagnetics}, in more complex media.