First-principles analysis of energy exchange in time-varying capacitors for energy trapping applications

TL;DR

This paper provides a first-principles analysis of how time-varying capacitors can be modulated to achieve reflectionless wave scattering and efficient energy transfer, enabling broadband pulse matching in active networks.

Contribution

It derives the required temporal modulation of capacitance for reflectionless scattering and clarifies the energy transfer mechanism from waves to the modulation source.

Findings

Capacitance modulation can be designed for reflectionless scattering.

Energy of incoming pulses is transferred to the modulation source.

Feasible implementation with DC voltage sources is demonstrated.

Abstract

Time-varying networks, consisting of lumped elements, such as resistors, capacitors, and inductors, actively modulated in time, have introduced a host of novel wave phenomena and witnessed a remarkable development during recent years. This paper investigates the scattering from a time varying capacitor and how such a load can be fully reflectionless when the capacitance is suitably modulated in time. We analytically derive the required temporal dependence of the capacitance and show how in contrast to other techniques it avoids extreme and negative values and, as a result, can be implemented in a feasible way, when the capacitor is charged with a DC voltage source. We also derive from first principles the energy balance of such a time-varying capacitor, proving that the energy of an incoming pulse is transferred to the modulation source. Our findings clarify scattering of waves from time-varying capacitors and open up a new way to matching of broadband pulses.