First-Principles Analysis of Energy Exchange in Time-Varying Capacitors for Energy Trapping Applications

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 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 derive for the first time the energy balance of such a reflectionless time-varying capacitor. Such energy balance is general in the sense that it is not restricted to incoming pulses with specific temporal shapes. Also, it unveils the interesting feature that, although the reflected signal is canceled, the energy of the incoming pulse is completely transferred to the modulation source instead of being stored in the capacitor. Our findings clarify scattering of waves from time-varying capacitors and open up a new way to matching of broadband pulses and converting electromagnetic energy to a different form of energy such as mechanical energy.