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Time-varying networks, consisting of lumped elements, such as resistors,capacitors, and inductors, actively modulated in time, have introduced a hostof novel wave phenomena and witnessed a remarkable development during recentyears. This paper investigates the scattering from a time varying capacitor andhow such a load can be fully reflectionless when the capacitance is suitablymodulated in time. We analytically derive the required temporal dependence ofthe capacitance and show how in contrast to other techniques it avoids extremeand 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 fromfirst principles the energy balance of such a time-varying capacitor, provingthat the energy of an incoming pulse is transferred to the modulation source.Our findings clarify scattering of waves from time-varying capacitors and openup a new way to matching of broadband pulses.

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