Perfect matching of reactive-loaded transmission lines through complex excitation

Any lossless transmission line terminated on an arbitrary reactive load suffers from reflections, due to the high impedance mismatch between the real characteristic impedance of the transmission line and the imaginary impedance of the load. Although several techniques have been proposed to achieve matching, a resistive lumped component must be always added at the end of the line for ensuring power dissipation and achieving the required zero reflection. Here, we present a way to achieve the perfect matching condition for purely reactive loads by exploiting the properties of complex frequency excitation. By exciting the circuit with a signal having a proper time profile, we demonstrate that the amplitude of the reflected wave can be brought to zero. Being the load purely reactive, energy is not dissipated, but stored in the load as long as the special excitation condition is satisfied, giving rise to an interesting singularity in the transient regime, referred to as virtual absorption. Then, the stored energy can be released at will by changing or stopping the applied complex excitation.