Perfect Matching of Reactive Loads Through Complex Frequencies: From Circuital Analysis to Experiments

The experimental evidence of purely reactive loads impedance matching is here provided by exploiting the special scattering response under complex excitations. The study starts with a theoretical analysis of the reflection properties of an arbitrary reactive load and identifies the proper excitation able to transform the purely reactive load into a virtual resistive load during the time the signal is applied. To minimize reflections between the load and the transmission line, the excitation must have a complex frequency, leading to a propagating signal with a tailored temporal envelope. The aim of this work is to design and, for the first time, experimentally demonstrate this anomalous scattering behavior in microwave circuits, showing that the time-modulated signals can be exploited as a new degree of freedom for achieving impedance matching without introducing neither a matching network nor resistive elements that are typically used for ensuring power dissipation and, thus, zero reflection. The proposed matching strategy does not alter the reactive load that is still lossless, enabling an anomalous termination condition where the energy is not dissipated nor reflected but indefinitely accumulated in the reactive load. The stored energy leaks out the load as soon as the applied signal changes or stops.