Beyond the Bode-Fano Bound: Wideband Impedance Matching for Short Pulses Using Temporal Switching of Transmission-Line Parameters

Impedance matching is one of the most important practices in wave engineering as it enables one to maximize the power transfer from the signal source to the load in the wave system. Unfortunately, it is bounded by the Bode-Fano criterion which states that, for any passive, linear, and time-invariant matching network, there is a stringent trade-off between the matching bandwidth and efficiency, implying severe constraints on various electromagnetic and acoustic wave systems. Here, we propose a matching paradigm that overcomes this issue by using a temporal switching of the parameters of a metamaterial-based transmission line, thus revoking the time-invariance assumption underlying the Bode-Fano criterion. Using this scheme we show theoretically that an efficient wideband matching, beyond the Bode-Fano bound, can be achieved for short-time pulses in challenging cases of very high contrast between the load and the generator impedances, and with significant load dispersion, situations common in, e.g., small antenna matching, cloaking, and with applications for ultrawideband communication, high resolution imaging, and more.