Electrical resonances and power transfer mechanisms for time-varying circuits and systems

The phenomena of resonances and power transfer mechanisms are pivotal in understanding the physical behavior and performance of electrical or electronic systems. These fundamental properties are of extreme significance, as they favorably or adversely impact a system’s overall electromagnetic response. However, to date, the definitions and physical understanding of these terms continue to remain restricted from a more general standpoint of traditional linear time-invariant systems, i.e., systems that do not change their intrinsic properties with time. Time-modulated systems, on the other hand, have garnered considerable recent attention due to their ability to exhibit extraordinary physical phenomena across a wide array of electromagnetic and optical applications. In the context of these time-modulated systems, the understanding of resonance behavior and power transfer methodologies from an electrical and electronic standpoint remains incomplete and elusive due to the current lack of an adequate theoretical foundation. In this study, accompanied by a detailed theoretical analysis, we demonstrate several paradigm shifts that can result from a thorough interpretation of these fundamental properties from the standpoint of time-modulated electromagnetic systems. For instance, we demonstrate here the possibility of achieving unprecedented control over resonances and anti-resonances, a capability to arbitrarily manipulate impedances and admittances by utilizing limited available component resources, an ability to perform extensive network synthesis through the generation, suppression, and control of anti-resonance phenomena, and a broader understanding of power transfer mechanisms, including source-specific transfer of electromagnetic power to a load. These inferences provide unprecedented degrees of freedom for harmonic engineering of a system’s electromagnetic response.