Time-Domain Physical Limitations on the Response of a Class of Time-Invariant Systems

We propose time-domain (TD) physical limitations on the system function of a linear, time-invariant system. Two approaches to derive TD physical bounds are presented. The first approach is based on Cauchy’s integral of the Laplace transform of a causal transfer function, while the second one relies on an integral representation of positive real (PR) functions. The analysis yields straightforward bounds on the output signal that can be readily used to benchmark the performance of time-varying electromagnetic (EM) structures. The results are illustrated on selected transmission-line problems and on the pulsed EM plane wave scattering by thin high-contrast sheets.