Extending scattering-parameter approach to characterization of linear time-varying microwave devices

In this paper, we apply the theory of linear time-varying differential syst ems of equations to defining an extension of the standard scattering parame ters. This extended parameter (S) over tilde (omega, t) is a function of bo th time and frequency. With this definition, we can accurately characterize rapidly time-and frequency-varying linear lumped causal microwave devices, in particular, photoconductive microwave switches. We discuss the similari ties between (S) over tilde (omega,t) and the standard S-parameter approach and describe a measurement technique. We also derive some important proper ties of the (S) over tilde (omega,t)-parameters and describe conditions und er which microwave devices such as photoconductive switches can be analyzed by this technique. To demonstrate the usefulness of (S) over tilde (omega, t), we derive the complete transfer function of the time-varying lumped-el ement model of a photoconductive switch. We also show the limitations of co nventional time-invariant assumptions (based on windowing or apodization) t o accurately model linear time-varying devices.