In this paper, we apply the theory of linear time-varying differential systems of equations to defining an extension of the standard scattering parameters. This extended parameter~() is a function of both time and frequency. With this definition, we can accurately characterize rapidly timeand frequency-varying linear lumped causal microwave devices, in particular, photoconductive microwave switches. We discuss the similarities between~() and the standard-parameter approach and describe a measurement technique. We also derive some important properties of the~()-parameters and describe conditions under which microwave devices such as photoconductive switches can be analyzed by this technique. To demonstrate the usefulness of~(), we derive the complete transfer function of the time-varying lumped-element model of a photoconductive switch. We also show the limitations of conventional time-invariant assumptions (based on windowing or apodization) to accurately model linear time-varying devices.
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