  Time-varying guiding structures introduce an additional degree of freedom,
besides spatial-variation, that enables better control over the guided wave in
a device. Periodically time-modulated structures which are usually considered
enable wave control over narrowband signals. However, for ultrawideband
short-pulse signals, time-variation in the form of temporal discontinuities is
required. Such a setup has recently been proposed as a mean to overcome the
Bode-Fano bound on impedance matching. While hard (abrupt) temporal
discontinuities are relatively simple to analyze by employing continuity of
magnetic flux and electric charge, soft (gradual) temporal switching of the
guiding structure parameters is more challenging. This work explores the case
of a short-pulse dynamics in a one-dimensional, metamaterial TL, medium with
general smooth time-variation of its parameters. In this time-varying TL,
wave-field solutions are obtained by a WKB approach which is more common in the
context of gradual spatial variations. Using this methodology a leading order
transmitted and reflected waves due to the time-variation are derived, followed
by a discussion of the energy balance in such switched media. A canonical
example of capacitor discharge into a long time-varied TL is given. These
results may be used as analysis/synthesis tools for time-varying wave devices
in electromagnetics and acoustics.
