Signal growth in a pure time-modulated transmission line and the loss effect

We present the first comprehensive study for signal growth in transmission
lines (TL) with purely time-modulated characteristic impedance Zo (infinite
superluminality). This study pioneers the investigation into the effects
of varying the cell’s electrical length and the impact of loss on momentum
band gaps and amplification levels. It also thoroughly examines how
time-modulated transmission line truncation by a static load influences
the sensitivity of amplification gain to the relative phase between the
incoming signal and modulation, comparing these findings to the case of
parametric amplification. Varying Zo is accomplished by loading TLs with a
sinusoidally time-modulated capacitor (TMC). The study starts with a
simple lumped model cell to facilitate understanding of the phenomena.
Following this, transmission lines are introduced, and the effects of
incorporating loss are examined. To accomplish this, three models are
investigated: a lossless L-C TL lumped model loaded with a shunt lossless
TMC and a TL loaded with a shunt lossless and lossy TMC. Dispersion
diagrams are plotted and momentum bandgaps are identified at a modulation
frequency double the signal frequency. Within the momentum bandgap, only
imaginary frequencies are found and correlated to momentum bandgap width
and signal growth level. Signal growth is confirmed using harmonic balance
and transient simulations, and the results are consistent with the
dispersion diagram outcomes.