DOI: 10.5061/dryad.qv9s4mwnx
title: Signal growth in a pure time-modulated transmission line and the loss effect

description: 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.
description: The datasets are generated by simulating various types of 9-unit
 cell transmission lines, each featuring a purely time-modulated
 characteristic impedance ( Z<sub>o</sub> ). The modulation of
 ( Z<sub>o </sub>) is achieved by loading the transmission
 lines with a sinusoidally time-modulated capacitor (TMC). These
 simulations are conducted using the Keysight Advanced Design System
 software.
description: # Signal growth in a pure time-modulated transmission line and the loss
 effect The dataset encompasses various studies on the simulated transient
 output voltage and power for 9-unit cell transmission lines, each
 featuring a purely time-modulated characteristic impedance, ( Zo ). The
 modulation of ( Zo) is achieved by loading the transmission lines with a
 sinusoidally time-modulated capacitor (TMC). [Datasets: contain the Excel
 files generated from the transient time simulator and plotted in the
 manuscript (named according to the manuscript)]. ## Variables used in the
 dataset: time: Time used in the transient simulations with an interval of
 400 ns and time step 0.01 ns. Po/Pout: Transient output power of the
 circuit. Vo/TRAN.Vo: The circuit's transient output voltage. Pin:
 Transient input power input to the circuit. ## Description of the data and
 file structure Plot_ID: identifier for study plot Fig.3(b): For 9 unit
 cells with 10 V input peak (1 Watt (rms)), time-modulated capacitor at MD
 = 0.66, L = 12.5 nH, Co = 5 pF, Fs = 0.5 GHz (main signal frequency), Fm =
 1 GHz (modulation frequency) loaded with a 50 Ω load impedance. [ Output
 voltage (transient)]. Fig.4(a): For 9 unit cells with 10 V input peak (1
 Watt(rms)), L = 12.5 nH, Co = 5 pF, Fs = 0.5 GHz (main signal frequency),
 Fm = 1 GHz (modulation frequency), loaded with a 50 Ω load impedance. [
 Output voltage (transient) at time-modulated capacitor at MD = 0.5].
 Fig.4(c): For 9 unit cells with 10 V input peak (1 Watt(rms)), L = 12.5
 nH, Co = 5 pF, Fs = 0.5 GHz (main signal frequency), Fm = 1 GHz
 (modulation frequency), loaded with a 50 Ω load impedance. [Output voltage
 (TS) at time-modulated capacitor with MD = 0.33]. Fig.5(a): For 9 unit
 cells with 10 V input peak (1 Watt(rms)), L = 12.5 nH, Co = 5 pF, Fs = 0.5
 GHz (main signal frequency), Fm = 1 GHz (modulation frequency), loaded
 with a 50 Ω load impedance. (a) Input instantaneous power (rms) in the
 absence of modulation (transient). Fig.5(b): For 9 unit cells with 10 V
 input peak (1 Watt(rms)), L = 12.5 nH, Co = 5 pF, Fs = 0.5 GHz (main
 signal frequency), Fm = 1 GHz (modulation frequency), loaded with a 50 Ω
 load impedance. Transient simulation output power (rms) with the
 time-modulated capacitor at MD = 0.66. Fig.5(c): For 9 unit cells with 10
 V input peak (1 Watt(rms)), L = 12.5 nH, Co = 5 pF, Fs = 0.5 GHz (main
 signal frequency), Fm = 1 GHz (modulation frequency), loaded with a 50 Ω
 load impedance. Transient simulation output power (rms) with the
 time-modulated capacitor at (c) MD = 0.5. Fig.5(d): For 9 unit cells with
 10 V input peak (1 Watt(rms)), L = 12.5 nH, Co = 5 pF, Fs = 0.5 GHz (main
 signal frequency), Fm = 1 GHz (modulation frequency), loaded with a 50 Ω
 load impedance. Transient simulation output power (rms) with the
 time-modulated capacitor at MD = 0.33. Fig.8(a): For 9 unit cells with 10
 V input peak (1 Watt (rms)), Co = 4 pF Fs = 0.5 GHz, Fm = 1 GHz, MD =
 0.58, and the TL with 90 Ω characteristic impedance (Zo) and different
 lengths loaded with a 50Ω load impedance. For 0.1λm (m = 0.1) TL: output
 voltage (transient). Fig.8(b): For 9 unit cells with 10 V input peak (1
 Watt (rms)), Co = 4 pF Fs = 0.5 GHz, Fm = 1 GHz, MD = 0.58, and the TL
 with 90 Ω characteristic impedance (Zo) and different lengths loaded with
 a 50Ω load impedance. For 0.15λm (m = 0.15) TL: output voltage
 (transient). Fig.8(g): For 9 unit cells with 10 V input peak (1 Watt
 (rms)), Co = 4 pF Fs = 0.5 GHz, Fm = 1 GHz, MD = 0.58, and the TL with 90
 Ω characteristic impedance (Zo) and different lengths loaded with a 50Ω
 load impedance. For 0.1λm (m = 0.1) TL: output power (transient).
 Fig.8(h): For 9 unit cells with 10 V input peak (1 Watt (rms)), Co = 4 pF
 Fs = 0.5 GHz, Fm = 1 GHz, MD = 0.58, and the TL with 90 Ω characteristic
 impedance (Zo) and different lengths loaded with a 50Ω load impedance. For
 0.15λm (m = 0.15) TL: output power (transient). Fig.10(a): For 9 unit
 cells with 10 V input peak (1 Watt (rms)), Co = 4 pF Fs = 0.5 GHz, Fm = 1
 GHz, MD = 0.58, and a 0.15λm (m = 0.15) TL with 90 Ω characteristic
 impedance (Zo) and different lengths loaded with a 50Ω load impedance. For
 Rc=5 Ω: output voltage (transient). Fig.10(b): For 9 unit cells with 10 V
 input peak (1 Watt (rms)), Co = 4 pF Fs = 0.5 GHz, Fm = 1 GHz, MD = 0.58,
 and a 0.15λm (m = 0.15) TL with 90 Ω characteristic impedance (Zo) and
 different lengths loaded with a 50Ω load impedance. For Rc=15 Ω: output
 voltage (transient). Fig.10(g): For 9 unit cells with 10 V input peak (1
 Watt (rms)), Co = 4 pF Fs = 0.5 GHz, Fm = 1 GHz, MD = 0.58, and a 0.15λm
 (m = 0.15) TL with 90 Ω characteristic impedance (Zo) and different
 lengths loaded with a 50Ω load impedance. For Rc=5 Ω: output Power
 (transient). Fig.10(h): For 9 unit cells with 10 V input peak (1 Watt
 (rms)), Co = 4 pF Fs = 0.5 GHz, Fm = 1 GHz, MD = 0.58, and a 0.15λm (m =
 0.15) TL with 90 Ω characteristic impedance (Zo) and different lengths
 loaded with a 50Ω load impedance. For Rc=15 Ω: output Power (transient).
 ### Variable used to define the datasets: MD: Modulation depth of
 capacitance time modulation. Fs: Input signal frequency Fm: Modulation
 frequency. Co: Nominal capacitance. λ: wavelength at input signal
 Frequency. λm: wavelength at the modulation frequency. Rc: Series
 resistance connected to the modulated capacitor. Ω: Ohm. rms: root mean
 square. TL: transmission line. ### Code/Software This folder contains two
 main directories: one for MATLAB codes related to all proposed models,
 which plot the real and complex frequency dispersion as well as the loss
 dispersion, and another for the simulator file (Advanced Design System)
 that validates the results obtained from the dispersion plots. ### Matlab
 files: This folder contains all the MATLAB scripts for the proposed
 models, which are used to plot real and complex frequency dispersion, as
 well as loss dispersion. Each folder contains the eigenshuffle.m script,
 which arranges the eigenvalues resulting from the solution of the
 eigenvalue problem. A.1. lumped model (Section 2(a)) L_C_Beta.m: Plots the
 real dispersion for the modulated TL lumped model. L_C_imagfre.m: Plots
 the complex dispersion for the modulated TL lumped model. A.2. Lossless
 and lossy TL (Section 2(b)) TL_RC_Beta.m: Plots the real dispersion for
 the modulated TL loaded with a shunt capacitor (lossy or lossless,
 depending on the value of Rc). TL_RC_imagfre.m: Plots the complex
 dispersion for the modulated TL loaded with a shunt capacitor (lossy or
 lossless, depending on the value of Rc). TL_RC_ALFA.m: Plots the loss
 dispersion for the modulated TL loaded with a shunt capacitor (lossy or
 lossless, depending on the value of Rc). ### Simulator File: This folder
 includes the Advanced Design System (ADS) files that validate the results
 obtained from the dispersion plots.