Nonlinear Transmission Line Model Research Articles

Role of gas composition in weakened nonlinear standing wave excitation and improved plasma radial uniformity in very-high-frequency asymmetric capacitive Ar/CF4 discharges

The higher harmonics generated by nonlinear sheath motion would enhance the standing wave effect, and thus lead to center-peaked plasma density profile in very-high-frequency (VHF) capacitive discharges. In this work, a nonlinear transmission line (NTL) model introduced in Zhou et al (2021 Plasma Sources Sci. Technol. 30 125017) has been extended, with radial transport of various particles and nonlinear sheath motion into account, to investigate the effects of CF4 fraction α on the nonlinear standing wave excitation and plasma radial uniformity in VHF (60 MHz) capacitively coupled Ar/CF4 plasmas at 3 Pa. The results indicate that for pure Ar discharges (i.e. α= 0%), the nonlinearly excited harmonics with short wavelength significantly enhance the electron power absorption at the radial center, resulting in a pronounced central-high plasma density profile. As α increases, the high-order harmonics are gradually damped due to the increase of resistance, as well as the longer wavelength caused by thicker sheath thickness. Thus, the radial profile of the electron absorbed power density shifts from center-peak to edge-high. Besides, at the radial center, the electron density and Ar+ ion density decrease with α , CF3 + ion density shows an increasing trend, while F− ion density initially rises and then decreases. Moreover, the density profiles of all the species become more uniform at higher CF4 fraction, due to the suppressed nonlinear standing wave excitation and the longer wavelength of the nonlinear harmonics.

A numerical approach for nonlinear transmission line analysis with bidirectional coupling to lumped-element and particle-in-cell models

In this article, an iterative method for nonlinear transmission lines (TLs) based on the Lax-Wendroff method has been established to describe a bidirectional coupling model of nonlinear lumped-element models, nonlinear transmission line models, and particle-in-cell (PIC) models. The proposed self-consistent global circuit model is achieved through the introduction of the charge conservation equation at the upper plate as the Robin boundary condition and its coupling with the PIC method used for plasma simulation. The effectiveness of the proposed model is validated through five numerical experiments, including nonlinear transmission line coupling to lumped circuits, and the most general case of plasma-TLs-lumped elements model (LEM) coupling systems. This non-linear global circuit coupling model provides a powerful tool for simulating the complex behavior of various physical systems, including but not limited to capacitively coupled plasmas, vacuum electronic devices, and Z-pinches.

Further physical research about soliton structures and phase portraits in nonlinear fractional electrical transmission line model

This paper presents several novel contributions in the field of nonlinear fractional low-pass electrical transmission line model (NFLETLM). Firstly, using the modified (G′G2)-expansion method and the extended modified Jacobi elliptic expansion method, we discovered new and accurate solutions for NFLETLM, which have not been reported in the existing literature (Tala-Tcbuc et al. 2014; Nuruzzaman et al. 2021). These solutions, denoted as U3,U4,U7,U8,U9,U10,U13,U14 and UJ1,UJ2,UJ3,UJ4 represent novel contributions to the fields. Secondly, by utilizing computer simulations, we observed various intriguing phenomena in the wave solution graphs, such as anti-kink waves, periodic waves, intense singular periodic waves, bright singular wave solutions, multi-periodic waves, intense double periodic waves, and alternating patterns of light and shade waves. These findings shed light on previously unexplored aspects of the problem. Thirdly, through an extensive study on the newly discovered solutions, we provided a comprehensive understanding of the solitons inherent in the NFLETLM, including comparison with other derivative solutions. Our conformable fractional derivative solutions showed similarities to beta derivative solutions, distinguishing them from Riemann–Liouville derivative solutions. Lastly, we explored the phase portrait, bifurcation analysis, sensitivity, and potential chaotic behaviors of the NFLETLM, which have not been addressed in previous works (Tala-Tcbuc et al. 2014; Nuruzzaman et al. 2021). This innovative contribution expands our understanding of the NFLETLM model and uncovers new dynamics and phenomena.

(Invited) Improved Thin Film Transistor Model Predicts TFT Operation in the THz Range

Novel Thin-film-transistor (TFT) TFT materials such as ZnO, InGaZnO, AMO-CNT, and organic materials dramatically improved the achieved and projected TFT performance. The low field mobility of oxide materials has reached values comparable to those for short-channel Si CMOS. The effects related to electron inertia and electron density oscillations in field effect transistors channels (FETs) diminish the role of the low field mobility as a figure of merit in short channel devices making the performance gap between TFTs and Si CMOS smaller enabling high frequency TFT applications even reaching sub-THz and THz frequencies (for the operating regimes using the rectification of the plasma oscillations. We report on an improved compact model based on the RPI TFT model [1] and using the Unified Charge Control Model (UCCM). [2, 3] This model accounts for a non-exponential slope in the subthreshold regime by introducing a varying subthreshold slope and accounts for non-trivial capacitance dependence on the gate bias. It also accommodates the inclusion of the parasitics related to the gate impedance. These new features allowed us to obtain an excellent agreement with the measured I-V/C-V characteristics for both long and short n-channel and p-channel TFTs. The application of this new TFT model to the analysis of the TFT response requires accounting for non-local potential distribution in the device channel. This is achieved by using a multi-segment nonlinear transmission line model of the TFT channel reproducing the approach that has been previously used for the THz SPICE/ADS Si CMOS model implementation. As a possible application example, we simulated a TFT complementary inverter. Our simulations showed that using the phase-matched THz signal feeding should yield a very sensitive detection of THz radiation impinging on a short channel TFT. These results show that the TFT RFID and other applications could be extended into the THz range of frequencies.

Lie group classification of the nonlinear transmission line model and exact traveling wave solutions

A nonlinear transmission line (NLTL) model is very essential tools in understanding of propagation of electrical solitons which can propagate in the form of voltage waves in nonlinear dispersive media. These models are often formulated using nonlinear partial differential equations. One of the basic tools available to study these equations are numerical methods such as finite difference method, finite element method, etc, have been developed for nonlinear partial differential equations. These methods require a great amount of time and memory due to the discretization and usually the effect of round-off error causes loss of accuracy in the results. So in this paper, we use one of the most famous analytical methods the Lie group analysis due to Sophus Lie. One of the advantages of this approach is that requires only algebraic calculations. The main aim of this study is to explore the nonlinear transmission line model with arbitrary capacitor's voltage dependence, through the use of Lie group classification, we show that the specifying form of arbitrary capacitor's voltage are power law nonlinearity, exponential law nonlinearity and constant capacitance. The exact solutions and similarity reductions generated from the symmetries are also provided. Furthermore, translational symmetries were utilized to find a family of traveling wave solutions via the \(\tanh\)-method of the governing nonlinear problem.

Optimal system, dynamical behaviors and exact solution of a nonlinear transmission line model by applying the Lie symmetry method

Optimal system, dynamical behaviors and exact solution of a nonlinear transmission line model by applying the Lie symmetry method

On some new analytical solutions to the (2+1)-dimensional nonlinear electrical transmission line model

In the present paper, from the field of communications in physics and engineering, we select the (2+1)-dimensional nonlinear electrical transmission line equation to be studied. The model under study is one of the models that has important applications in the field of physics and telecommunications engineering. We acquire the soliton solutions by using two simple methods. We present some figures in two and three dimensions to show that these solutions actually have the properties of soliton waves.

Nonlinear transmission line (NTL) model study of electromagnetic effects in high-frequency asymmetrically driven capacitive discharges

In this work, we generalize a nonlinear transmission line (NTL) model introduced in a previous work [Liu et al. Plasma Sources Sci. Technol. 30, 045017 (2021)] to achieve more comprehensive simulations. The improved NTL model allows a variable-sized (instead of a one grid cell) vacuum spacer between the powered and grounded electrodes and takes into account the (previously neglected) electron-neutral elastic collision frequency term in the plasma dielectric constant, and the radial variation of the plasma density. Using this model, we study the effects of the spatial and series resonances, associated with the (axially) z-antisymmetric and z-symmetric radially propagating surface wave modes, and the nonlinear harmonic excitations on the plasma uniformity. We conduct simulations in which we increase the driving frequency f from 30 to 120 MHz for an asymmetric capacitive argon discharge at a fixed pressure and electron power of pg=20 mTorr and Pe=40 W, respectively. The first antisymmetric mode resonance frequency fa1 occurs between 80 and 90 MHz, and the first symmetric mode resonance frequency fs1 occurs at about 100 MHz. The powered electrode sheath becomes smaller than the grounded electrode sheath for f≈fa1, and the source voltage reaches a minimum for f≈fs1. The radially varying electron power density shows a narrow center peak due to the finite mode wavelengths and the nonlinearly excited harmonics, which can be further enhanced by spatial or series resonances. A second peak appears above the vacuum spacer edge as f exceeds fs1 at 120 MHz because the shorter wavelengths at higher f allow secondary maxima of the surface waves to form within the reactor.

Simulation of nonlinear standing wave excitation in very-high-frequency asymmetric capacitive discharges: roles of radial plasma density profile and rf power

It is recognized that in large-area, very-high-frequency capacitively coupled plasma (VHF CCP) reactors, the higher harmonics generated by nonlinear sheath motion can lead to enhanced standing wave excitation. In this work, a self-consistent electromagnetic model, which couples a one-dimensional, radial nonlinear transmission line model with a bulk plasma fluid model, is employed to investigate the nonlinear standing wave excitation in a VHF driven, geometrically asymmetric capacitive argon discharge operated at low pressure. By considering a radially non-uniform plasma density profile (case I) calculated self-consistently by the nonlinear electromagnetic model and the corresponding radially-averaged, uniform plasma density profile (case II), we first examine the effect of the plasma density non-uniformity on the propagation of electromagnetic surface waves in a 3 Pa argon discharge driven at 100 MHz and 90 W. Compared to case II, the higher plasma density at the radial center in case I determines a higher plasma series resonance frequency, yielding stronger high-order harmonic excitations and more significant central peak in the harmonic current density J z,n and the harmonic electron power absorption p n profiles. Therefore, under the assumption of the radially uniform plasma density in a CCP discharge, the self-excitation of higher harmonics at the radial center should be underestimated. Second, using the self-consistent electromagnetic model, the effect of the rf power on the excitation of nonlinear standing waves is investigated in a 3 Pa argon discharge driven at 100 MHz. At a low power of 30 W, the discharge is dominated by the first two harmonics. The higher harmonic excitations and the nonlinear standing waves are observed to be enhanced with increasing the rf power, resulting in a more pronounced central peak in the radial profiles of the total electron power absorption density p e, the electron temperature T e, and the electron density n e. For all rf powers, the calculated radial profiles of n e show good agreement with the experimental data obtained by a floating double probe.

Invariant solutions and bifurcation analysis of the nonlinear transmission line model

In this paper, the nonlinear transmission line model with the power law nonlinearity and the constant capacitance and voltage relationship is studied using Lie symmetry analysis. Corresponding to the infinitesimals obtained, using commutation relations, abelian and non-abelian Lie subalgebras are obtained. Also, using the adjoint table, a one-dimensional optimal system of subalgebra is presented. Based on this optimal system, the corresponding Lie symmetry reductions are obtained. Moreover, variety of new similarity solutions in the form of trigonometric functions, hyperbolic functions, are obtained. Corresponding to one similarity reduction, by bifurcation analysis of dynamical system, the stable and unstable regions are determined, which show the existence of soliton solutions from the nonlinear dynamics point of view. Some of the obtained solutions represented graphically and observations are also discussed.

Regarding New Traveling Wave Solutions for the Mathematical Model Arising in Telecommunications

This research paper focuses on the application of the tanh function method to find the soliton solutions of the (2+1)-dimensional nonlinear electrical transmission line model. Materials used to form a transmitting line are very important to transmit electric charge. In this sense, we find some new voltage behaviors such as dark, trigonometric, and complex function solutions. Choosing some suitable values of parameters, we present some various surfaces of results obtained in this paper. These results play an important role in telecommunications lines used to stand for wave propagations.

A new survey to the nonlinear electrical transmission line model

In this paper, we find new travelling wave solutions to the nonlinear electrical transmission line model. Exponential function method is applied. This model is used to the voltage behaviors in electrical transmission lines. Under a suitable choice of control parameters, we plot the figures along with contour surfaces of new solutions by using computational programs such as Mathematica, Maple and Matlab. Some information about the behavior of voltage on the electrical lines is extracted. The hyperbolic, periodic or singular properties are reported.

Construction of new traveling and solitary wave solutions of a nonlinear PDE characterizing the nonlinear low-pass electrical transmission lines

In this study, we intend to analyze the traveling and several other solitary wave solutions in the nonlinear low-pass electrical transmission line model using the new mapping method, the new extended auxiliary equation method, and the extended Kudryashov method. A type of traveling and solitary wave solutions emerge, consisting of hyperbolic function, trigonometric, rational, periodic, and doubly periodic solutions that reflect kink, anti-kink wave solitons, bright-dark optical solitons, singular solitons, and other traveling waves. The three integration techniques applied are efficient, effective, and versatile for the creation of new bright, dark, singular, and non-singular periodic and solitary wave propagation solutions in nonlinear low-pass electrical transmission lines. To see the extant physical significance of the considered equation, we present some 2D and 3D figures for some solutions. We compare the obtained results with those obtained in the literature. We investigate and demonstrate the stability of the soliton solutions.

Nonlinear harmonic excitations in collisional, asymmetrically-driven capacitive discharges

The standing wave effect, which may lead to center-high density profiles in high frequency capacitive discharges, can be enhanced by nonlinearly excited harmonics. In this work, a nonlinear transmission line model, which solves for the electromagnetic fields in the time domain, is coupled to a two-dimensional bulk plasma fluid model to study nonlinear effects in asymmetric cylindrical capacitive argon discharges. An analytical collisional or collisionless (ion) sheath model is used to determine the stochastic and ohmic sheath heating and the nonlinear dependence of sheath voltage on sheath charge. We first examine a base case of a 20 mTorr argon discharge driven with an electron power P e = 40 W at a frequency f = 60 MHz, using collisionless and collisional sheath models. For the collisionless sheath model, the nonlinearly excited harmonics near the series and spatial resonance frequencies significantly enhance the on-axis power deposition and lead to a sharp peak of electron density at the discharge center. The collisional sheath model gives a smaller sheath width, leading to lower series and spatial resonance frequencies and a smaller source voltage for the fixed electron power. As a result, lower harmonics with broader spatial profiles and decreased magnitude are excited, reducing the center-high plasma nonuniformity. Then, we examine the discharge in a pressure range of 20–100 mTorr at fixed P e = 40 W and f = 60 MHz, using the collisional sheath model. As pressure increases, the harmonics gradually damp out, and the enhancement of on-axis power deposition becomes less significant. At the same time, more power is localized near the powered electrode edge due to decreased skin depth and smaller energy diffusion. As a result, the density peak shifts from the radial center to the powered electrode edge.

Traveling and localized solitary wave solutions of the nonlinear electrical transmission line model equation

Analytical solutions describing the kink–antikink type, hyperbolic, trigonometric, doubly periodic, localized bright and dark soliton like, breather and rational periodic train solutions to the discrete nonlinear electrical transmission line in $$(2+1)$$ -dimensions have been investigated with the Kudryashov method, the fractional linear transform method, and the simplest equation method with its modified and extended versions. Consequently, many new and more general explicit forms of traveling waves are retrieved under parametric conditions. The 3D, 2D, and density profile of some of the obtained results are numerically simulated by selecting suitable values of the various parameters of the NLTL model equation. Furthermore, all the obtained results were checked and verified by putting back into the considered nonlinear transmission line model equation with Maple and Mathematica software. The acquired results show the validity and reliability of the proposed schemes to the studied nonlinear electrical transmission line model.

A Nonlinear Transmission Line Model for Simulating Distributed SIS Frequency Multipliers

Superconductor/insulator/superconductor (SIS) jun-ctions have extremely nonlinear electrical properties, which makes them ideal for a variety of applications, including heterodyne mixing and frequency multiplication. With SIS mixers, the SIS junctions normally have circular cross sections, but they can also be fabricated in the form of microstrip transmission lines, known as distributed SIS junctions (DSJs). By using a DSJ as an open-circuit stub, it is possible to create a large SIS junction with a low effective input reactance. This is beneficial for SIS frequency multipliers because their output power is proportional to the area of the junction. It is challenging, however, to simulate the behavior of DSJs because they have to be modeled as transmission lines and the model has to take into account the quasiparticle tunneling current, which is a nonlinear function of the ac voltage. In this article, we present a new nonlinear transmission line model to accurately describe the behavior of DSJs and to simulate the performance of distributed SIS frequency multipliers (DSMs). This model is compared to experimental data from a recent DSM device and good agreement is found between the dc tunneling currents and the output powers at the second harmonic. Based on this success, an improved DSM design is proposed that has a higher output power and a higher conversion efficiency than previous designs.

Catastrophe theory in the phenomenological description of the avalanche effect in dc-biased microwave HTSC transmission lines

Within the framework of the proposed generalization of the phenomenological model of a microwave nonlinear HTSC transmission line, the effects of direct current on the transmission line are studied. Taking into account the next term in the expansion of the nonlinear dependence of the resistance on current allows us to explain the anomalous dependence of the insertion loss on the input power level observed in the experiment at subcritical temperatures. An additional direct current through the microwave waveguide can lead to the appearance of a bifurcation region in the space of control parameters. This is manifested in the possibility of an abrupt change in the properties of the waveguide at the boundaries of this region and the transition of the HTSC waveguide to a strongly dissipative state. The qualitative correspondence of the properties of the generalized phenomenological model to the data of experimental studies of the HTSC coplanar waveguide is obtained.

New Complex Solutions to the Nonlinear Electrical Transmission Line Model

AbstractIn this paper, with the help of an analytical approach, new complex singular and travelling dark solutionsto the nonlinear electrical transmission line are successfully constructed. 2D and 3Dfigures along with contour figures are plotted. Finally, at the end of manuscript, general conclusions about these novel findings, which differ from existing results, are given.

Variable Frequency Signal Carrying Nonlinear Transmission Line - Modeling using Machine Learning

in modeling of complex systems, manual creation and maintenance of the appropriate behavior is found to be the key problem. Behavior modeling using machine learning has found successful in modeling and simulation. This paper presents artificial neural network (ANN) modeling of transmission line carrying frequency varying signal using machine learning. This work uses proper orthogonal decomposition (POD) based reduced order modeling. In this proposed work, snapshot sets of complex mathematical model of nonlinear transmission line and also linear model are obtained at different time interval. These snapshot sets are arranged in matrix form separately for nonlinear and linear models. POD method is applied on both the matrices separately. This reduces the order of the matrix which is used as input and output data set for neural network training through machine learning technique. Trained neural network model has been verified using different untrained data set. The proposed algorithm determines the dimension of the interpolation space prompting a considerable decrease in the computational expense. The proposed algorithm doesn't force any imperatives on the topology of the appropriate circuit or kind of the nonlinear segments and hence relevant to general nonlinear systems.

Modulational instability and peak solitary wave in a discrete nonlinear electrical transmission line described by the modified extended nonlinear Schrödinger equation

The present work describes the propagation of plane and peak solitary waves in a modified extended nonlinear Schrodinger (MENLS) equation that was earlier shown to govern the dynamics of modulated waves in a discrete nonlinear electrical transmission line (DNLETL). Firstly, the analytic expression for the modulational instability gain is found and the influence of wavenumber and wave amplitude on the gain is derived. It is predicted that they can be used to control the occurrence of modulation instability phenomenon in the network. Afterwards, using the MENLS equation, we show that this model of nonlinear electrical transmission line admits peak solitary wave for physically realistic parameters of the system. Direct numerical simulations are performed on the exact equations of the lattice and the obtained results are in very good agreement with the analytical predictions.