Nonlinear Transmission Line Model Research Articles

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.

Two-dimensional particle-in-cell simulations of standing waves and wave-induced hysteresis in asymmetric capacitive discharges

Asymmetrically excited, high frequency cylindrical capacitive discharges are widely used for materials etching and thin film deposition. Two-dimensional (2D) electrostatic particle-in-cell (PIC) simulations show the existence of standing waves and wave-induced hysteresis of the plasma density, i.e. two different steady states for the same driving rf voltage amplitude, when the voltage is increased from a low value or decreased from a high value. The phenomenon is explored over a range of pressures (10–30 mTorr) and frequencies (60–80 MHz). Examined at 73 MHz, with increasing gas pressure, the hysteresis loop gradually shrinks and vanishes. To understand the hysteresis induced by z-symmetric and z-antisymmetric radial wave propagation modes, the PIC results are compared with a nonlinear transmission line model assuming uniform bulk plasma density, to determine the symmetric and antisymmetric voltage amplitudes. The model results are in good agreement with the PIC observations, showing central-low and central-high profiles of the antisymmetric mode voltage at low density and high density, respectively. The results are then used to determine the parameters of a lumped circuit model of the two modes, from which the hysteresis is induced by the density dependence of the symmetric and anti-symmetric wave mode absorbed electron powers. For the low density state, the discharge is sustained mainly by the symmetric mode excitation. At high density, the discharge is sustained by both symmetric and anti-symmetric modes, with the latter partly showing a spatial resonance. The results are also shown to be frequency dependent, with an onset of the hysteresis at about 66 MHz.

On solitons: the biomolecular nonlinear transmission line models with constant and time variable coefficients

The article studies the dynamics of solitons in electrical microtubule model, which describes the propagation of waves in nonlinear dynamical system. Microtubules are not only a passive support of a cell but also they have highly dynamic structures involved in cell motility, intracellular transport and signaling. The underlying model has been considered with constant and variable coefficients of time function. The solitary wave ansatz has been applied successfully to extract these solitons. The corresponding integrability criteria, also known as constraint conditions, naturally emerge from the analysis of these models.

A Nonlinear Transmission Line Model of the Cochlea With Temporal Integration Accounts for Duration Effects in Threshold Fine Structure

A Nonlinear Transmission Line Model of the Cochlea With Temporal Integration Accounts for Duration Effects in Threshold Fine Structure

Nonlinear Two-Dimensional Transmission Line Models for Electrochemically Driven Conducting Polymer Actuators

The electronic and ionic conductivities of conducting polymers can change as a function of oxidation state, and yet, these properties are not generally considered in modeling the electrochemistry and electrochemically driven actuation of these materials. These effects can be significant particularly over large ranges of oxidation state and in long films where electrical contact is made from one end. In this study, a transmission line model is implemented, in which conductivities vary as a function of local oxidation state, with this variation being based on measured values. Our time-domain model is based on a 2-D RC transmission line model implemented using a state-space representation. Voltage drop along the length of the film away from the attachment point and the variation in electronic conductivity with state of charge along this length necessitated the use of a 2-D nonlinear model to obtain effective predictions of response for the film dimension used. The general approach demonstrated may be applied to any situation where properties vary with position and oxidation state, such as in batteries and supercapacitors. The last step showed the successful application of the model to predict actuation of a polypyrrole linear actuator.

Exact and soliton solutions to nonlinear transmission line model

A nonlinear transmission line (NLTL) is comprised of a transmission line periodically loaded with varactors, where the capacitance nonlinearity arises from the variable depletion layer width, which depends both on the DC and AC voltages of the propagating wave. An equivalent circuit model of NLTL is discussed analytically, in this article, and different type of solutions are celebrated. The improved extended tanh-function method has been applied successfully to extract the solutions. The obtained solutions are solitary wave solutions, singular periodic solutions, singular soliton solutions, Jacobi elliptic doubly periodic type solutions and Weierstrass elliptic doubly periodic type solutions. It is a very convenient tool to study the propagation of electrical solitons which propagate in the form of voltage waves in nonlinear dispersive media.

Nonlinear Multiconductor Transmission Line Analysis of Broadband Switching Metamaterials

In this paper, we present a nonlinear multiconductor transmission line model to analyze the time-domain and nonlinear responses of broadband switching metamaterials. This analysis employs coupled transmission lines loaded with nonlinear elements to model the response of the metamaterial structures to a vertically polarized free-space excitation. Using this analysis we first examine the time-domain response of a broadband switching metamaterial structure loaded with high-speed Schottky diodes. We then show that this structure’s response to incident power can be effectively inverted by replacing these Schottky diodes with varactor diodes. Experimental results are presented for both structures in WR-284 waveguide, which show good agreement with results generated from full-wave and transmission line analysis. We also use the circuit model to simulate power-dependent material parameters and both the input and output third-order intercept point for both the Schottky-loaded and varactor-loaded metamaterials.

Physiological motivated transmission-lines as front end for loudness models.

The perception of loudness is strongly influenced by peripheral auditory processing, which calls for a physiologically correct peripheral auditory processing stage when constructing advanced loudness models. Most loudness models, however, rather follow a functional approach: a parallel auditory filter bank combined with a compression stage, followed by spectral and temporal integration. Such classical loudness models do not allow to directly link physiological measurements like otoacoustic emissions to properties of their auditory filterbank. However, this can be achieved with physiologically motivated transmission-line models (TLMs) of the cochlea. Here two active and nonlinear TLMs were tested as the peripheral front end of a loudness model. The TLMs are followed by a simple generic back end which performs integration of basilar-membrane "excitation" across place and time to yield a loudness estimate. The proposed model approach reaches similar performance as other state-of-the-art loudness models regarding the prediction of loudness in sones, equal-loudness contours (including spectral fine structure), and loudness as a function of bandwidth. The suggested model provides a powerful tool to directly connect objective measures of basilar membrane compression, such as distortion product otoacoustic emissions, and loudness in future studies.

2D fluid-analytical simulation of electromagnetic effects in low pressure, high frequency electronegative capacitive discharges

A fast 2D axisymmetric fluid-analytical multifrequency capacitively coupled plasma (CCP) reactor code is used to study center high nonuniformity in a low pressure electronegative chlorine discharge. In the code, a time-independent Helmholtz wave equation is used to solve for the capacitive fields in the linearized frequency domain. This eliminates the time dependence from the electromagnetic (EM) solve, greatly speeding up the simulations at the cost of neglecting higher harmonics. However, since the code allows up to three driving frequencies, we can add the two most important harmonics to the CCP simulations as the second and third input frequencies. The amplitude and phase of these harmonics are estimated by using a recently developed 1D radial nonlinear transmission line (TL) model of a highly asymmetric cylindrical discharge (Lieberman et al 2015 Plasma Sources Sci. Technol. 24 055011). We find that at higher applied frequencies, the higher harmonics contribute significantly to the center high nonuniformity due to their shorter plasma wavelengths.

Boolean gates on actin filaments

Actin is a globular protein which forms long polar filaments in the eukaryotic cytoskeleton. Actin networks play a key role in cell mechanics and cell motility. They have also been implicated in information transmission and processing, memory and learning in neuronal cells. The actin filaments have been shown to support propagation of voltage pulses. Here we apply a coupled nonlinear transmission line model of actin filaments to study interactions between voltage pulses. To represent digital information we assign a logical Truth value to the presence of a voltage pulse in a given location of the actin filament, and False to the pulse's absence, so that information flows along the filament with pulse transmission. When two pulses, representing Boolean values of input variables, interact, then they can facilitate or inhibit further propagation of each other. We explore this phenomenon to construct Boolean logical gates and a one-bit half-adder with interacting voltage pulses. We discuss implications of these findings on cellular process and technological applications.

Lightning strikes to tall objects: A study of wave interactions at the return‐stroke front using a nonlinear transmission line model

AbstractA theoretical study is presented to investigate lightning strikes to towers, with focus on wave interactions occurring at the return‐stroke front due to the arrival of current pulses that propagate upward on the channel after being transmitted from the tower. The lightning channel is represented as a transmission line including corona and nonlinear losses. Analyses for the hypothetical case of a lossless channel considering matched tower and channel impedances show that the arrival of current pulses at the upward moving return‐stroke front leads to an increase in corona currents leaving the channel. This transient process generates current pulses whose arrival at the tower top can be interpreted as the effect of a current reflection at the upward moving front, even though no impedance discontinuity exists at that point if return‐stroke and leader channel properties are assumed the same. In the more realistic case of a lossy channel considering unmatched channel and tower impedances, the nonlinear channel resistance modifies the current pulses that propagate along the channel so that they merge smoothly with the return‐stroke front. In this case, the interaction of the current pulses transmitted from the tower to the channel with the upward moving return‐stroke front does not lead to features that can be clearly interpreted as the result of current reflections at that point in the evaluated conditions. Finally, it is argued that the current reflection coefficient at the tower top should be viewed as a current dependent parameter as opposed to a constant, linear value.

Enhanced charging kinetics of porous electrodes: surface conduction as a short-circuit mechanism.

We use direct numerical simulations of the Poisson-Nernst-Planck equations to study the charging kinetics of porous electrodes and to evaluate the predictive capabilities of effective circuit models, both linear and nonlinear. The classic transmission line theory of de Levie holds for general electrode morphologies, but only at low applied potentials. Charging dynamics are slowed appreciably at high potentials, yet not as significantly as predicted by the nonlinear transmission line model of Biesheuvel and Bazant. We identify surface conduction as a mechanism which can effectively "short circuit" the high-resistance electrolyte in the bulk of the pores, thus accelerating the charging dynamics and boosting power densities. Notably, the boost in power density holds only for electrode morphologies with continuous conducting surfaces in the charging direction.

A study on the influence of corona on currents and electromagnetic fields predicted by a nonlinear lightning return‐stroke model

AbstractThis paper investigates the influence of corona on currents and electromagnetic fields predicted by a return‐stroke model that represents the lightning channel as a nonuniform transmission line with time‐varying (nonlinear) resistance. The corona model used in this paper allows the calculation of corona currents as a function of the radial electric field in the vicinity of the channel. A parametric study is presented to investigate the influence of corona parameters, such as the breakdown electric field and the critical electric field for the stable propagation of streamers, on predicted currents and electromagnetic fields. The results show that, regardless of the assumed corona parameters, the incorporation of corona into the nonuniform and nonlinear transmission line model under investigation modifies the model predictions so that they consistently reproduce most of the typical features of experimentally observed lightning electromagnetic fields and return‐stroke speed profiles. In particular, it is shown that the proposed model leads to close vertical electric fields presenting waveforms, amplitudes, and decay with distance in good agreement with dart leader electric field changes measured in triggered lightning experiments. A comparison with popular engineering return‐stroke models further confirms the model's ability to predict consistent electric field waveforms in the close vicinity of the channel. Some differences observed in the field amplitudes calculated with the different models can be related to the fact that current distortion, while present in the proposed model, is ultimately neglected in the considered engineering return‐stroke models.

Modeling cochlear dynamics: Interrelation between cochlea mechanics and psychoacoustics

A model of the cochlea was used to bridge the gap between model approaches commonly used to investigate phenomena related to otoacoustic emissions and more filter-based model approaches often used in psychoacoustics. In the present study, a nonlinear and active one-dimensional transmission line model was developed that accounts for several aspects of physiological data with a single fixed parameter set. The model shows plausible excitation patterns and an input-output function similar to the linear-compressive-linear function as hypothesized in psychoacoustics. The model shows realistic results in a two-tone suppression paradigm and a plausible growth function of the 2f(1)-f(2) component of distortion product otoacoustic emissions. Finestructure was found in simulated stimulus-frequency otoacoustic emissions (SFOAE) with realistic levels and rapid phase rotation. A plausible "threshold in quiet" including finestructure and spontaneous otoacoustic emissions (SOAE) could be simulated. It is further shown that psychoacoustical data of modulation detection near threshold can be explained by the mechanical dynamics of the modeled healthy cochlea. It is discussed that such a model can be used to investigate the representation of acoustic signals in healthy and impaired cochleae at this early stage of the auditory pathway for both, physiological as well as psychoacoustical paradigms.

Suppression of the standing wave effect in high frequency capacitive discharges using a shaped electrode and a dielectric lens: Self-consistent approach

The standing wave effect causes nonuniform plasma excitation in high frequencies capacitive discharges when the electrode size is not considerably smaller than the excitation wavelength. A shaped electrode was proposed by Sansonnens and Schmitt [Appl. Phys. Lett. 82, 182 (2003)] to suppress this unwanted effect. The shape of the electrode was calculated in the vacuum approximation (no plasma was present between the electrodes), and was found to be Gaussian. The authors postulated that the presence of plasma would not significantly modify the solution. However, it was shown [Chabert et al., Phys. Plasmas 11, 1775 (2004)] using a self-consistent nonlinear transmission line model that the presence of plasma significantly shortens the wavelength for a system composed of two parallel plate electrodes. It was therefore legitimate to expect the optimized shape of the electrode and lens to be different when a plasma is present. Here it is shown that to suppress the standing wave effect the current flowing in the electrodes must be proportional to the discharge radius. This condition is independent of the medium present between the plates and indeed requires a Gaussian electrode.

Self-consistent nonlinear transmission line model of standing wave effects in a capacitive discharge

It has been shown previously [Lieberman et al., Plasma Sources Sci. Technol. 11, 283 (2002)], using a non-self-consistent model based on solutions of Maxwell’s equations, that several electromagnetic effects may compromise capacitive discharge uniformity. Among these, the standing wave effect dominates at low and moderate electron densities when the driving frequency is significantly greater than the usual 13.56 MHz. In the present work, two different global discharge models have been coupled to a transmission line model and used to obtain the self-consistent characteristics of the standing wave effect. An analytical solution for the wavelength λ was derived for the lossless case and compared to the numerical results. For typical plasma etching conditions (pressure 10–100 mTorr), a good approximation of the wavelength is λ/λ0≈40 V01/10l−1/2f−2/5, where λ0 is the wavelength in vacuum, V0 is the rf voltage magnitude in volts at the discharge center, l is the electrode spacing in meters, and f the driving frequency in hertz.

Application of the two-dimensional Fourier transform to nonlinear wave propagation phenomena

A new technique based on the two-dimensional Fourier transform is presented and applied to the study of nonlinear wave propagation phenomena in one-dimensional, finite, nonlinear transmission lines. The technique permits determining the effects of nonlinearities and boundary conditions on the Fourier transform and identifying incident and reflected waves and solitons which may propagate through the transmission line at constant speed. The effects of windows on the Fourier transform are also assessed in both linear and nonlinear transmission line models. >

Prediction of inner ear properties by the dynamics of the cochlear amplifiers

The role of the outer hair cells as cochlear amplifiers has been recently shown experimentally and theoretically. The nonlinear transmission line model was chosen as a framework to test the role of the cochlear amplifiers to different cochlear properties. It was found that there are phenomena such as rate suppression, or threshold microstructure in the vicinity of spontaneous otoacoustic emission, that can be predicted by such a model only if it is assumed that the local cochlear amplification is dynamically changing as a function of the stimulus. The dynamics of the cochlear amplifiers was achieved in the model by assuming that each outer hair cell amplification gain depends on the electrical potential across its membrane. It is most probable that the cochlear microphonics, which represent the potential changes in the scala media, are indication to the electromechanical feedback loop. The electrical potential in the model is derived by assuming that it produces an external mechanical force that is applied to the outer hair cells that in return act as a damped-spring mass. The model was simulated in the time domain, and its prediction to various cochlear phenomena will be discussed.

Measurement of magnetostriction in self-biased shielded magnetoresistive heads

We report a method of measuring the magnetostriction of self-biased shielded magnetoresistive (MR) elements. In this technique the optimum bias current for the MR element, defined as the point where the head delivers the maximum output per unit current, is determined by measuring the head output from a flux source while varying the bias current fed to the element. A mechanical fixture is then used to bend the head and strain the MR film. Because of magnetoelastic effects, the change in stress alters the MR element anisotropy and causes a shift of the optimum bias point. The optimum bias point is measured as a function of the stress applied to the MR element and the dependence modeled using a nonlinear transmission-line model for a shielded MR head with shunt and/or offset bias. Parameters for the model are set by fitting the full output voltage versus bias current curve. The changes in the value of the MR element anisotropy required to fit the experimental data are attributed to changes in the magnetoelastic anisotropy and the magnetostriction calculated. This measurement technique does require the removal of one of the shields in order to guarantee a uniform and reproducible strain of the MR film when the head is bent. >

Numerical property and efficient solution of a transmission-line model for basilar membrane wave motions

In this paper we study numerical properties of a finite difference scheme for the solution of a one-dimensional nonlinear transmission line model for basilar membrane wave motions. In particular, we apply the Von Neumann method to obtain a sufficient condition under which the finite difference solution to the model is guaranteed to be stable. The significance of this condition is that it determines the optimal time and spatial mesh which would invoke a minimal amount of computation for obtaining stable and accurate model outputs.