Nonlinear Transmission Line Research Articles

The pulse narrowing nonlinear transmission lines model within the local fractional calculus on the Cantor sets

PurposeThe fractal and fractional calculus have obtained considerable attention in the electrical and electronic engineering since they can model many complex phenomena that the traditional integer-order calculus cannot. The purpose of this paper is to develop a new fractional pulse narrowing nonlinear transmission lines model within the local fractional calculus for the first time and derive a novel method, namely, the direct mapping method, to seek for the nondifferentiable (ND) exact solutions.Design/methodology/approachBy defining some special functions via the Mittag–Leffler function on the Cantor sets, a novel approach, namely, the direct mapping method is derived via constructing a group of the nonlinear local fractional ordinary differential equations. With the aid of the direct mapping method, four groups of the ND exact solutions are obtained in just one step. The dynamic behaviors of the ND exact solutions on the Cantor sets are also described through the 3D graphical illustration.FindingsIt is found that the proposed method is simple but effective and can construct four sets of the ND exact solutions in just one step. In addition, one of the ND exact solutions becomes the exact solution of the classic pulse narrowing nonlinear transmission lines model for the special case 9 = 1, which strongly proves the correctness and effectiveness of the method. The ideas in the paper can be used to study the other fractal partial differential equations (PDEs) within the local fractional derivative (LFD) arising in electrical and electronic engineering.Originality/valueThe fractional pulse narrowing nonlinear transmission lines model within the LFD is proposed for the first time in this paper. The proposed method in the work can be used to study the other fractal PDEs arising in electrical and electronic engineering. The findings in this work are expected to shed a light on the study of the fractal PDEs arising in electrical and electronic engineering.

W-Shaped Bright Soliton of the (2 + 1)-Dimension Nonlinear Electrical Transmission Line

In this paper, we investigate solitary wave solutions of the nonlinear electrical transmission line by using the Jacobi elliptic function and the auxiliary equation methods. We obtain Jacobi elliptic function solutions as well as kink, bright, dark, and W-shaped solitons as a result. For specific values of the Jacobi elliptic modulus, we depict bright, dark, and W-shaped soliton solutions as suitable parameters of the structure. Using the auxiliary equation method gives the combined bright–bright and dark–dark optical solitons in optical fibers. One result emerges from this analysis: the potential parameters and free parameters of the method can be employed to degenerate W-shaped bright and dark solitons. The acquired results are general and can be used for many applications in nonlinear dynamic systems.

Symplectic Integration Schemes for Systems With Nonlinear Dissipation

In previous work a variational integration scheme for mechanical systems containing linear dissipation was developed (Limebeer et al., 2020). The key idea is to use a transmission line as the solution to a power-balancing control problem—in the physics literature controllers of this type are known as “heat baths.” The power-balanced closed-loop system is thereby made amenable to analysis with Hamilton's principle. As a consequence, variational principles can be used to find symplectic integration schemes for dissipative systems. The outcome of this work is a coherent physical explanation as to why variational/symplectic integration algorithms for the open dissipative system can perform as well as their conservative counterparts. An important application of these integration algorithms is the solution of long-time-horizon optimal control problems. In this article, these ideas are extended to systems with smooth memoryless nonlinear dissipation. This extension employs a nonlinear lossless transmission line, which is again the solution to a power-balancing control problem. As in the case of linear dissipation, the resulting variational integration schemes are demonstrated to have excellent numerical properties, which are significantly less demanding computationally than their implicit nonvariational counterparts.

Spectral stability and dynamics of solitary waves in a coupled nonlinear left-handed transmission line

Spectral stability and dynamics of solitary waves in a coupled nonlinear left-handed transmission line

Propagating intrinsic localized mode in a cyclic, dissipative, self-dual one-dimensional nonlinear transmission line.

A well-known feature of a propagating localized excitation in a discrete lattice is the generation of a backwave in the extended normal mode spectrum. To quantify the parameter-dependent amplitude of such a backwave, the properties of a running intrinsic localized mode (ILM) in electric, cyclic, dissipative, nonlinear 1D transmission lines, containing balanced nonlinear capacitive and inductive terms, are studied via simulations. Both balanced and unbalanced damping and driving conditions are treated. The introduction of a unit cell duplex driver, with a voltage source driving the nonlinear capacitor and a synchronized current source, the nonlinear inductor, provides an opportunity to design a cyclic, dissipative self-dual nonlinear transmission line. When the self-dual conditions are satisfied, the dynamical voltage and current equationsof motion within a cell become the same, the strength of the fundamental, resonant coupling between the ILM and the lattice modes collapses, and the associated fundamental backwave is no longer observed.

Soliton wave parameter estimation with the help of artificial neural network by using the experimental data carried out on the nonlinear transmission line

In this study, an artificial neural network (ANN) model is generated, which is used to estimate the output parameters of soliton waves produced as a result of nonlinear transmission lines (NLTLs). Three different output parameters are acquired as a consequence of the experiments carried out utilizing the five various input parameters that are set in the ANN-based study. Input parameters for NLTL designs with 116 different experiments; inductor (L), input voltage (Vi) value, number of nodes (n), capacitance (C(V)) and load resistance (RLoad) values. Output parameters values, which are maximum voltage (Vmax), center frequency (fcenter), and voltage modulation depth (VMD). Input and output data; 70 % is set aside for training, 15 % for validation and the remaining 15 % for testing. Training, validation, and testing steps are repeated for the output parameters, in which case more than 99 % correlation is found as a result of each operation. An absolute percentage error value is found for each output parameter. Moreover, Mean absolute percentage error (MAPE) is calculated for these output datasets. The data set is tested for the experimental studies carried out in the literature, and it is observed that there is a compliance of over 99 % for this situation.

Systems and technologies based on nonlinear transmission lines with ferrite (Review)

Nonlinear transmission lines with ferrite have been actively developed and studied for about two decades. At the same time, the first works on this topic date back to the middle of the last century. Nonlinear transmission lines with ferrite find their application in various problems of electrophysics, with the greatest application being found in the problems of pulse sharpening, as delay lines and generators of high-power pulses of microwave radiation. The main scientific and technical results of the development of technologies of nonlinear transmission lines with ferrite are presented in chronological order, starting from lines for sharpening the fronts of voltage pulses, ending with multichannel microwave sources based on them. Keywords: high power microwaves, ferromagnetic materials, pulsed power, electromagnetic shock waves.

Системы и технологии на основе нелинейных передающих линий с ферритом (обзор)

Nonlinear transmission lines with ferrite have been actively developed and studied for about two decades. At the same time, the first works on this topic date back to the middle of the last century. Nonlinear transmission lines with ferrite find their application in various problems of electrophysics, with the greatest application being found in the problems of pulse sharpening, as delay lines and generators of high-power pulses of microwave radiation. The main scientific and technical results of the development of technologies of nonlinear transmission lines with ferrite are presented in chronological order, starting from lines for sharpening the fronts of voltage pulses, ending with multichannel microwave sources based on them.

Theory and practice of pulse compression in hybrid and gyromagnetic non-linear transmission lines

This paper presents a comprehensive analysis of pulse compression capability in hybrid and gyromagnetic non-linear transmission lines (NLTLs). The corresponding theoretical analysis in the hybrid NLTLs is derived and discussed in detail with the generation and sharpening aspects of leading and trailing pulse edges. The parameters responsible for pulse sharpening are examined and their corresponding pulse compression capability is modelled by providing the output waveform while varying these parameters. A holistic overview and mathematical development of gyromagnetic NLTLs are also conducted, which are modeled and validated through an equivalent lumped element model. Important parameters such as saturation magnetization, gyromagnetic NLTL sections, and damping parameter are elaborated and their influences on pulse sharpening and compression capability are studied. Validation of the theoretical and parametric analysis is performed by an experimental demonstration. The results achieved from hybrid and gyromagnetic NLTLs are briefly summarized, and their corresponding advantages and disadvantages are highlighted. This research is set to provide a fresh and successful debut for investigating gyromagnetic and hybrid NLTLs and their inherent effects on pulse compression for future ultrafast electronic systems and interconnects.

Ku-band multichannel frequency comb Doppler reflectometer on the GAMMA 10/potential control and divertor simulating experiment (PDX) tandem mirror.

A Ku-band (12-18GHz) multichannel Doppler reflectometer (DR) has been developed in the GAMMA 10/potential control and divertor simulating experiment (PDX) tandem mirror device to improve the applicability of DR measurement for simultaneous monitoring of velocity of electron density turbulence at different locations. Our previous single-channel DR circuit has been replaced by the multichannel microwave system using a nonlinear transmission line based comb generator with heterodyne technique. The multichannel DR system has been installed in the central cell of GAMMA 10/PDX. Initial results of application to GAMMA 10/PDX plasma are presented, showing Doppler frequency shifts during an additional ion cyclotron resonance frequency heating and gas-puffing experiment.

Nonlinear Transmission Line Performance as a Combined Pulse Forming Line and High-Power Microwave Source as a Function of Line Impedance

Nonlinear transmission lines (NLTLs) offer compact, low-cost, all solid-state high-power microwave (HPM) generation. This article experimentally investigates the RF output power for composite-based 10, 25, and 50 Ω NLTLs used as a combined pulse forming line and HPM source. We manufactured coaxial NLTLs containing 10% barium strontium titanate and 15% nickel zinc ferrite encased in polydimethylsiloxane. The output voltage and power in the time and frequency domains, respectively, showed that the 10 Ω NLTL generated the greatest RF output. The 25 Ω NLTL generated greater output power from 500–1100 MHz than the 50 Ω NLTL. This occurs because reducing the NLTL impedance induces a larger transient current for a given charging voltage. This transient current corresponds to a stronger transient magnetic field, which facilitates magnetic moment alignment to allow for coherent magnetic moment rotation to occur. This setup eliminates the separate pulse forming network and magnetic field bias that typically occurs in other NLTL systems, which provides additional flexibility in tuning the NLTL impedance and reducing device footprint.

Interpolatory proper order decomposition of nonlinear transmission line circuits

PurposeThe paper is concerned with interpolatory proper orthogonal decomposition (IPOD) methods for nonlinear transmission line circuits. This paper aims to examine several factors that must be considered when applying such model reduction techniques to this kind of circuit.Design/methodology/approachTwo types of POD will be implemented. In each case, the choice of the order of the reduced model and the order of the interpolation space shall be considered. The stability of the models shall be explored.FindingsThe results indicate that the order for the reduced model to obtain accurate results depends on the chosen method when considering nonlinear transmission lines. The results also indicate that the structure of the nonlinear transmission line is crucial for determining the stability of the reduced models.Originality/valueThe work compares two IPOD methods and discusses the issues involved in achieving an accurate and stable reduced-order model for a nonlinear transmission line.

(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.

Brain Microtubule Electrical Oscillations-Empirical Mode Decomposition Analysis.

Microtubules (MTs) are essential cytoskeletal polymers of eukaryote cells implicated in various cell functions, including cell division, cargo transfer, and cell signaling. MTs also are highly charged polymers that generate electrical oscillations that may underlie their ability to act as nonlinear transmission lines. However, the oscillatory composition and time-frequency differences of the MT electrical oscillations have not been identified. Here, we applied the Empirical Mode Decomposition (EMD) to bovine brain MT sheet recordings to determine the number and fundamental frequencies of the Intrinsic Modes Functions (IMF) and evaluate their energetic contribution to the electrical signal. As previously reported, raw signals were obtained from cow brain MTs (Cantero et al. Sci Rep 6:27143, 2016), sampled, filtered, and subjected to signal decomposition from representative experiments. Filtered signals (200Hz) allowed us to identify either six or seven IMFs. The reconstructed tracings faithfully resembled the original signals, with identifiable frequency peaks. To extend the analysis to obtain time-frequency information and the energy implicated in each IMF, we applied the Hilbert-Huang Transform (HHT) and the Continuous Wavelet Transform (CWT) to the same samples. The analyses disclosed the presence of more fundamental frequency peaks than initially reported and evidenced the advantages and disadvantages of each transform. The study indicates that the EMD is a robust approach to quantifying signal decomposition of brain MT oscillations and suggests novel similarities with human brain wave electroencephalogram (EEG) recordings. The evidence points to the potentially fundamental role of MT oscillations in brain electrical activity.

Tunability Behavior of (Ba, Ca)(Zr, Ti)O Ceramic Capacitors Powered by Thermally Induced Phase Transitions With Applications to Nonlinear Transmission Lines

Ferroelectric ceramics with low loss dielectric, high permittivity, and nonlinear behavior are essential in capacitive nonlinear transmission lines (NLTLs) for radio frequency (RF) generation. NLTLs have the potential to generate soliton waves for high-power microwave (HPM) applications in mobile defense platforms and satellite communications. In this work, we synthesize, characterize, and investigate the nonlinear behavior of (Ba,Ca)(Zr,Ti)O3 ceramics system to be applied as nonlinear elements in capacitive NLTLs. The ceramics were structurally and microstructural characterized. Anomalies in dielectric and pyroelectric curves access the temperatures of phase transitions. The permittivity tunability was studied as a function of electric field and frequency in temperatures near phase transitions. The phase transitions of materials are identified by temperature where the permittivity and percentage of nonlinear tunability factor (NTF) are higher, which are required to produce RF on NLTLs.

A wideband high-power microwave radiation source based on gyromagnetic nonlinear transmission line and Vlasov antenna.

The gyromagnetic nonlinear transmission line (GNLTL) is a special kind of coaxial transmission line partially loaded with the ferrite material. A GNLTL system can modulate the input high-power pulses into wideband high-power microwaves without relying on the electron beam and confining magnetic field. The unique working mechanism gives the GNLTL system the potential to be a small portable wideband high-power microwave radiation source. In this study, a wideband high-power microwave radiation source based on a GNLTL system is designed and constructed. In order to effectively radiate the wideband microwaves into the air, a high-power wideband Vlasov antenna and a special absorption high-pass filter are developed. The designs of key subsystems and high-power radiation experiments have been introduced and discussed in detail. In the test experiments, a radiated pulse with a peak electric field strength of 23 kV/m was measured at 20m away from the transmitting antenna and the effective potential of radiation is 460 kV/m. The pulse width of the radiation pulse is about 4ns, the center frequency is about 2.25GHz, and the highest repetition rate can reach 25Hz.

Diverse Soliton Structures of the ( 2 + 1 )-Dimensional Nonlinear Electrical Transmission Line Equation

In this work, the ( 2 + 1 )-dimensional nonlinear electrical transmission line equation (NETLE) is investigated by applying three recent technologies, namely, the variational approach, Hamiltonian approach, and energy balance approach. Diverse exact soliton solutions such as the bright, bright-like, kinky bright, bright-dark soliton, and periodic soliton solutions are successfully constructed. The outlines of the different solutions are shown in the form of the 3-D plot with the help of the Wolfram Mathematica. It reveals that the used methods are concise and effective and are expected to provide some inspiration for the study of travelling wave solutions of the PDEs in physics.

High-Voltage Microwave Systems Based on Ferrite Gyromagnetic Nonlinear Transmission Lines

Test results of high-voltage stationary four-channel generators based on the coaxial gyromagnetic ferrite-filled nonlinear transmission lines (NLTLs) with external magnetic bias and modulation frequency of the rapidly damping oscillations of ~ 8.7 GHz are presented. The peak amplitude of the output oscillations of −350 kV in the channel had a maximum modulation depth more than 80%. The single-channel stationary microwave system increased the peak amplitude to record value −695 kV in the frequency range ~ 10 (11.5) GHz. The compact two-channel gyromagnetic ferrite line system was also tested. The peak amplitude of output oscillations reached −170 kV when the modulation frequency is of ~ 6.5 GHz. Electrical strength of oil-isolated ferrite line was tested in the compact one-channel system at a repetition rate of 25 pps when an electrical field in the line reached ~ 185 kV/mm.

100-MW-Level Experiments of a Gyromagnetic Nonlinear Transmission Line System

The wideband high-power microwave systems have the advantages of wide energy spectrum, electron beam independence, compactness, and low cost. The gyromagnetic nonlinear transmission line (GNLTL) has drawn much attention for its potential as a novel solid-state, frequency-agile, and compact wideband source. The working mechanism of GNLTL is different from that of the traditional electric vacuum tubes, and the strong dispersion and nonlinear characteristics make it difficult to be accurately theoretically calculated and simulated. In this article, a 100-MW-level GNLTL system based on a Tesla-type driver was designed and constructed. A series of test experiments were then carried out to investigate the effects of different configurations, including delay line length, ferrite cores’ assembly orientation, transmission line length, bias magnetic field magnitude, and excitation voltage. The changing laws of the key parameters of the output microwaves including the peak power, modulation depth, center frequency, and percentage band are summarized and the underlying physical mechanisms are analyzed. The results may be instructive for the predesign of GNLTLs, especially for the devices operating at high power. In addition, a multiple center frequency points’ phenomenon was discovered in the output signal, which may bring new application possibilities for GNLTL.

Design and Performance of a Ferrite Transmission Line Sharpener for Trigger Generator Used in FLTD

Tens of thousands of gas switches in fast linear transformer driver (FLTD) need to be switched ON synchronously, which requires gas switch triggers with fast rise time and low jitter. At present, the pulse rise time of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 100$ </tex-math></inline-formula> -kV gas switch trigger is often sharpened by a gas switch. Although the gas switch sharpener can reduce pulse rise time, it is difficult to control the pulse jitter because of the dispersion of gas discharge. Using a ferrite nonlinear transmission line to steepen pulse rise time has been widely used in high-power microwave fields. In this article, a ferrite transmission line is proposed to replace the gas switch sharpener. By establishing the simulation model of the ferrite transmission line, the effects of pulse amplitude, transmission line length, and structural parameters on the sharpening rise time are analyzed. An experimental platform was established to test the sharpening performance of two different structural ferrite transmission lines. The test results show that the ferrite transmission lines can reduce the trigger pulse rise time from 124 ns to less than 16 ns, and the jitter of the whole trigger device is less than 2.5 ns, which can be used to replace the gas switch sharpener.