Transmission Line Of Finite Length Research Articles

Two-port quantum model of finite-length transmission lines coupled to lumped circuits

Two-port quantum model of finite-length transmission lines coupled to lumped circuits

Freestanding niobium pentoxide-decorated multiwalled carbon nanotube electrode: Charge storage mechanism in sodium-ion pseudocapacitor and battery

This study investigated flexible, freestanding niobium pentoxide (Nb2O5) decorated multiwalled carbon nanotube (MWCNT) electrode material in a sodium-ion pseudocapacitor and its respective energy storage mechanism. Sodium is an abundant element in the Earth's crust, with attractive sustainability and low-cost appeal for the scientific community and energy markets such as electric vehicles and renewable energies. Combined with niobium pentoxide and carbon nanotubes, sodium ions can perform ultra-fast intercalation into niobium pentoxide and electrostatic adsorption onto carbon high surface areas. Niobium pentoxide particles were investigated using X-ray diffraction via Rietveld refinement, a powerful technique to study crystalline materials' electronic and structural properties that directly influence Na+-ion diffusion. The niobium pentoxide-decorated MWCNT electrode material was investigated within a symmetric supercapacitor (SIC) and as an anode for sodium-ion batteries (SIBs). A finite-length transmission line was used to model the impedance behavior of the solid and liquid phases that comprised the material/solution interface. This numerical modelling allowed investigators to infer the presence of MWCNT as a nanostructured matrix since Nb2O5 dispersive nanoparticles increased the overall pseudopacacitance by 63.2% for Nb2O5/MWCNT compared to MWCNT nanostructured electrodes. Electrochemical findings revealed a maximum capacitance of 192 F g−1 for the SIC full cell, with capacitance retention of 96% after 10,000 cycles. In addition, the SIC delivered outstanding power density from 98.7 to 24,671 W kg−1 and high energy density from 5.4 to 2.7 W h kg−1. In an SIB half-cell configuration, the electrode delivered a reversible sodium-ion storage capacity of ~163 mA h g−1, with a retention capacity of ~68 mA h g−1 after 100 cycles at 25 mA g−1. These systems bridge the gap between supercapacitors and batteries by employing the best properties of them both.

Development of a Mobile Application for Teaching Transmission Line Theory

<p>The teaching of transmission line theory in electrical engineering courses must be tailored to an audience which is increasingly reluctant to adhere to abstract disciplines. In our opinion, the best solution to make transmission line courses more attractive is to offer practical applications and intensively use of mathematical computer-aided teaching tools to overcome, at the beginning, the difficulties linked to the theory. Indeed, transmission line theory comes alive when the travelling waves are animated on a screen (smartphone, tablets, laptop, etc.). Fundamental concepts such as “progressive wave”, “reflected wave” and “load matching” could be easily demonstrated in the classroom or at home. Transmission line simulations are applied to problems using connections to shunt, open, matched and unmatched loads, and show how the signal waveforms arise from one end to another. The proposed Android-based animations are used with a sinusoidal generator to illustrate the evolution to the sinusoidal steady state and allow learners to easily handle the corresponding Smith chart. Students are encouraged to run those applications at home as a computational laboratory to verify their solutions to homework problems. <br />This article introduces simple Android-based virtual tools for the investigation and visualization in real time of waves traveling along a terminated finite-length transmission line, without and with faults between the source and the load. The package can be used as an educational tool in various lectures or homework to aid teaching high frequency electronics and transmission lines theory.</p>

High-Frequency Electromagnetic Coupling to Multiconductor Transmission Lines of Finite Length

This paper presents a theory and an efficient solution approach for the problem of electromagnetic field coupling to a long multiconductor line with arbitrary terminations. The theory is applicable for a high-frequency plane wave electromagnetic field excitation, when the transmission line approximation conditions are no longer satisfied.

Analysis of the transient response of a dual-fed RC transmission line.

The transient analysis of a uniform transmission line of finite length is considered in this paper. For the first time this paper provides an analytical expression for the time-domain response of an RC transmission line, which is stimulated by a step function that is fed into both ends of the transmission line. In particular, we find an analytical expression for the step response at the center of the transmission line, in order to determine the worst-case rise time. This is of interest, for example, in large charge-coupled device (CCD) arrays, where long polysilicon lines are dual-fed in order to mitigate degradation in rise time. The analytical expressions for the RC transmission line are supported by computer-simulated lumped RC models.

Inverse Scattering for Soft Fault Diagnosis in Electric Transmission Lines

Today's advanced reflectometry methods provide an efficient solution for the diagnosis of electric transmission line hard faults (open and short circuits), but they are much less efficient for soft faults, in particular, for faults resulting in spatially smooth variations of characteristic impedance. This paper attempts to fill an important gap for the application of the inverse scattering transform to reflectometry-based soft fault diagnosis: it clarifies the relationship between the reflection coefficient measured with reflectometry instruments and the mathematical object of the same name defined in the inverse scattering theory, by reconciling finite length transmission lines with the inverse scattering transform defined on the infinite interval. The feasibility of this approach is then demonstrated by numerical simulation of lossless transmission lines affected by soft faults, and by the solution of the inverse scattering problem effectively retrieving smoothly varying characteristic impedance profiles from reflection coefficients.

Travelling Modes in Wave-Heated Plasma Sources

This paper describes a theoretical and experimental study of surface- and helicon-wave-heated plasma sources in which standing waves are set up in the cavity between the closed end plate to a plasma vessel and a wave launcher while travelling waves propagate from the opposite side of the launcher into a region which is long compared with the attenuation distance of the waves. We model the situation as a lossy transmission line of finite length coupled at the launcher to a lossy transmission line of infinite extent. RF power applied to the launcher divides in the ratio of the input impedances of the two transmission lines. For a conducting end plate, the power delivered to the travelling waves is a maximum when the cavity length is an odd number of 1/4 wavelengths long for which its input impedance is a maximum. Similarly, for an insulated end plate, the power delivered to the travelling waves is a maximum for a cavity with a length equal to an integer number of half wavelengths for which its input impedance is again a maximum.

Practical electromagnetics: from biomedical sciences to wireless communication

Preface. 1. INTRODUCTION. 1.1 Electrical sources and fundamental quantities. 1.2 Static and dynamic fields. 1.3 Working with complex numbers and functions. 2. VECTORS AND FIELDS. 2.1 Working with vectors. 2.2 Coordinate systems. 2.3 Differentiation and integration of vectors. 2.4 Gradient of the scalar field and its applications. 2.5 Divergence of the vector field and its applications. 2.6 Curl of the vector field and its applications. 2.7 The divergence theorem. 2.8 Stokes' theorem. DELTA. 2.9 Other operations involving 2.10 Helmholtz theorem. 3. BASIC LAWS OF ELECTROMAGNETICS. 3.1 Maxwell's equations in large scale/integral form. 3.2 Maxwell's equations in point/differential form. 3.3 Constitutive relations. 3.4 Boundary conditions. 3.5 Lorentz force equation. 3.6 Poynting vector and power flow. 4. UNIFORM PLANE WAVES. 4.1 The wave equation and uniform plane wave solutions. 4.2 Plane electromagnetic waves in Lossy media. 4.3 Uniform plane wave incident normally on an interface. 4.4 Uniform plane wave incident obliquely on an interface. 5. TRANSMISSION LINES. 5.1 Transmission line equations. 5.2 Finite length transmission line. 5.3 Smith chart. 5.4 Transients on transmission lines. 6. MODIFIED MAXWELL'S EQUATIONS AND POTENTIAL FUNCTIONS. 6.1 Magnetic charge and current. 6.2 Magnetic vector and electric scalar potentials. 6.3 Electric vector and magnetic scalar potentials. 6.4 Construction of solution in rectangular coordinates. 6.5 Construction of solution in cylindrical coordinates. 6.6 Construction of solution in spherical coordinates. 7. SOURCE IN INFINITE SPACE. 7.1 Fields of an infinitesimal source. 7.2 Antenna parameters. 7.3 Linear antennas. 7.4 Antenna arrays. 7.5 Friis transmission formula and the radar range equation. 8. ELECTROSTATIC FIELDS. 8.1 Laws of electrostatic fields. 8.2 Gauss' law. 8.3 Poisson's and Laplace's equations. 8.4 Capacitors and energy storage. 8.5 Further applications of Poisson's and Laplace's equations. 9. MAGNETOSTATIC FIELDS. 9.1 Laws of magnetostatic fields. 9.2 Inductors and energy storage. 9.3 Magnetic materials. 9.4 Magnetic Circuits. 10. WAVEGUIDES AND CAVITY RESONATORS. 10. 1 Metallic rectangular waveguide. 10. 2 Metallic circular cylindrical waveguide. 10.3 Rectangular cavity resonators. 10.4 Circular cylindrical cavity resonators. 11. NUMERICAL TECHNIQUES. 11.1 Finite difference methods. 11.2 The method of moments. 11.3 Scattering of plane EM waves from an infinitely long cylinder. Appendix A. Mathematical formulas. Appendix B. Delta function and evaluation of fields in unbounded media. Appendix C. Bessel functions. Appendix D. Legendre functions. Appendix E. Characteristics of selected materials. Appendix F. Physical constants. Appendix G. Decibels and Neper. Appendix H. Nomenclature and characteristics of standard rectangular waveguides. SELECTED REFERENCE BOOKS . Index.

Generalized Form of Telegrapher's Equations for the Electromagnetic Field Coupling to Finite-Length Lines Above a Lossy Ground

In this paper, a generalized form of the Telegrapher's equations for electromagnetic field coupling to finite-length transmission lines above a lossy ground is derived. The approach is fully based on the thin-wire antenna theory. The effect of a lossy half-space is taken into account by means of the reflection coefficient approximation. The conductor losses can also be taken into account via surface impedance per unit length. The resulting equations are handled numerically via the Galerkin--Bubnov indirect boundary element method. Numerical results are presented for induced current along the line, and compared with transmission line (TL) approximation, for the case of lossless conductor. It is shown that the TL approximation can result in a significant underestimation of the induced currents.

A MATLAB-based transmission-line virtual tool: finite-difference time-domain reflectometer

This article introduces a simple virtual tool, TDRMeter, for the investigation and visualization of time-domain pulsed voltage/current, traveling along a terminated finite-length transmission line, without and with faults somewhere between the source and the load. The package can be used as an educational tool in various undergraduate lectures to aid in teaching electromagnetics as well as transmission lines.

Analysis of Crosstalk between Finite-Length Multiconductor Transmission Lines on a PCB by Using Circuit-Concept Approach

In this paper, crosstalk between multiconductor transmission lines of finite length in arbitrary directions on a printed circuit board is studied by using a circuit-concept approach. The circuit-concept approach of (2+1) finite-length lines is expanded for the crosstalk calculation of (n + 1) lines where n > 2. 2n-port network expression is derived from the modified telegrapher equations. The effect of via currents flowing through the vertical short line sections at the line terminals is also investigated. Due to this expansion the derived equations for (n + 1) lines are expected to be easily applied for crosstalk analysis of a variety of complex structures such as via fences and guard traces, etc.

Thermal Noise of Microwave Superconducting Filter-Amplifier Combinations

Superconducting filters in radioastronomical receiver frontends at cm-wavelengths may eliminate nearby terrestrial interference signals since they offer very high frequency selectivity and extremely small insertion loss. Moreover, power in unwanted intermodulation signals is sufficiently small at the expected input levels. On the other hand thermal noise outside the passband of a filter-amplifier combination may affect the receiver performance. The overall thermal noise of superconducting filters with Butterworth or quasi-elliptic characteristic connected via a 50 /spl Omega/ transmission line of finite length with a low noise amplifier is investigated. Arrangements with very low noise outside the passband are described. Simulated and measured thermal noise spectra are in reasonable agreement.

Analysis of a double step microstrip discontinuity using generalized transmission line equations

In this paper, a new analysis for a double step microstrip discontinuity is presented by using generalized transmission line equations . The new analysis is based on a new concept of a finite-length transmission line integrated with its double step discontinuity so that the double step discontinuity is regarded as a finite-length nonuniform transmission line and the generalized equations could be directly implemented. Since the generalized equation coefficients are determined by dynamic numerical methods and the coefficients are invariant with the line excitation and load, the equations are dynamic rather than TEM. The interested discoveries are that the generalized equations for the whole double step structure or a partial double step structure can give us the same results and the generalized equations have broadband frequency characteristics. For the double step structure used in this paper for the analysis, the S-parameters for a frequency band from 0.5 GHz to 10 GHz can be well calculated by using only two separately generalized equations at frequency of 3 GHz and 8 GHz.

Technique for computing the response of a line of finite length excited by high frequency electromagnetic fields

The important EMC problem of the high-frequency electromagnetic field coupling to a single-conductor transmission line of finite length is considered. In particular, a general method to determine the current induced on the line subjected to a generic incident field wave is proposed. The governing integro-differential equation of the problem is solved by means of a numerical procedure based on a Fourier series transformation. It can be proved that the series in which the unknown of the problem, namely the current along the line, is developed converges to the exact solution and only few terms are needed. The proposed approach represents a more accurate alternative to the transmission line (TL) approximation, since it allows the removal of its typical limitations, namely assumptions about the absence of a common mode current and about the TEM (or quasi-TEM) propagation mode. Such assumptions determine restrictions on the maximum value of line height and width with respect both to the line length and to the minimum field wavelength. Numerical results obtained on a test line excited by a suitable electromagnetic pulse are compared with those provided by the numerical electromagnetic code (NEC) and a good agreement is highlighted.

Analytical expressions for per-unit-length parameters of finite length transmission lines with discontinuities

Analytical expressions for per-unit-length parameters of finite-length transmission lines are derived and verified by the method of moments in this paper. The line can be a conductor with bends and varying sizes. The expressions are explicit in form and can be used to model and analyze the effects from ends and bends on the line effectively.

有限長伝送線路の立ち上がり部分の影響について(2)(EMC関連および一般)

有限長伝送線路の立ち上がり部分の影響について(2)(EMC関連および一般)

Analysis of crosstalk between nonparallel transmission lines by using a circuit concept

Crosstalk between two nonparallel transmission lines of finite length is studied. Nonhomogeneous differential equations for transmission lines excited by external fields are used in this analysis. The electromagnetic fields around the finite-length transmission lines are generated by currents in a transmission line section and terminal transitions, which are expressed using vector potentials. By manipulating a solution of the differential equations, a four-port network expression in terms of terminal voltages and currents is obtained. Experimental results for some models show the validity of the theory. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80(11): 45–53, 1997

Closed-form solution for lossy exponential transmission line problem in frequency and time domains

An exact and explicit solution for the reflection and transmission problem of a lossy exponential transmission line of finite length is derived in both the frequency and the time domain via a wave-splitting approach. The problem is formulated first in the frequency domain. Wave-splitting is defined and the solution for internal voltages and currents is derived. Closed-form solutions for the reflection and transmission coefficients are obtained. The explicit solution for a transmission line consisting of several exponential pieces (each with different taper) in series is then easily written down. To obtain the transient response of the lossy exponential line, a time domain Green function approach based on wave-splitting is used. Linear partial differential equations for the Green functions together with the initial and boundary conditions are derived and solved explicitly. The exact and explicit solutions for the transient reflection and transmission up to arbitrary large times are given.

Cooper-pair current through ultrasmall Josephson junctions.

The current-voltage characteristics of ultrasmall Josephson junctions sensitively depend on the electromagnetic environment of the junction. When the charging energy exceeds the Josephson coupling energy, the usual supercurrent at zero voltage is completely suppressed. However, for typical environmental impedances, which are small compared to the resistance quantum, stochastic Cooper-pair tunneling leads to a supercurrent peak at a small finite voltage which is proportional to the temperature and the low-frequency resistance of the external circuit. An analytic expression for the form of this universal peak, which is independent of the high-frequency behavior of the environment, is given. With increasing Josephson coupling the peak merges into the usual supercurrent of a Josephson junction. At larger voltages the Cooper-pair current depends on details of the environment. Current peaks are shown to result from resonances in the environmental impedance. Specifically, the case of an [ital LC] transmission line of finite length is discussed.

Frequency and Time Domain Green Function Technique for Nonuniform LCRG Transmission Lines with Frequency-Dependent Parameters

The reflection and transmission of waves on a nonuniform LCRG transmission line of finite length with frequency-dependent parameters are considered. A Green function technique combined with wave splitting is used both in the frequency domain and the time domain. In the frequency domain ordinary differential equations (ODEs) for the time-harmonic Green functions are obtained. In the time domain the transmission line model is established through a set of dispersion kernels. Partial differential equations (PDEs) for the time-domain Green functions are derived. Numerical results for transient reflected, transmitted and internal currents are presented. Furthermore, it is noted that a special case of the present formalism can be used to determine the reflected, transmitted and internal fields for normal plane wave incidence on a stratified dispersive and dissipative slab.