Analysis of Transmission Line with Distributed Series Voltage Sources Using Green’s Function

The vast majority of nonuniform transmission lines are no analytical solution except for a few special forms of transmission line. Dividing nonuniform transmission line into several equal parts, then each part can be regarded as uniform transmission line approximately. Using the theory of uniform transmission line to analyze nonuniform transmission line's transient response is the commonly used method. Composite Simpson's rule for transient analysis of nonuniform transmission lines is proposed in this paper. The exponential transmission matrix of nonuniform transmission line's equation is transformed into a general algebraic equation, which greatly simplifies the analysis on transient response for nonuniform transmission line. The simulation results illustrate the accuracy of the presented approach with examples.

This paper presents a novel time-domain integration method for transient analysis of nonuniform multiconductor transmission lines (MTLs). It can solve the time response of various kinds of transmission lines with arbitrary coupling status. The spatial discretization in this method is the same as the finite-difference time-domain (FDTD) algorithm. However, in order to eliminate the Courant-Friedrich-Levy condition constraint, a precise time-step integration method is utilized in time-domain calculation. It gives an analytical solution in the time domain for the spatial discretized Telegrapher's equations with linear boundary conditions. Large time steps can be adopted in the integration process to achieve accurate results efficiently. In the analysis of transmission lines with frequency-dependent parameters, a passive equivalent model is introduced, which leads to the similar semidiscrete model as that for the frequency-independent case. In addition, a rigorous proof of the passivity of the model is provided. Numerical examples are presented to demonstrate the accuracy and stability of the proposed method.

By using electromagnetic topology (EMT) method, this paper discusses the issue of the electromagnetic field penetration through an aperture to a cavity and coupling to a two-wire transmission line in the cavity. By representing the electromagnetic field propagation path as “tube”, and combining with transmission line theory, this paper creates the Baum-Liu-Tesche (BLT) equation of radiation coupling. Then, by employing the BLT equation, the semi-analytic solutions of the load response of the two-wire transmission line in the cavity are obtained. Numerical examples are constructed to demonstrate the validity of this technique.

This paper presents an analytical method of predicting and eliminating limit cycle conditions in hydraulic drive systems, where backlash in the actuator seal is the dominant nonlinearity. It is shown that limit cycle conditions are a strong function of certain plant parameters. The elimination of limit cycle conditions may thus be achieved by the alteration of certain inherent plant parameters. Fluid flow in a hydraulic pipe is modelled using transmission line theory. The sinusoidal-input describing function is used to indicate which values of the plant parameters would result in limit cycle conditions. The analytical results were verified on an experimental test bench.

The problem of coupling between the transmission line and the external electromagnetic waves is analyzed more easily and more effectively if it is treated via transmission line theory rather than scattering theory if the cross section of the transmission line is much smaller than the wavelength and the principal mode of the induced current is TEM. This paper derives the transmission line equations by which the induced current is excited by the electric field components in the transmission direction and between the lines among the electromagnetic field components. the relation with the conventional theory, physical meanings and the equivalent circuits are discussed. In the experiment in which a plane wave is used as the external electromagnetic field, the results agree well with the present theory and the validity of the theory is confirmed if the transmission line cross section is extremely small. Further, a compensation method is discussed for the transmission line height for which the principal mode is considered TEM. the theoretical accuracy is shown and the fact that the line width restricts the range of applicability of this theory is confirmed experimentally.

In this paper we perform an in-depth theoretical study of a sensing platform based on epsilon-near-zero (ENZ) metamaterials. The structure proposed for sensing is a narrow metallic waveguide channel. An equivalent circuit model is rigorously deduced using transmission line theory, considering several configurations for a dielectric body (analyte sample) inserted within the narrow channel, showing good agreement with results obtained from numerical simulations. The transmission line model is able to reproduce even the most peculiar details of the sensing platform response. Its performance is then evaluated by varying systematically the size, position and permittivity of the analyte, and height of the ENZ channel. It is shown that the sensor is capable of detecting changes in the permittivity/refractive index or position even with deeply subwavelength analyte sizes (∼0.05λ0), giving a sensitivity up to 0.03 m/RIU and a figure of Merit ∼25. The effective medium approach is evaluated by treating the inhomogeneous cross-section of the analyte as a transmission line filled with a homogeneous material.

This paper presents an analysis of external electromagnetic field coupling on the single-conductor coupling, using transmission line theory, the shielding theory, two-port network theory and antenna theory. transmission line theory, the calculation method of the induced current and voltage generated on the transmission line which is generated by external electromagnetic field is desirably in this paper.

Transmission line theory in electromagnetics comes alive when the travelling waves are animated on a computer screen, using program "BOUNCE". Fundamental concepts such as "travelling wave", "reflected wave", and "load matching" are forcefully demonstrated in the classroom. Problems using series connections of dissimilar line, shunt loads and branches can be readily examined. Transmission line theory is applied to problems in the design of tri-state logic circuits that cannot be solved readily by hand, using animation to show how the voltage waveforms arise. Animation is used with a sinusoidal generator to illustrate the evolution to the sinusoidal steady state, as an introduction to solving transmission line circuits with phasors. Students are encouraged to run BOUNCE at home as a computational laboratory to verify their solutions to homework problems. This paper presents the BOUNCE program, and some of the demonstrations with BOUNCE that are used in the classroom.

This paper presents the application of transmission line theory to analyze grounding arrangements composed of multiple parallel electrodes. The grounding system is treated as a multiconductor transmission line and a solution method based on a similarity transformation is used to solve the resultant equations. The impulse response of grounding arrangements composed of multiple grounding rods and horizontal electrodes are simulated, and the results are presented in terms of the grounding potential rise and impulse coefficient. The accuracy of the results is assessed by comparison with simulations of the same cases using an electromagnetic field approach. The proposed model is useful to estimate quantities related to the lightning response of typical grounding arrangements of transmission and distribution lines.

A generalized method of moments (MoM)-SPICE iterative technique for field coupling analysis of multiconductor transmission lines (MTLs) in the vicinity of complex structures is presented. Telegrapher's coupling equations are modified with additional distributed voltage and current sources for more accurate analysis of the total current induced onto transmission line bundles in the presence of complex structures. These additional voltage and current sources are introduced to enforce the electric field boundary condition and continuity equation on MTLs beyond the quasi-static regime. The surrounding structure is modeled via the MoM and a SPICE-like simulator is used to simulate equivalent circuit model of the MTLs extracted via the partial element equivalent circuit method. The proposed technique is based on perturbation theory with the quasi-static current distributions on the transmission lines still assumed to be dominant. Validation examples for single and MTLs are given in the presence of complex structures.

In this paper, the two-dimensional Fourier transform and wave decomposition technique are used to transform Maxwell’s equation in transversely isotropic (TI) formation into two independent sets of transmission line equations about transverse magnetic (TM) wave and transverse electric (TE) wave. According to both transmission line theory and superposition principle, an improved transmission line method is advanced to simplify the computational process of TM wave and TE wave only by introducing the transmission line Green’s functions of the current source. Thus, the new algorithm and the new expressions of current source electromagnetic (EM) dyadic Green’s functions in frequency-wavenumber domain are established for realizing the efficient simulation of marine controlled-source electromagnetic (MCSEM) responses in the horizontally layered TI formation. On this base, the basic solutions of the transmission line Green’s functions and EM boundary conditions are utilized to derive the recursive formula of the generalized reflections and amplitudes of the TE and TM waves, and the analytic solutions of the Green’s functions in each bed are obtained. Then, by using Fourier inverse transform and Bessel integral formula, the MCSEM responses in frequency-spatial domain are expressed in the Sommerfeld integral form. A combination of the cubic spline interpolation with the Lommel integral is used to efficiently compute the MCSEM responses. Finally, we validate the modeling algorithm and investigate the influences of changes in operation frequency and anisotropic coefficient on the MCSEM response in the TI formation.

Imagining a specific SPICE model for the Cable Discharge Event (CDE) is impossible because the model depends on the cable length, material, and type. This paper aims to propose an instruction to extract a SPICE model for Flat Ribbon Cables (FRCs), which have a wide range of applications in electronics. This work introduces general information and considerations about the CDE in FRCs, and the conductor of the FRC considers a transmission line which to Extract its equivalent circuit; a technique based on S-Parameter measurement and transmission line theory is demonstrated. Also, this work regards the mutual capacitance between the conductor of FRC in the extracted SPICE model. In this work, the analytical technique and the 3D full-wave software synergize with each other to increase the reliability of the proposed SPICE model. This work evaluates the effect of cable length and termination resistance on the discharge waveform. The proposed instruction can be expanded to the other cables. It helps the designers observe the CDE impacts besides other transient events on their circuits and systems without spending much time and expense.

A novel method for transient analysis of Iossy transmission lines with arbitrary nonlinear terminal networks is presented. The uniqueness of this approach is that we develop time-domain Green's functions for the multiport transmission-line systems by terminating the ports in quasi-matched loads. This ensures Green's functions of a short duration. Hence, the amount of frequency-domain data necessary to obtain time-domain Green's functions is modest. These Green's functions are then convolved with the line port voltages. With this technique one can analyze responses of multiconductor transmission lines with arbitrary nonlinear loads (even with memory) as we have at any instant of time Thevenin's equivalent of the linear portion of the system. An example is presented to illustrate the application of this technique to multiconductor nonlinearly loaded transmission lines.

Introduction: Electromagnetic wave coupling to transmission lines has received much attention for many years. This classical EMC problem has recently evolved from deterministic models to statistical analysis [1]. This latter approach has been shown to be more suited to the modelling of realistic situations when transmission lines are immersed in diffused wireless communication systems. In the related works, the localisation and polarisation of the interference sources are considered as random variables, and closed form expressions or numerical approximations are derived concerning the statistical distribution of the induced voltage. A usual limitation of this approach is however the single interference source assumption leading to a single interference field impinging the lines. In confined situations, dense multipath environment, or when several transmitters are present, a better modelling might be obtained by considering a more complex excitation of the lines. In this Letter, a general formalism based on a plane wave spectrum illumination is proposed to study such a case. Formalism: Let a uniform and lossless bi-filar transmission line be located at the origin of a Cartesian co-ordinate system. The line is directed along the z axis, the spacing between the conductors is b ,t he conductor radius a, and the line length s. At z ¼0, the line is fed by a sinusoidal source V0 of impedance Z0. At the far-end, a load impedance Zs terminates the line. Using transmission line theory, the current flowing on the line is given by

Electromagnetic waves in loaded cylindrical structures : a radial transmission line approach