Equations Of Nonuniform Transmission Lines Research Articles

A simplified numerical modeling of the transient behavior of grounding systems considering soil ionization

The analysis of the transient performances of grounding systems during a lightning discharge is proposed in the literature by modeling in time or in frequency domain. The frequency modeling makes it generaly possible to take into account the electromagnetic effects observed during the rise time of the pulse while temporal modelling makes it possible to introduce the nonlinear phenomenon (soil ionization) observed following an injection of a very high intensity lightning strike. In this work we propose a modeling with a simplified implementation which takes into account the various electromagnetic couplings which arise after spatial discretization of the grounding system as well as the ionization of the soil. This new formalism is developed from the equations of nonuniform Transmission Lines (nuTL) and the Finite-Difference Time-Domain (FDTD) method. This simplified modeling is carried out solely by spatial discretization of the grounding system conductors, is done without loss of precision and with very low calculation times. Our calculation results are compared to those already published and carried out by simulation or by the measurements.

Introducing Nonuniform Grids into the FDTD Solution of the Transmission-Line Equations by Renormalizing the Per-Unit-Length Parameters

A challenging aspect of using the finite-difference time-domain (FDTD) method to solve nonuniform transmission-line equations is to choose a discretization grid with an adequate spatial resolution. When the per-unit-length parameters have strong variations, an efficient problem-solving strategy requires the use of a nonuniform discretization grid. This paper presents a nonuniform gridding method that makes use of an analytically defined coordinate transformation to map a nonuniformly spaced grid onto a uniformly spaced grid where the standard FDTD time stepping equations can be applied. This approach absorbs all the details of the nonuniform grid into effective or renormalized per-unit-length parameters.

Analytic solution of non-uniform transmission lines at low frequencies

A simple approximated analytical solution is introduced to analyse arbitrary non-uniform transmission lines (NTLs) at low frequencies. First, the differential equations of NTLs are written as a suitable matrix differential equation. Then, the matrix differential equation is solved to obtain the chain parameter matrix of NTLs. Later, the voltage and current of the line are obtained at any point using the obtained chain parameter matrix. Finally, the validation of the introduced solution is studied.

Modeling the Terminal Response of a Bundle of Twisted-Wire Pairs Excited by a Plane Wave

The proposal to use multiple-input multiple-output vectored transmission in digital subscriber line (DSL) systems has prompted a revision of the channel noise models used to characterize twisted-wire pairs (TWPs). In this context, a transmission-line model for predicting the terminal response of a bundle of TWPs to an illuminating plane-wave electromagnetic field is introduced. The corresponding nonuniform transmission-line equations for the multiconductor system are solved numerically. The goal of the model is to provide a tool for solving a wide variety of radio-frequency interference problems in DSL systems. Computed results for a variety of TWP structures are presented, and the issue of small random twisting nonuniformities is explored.

ANALYSIS OF NONUNIFORM TRANSMISSION LINES USING THE EQUIVALENT SOURCES

A new method is introduced to analyze arbitrary nonuniform transmission lines. In this method, the equations of nonuniform transmission lines are converted to the equations of uniform transmission lines, which have been excited by distributed equivalent sources. Then, the voltage and current distributions are obtained using an iterative method. The validity of the method is verified using a comprehensive example.

Generalized non‐uniform transmission‐line models for local radiation from microstrip bends in MMICs

AbstractAlthough microstrip bends in high‐speed digital MMICs have been widely investigated for the past two decades, their local radiation characteristics rather than their reflection characteristics have not been completely explored yet. In this paper, the generalized non‐uniform transmission‐line equations are used in analysing the microstrip bends including their local radiations. In our new models, the whole structure of a bend is regarded as a non‐uniform transmission line that is totally governed by the generalized non‐uniform transmission‐line equations. Except for analytical simplification and broad bandwidth performance, the new analysis could indicate where the strongly local radiations along a bend structure come from. Copyright © 2003 John Wiley & Sons, Ltd.

Crosstalk and reflection for curvilinear conductors by utilizing a non-uniform transmission line approach

A novel approach to analyze curvilinear multiconductor transmission line systems is presented. Non-uniform transmission line equations for the systems are obtained and solved by using chain matrix approach. Crosstalk and reflection due to discontinuities such as bend and changes of radii are investigated. Per-unit-length parameters for the lines are discussed as well. It is observed that the discontinuities will increase the crosstalk significantly and bending will substantially increase crosstalk at the driving end.

Algebraic solution of time-domain nonuniform transmission-line equations by 2-D wavelet transform

In this paper, the numerical solution of nonuniform transmission lines is treated. The method proposed is based on the double wavelet expansion of the multiconductor transmission lines (MTL) equations; the expansion is performed both in the time domain and in the space domain, and the coupled partial differential equations become an algebraic system in the Lyapunov form which is solved by the use of standard techniques. The method has been tested in many cases and has demonstrated to require low CPU time consumption and low memory occupation.

A New Approach To Derive and Analyze Nonuniform Transmission Line Equations for Curvilinear Multiconductor Systems

A novel approach to derive nonuniform transmission line equations for curvilinear multiconductor systems is presented by directly using the scalar and vector potentials associated with boundary conditions. The per-unit-length parameters of the line can be obtained simultaneously in derivation and are explicitly given for straight conductor systems as an example. Results for a bent conductor of different radii over ground plane also verify the approach.

Radiation parameter extraction for transmission‐line interconnects by using method‐of‐moments solutions

AbstractIn this paper, an extraction technique of radiation sources for nonuniform transmission lines is proposed for the first time. The technique, based on solutions of the method of moments (MoM), can numerically determine the coefficients of nonuniform transmission‐line equations, in which radiation parameters are included. Numerical examples show that the radiation effect of a right‐angle microstrip‐line bend is indeed stronger than that of a corresponding 45° mitered bend at high frequency. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 37–39, 2001.

Space–time wavelet expansion iterative solution of non‐uniform transmission lines with arbitrary loads

AbstractIn this paper a method based on the double expansion by wavelet on the interval in space and time of non‐uniform transmission line equations with arbitrary loads is presented. The differential time domain equations are transformed into a Lyapunov equation which is adaptively solved. Hence, a Fourier‐like approach for the time‐domain solution of transient electromagnetics problems is obtained avoiding the typical problems of time‐stepping techniques. The accuracy of the solution can be selected by choosing an adequate number of components of the wavelet basis. Different cases have been studied to show the effectiveness of the method. Copyright © 2001 John Wiley & Sons, Ltd.

A nonuniform transmission-line approach for modeling bends on transmission lines

A novel approach for modeling the discontinuities of transmission lines such as conductors with bends and varying size is proposed. The effect from the discontinuities is incorporated in the per-unit-length parameters of nonuniform transmission-line equations. For canonical problems, our approach yields correct results. For a more general case, a comparison between our calculations and experimental data reported in the literature shows good general agreement. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 71–74, 2001.

The Nonuniform Transmission Line as a Broadband Termination

The problem of obtaining a broadband microwave termination is considered from the point of view of nonuniform transmission line theory. Attention is restricted to lines in which only the distributed shunt admittance may be varied. An optimization argument is presented which leads to the consideration of a line in which the fractional increase in admittance per wavelength in the line is constant. The nonuniform transmission line equations are solved exactly for this case, and the results are expressed in terms of readily interpretable elementary functions. It is shown that a fixed geometrical length of line can lead to an arbitrarily large effective length without destroying the match at the input. The introduction of a small loss term makes the line almost totally absorbing regardless of its termination. The line has a long-wavelength cutoff given by 4Π times the actual length of the line. If the line is short-circuited at its far end, a return loss of greater than 11.4 db is obtained at all frequencies above twice the cutoff frequency. The effect of certain practical limitations on the performance of this line is also discussed.