Lossy Nonuniform Transmission Lines Research Articles

Fast transient analysis method for lossy nonuniform transmission line with nonlinear terminations

A fast and effective approach for simulating lossy nonuniform transmission line with the nonlinear terminations is presented. The method based on the improved delay extraction-based macromodeling algorithm (DEPACT) for the lossy uniform transmission line. Meanwhile, by reducing the approximation order, the macromodel is simplified and the simulation time is reduced. The simulation results are compared with the finite difference time domain (FDTD) method and good agreement is obtained.

Efficient Method for Time-Domain Analysis of Lossy Nonuniform Multiconductor Transmission Line Driven by a Modulated Signal Using FDTD Technique

In this paper, an unconditionally stable finite-difference time-domain algorithm is presented for analysis of lossy nonuniform multiconductor transmission line (MTL). The results of the proposed algorithm are confirmed by those of the Leap-Frog algorithm. The unconditionally stable algorithm alone cannot decrease the time consumption, especially when the MTL is excited by modulated signals. The complex phasor transformation approach is used to separate the modulating signal from the carrier signal when an MTL is excited by a modulated signal. A new set of equations is generated using this approach. The new equations are based on the modulating signal, and the carrier signal is eliminated in these equations. The derived equations are solved by Leap-Frog algorithm, and the results confirm the accuracy of these equations. Finally, the proposed equations are solved by the unconditionally stable algorithm at several temporal step sizes. The results indicate that this method has much lower CPU time compared with the conventional method and also has a very good accuracy.

Sensitivity Analysis of Lossy Nonuniform Multiconductor Transmission Lines With Nonlinear Terminations

This paper applies the Lax-Friedrichs technique, usually used in fluid dynamics, to transmission line sensitivity analysis. The Lax-Friedrichs difference scheme for sensitivity analysis of both uniform and nonuniform transmission lines is derived. Based on this scheme, a method for analyzing multiconductor transmission line sensitivity, which does not need to be decoupled, is presented by combining with matrix operations. Using numerical experiments, the proposed method is compared with the characteristic method and the fast Fourier transform approach. With the presented method, the sensitivity of a nonlinear circuit including nonuniform multiconductor transmission lines is analyzed and the results are verified by the HSPICE perturbation method. The proposed method can be applied to either linear or nonlinear circuits, which include lossy nonuniform multiconductor transmission lines, and is proved to be efficient.

Sensitivity analysis of lossy nonuniform multiconductor transmission lines based on the Lax‐Wendroff technique

AbstractThis paper applies the Lax‐Wendroff technique, usually used in fluid dynamics, to transmission line sensitivity analysis. A second‐order‐accurate Lax‐Wendroff difference scheme for sensitivity analysis of both uniform and nonuniform transmission lines is derived. Based on this scheme, a new method for analyzing multiconductor transmission line sensitivity, which does not need to be decoupled, is presented by combining with matrix operations. Using numerical experiments, the proposed method is compared with the characteristic method and the fast Fourier transform approach. With the presented method, the sensitivity of a nonlinear circuit including nonuniform multiconductor transmission lines is analyzed and the results are verified by the HSPICE perturbation method. The proposed method can be applied to either linear or nonlinear circuits, which include lossy nonuniform multiconductor transmission lines and is proved to be efficient. Copyright © 2009 John Wiley & Sons, Ltd.

Analysis of Hermite Lossy Nonuniform Transmission Lines Based on Hermite Function and Confluent Hypergeometric Function

The rigorous analytical solutions of the lossy Hermite nonuniform transmission lines (HNTL) are presented in this paper. These solutions are based on two special functions, namely, Hermite function and confluent hypergeometric function. The ABCD matrix of HNTL is given to obtain the corresponding frequency characteristic of the HNTL transformer. Through numerical simulations in different terminated cases, it is found that the lossless HNTL can be matched by resistance loads. This conclusion is different from the lossless one presented by D.torrungrueng. etc. In addition, the distributed power values of HNTL in the lossy case are calculated to show the attenuation character.

Time-Domain Analysis of a Lossy Nonuniform Transmission Line

An analytical solution of the coupled Telegrapher's equations for the voltage and current on a homogeneous lossy transmission line is presented. The resulting expression is obtained in the form of an exact time-domain propagator operating on the line voltage and current. It is shown that an application of Simpson's rule yields a simple accurate numerical representation of the propagator that can be used to analyze both homogeneous and inhomogeneous transmission lines. Numerical dispersion in lossy media is examined proving that this method has no numerical dispersion.

A Precise Time-Step Integration Method for Transient Analysis of Lossy Nonuniform Transmission Lines

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.

A Novel Time-domain Integration Method for Transient Analysis of Nonuniform Transmission Lines

This paper presents a precise time-step integration method for transient analysis of lossy nonuniform transmission lines. The spatial discretization in this method is the same to the finite difference time domain (FDTD) algorithm. However, in order to eliminate the Courant condition constraint, the precise integration method is utilized in the time-domain calculation. It gives quasi-exact solutions in time domain for the spatial discretized Telegrapher’s equations. Since the exponential matrix is calculated precisely, large time step can be adopted in the integration process to achieve accurate results efficiently. A numerical example is presented to demonstrate the accuracy and stability of the proposed method. DOI: 10.2529/PIERS060904030908

Accurate modeling of lossy nonuniform transmission lines by using differential quadrature methods

This paper discusses an efficient numerical approximation technique, called the differential quadrature method (DQM), which has been adapted to model lossy uniform and nonuniform transmission lines. The DQM can quickly compute the derivative of a function at any point within its bounded domain by estimating a weighted linear sum of values of the function at a small set of points belonging to the domain. Using the DQM, the frequency-domain Telegrapher's partial differential equations for transmission lines can be discretized into a set of easily solvable algebraic equations. DQM reduces interconnects into multiport models whose port voltages and currents are related by rational formulas in the frequency domain. Although the rationalization process in DQM is comparable with the Pade approximation of asymptotic waveform evaluation (AWE) applied to transmission lines, the derivation mechanisms in these two disparate methods are significantly different. Unlike AWE, which employs a complex moment-matching process to obtain rational approximation, the DQM requires no approximation of transcendental functions, thereby avoiding the process of moment generation and moment matching. Due to global sampling of points in the DQM approximation, it requires far fewer grid points in order to build accurate discrete models than other numerical methods do. The DQM-based time-domain model can be readily integrated in a circuit simulator like SPICE.

Transient analysis of lossy nonuniform transmission line using the finite difference time domain method

AbstractWith a view to carrying out a highly accurate and fast time domain analysis of a lossy nonuniform transmission line, a method is described for application of the FDTD method to a finitely long lossy nonuniform transmission line. The present method is applied to a parabolic transmission line as one variety of nonuniform transmission line and a step response analysis is performed. By comparison with an analytical solution and other methods, the effectiveness of the method is confirmed. Also, the step response at the output end of a lossy nonuniform transmission line is almost a step waveform under conditions different from the distortionless transmission condition of a uniform line. Based on this result, a method is described for approximating the step response waveform at the output end of a lossy parabolic line to a step waveform. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(8): 1–10, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10006

Time‐domain study of lossy nonuniform multiconductor transmission lines with complex nonlinear loads

Time‐domain study of lossy nonuniform multiconductor transmission lines with complex nonlinear loads

Time‐domain study of lossy nonuniform multiconductor transmission lines with complex nonlinear loads

AbstractThis paper deals with a computational approach based upon the centered‐points finite‐difference time‐domain (FDTD) technique for evaluating voltages and currents along lossy nonuniform multiconductor transmission lines terminated with arbitrary loads. We emphasize the case of complex nonlinear loads, such as a metal semiconductor field‐effect transistor (MESFET). We illustrate and validate the FDTD technique with time‐domain reflectometer (TDR) experiments. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 296–301, 2001.

Accurate non-uniform transmission line model and its application to the de-embedding of on-wafer measurements

An accurate model for lossy non-uniform transmission lines is presented. The technique provides a coplanar waveguide (CPW) taper model, which has been used to accurately de-embed measurements of passive CPW components in line geometries differing from the nominal 50/spl Omega/ geometry of the calibration. The model accounts for both dielectric and conductor losses, and is shown to be in excellent agreement with measured results from 45 MHz to 120 GHz.

Simulation of single and coupled transmission lines using time-domain scattering parameters

A new method of transient analysis and simulation of interconnects is introduced. The presented approach permits calculation of scattering parameters of lossy nonuniform transmission lines and n-wire lossy coupled uniform lines directly in the time domain. In both cases, the procedure is the same. First, the partial differential equations are converted to integral telegrapher's equations, using the method of characteristics. Next, these integral equations are solved by the method of successive approximations, and infinite series expansions of scattering parameters in the time domain are obtained. The terms of the series expansions are expressed by elementary functions. The infinite series obtained are generally fast convergent and can be truncated after a few first terms, with the small relative truncation error previously defined. The number of terms in the truncated series can be determined on the basis of transmission line parameter values and the assumed relative truncation error. Finally, test examples for single and n-wire coupled line are presented. Simulation time and memory occupation are very small.

Blind deconvolution of sources from the transmission responses of one-dimensional inhomogeneous continuous and discrete layered absorbing media

Non-destructive testing and reconstruction of lossy non-uniform transmission lines require solving inverse scattering problems for inhomogeneous one-dimensional (1D) lossy media. Often the source waveform used to probe the medium is unknown, since it cannot be measured separately. This paper shows that the blind deconvolution problem of reconstructing both an unknown source and an unknown lossy 1D medium can be solved, provided the medium absorption is sufficiently large. We generalize the minimum-phase property of the transmission response to a more severe property for lossy media. We also show how partial knowledge of the source can be used to reconstruct low-loss and lossless 1D media. Both discrete and continuous 1D layered media are considered. Numerical examples are presented.

Equivalent Representations of Lossy Nonuniform Transmission Lines

Equivalent transformations, which were recently derived for mixed lumped and distributed circuits, may be extended to circuits consisting of lumped reactance, resistors, and Iossy transmission lines. It is shown that circuits consisting of a cascade connection of lumped element sections and Iossy uniform transmission lines are equivalent to circuits consisting of a cascade connection of lossy nonuniform transmission lines, lumped elements, and ideal transformers. Furthermore, by considering the limiting case of these transformations, equivalent transformations for circuits consisting of a cascade connection of lumped reactance, resistors, and nonuniform transmission lines are obtained. Exact equivalent circuits of Iossy even-order binomial form transmission lines are derived from these equivalent transformations.