Multiconductor Transmission Line Equations Research Articles

Characterization of Via Structures in Multilayer Printed Circuit Boards With an Equivalent Transmission-Line Model

Vias are typical discontinuities for high-speed signal transmission in printed circuit boards (PCBs). This paper proposes an equivalent multiconductor transmission-line model for via structures in multilayer PCBs. The proposed model is based on the physic-based circuit model, taking into account distributed effects. Various via structures with arbitrary via number, trace connections, and via stubs can be effectively handled in the equivalent transmission-line model, which is sufficiently accurate and fast to be integrated into circuit simulators for via and link-path analysis. With the proposed model, well-known transmission-line theories can be borrowed for via modeling and characterization for signal integrity in high-speed digital circuits. The proposed model is validated with both full-wave simulations and measurements for multilayer PCBs with different via structures.

A coupled nonuniform transmission line analysis using FEM

This paper presents a finite element frequency domain model for numerical solution of the coupled nonuniform transmission line (NTL) problem. Based on the finite element method (FEM), a novel numerical procedure for solution of a system of the nonuniform multi-conductor transmission line equations in the frequency domain is presented. The results obtained by the proposed method has been compared to the analytical solution.

A Generalized Multiconductor Transmission Line Model and Optimized Method for the Solution of the MTL Equations

A generalized multiconductor transmission line (MTL) model is developed for modeling of wide frequency transient response on busbars, cables and core-type transformer windings. Different from the traditional MTL model, the equations of the generalized MTL model are built in the cylindrical coordinate system beside rectangular coordinate system. Based on further discussion, it is found that generalized MTL model could be changed to MTL model where all lines have the same length as to the core-type transformer windings. Then, the optimized solution based on Time domain finite element method (TDFEM) is developed for the above MTL equations. It avoids numerical oscillation of the finite difference time domain (FDTD) method. The numerical results are in agreement with ones calculated by Bergeron's method and FDTD method.

A spice model for multiconductor microstrip lines excited by an incident plane wave

AbstractThis article presents a SPICE model to analyze the terminal response of multiconductor microstrip lines excited by an incident plane wave. The analysis is based on multiconductor transmission line equations with the quasi‐TEM propagation mode approximation on microstrip lines and an accurate calculation of electromagnetic fields in the air/dielectric medium. The proposed SPICE model can be directly used for both the time‐domain and frequency‐domain analyzes and allows incorporating nonlinear and time‐varying loads. Several cases with an arbitrary plane wave incidence are simulated by using the proposed SPICE model. The results are in good agreement with those obtained using the Baum‐Liu‐Tesche equations model and full‐wave analysis simulator (by CST Microwave Studio Software). © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:2754–2761, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26396

EFFICIENT TIME-DOMAIN NOISE MODELING APPROACH FOR MILLIMETER-WAVE FETS

Based on the active coupled line concept, a novel approach for e-cient noise performance modeling of millimeter-wave fleld-efiect transistors is proposed. This distributed model considers the efiect of wave propagation along the device electrodes, which can signiflcantly afiect the noise performance especially in the millimeter-wave range. By solving the multi-conductor transmission line equations, using the Finite-Difierence Time-Domain technique, this procedure can accurately determine the noise correlation matrix of the transistor and then its noise performance.

Upper Bound and Dispersion of the Outdoor Powerline Channel Frequency-Response

In this paper, multiconductor transmission line (MTL) modelling is used to characterize the frequency response and dispersion of the low-voltage outdoor powerline channel. The analysis focuses on a single transmitter-to-receiver link and all the possible connection schemes associated with that link. By resorting to modal analysis, approximate analytical upper bounds of the channel frequency-response are derived for simplified but representative network configurations involving power cables with star-quad cross-section. Numerical solution of the MTL equations is used to validate the theoretical work and to show the dispersion of the channel frequency-responses, which results to be of the order of 20dB.

Nonlinear and fully distributed field effect transistor modelling procedure using time-domain method

An accurate and efficient modelling approach for field effect transistors (FET) as nonlinear active transmission lines is presented. The nonlinear active multiconductor transmission line (NAMTL) equations are obtained by considering the transistor as three active coupled lines operating in a nonlinear regime. This modelling procedure accurately spots the effect of wave propagation along the device electrodes. This modelling approach is applied to an FET by solving the NAMTL equations using a finite-difference time-domain technique. The results of this model are compared with the semi-distributed (slice) model. This method produces more accurate results than the slice model, especially at high frequencies.

Incident field excitation of random cables

This work considers the problem of characterizing the response of a cable bundle in the presence of an external electromagnetic field when the orientation of the cable is not well defined or is unknown. To do this, cable bundles are modeled as multiconductor transmission lines. Because of the random nature of the cable, an exact solution is not in general possible. Therefore a solution is approximated by segmenting the cable into a number of small uniform sections that can be solved and combined to form an overall solution. The orientation of these sections is allowed to vary randomly, thereby modeling the various twists and bends that may be found in a practical application. The line is excited by an external electromagnetic field. The voltages and currents generated at the terminations of the cable are calculated using a numerical approach to solve the multiconductor transmission line equations in the frequency domain. Because the exact positioning of the cable is not known, statistical data for the response are needed. To obtain statistical data, a large number of randomly generated cables are generated and solved.

TIME DOMAIN ANALYSIS OF ACTIVE TRANSMISSION LINE USING FDTD TECHNIQUE (APPLICATION TO MICROWAVE/MM- WAVE TRANSISTORS)

In this paper, an accurate modeling procedure for GaAs MESFET as active coupled transmission line is presented. This model can consider the effect of wave propagation along the device electrodes. In this modeling technique the active multiconductor transmission line (AMTL) equations are obtained, which satisfy the TEM wave propagation along the GaAs MESFET electrodes. This modeling procedure is applied to a GaAs MESFETs by solving the AMTL equations using Finite-Difference Time-Domain (FDTD) technique. The scattering parameters are computed from time domain results over a frequency range of 20-220 GHz. This model investigates the effect of wave propagation along the transistor more accurate than the slice model, especially at high frequencies.

Experimental and Numerical Investigation of Crosstalk Effect in Coupled Coplanar Waveguides—Part II: Multimode Coupled Line Representation

An approach for the crosstalk effect description in coupled coplanar waveguides with ideally grounded central strip conductor (C-CPWGS) that, for the first time, takes into account nonideal grounding by means of multimode propagation is presented in this paper. The frequency-domain full-wave computations of modal eigenvectors and propagation delays combined with multiconductor transmission line equations have been employed to obtain near- and far-end crosstalk waveforms. Developed theory has been verified experimentally by comparison with results of the time-domain crosstalk measurement of selected test structures. A very good degree of coherence between numerically computed and experimentally measured data has been achieved

Modeling of striplines between a power and a ground plane

In this paper, a stripline model is presented for coupled signal lines routed between a power and a ground plane based on multiconductor transmission line (MTL) theory. Through a suitable diagonalization of the MTL equations for striplines, the transverse electromagnetic (TEM) parallel-plate mode is decoupled from the stripline mode. In this way, stripline models that are obtained assuming ideal planes at ground potential can be extended to take into account the nonideal behavior of the planes. The presented model is applied to represent mode conversion due to vias, holes in the reference planes, and terminations of the stripline. Influence of inhomogeneous media is discussed.

Deterministic modeling of the (shielded) outdoor power line channel based on the multiconductor transmission line equations

In this paper, a complete methodology is proposed for the deterministic modeling of the channel transfer functions associated with underground power line access networks, in the light of the Multiconductor Transmission Line Theory. Some multiconductor power line cables are analyzed in detail, and their fundamental propagation characteristics (definition of eigenmodes, phase velocity, characteristic impedance, lineic attenuation) are related to the geometry of the conductors and the material properties. A multidimensional scattering matrix formalism is then introduced to perform an accurate analysis of the global power line network including multiconductor cable segments, derivation points, and termination loads. An illustrative example of a power line access network with three types of cables (with different numbers of conductors), 20 derivations, and five remote terminals, is finally proposed.

Transmission line formulation for the full-wave analysis of two-dimensional dielectric photonic crystals

Using a matrix formulation it is shown how the full-wave analysis of multilayer photonic crystals can be reduced to the analysis of an equivalent multiconductor transmission line (TL). In the special case of single-layer two-dimensional photonic crystals the inductance and capacitance matrices of this equivalent TL provide the propagation characteristics of the crystal under investigation. Specifically, the determinants of these matrices contain the required information for determining propagation constants and consequently the field distribution of TM and TE propagation modes inside the crystal. Comparison of the numerical results presented in this work with those available in the literature verifies the soundness of the TL formulation introduced. Although the numerical results are presented for lossless isotropic dielectrics, the method is applicable to photonic crystals made of lossy and/or anisotropic dielectrics.

Spice Equivalent Circuit of a Two-Parallel-Wires Shielded Cable for Evaluation of the RF Induced Voltages at the Terminations

A SPICE circuit model is developed for the evaluation in frequency and time domain, of the common and differential mode voltages at the terminals of a two-parallel-wires shielded cable during a current injection test. The proposed circuit is an exact equivalent of the model's governing multiconductor transmission line equations without the need of any subdivision in elementary cells and takes into account the presence of both transfer impedance and admittance.

Radiation analysis of PCB layout using a hybrid MoM-MTL method

A new hybrid method which combines the method of moments and the multiconductor transmission line equations is presented. Both methods are combined by an iterative algorithm which utilizes an integral description for the electric field strength. In order to choose the appropriate method for the several parts of a printed-circuit-board layout, it is necessary to divide the structure. Based on a capacitive coupling model, an error coefficient is described which enables the prediction of worst-case error of the current distribution. The comparison of measurements with results of the hybrid method exposes the applicability of the hybrid method.

Mirror-transformations of matrices and their application on odd/even modal decomposition of mirror-symmetric multiconductor transmission line equations

We employ mirror-transformations of matrices in this paper to represent the mirror reflection relations in the per-unit-length (PUL) matrices of multiconductor transmission lines (MTL) with mirror symmetry. From the theory of mirror-symmetric matrices, we propose a generalized odd/even modal decomposition scheme of mirror-symmetric MTL equations. We effectively divide PUL impedance matrix Z and admittance matrix Y into even- and odd-mode PUL matrices. Special cases and applications are discussed within the general theory. The rotational structure is studied specially from the view of mirror symmetry besides the view of rotational symmetry.

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.

Full-wave analysis of shielded cable configurations by the FDTD method

A numerical method is proposed to model transients in a shielded cable embedded in a three-dimensional field domain by using the finite-difference time-domain (FDTD) method. The coaxial shielded cable is assumed to be a multiconductor transmission line (MTL). The in cell voltage and the current on the external shield surface are calculated by a full-wave method, while the core current and the core-to-shield voltage are analyzed by assuming the validity of the quasi-TEM propagation mode inside the shield. The internal and external shield surfaces are coupled by the transfer admittance and by the transfer impedance of the cable shield. The solution is obtained by the FDTD method combining the MTL equations with the field equations. The proposed time-domain method takes into account the frequency-dependent parameters of the cable conductors by recursive convolution techniques. The validation of the procedure is performed in simple test configurations.

Lightning-induced effects on lossy MTL terminated on arbitrary loads: a wavelet approach

Lightning-induced electromagnetic effects propagating on multiconductor transmission-line (MTL) structures are a severe threat for many electronic devices. The solution of uniform MTL equations with frequency-dependent losses and nonlinear loads is proposed in the wavelet domain. Some remarkable features of the wavelets are presented and applied in order to speed up the solution time of the induced effects and to open possibilities to use them for signal integrity analysis. Validation of the obtained results with others given by well-established numerical techniques is also presented.

An efficient characterization of interconnected multiconductor-transmisslon-line networks

The numerical solution of the multiconductor-transmission-line (MTL) equations for lossy interconnected transmission lines (TLs) is investigated in this paper. The solution for the transmission line segments is accomplished through the finite-difference time-domain method, whereas the terminations and interconnection networks (which may contain nonlinearities) are characterized with an efficient state-variable representation. High-frequency skin-effect losses in the TLs are included in the MTL equations through convolution integrals in the MTL equations. The computation of these convolution integrals represents the bulk of the solution effort. Two methods, the singular-value-decomposition method and the matrix-pencil method, are shown to significantly reduce the computation time and improve the solution accuracy.