Computation of Crosstalk in a Multiconductor Transmission Line

Closed-form solutions for the terminal currents of a multiconductor transmission line are obtained. The results allow a numerically efficient computation of the crosstalk associated with an (n + 1)-conductor line when a large number of frequencies are of interest and bypass the usual requirement for the repeated solution of n simultaneous equations at each frequency. The results show the effect of parasitic circuits in the line on the coupling between any two circuits. It is also shown that the usual low-frequency notion of superimposing inductive and capacitive coupling which has been used for lines with only two circuits is valid, for an electrically short line and a sufficiently low frequency, for a multiconductor line containing any number of coupled circuits. Some additional qualitative details concerning the crosstalk are evident in this formulation.     

Prediction of Crosstalk in Ribbon Cables: Comparison of Model Predictions and Experimental Results

The prediction of crosstalk in ribbon cables is investigated. Experimental results are obtained for a 20-wire ribbon cable and compared to the predictions of the multiconductor transmission line (MTL) model. Based on the experimental configuration tested, it would appear that accurate predictions of crosstalk can be achieved in these controlled-characteristic cables. The prediction accuracies are typically within ±1 dB for frequencies such that the line is electrically short and ±6 dB for frequencies such that the line is electrically long. It was found that the parasitic wires in the cable can have a significant effect (as much as 40 dB) on the coupling between a generator circuit and a receptor circuit in the cable. Therefore, to achieve accurate predictions in ribbon cables, one must consider the interactions between all wires in the cable. The wire insulation evidently cannot be ignored for frequencies such that the line is electrically long. The impedance of the reference wire cannot be ignored for low frequencies where the common-impedance coupling dominates the electromagnetic-field coupling.     

Equivalent Transformations for Mixed-Lumped and Multiconductor Coupled Circuits

Distributed circuits consisting of a cascade connection of m -port stab circuits and multiconductor coupled transmission lines are equivalent to ones consisting of cascade connections of multiconductor coupled transmission lines whose characteristic impedances are different from original ones, m-port stub circuits, and an m-port ideal transformer bank. Because of the reciprocity of the circuit, values of transformer ratio must be identified. In the special case of a one conductor transmission line, these equivalent transformations are equivalent to Kuroda's identities. These extended equivalent transformations may be applied to mixed-lumped and multiconductor coupled circuits. By using these equivalent transformations, equivalent circuits and exact network functions of multiconductor nonuniform coupled transmission lines can be obtained.     

Calculation of the characteristics of two-wire lines in multiconductor cables

A rigorous method is proposed for calculating the parameters of two-wire lines (twisted pairs) surrounded by a single metal shield and the mutual coupling between these lines. It is shown that coupling between the lines in multiconductor cables results in electromagnetic interference (crosstalk) in communications channels and that inphase currents in the lines are caused by the asymmetry of excitation and loads. The stray voltages induced across the impedances placed at the beginning and the end of an adjacent line are determined at a given power in the main line. The effect produced by the loads placed between the wires and the shield is considered. The proposed method allows generalization of the obtained results to the case of lossy multiconductor cables.     

Estimation of Crosstalk in Three-Conductor Transmission Lines

A simple method for sketching the frequency response of crosstalk in three-conductor transmission lines is presented. The line is composed of three perfect conductors immersed in a lossless homogeneous medium. The method allows one to obtain a logarithmic asymptote plot (Bode plot) common to automatic control and electric circuit problems. In addition, it is shown that the maximum crosstalk may occur for frequencies where the line is electrically short. The magnitude of this maximum crosstalk can be estimated from the plot.     

Electromagnetic Field-to-Wire Coupling in the SHF Frequency Range And Beyond

Methods have been developed for the treatment of field-to-wire coupling at superhigh frequencies (SHF's) and beyond. In this region, transmission-line lengths and wire separations become very large electrically, and field-to-wire coupling problems become intractable. Several types of transmission lines have been examined in the SHF range, including uniform and nonuniform transmission lines, coaxial transmission lines, and multiconductor transmission lines. Current distributions are found to be predominantly of a standing-wave or traveling-wave form. The higher order modes are not significant for those cases examined. Bounds may be obtained for induced currents in the field-to-wire problem by considering the transmission line as a receiving antenna. The maximum value of induced current under conditions of maximum susceptibility is shown to vary little with frequency.     

Coupled mode analysis of forward and backward coupling in multiconductor transmission lines

The nonorthogonal coupled mode theory is extended to the analysis of multiconductor transmission lines by including backward coupling. Coupling coefficients are expressed as overlap integrals of the eigenfields and currents belonging to individual lines. These eigenmode solutions are calculated using the finite-difference time-domain method, which can provide a broadband solution through a single simulation. General termination conditions are given, and scattering parameters of a multiconductor transmission line can be obtained directly by solving the coupled mode equations subject to these termination conditions. As illustrative examples, several configurations of coupled microstrip lines are analyzed, and numerical results are presented. It is observed that both the forward and backward coupling results agree fairly well with results from Advanced Design System Momentum software.     

Literal solutions for time-domain crosstalk on losslesstransmission lines

The transmission line equations for a three-conductor lossless line in a homogeneous medium are solved in literal (symbolic) form in the time domain. The resulting formulas for the crosstalk voltages are exact and are given in terms of the line parameters and the termination impedances. These formulas demonstrate the effect of the various line parameters on the resulting crosstalk and show how to adjust the line parameters to achieve a desired time-domain crosstalk. In addition, other solution methods are discussed and used to verify the literal solution     

Closed-Form Expressions for the Total Power Radiated by an Electrically Long Multiconductor Line

Two analytical solutions based on transmission-line theory for the total power radiated by a multiconductor line above a ground plane are proposed. The line is not assumed to be electrically short or close to the ground plane, thus making the proposed model suitable for assessing the emission/immunity of actual transmission lines employed in industrial contexts such as in the automotive domain, railway lines, and power-distribution lines. The model allows an imperfect ground plane to be considered through the complex-image approximation together with propagation losses. Numerical and experimental results are provided as a validation, while an empirical rule to assess the accuracy of the results is proposed. The two expressions aim at allowing fast parametric analysis of radiation during the design phase of the electrical and geometrical configuration of an unshielded multiconductor transmission line.      

Time-domain response of multiconductor transmission lines

Evaluation of the time-domain response of multiconductor transmission lines is of great importance in the analysis of the crosstalk in fast digital circuit interconnections, as well as in the analysis of power lines. Several techniques for the computation of the line response, starting from the known circuit-theory parameters, are presented and evaluated. These methods are: time-stepping solution of the telegrapher equations, modal analysis in the time domain, model analysis in the frequency domain, and a convolution technique which uses line Green's functions. The last method can treat the most general case of lossy transmission lines with nonlinear terminal networks. Numerical and experimental results are presented to illustrate these techniques and to give insight into the crosstalk problems in fast digital circuits.     

Simulation and modeling-simulating crosstalk and field to wirecoupling with a SPICE simulator

The simulation of two electromagnetic compatibility (EMC) problems, namely crosstalk and field-to-wire coupling, using SPICE are described. These modeling techniques for simulation of EMC of multiconductor transmission lines allow calculation in the time domain, as well as the frequency domain. Nonlinearities, protective devices, and even complex circuitry can be included at both ends of the transmission line. Disturbing voltages can also be studied at any node in a susceptor network. The techniques also offer the possibility of including arbitrary sources of radiated disturbances, which could allow the simulation of aperture coupling in an enclosure     

Propagation Modes, Equivalent Circuits, and Characteristic Terminations for Multiconductor Transmission Lines with Inhomogeneous Dielectrics

The theory of wave propagation on Iossless multiconductor transmission lines with inhomogeneous dielectrics is developed using matrix analysis. The treatment is concise and complete and has the advantage of identifying propagation modes in a way that permits straightforward physical interpretation. The equivalent circuit for the general line is derived and its application to the solution of wave problems with reflections is demonstrated. Special consideration is given to the problem of characteristically terminating a multiconductor line, i.e., terminating without reflections. The realizability of such a characteristic termination network is discussed, and proofs of realizability are given for the important cases of all lines with homogeneous dielectrics and all three-conductor lines, regardless of dielectric inhomogeneities. Symmetric three-conductor lines are discussed to exemplify the general theory, and an application to the problem of mode conversion on symmetric and asymmetric shielded strip lines is given.     

Generalized Theory of Impedance Loaded Multiconductor Transmission Lines in an Incident Field

A general theory is advanced for determining the currents in the load impedances of an N-conductor isolated transmission line excited by an electromagnetic field with the electric vector directed parallel to the wires. The number of impedance loads in the circuit is 2N. An impedance is connected in series with each conductor at its ends. At each end of the transmission line the impedances emanate from a common node. There is no requirement that the conductors be of the same radius, be equally spaced, or lie in a common plane; however, their axes must be parallel. Evidently the cross section of the line must be sufficiently small in terms of the wavelength that transmission line theory applies. Numerical values for the load currents In a three-conductor model are given. Scattering from end loaded multiconductor transmission lines is considered. It is shown that for configurations lacking geometrical symmetry such problems become arduous if not solved by computer.     

Binder MIMO Channels

This paper introduces a multiple-input multiple-output channel model for the characterization of a binder of telephone lines. This model is based on multiconductor transmission line theory, and uses parameters that can be obtained from electromagnetic theory or measured data. The model generates frequency-dependent channel/binder transfer function matrices as a function of cable type, geometric line-spacing and twist-length parameters, and source--load configurations. The model allows the extraction of the magnitude and the phase of individual near end crosstalk, far end crosstalk, split-pair, and phantom transfer functions from the transfer function matrix of the binder. These individual crosstalk transfer functions are often found to be very sensitive to small imperfections in the binder. Examples of category 3 twisted pair American telephone lines and ldquoquadrdquo telephone cables are also presented.     

Transmission Modes in a Braided Coaxial Cable and Coupling to a Tunnel Environment

Radio frequency transmission in a semicircular tunnel containing a braided coaxial cable is considered. The general formulation accounts for both the ohmic losses in the tunnel wall and a thin lossy film layer on the outer surface of the dielectric jacket of the cable. Using a quasi-static approximation, it is found that the propagation constants of the low-frequency transmission line modes are obtained through the solution of a cubic equation. However, for the special case when the conductivity thickness product of the Iossy film layer vanishes, this cubic equation reduces to a quadratic. The spatially dispersive form of the braid transfer impedance is also accounted for. It is shown that the quasistatic theory is well justified for frequencies as high as 100 MHz for typical tunnel geometries. Finally, special characteristic impedances are derived for the various modes of the equivalent multiconductor transmission line.     

Natural frequencies of piecewise uniform transmission lines

A transmission line composed of a number of cascaded uniform lines with different characteristic impedances and lengths is considered. Approximate expressions for the chain parameters and natural frequencies useful to a variational synthesis are given.     

Experimental Characterization of Multiconductor Transmission Lines in the Frequency Domain

Although a number of papers have been published on the experimental characterization of multiconductor transmission lines, they are limited to the time domain for lossless multiconductor lines in homogeneous media. This paper presents a method for the characterization of multiconductor transmission lines in inhomogeneous media. The experimental technique for the measurement of multiconductor line parameters is presented and the appropriate multiconductor line equations are solved to obtain these parameters. The experimental method involves only the short-and open-circuit impedance measurements for different configurations. The experimental results for a four-conductor line are found to be in good agreement with computed results and a low-frequency lumped model.     

非均匀传输线间的串扰研究

应用时域有限差分法对非均匀传输线间的串扰耦合进行分析。基于细线散射的时域有限差分法分析非均匀结构时,采用阶梯式均匀传输线模型,对非均匀传输线进行分段逼近。针对不等长、线径变化、非平行线和交叉线4种情况分析其参数变化对串扰的影响。研究表明：不等长电缆超出部分长度对串扰耦合幅度影响较小,对谐振频率影响较大;电缆线径的变化对其串扰耦合影响较小;非平行线和交叉线的角度对电缆间串扰的影响较大。     

Riccati matrix differential equation formulation for the analysisof nonuniform multiple coupled microstrip lines

A Riccati matrix differential equation (RMDE) is formulated for analyzing nonuniform coupled microstrip lines (NCML's) in the frequency domain. The formulation is based on a reciprocity-related definition in the theory of multiconductor transmission lines under quasi-TEM assumption. The hybrid-mode nature of modal phase velocities and strip characteristic impedances for multiconductor microstrip structure is included. The nonlinear RMDE is first transformed into a first-order linear differential matrix equation which can be efficiently solved using method of moments. A convergence study is performed to investigate the sufficient number of basis functions used in the method. The voltage-scattering parameters of a tapered microstrip and two three-line structures are presented. The frequency responses of a pair of nonuniform coupled lines are measured and compared with calculated results