On the contribution of the electromagnetic field components infield-to-transmission line interaction

Based on the transmission line approximation, three different equivalent formulations have been proposed for evaluating the interaction between an external electromagnetic field and a transmission line, The difference among these “coupling” formulations, which are summarized for the case of a lossless line, lies essentially in the representation of the source terms as a function of the external electromagnetic field components. The authors show that the contribution of a given electromagnetic field component is different depending on the particular adopted formulation, To show that, the three formulations are employed to calculate the voltages induced on an overhead line by a nearby lightning strike, and the contribution to the induced voltage of the various electromagnetic field components explicitly appearing in each formulation is emphasized. The authors conclude that it is misleading to speak about the contribution of a given electromagnetic field component to the total induced voltages without first specifying the coupling formulation one is using     

Equivalent edge currents for arbitrary aspects of observation

Explicit expressions for equivalent edge currents are derived for an arbitrary local wedge angle and arbitrary directions of illumination and observation. Thereby the method of equivalent currents (MEC) is completed as a practically applicable theory of the electromagnetic high-frequency diffraction by edges. The derivation is based on an asymptotic relationship between the surface radiation integral of the physical theory of diffraction (PTD) and the line radiation integral of MEC, and the resulting expressions are deduced from the exact solutions of the canonical wedge problem.     

On the coupling of an external electromagnetic field to a printedcircuit board trace

Compact analytical solutions are developed for the terminal responses of a printed circuit board (PCB) trace exposed to an external electromagnetic field in the frequency and time domain. The analysis based on transmission line theory in a scattered voltage formulation uses a quasi-TEM propagation model for the trace and the exact distribution of the external electric field within the air/dielectric medium for the excitation terms. From the general solutions obtained for arbitrary wave incidence and terminal impedances, several much simpler approximations are derived revealing the principal behavior and indicating the relevant parameters to minimize the coupling. Practical examples with a comparison of the different results are presented     

外电磁场对近面有限长电缆的影响

采用传输线理论,提出有损耗地面的情况下外电磁场对近面有限长导线的感应电流和分布电压的公式.讨论不同的高度、地电导率、外场入射角等对近面有限长导线感应电流和分布电压幅度的影响.计算结果表明,近地面处一根暴露于外场环境中的几十米长电缆,其感应电流峰值一般可达上千安培.     

Comparison of the transmission line and scattering models forcomputing the HEMP response of overhead cables

The author discusses the use of transmission line and electromagnetic scattering models for computing the induced currents on long above-ground electrical cables, subjected to a transient plane wave excitation. The pertinent equations for determining the excitation electric field along the cable are summarized, along with the expressions which relate the line current to the excitation field. For the transmission line case, the cable current can be expressed in terms of per-unit-length impedance and admittance parameters which are functions of only the line geometry and the frequency. For the scattering case, similar line parameters can be inferred from the form of the solution for the current, but with the line parameters depending on the angles of incidence. Several numerical calculations of the line responses are provided, and these indicate that the transmission line analysis appears to provide response estimates which are smaller than those obtained using the more accurate scattering theory     

Circuit-Concept Approach to Externally Excited Transmission Lines

The coupling of external electromagnetic waves to transmission lines is developed using a circuit-analysis concept. The validity of forcing terms of line equations reported in the literature is confirmed by experimental results of a wire model that is installed above a ?perfectly? conducting ground plane and excited by plane waves of parallel and perpendicular polarizations. Equivalent-circuit representations are derived from solutions of the equations. These are versatile expressions for prediction of coupling of external waves to various types of lines. Coupling, externally excited transmission line, line equations, forcing terms.     

动车组内电磁场对线缆耦合及抑制措施分析

分析动车组在运行的时候产生的空间电磁干扰源,采用Agrawal传输线理论对场线耦合进行分析计算;分析干扰源参数变化对传输线终端负载电流的影响;通过计算数据分析线缆的抗干扰措施,为车辆布线电磁兼容性设计提供参考。     

Electromagnetic field coupling to a line of finite length: theoryand fast iterative solutions in frequency and time domains

A system of integral-differential equations for evaluating currents and voltages induced by external electromagnetic fields on a finite-length horizontal wire above a perfectly conducting ground is derived under the thin wire approximation. Based on perturbation theory, an iterative procedure is proposed to solve the derived coupling equations, where the zeroth iteration term is determined by using the transmission line (TL) approximation. The method can be applied both in the frequency and in the time domains. The proposed iterative procedure converges rapidly to the exact analytical solution for the case of an infinite line, and to the NEC solution for a line of finite length. Moreover, with only one iteration, an excellent approximation to the exact solution can be obtained. The method is applied to assess the validity of the TL approximation for plane wave coupling to an overhead line of finite length. It is shown that the resulting errors for the early-time response are generally higher than those corresponding to infinite lines     

Field coupling to nonuniform and uniform transmission lines

We study time-domain and frequency-domain responses of nonuniform and uniform transmission lines excited by incident electromagnetic waves. Externally excited uniform transmission lines permit closed-form solutions in terms of inverse chain matrix, whereas nonuniform lines cannot be analytically solved, in general. We adopt a method of equivalent cascaded network chain as the method of solving the latter situation. Useful and compact expressions for the load currents induced at terminal loads are derived. To confirm the validity of this method and the forcing terms, theoretical and experimental results of coupling calculations for a few typical (uniform/nonuniform) line geometries, relevant in the EMC field, are presented and discussed     

基于积分方程等效电路和BLT方程的传导耦合效应仿真分析

提出了基于积分方程等效电路和Baum-Liu-Tesche(BLT)方程的电磁脉冲传导耦合效应分析方法, 建立外部电磁干扰等效源模型, 提取等效电流和阻抗参数.对内部含复杂传输线网络和集成电路插件的电子设备建立了电磁拓扑模型, 采用BLT方程分析电磁脉冲响应.仿真分析了内部传输线连接关系、外部信号线长度和半径大小、节点负载等因素对传导耦合效应的影响.将计算结果和商用电磁仿真软件CST的结果进行了对比, 分析了所提方法的有效性, 可为电子设备电磁脉冲防护设计提供参考.     

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.      

Fast transient analysis of incident field coupling to multiconductor transmission lines

Due to the rapid surge in operating frequencies and complexity of modern electronic designs, accurate/fast electromagnetic compatibility/interference analysis is becoming mandatory. This paper presents a closed-form SPICE macromodel for fast transient analysis of lossy multiconductor transmission lines in the presence of incident electromagnetic fields. In the proposed algorithm, the equivalent sources due to incident field coupling have been formulated so as to take an advantage of the recently developed delay extraction based passive transmission line macromodels. Also, a method to incorporate frequency-dependent per-unit-length parameters is presented. The time-domain macromodel is in the form of ordinary differential equations and can be easily included in SPICE like simulators for transient analysis. The proposed algorithm while guaranteeing the stability of the simulation by employing passive transmission line macromodel, provides significant speed-up for the incident field coupling analysis of multiconductor transmission line networks, especially with large delay and low losses.     

Analyzing electromagnetic pulse coupling by combining TLT, MoM, andGTD/UTD

An important problem in electromagnetic compatibility (EMC) analysis is to determine the coupling of an electromagnetic field into a shielded cable. Using the transmission line theory (TLT), the disturbance voltage induced inside the cable is easily calculated from the current distribution on its shield. This current distribution depends on the incident electromagnetic field and is efficiently determined by the method of moments (MoM). Extending the MoM with the geometrical and uniform theory of diffraction (GTD/UTD) makes it possible to solve scattering problems that are too large and too complex for the plain MoM. The combination of the three approaches-TLT, MoM, and GTD/UTD-allows calculation of the disturbance voltage inside a shielded cable, which is part of a complex scattering structure. The fundamentals of each method and the way of putting them together are shown in this paper. The application of the proposed method is demonstrated by an example: the pulse coupling between a monopole antenna and a shielded cable is analyzed, taking into account a large conducting structure in the vicinity     

Circuit-Based Analysis of Electromagnetic Field Coupling With Nonuniform Transmission Lines

This paper presents a new algorithm for simulating electromagnetic (EM) field coupling with nonuniform multiconductor transmission lines in a circuit simulation environment. The proposed algorithm is based on the concept of passive model-order reduction, whereby an algorithmically developed passive reduced-order model, coupled with a set of equivalent sources representing the incident filed, are shown to accurately capture the behavior of the transmission line under EM excitation. The reduced-order model is developed independently from the particular shape of the incident field pulse, in the sense that, in constructing the model, one does not need prior knowledge about the waveform of the incident pulse of the EM field. In addition, it is also shown that the model developed can be used to simulate the transmission line in the absence of the EM field. The derived equivalent sources, representing the field coupling, are given directly in the time domain, thereby making simulation under nonlinear circuit terminations an easy task. Although the proposed work is aimed mainly at simulating nonuniform transmission lines, it can be applied to uniform lines as a special case. The proposed algorithm has been validated numerically with several examples.     

Excitation of Surface Waves and the Scattered Radiation Fields by Rough Surfaces of Arbitrary Slope

Surface waves as well as Iateral waves are excited when a rough surface is illuminated by the radiation fields. In view of shadowing, these terms of the complete field expansions contribute significantly to the total fields when the transmitter or receiver are near the rough surface. In this work explict expressions are derived for the coupling between the radiation fields and the surface waves which are guided at the irregular interface between two media. In the analysis, the slope of the rough surface is not restricted and the solutions for both the horizontally and vertically polarized waves are shown to satisfy reciprocity and duality relationships in electromagnetic theory. Special consideration is given to Brewster angles of incidence and scatter and stationary phase techniques. The fufl-wave solutions are also applied to random and periodic rough surfaces.     

Efficient Modeling of Transmission Lines With Electromagnetic Wave Coupling by Using the Finite Difference Quadrature Method

This paper proposes an efficient numerical technique, called the finite difference quadrature (FDQ) method, to model the transmission line with radiated electromagnetic (EM) wave noise coupling. A discrete modeling approach, the FDQ method adapts coarse grid points along the transmission line to compute the finite difference between adjacent grid points. A global approximation scheme is formulated in the form of a weighted sum of quantities beyond the local grid points. Unlike the Gaussian quadrature method that computes numerical integrals by using global approximation framework, the FDQ method uses a global quadrature method to construct the approximation schemes for the computation of, however, numerical finite differences. As a global approximation technique, the FDQ method has superior numerical dispersion to the finite difference (FD) method, and, therefore, needs much sparser grid points than the FD method to achieve comparable accuracy. Equivalent voltage and current sources are derived, exciting the transmission line at the grid points. Equivalent circuit models are consequently derived to represent the transmission line subject to radiated electromagnetic wave noise. The FDQ-based equivalent models can be integrated into a simulator like SPICE.     

A UTD type analysis of the plane wave scattering by a fullyilluminated perfectly conducting cone

A uniform high-frequency asymptotic solution, based on the physical optics (PO) approximation, is obtained in the format of the uniform geometrical theory of diffraction (UTD) to describe the fields diffracted by the tip of a semi-infinite, perfectly conducting cone when it is fully illuminated by an electromagnetic plane wave. The solution is expressed in terms of an integral, over finite limits which can be integrated numerically without difficulty. The results computed from the uniform asymptotic PO solution compare well with previously published results given for narrow-angle semi-infinite cones. In addition, they compare well with measurement and with an independent moment method (MM) solution for the scattering by a finite flat-backed cone in which several higher order wave interactions are found to be significant; one such interaction is between the tip and the base of the cone. Expressions are provided which are useful for calculating this tip-base interaction and confirm its relative importance. These expressions also provide tip diffraction effects which are important within the forward paraxial zone for the radiation by antennas on cones     

Transient response of coupled linear dipole antennas

Transient responses of coupled linear dipole antennas are measured for a basic understanding of coupling in the time domain. A very short pulse for excitation is used and it is shown that the measured data represent the quasi-impulse responses. For further investigation and comparison with the measured data, a simple formula of the impulse response of this configuration is derived by using the transmission line approximation. They suggest that the tips and feed points of each antenna have a significant role in the electromagnetic coupling.     

Linear two-wire transmission line coupling to an externalelectromagnetic field. I. Theory

The telegrapher's equations have been derived electrodynamically for the transmission line of two linear parallel conductors separated by a dielectric layer and excited by an electromagnetic field. The line coupling to a plane electromagnetic wave is illustrated for an arbitrary orientation of Poynting's vector and various polarization angles. The results are compared with the ones of other papers. The role of the magnetic field, while exciting the line, is clarified. The equations obtained in the paper are solved analytically in the case of the line excitation source being an electromagnetic pulse of arbitrary form