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A Generalized Multiple-Scattering Method for Modeling a Cable Harness With Ground Connections to a Nearby Metal Surface
Abstract
This paper proposes a generalized multiple-scattering (GMS) method to evaluate the current distribution on a cable harness with ground connections to a nearby metal surface. The GMS method is a hybrid method combining the transmission line theory and the method of moments. The GMS method uses the generalized multiconductor transmission line (GMTL) solver for the cable harness part and the mixed-potential integral equation (MPIE) solver for the rest of the structure including the metal surface and the grounding wires. Neither the GMTL nor the MPIE solver alone takes into account the mutual interactions between the cable harness and the rest of the structure. Therefore, an iterative scheme is arranged in the GMS method to compensate the above-mentioned interactions. These interactions occur via not only field couplings, but also current conducting through the grounding points on the cable harness. A numerical test case is provided to benchmark the proposed GMS method.
... With the increasing frequency and integration of current power equipment, the problem of crosstalk between transmission lines cannot be ignored [1], [2]. Crosstalk is an unintentional coupling phenomenon, which means that the electromagnetic field generated by the voltage and current on the excitation line will affect the adjacent transmission lines and generate induced signals at their endpoints [3]. ...
... In [8], a new non-uniform TWP modeling method is proposed to simulate the change of the center position of the TWP. G. Spadacini et al. proposed a prediction model of low-frequency nonuniform TWP crosstalk under plane wave excitation [1][2]. The equivalent cable bundle method (ECBM) is used with some modifications to predict crosstalk within a bundle of TWP [11]. ...
In this paper, a new algorithm for predicting per unit length (p.u.l) parasitic parameters of transmission line is proposed. In the twisted-wire pair (TWP), different rotation degrees correspond to different parasitic parameters, which brings difficulties to the solution of telegraph equation. At present, the mainstream method is to divide TWP and use the cascade theory to solve each segment as a parallel transmission line. Therefore, we propose to use the beetle swarm optimization (BSO) algorithm to optimize the weights of the back propagation neural network, use a certain sample to train the network. This algorithm is used to predict the p.u.l parameters of uniform and non-uniform TWP, and the finite-difference time-domain (FDTD) method is used to solve telegraph equation. Among them, the crosstalk value of the uniform TWP is compared with the simulation value in the CST to verify the effectiveness of the proposed algorithm; the non-uniform TWP performs 500 random generation calculations to give the maximum envelope value of the crosstalk.
... Note that the values of the power loss crosstalk (PL NEXT , PL FEXT ) in decibels can be calculated as follows [15][16][17][18] (19) where H NEXT and H FEXT are the transfer function. The PL expression can be written as follows: ...
Introduction. In this paper, the equivalent cable harness method is generalized for predicting the electromagnetic emissions problems of twisted-wire pairs. The novelty of the proposed work consists in modeling of a multiconductor cable, in a simplified cable harness composed of a reduced number of equivalent conductors, each one is representing the behavior of one group of conductors of the initial cable. Purpose. This work is focused on the development and implementation of simplified simulations to study electromagnetic couplings on multiconductor cable. Methods. This method requires a four step procedure which is summarized as follows. Two different cases, of one end grounded and two ends grounded configurations can be analyzed. Results. The results had shown that the model complexity and computation time are significantly reduced, without, however, reducing the accuracy of the calculations.
... The different wires are randomly gathered and fixed together by hand bundling. As the operating frequency increases and the types of cable bundles increase, the effects of crosstalk between these cable bundles cannot be ignored [1], [2]. ...
Accurate analytical solution for the crosstalk of random cable bundle is difficult to obtain, but the limit of the crosstalk can be predicted. This paper proposes a method to predict the crosstalk of random cable bundle. Based on the idea of cascade method, the model takes into account the random rotation of the cross-section and the random transposition of the core. A neural network algorithm based on back propagation optimized by the beetle antennae search method (BAS-BPNN) is introduced to mathematically describe the random rotation of the cross-section. The elementary row-to-column transformation of the unit length RLCG parameter matrix is used to deal with the random transposition of the core. The discontinuity between segments generated by transposition is solved by introducing transition probability parameters. Finally, combined with the finite-difference time-domain (FDTD) algorithm, the crosstalk of the random cable bundle is obtained. The numerical experimental results show that the new method can reduce a lot of experimental work in the crosstalk problem of random cable bundle, and has higher accuracy and a wider frequency range.
In this article, deep neural network (DNN) and chain parameter methods are used to analyze the crosstalk coupling of a star‐quad and a twisted bundle of twisted wire pairs (TBTWP) cables for different excitations, respectively. A DNN is used to extract the per‐unit‐length (p.u.l) resistance, inductance, capacitance, and conductance (RLCG) parameters at any position for the star‐quad and TBTWP cables. The induced common mode (CM) and differential mode (DM) currents due to crosstalk are calculated by combining the obtained RLCG parameters with the chain parameter method. The obtained results show good agreement with that of FEKO software. Moreover, it is found that the star‐quad cable can reduce the external coupling more effectively than that of the TBTWP cable. Finally, measurements are performed to further validate the accuracy of our proposed algorithm.
This paper presents a general formulation of the generalized multiconductor transmission line (GMTL) method to model a parallel cable harness including straight and bent wires. The parallel cable harness here indicates the uniform cross-sectional wire distribution. The GMTL equations are solved recursively based on the perturbation theory. This GMTL method facilitates an accurate evaluation of the current distributed on a cable harness. On top of that, the current obtained in a radiation problem is decomposed into two traveling currents, i.e., the positive-going and the negative-going currents, based on the least-squares method. With the decomposed currents, the steepest descent method is further adopted to achieve a fast approximation of the total radiated power. Finally, the capability and the limitations of the GMTL method in terms of the electrical wire separation and length are investigated. The necessity of the recursive corrections is also studied.
Interactions between a cable harness containing multiple wires and the nearby metal surface can be evaluated by full-wave methods. Though these methods can calculate the interactions with great accuracy, they have long simulation times and large memory requirements when dealing with complex wire structures. The multiple scattering (MS) approach by treating the cable harness and the surface separately using different algorithms has been proven to be superior to the full-wave methods when evaluating these interactions. However, the cable harness solver in the previous MS approach is restricted to two-wire structures since the per-unit-length (pul) inductance (L) and capacitance (C) are derived based on the antenna and differential modes assumption between two wires. In this paper, a generalized multiconductor transmission-line (GMTL) approach is proposed to overcome the two-wire limitation. In the GMTL approach, all wires take the infinity as the reference. The extraction of the pul L and C for the cable harness is not limited by the number of wires. Thus, the GMTL approach can conveniently model multiple wire structures. The application of the GMTL approach to the multiple wires enables the MS approach to accurately evaluate the interactions between the cable harness and the metal surface.
Due to the static magnetic field, the conductivity for graphene becomes a
dispersive and anisotropic tensor, which complicates most modeling
methodologies. In this paper, a novel equivalent circuit model is proposed for
graphene with the magnetostatic bias based on the electric field integral
equation (EFIE). To characterize the anisotropic property of the biased
graphene, the resistive part of the unit circuit is replaced by a resistor in
series with current control voltage sources (CCVSs). The CCVSs account for the
off-diagonal parts of the surface conductivity tensor for the magnetized
graphene. Furthermore, the definitions of the absorption cross section and the
scattering cross section are revisited to make them feasible for derived
circuit analysis. This proposed method is benchmarked with several numerical
examples. This paper also provides a new equivalent circuit model to deal with
dispersive and anisotropic materials.
Power radiation and radiated coupling among different structures represent an important area for research study. The partial element equivalent circuit method (PEEC) is a powerful technique which bridges the gap between the electromagnetic and circuit theories. In this paper, we develop a new approach for PEEC to calculate the distributive power radiation and couplings. With this approach, formulations for both the radiated power and the transferred power can be evaluated. Further, the physical meanings of the power results are interpreted according to the conservation of energy law. We use electric dipoles, magnetic dipoles and patch antennas as well as coupled microstrip lines to benchmark the method. The approach can also be applied to EMC/EMI and other power dissipation computations. Index Terms—Energy conservation, partial element equivalent circuit method (PEEC), radiated power, transferred power.
This work presents a thorough derivation of the full-wave transmission-line equations on the basis of Maxwell’s theory. The
multiconductor system is assumed to be composed of nonuniform thin wires. It is shown that the mixed potential integral equations
are equivalent to generalized telegrapher equations. Novel, exact, and compact expressions for the multiconductor transmission-line
parameters are derived, and their connection to radiation effects is shown. Iteration and perturbation procedures are proposed
for the solution of the generalized transmission-line equations.
KeywordsElectromagnetic compatibility-Nonuniform transmission lines-Generalized telegrapher equations-Product integral-Radiation-Complex transmission line parameters
The DC power-bus is a critical aspect in high-speed digital
circuit designs. A circuit extraction approach based on a
mixed-potential integral equation is presented herein to model arbitrary
multilayer power-bus structures with vertical discontinuities that
include decoupling capacitor interconnects. Green's functions in a
stratified medium are used and the problem is formulated using a
mixed-potential integral equation approach. The final matrix equation is
not solved, rather, an equivalent circuit model is extracted from the
first-principles formulation. Agreement between modeling and
measurements is good, and the utility of the approach is demonstrated
for DC power-bus design
In this paper, we derive an integral equation describing the antenna-mode currents along a two-wire transmission line (TL). We show that when the cross-sectional dimensions of the line are electrically small, the integral equation reduces to a pair of TL-like equations with equivalent line parameters (inductance and capacitance). The derived equations make it possible to compute the antenna-mode currents using any traditional TL coupling code with appropriate parameters. The derived equations are tested against numerical results obtained using numerical electromagnetics code (NEC), and reasonably good agreement is found
In this paper, the telegrapher equations are extended to general modes and very high frequencies to include radiation effects. It is shown, that the new line parameters are gauge dependent. However, there is also a gauge-independent representation of these parameters. In this representation, the per-unit-length capacitance is not correlated with the radiation resistance, only the per-unit-length inductance (strictly speaking, the imaginary part of it) constitutes it. The generalization to multiconductor and to finite straight transmission lines is straightforward.
A modal approach for parallel plate impedance and equivalent inductance extraction for power integrity analysis including ball grid arrays (BGAs) between two parallel plates is presented. Since the BGAs are placed close to each other, the current flowing through each ball is not uniformly distributed due to the proximity effect. In this paper, a modal-based cavity method is proposed to count for this proximity effect. Analytical solutions for both the parallel plate impedance and the equivalent inductances associated with the BGAs are derived from the modal-based cavity method. The proposed method is validated by finite element method simulations and the application of the proposed method for power distribution network design is demonstrated.
The ball grid array (BGA) structure is the interconnection between package to printed circuit board and the discontinuity from BGA affects the performance for the whole link path in the high-speed digital system. So, it is important to accurately model the BGA structures. In current methods, the current distribution of conductors is treated as isotropic. However, the pitch size of solder balls is comparable to the diameter. The current is no longer uniformly distributed. In this paper, a fast modal-based approach is developed to accurately and efficiently capture the proximity effect. Image theory is also applied in the proposed approach to reduce the computational domain from 3-D structure to 2-D. The matrix reduction approach is applied to obtain the physical loop inductance. The lumped capacitance is obtained in . A $\pi $ topology equivalent circuit model for the BGA structure is built. Good agreement between the equivalent circuit model and full-wave simulation can be achieved up to 40 GHz.
The China high-speed trains use cable trays to neatly arrange the cables running through the distributed systems. On one hand, they protect cables against external electromagnetic interference and reduce external radiation from the cables. On the other hand, the cable trays create waveguide structures that affect the coupling among cables inside the cable trays. To simplify coupling analysis for cables going through a cable tray, a lumped circuit model was built using admittance blocks extracted from a mixed-potential integral equation (MPIE) formulation. In the MPIE formulation, either the half-free space or the waveguide dyadic Green's function was used depending on the region where the cables were. A test case was investigated. Results by the proposed circuit model were validated by measurement and full-wave simulation results.
In this paper, a multiconductor modified enhanced transmission line theory is presented. The constitutive equations of this theory are directly derived from Maxwell's equations without the restriction to the transverse electromagnetic mode, while conserving the mathematical formalism of the classical transmission line theory (TLT). However, the per-unit-length (p.u.l.) parameters become complex and frequency dependent but still have an RLCG form. Besides, these new parameters are expressed as a combination of the classical ones and a high-frequency correction. These equations can be easily solved by the existing classical TLT solvers. The results obtained by this theory are in a much better agreement than the classical TLT with those predicted by a full-wave solver or measurements.
Interactions between cable harness and vehicle body can be calculated using the full-wave method-of-moments (MoM) formulation. Although the full-wave MoM formulation can help us to calculate these interactions with great accuracy, it can be fairly time consuming when dealing with complex wire structures. On the other hand, the conventional multiconductor transmission-line theory can be used to obtain a simple model of the interactions, but only the effect of the transmission-line (TL)-mode current can be accounted for in this method. Starting with the complete electrical field integral equations, the current on a two-conductor thin wire structure due to incident field illumination can be decomposed into TL and antenna modes. Both modes can be solved using a SPICE solver in the form of Telegrapher's equations. A proposed multiple scattering (MS) method based on a hybrid of TL and surface MoM can then be used to calculate interactions between thin wire structures, such as cable harness, and conductive surfaces, such as vehicle body. A test case shows that wire current computation using the proposed MS method takes less time but reaches the same accuracy compared to the full-wave MoM.
The main goal of this paper is the analytic approximation of the singularity expansion method poles of a long finite wire with vertical risers above a perfectly conducting ground. For wavelengths in the same order of magnitude or smaller than the height of the wire above the ground, the classical transmission-line theory is not valid. Therefore, an asymptotic approach is used to approximate the current on the thin wire, which is expressed in terms of current reflection and scattering coefficients. The perturbation theory is used for their analytic calculation. The complex current is analytically approximated and compared to a numerical simulation for illustration purposes. A very good agreement between the analytic approximations and the numerical ones from literature and simulations is observed.
The electromagnetic (EM) characterization of graphene under general EM environments is becoming of interest in the engineering and scientific research fields. However, its numerical modeling process is extremely cost prohibitive due to the huge contrast between its thickness and other dimensions. In this work, for the first time, the EM features of graphene are characterized by a circuit model through the partial element equivalent circuit (PEEC) method. The atomically thick graphene is equivalently replaced by an impedance boundary condition. After incorporating the PEEC method, a novel surface conductivity circuit model is derived for graphene. A physical resistor and inductor are added into the conventional PEEC cell due to the dispersive conductivity property of graphene. The proposed novel method significantly reduces the memory and CPU time consumption for general graphene structures when compared with standard numerical finite element method (FEM) or finite difference (FD) methods, where 3-D meshing is unavoidable. This model also transforms the surface conductivity of graphene into a vivid circuit, and physical properties of the material can be conveniently obtained, such as radiation, scattering, and resistance properties, when compared with method of moments (MOM). In addition, the radiation and scattering calculation by MOM entail the cumbersome steps of defining a bounding surface and implementing a multidimensional integrand, while in PEEC, these complications are entirely bypassed by the concise vector-matrix-vector product (VMVP) formulas. To validate the introduced algorithm, various numerical examples are presented and compared with existing references.
This paper presents a theory and an efficient solution approach for the problem of electromagnetic field coupling to a long multiconductor line with arbitrary terminations. The theory is applicable for a high-frequency plane wave electromagnetic field excitation, when the transmission line approximation conditions are no longer satisfied.
Effective computational techniques for Multi-Transmission Line (MTL) based on Lumped Circuit Transmission Line (LCTL) method are suggested and applied for EMC analysis of complex cable harness. Accuracy of developed algorithms is validated by comparisons with measurements.
Interaction between cable harness structures and antennas is simulated by means of combination of two methods: multi-transmission line (MTL) based Lumped Circuit Transmission Line (LCTL) method and Method of Moments (MoM). Simulation is validated by comparison with measurements. Proposed methodology can be applied to prediction of electromagnetic compatibility (EMC) characteristics of complex antenna-harness systems.
A hybrid approach is presented that combines the method of transmission lines (MTL) with the method of moments (MoM) to solve electromagnetic radiation problems on structures consisting of wires with complex terminations and three-dimensional conducting bodies. This approach is based on calculating the currents on wires using MTL and converting them to external sources for the remaining geometry to be handled by MoM. Validation of the MTL/MoM approach is done, its application to different wire, circuit and body configurations, including wire bunches, is illustrated, and its advantage over direct MoM calculations is shown.
The paper presents a generalized transmission line model able to describe the high-frequency mixed-mode propagation along electrical interconnects. The model is derived from a full-wave formulation and extends the validity of the standard transmission line (TL) model to frequency ranges where the propagation is no longer of transmission electron microscopy (TEM)-type. This generalized TL model describes the high-frequency differential and common mode propagation and the mode conversion. Within its validity limits, the proposed model provides solutions in good agreement with those obtained through full-wave models. Case studies are carried out to evaluate the high-frequency mode conversion in asymmetric interconnects.
An enhanced transmission line model (ETL) has been recently proposed to describe the propagation along two parallel wires with circular cross sections up to wavelengths comparable to the distance between the wires. In this paper, a general ETL model is proposed to describe the propagation along interconnects consisting of wires with arbitrary cross sections. Since the ETL model has the same simplicity of the standard transmission line model, it allows investigating high-frequency effects, like radiation and dispersion, with a computational cost which is sensibly lower than that required by a full-wave numerical simulation. The ETL model is obtained, with suitable approximations, starting from a full-wave analysis of the propagation problem and using an integral formulation based on the electromagnetic potentials satisfying the Lorentz gauge. Some case studies are carried out and discussed, including a benchmark test with existing literature, performed to check the validity and accuracy of the proposed model.
A fast and comprehensive time-domain method for analyzing electromagnetic compatibility (EMC) and electromagnetic interference (EMI) phenomena on complex structures that involve electrically large platforms (e.g., vehicle shells) along with cable-interconnected antennas, shielding enclosures, and printed circuit boards is proposed. To efficiently simulate field interactions with such structures, three different solvers are hybridized: (1) a time-domain integral-equation (TDIE)-based field solver that computes fields on the exterior structure comprising platforms, antennas, enclosures, boards, and cable shields (external fields); (2) a modified nodal-analysis (MNA)-based circuit solver that computes currents and voltages on lumped circuits approximating cable connectors/loads; and (3) a TDIE-based transmission line solver that computes transmission line voltages and currents at cable terminations (guided fields). These three solvers are rigorously interfaced at the cable connectors/loads and along the cable shields; the resulting coupled system of equations is solved simultaneously at each time step. Computation of the external and guided fields, which constitutes the computational bottleneck of this approach, is accelerated using fast Fourier transform-based algorithms. Further acceleration is achieved by parallelizing the computation of external fields. The resulting hybrid solver permits the analysis of electrically large and geometrically intricate structures loaded with coaxial cables. The accuracy, efficiency, and versatility of the proposed solver are demonstrated by analyzing several EMC/EMI problems including interference between a log-periodic monopole array trailing an aircraft's wing and a monopole antenna mounted on its fuselage, coupling into coaxial cables connecting shielded printed circuit boards located inside a cockpit, and coupling into coaxial cables from a cell phone antenna located inside a fuselage.
The feature selective validation (FSV) method has been proposed as a technique to allow the objective, quantified, comparison of data for inter alia validation of computational electromagnetics. In the companion paper "Feature selective validation for validation of computational electromagnetics. Part I-The FSV method," the method was outlined in some detail. This paper addresses two specific issues related to the implementation of the FSV method, namely "how well does it produce results that agree with visual assessment?" and "what benefit can it provide in a practical validation environment?" The first of these questions is addressed by comparing the FSV output to the results of an extensive survey of EMC engineers from several countries. The second is approached via a case study analysis
A goal for the validation of computational electromagnetics (CEM) is to provide the community with a simple computational method that can be used to predict the assessment of electromagnetic compatibility (EMC) data as it would be undertaken by individuals or teams of engineers. The benefits of being able to do this include quantifying the comparison of data that has hitherto only been assessed qualitatively, to provide the ability to track differences between model iterations, and to provide a means of capturing the variability and range of opinions of groups and teams of workers. The feature selective validation (FSV) technique shows great promise for achieving this goal. This paper presents a detailed analysis of the FSV method, setting it firmly in the context of previous comparison techniques; it suggests the relationship between validation of graphically presented data and the psychology of visual perception. A set of applicability tests to judge the effectiveness of computer-based CEM validation techniques is also proposed. This paper is followed by a detailed comparison with visual assessment, which is presented in Part II
A generalized method of moments (MoM)-SPICE iterative technique for field coupling analysis of multiconductor transmission lines (MTLs) in the vicinity of complex structures is presented. Telegrapher's coupling equations are modified with additional distributed voltage and current sources for more accurate analysis of the total current induced onto transmission line bundles in the presence of complex structures. These additional voltage and current sources are introduced to enforce the electric field boundary condition and continuity equation on MTLs beyond the quasi-static regime. The surrounding structure is modeled via the MoM and a SPICE-like simulator is used to simulate equivalent circuit model of the MTLs extracted via the partial element equivalent circuit method. The proposed technique is based on perturbation theory with the quasi-static current distributions on the transmission lines still assumed to be dominant. Validation examples for single and MTLs are given in the presence of complex structures.
The "standard" transmission line model describes accurately the propagation of electric signals along conducting wires, if the distance between them is much smaller than both their length and the smallest characteristic wavelength of the signals. This paper presents an "enhanced" transmission line model that is able to describe the propagation along perfectly conducting wires in a homogeneous dielectric, and also when the distance between the wires is comparable with the smallest characteristic wavelength of the signals. The enhanced model is obtained, with suitable approximations, starting from a full-wave analysis of the problem and using an integral formulation based on the electromagnetic potentials satisfying the Lorentz gauge. It differs from the standard transmission line model, only in its constitutive relations, that is, in the relation between the per unit length (p.u.l.) magnetic flux and the current intensity, and in the relation between the electric voltage and the p.u.l. electric charge. In the standard model, these relations are of the algebraic type, and in the enhanced one they are of the convolution type, expressing nothing more than a very simple physical fact: the values of the p.u.l. flux and voltage at the generic abscissa along the wires depend on the entire distribution of the current and the p.u.l. charge, respectively. The kernels of the convolution integrals have the logarithmic singularity typical of the surface distributions and takes into account proximity effects. The solution of the enhanced model highlights the high-frequency effects due to dispersion and radiation that the standard model is unable to provide. Good agreement with the solutions obtained by a full-wave electromagnetic numerical code is achieved.
Via interconnects in multilayer substrates, such as chip scale packaging, ball grid arrays, multichip modules, and printed circuit boards (PCB) can critically impact system performance. Lumped-circuit models for vias are usually established from their geometries to better understand the physics. This paper presents a procedure to extract these element values from a partial element equivalent circuit type method, denoted by CEMPIE. With a known physics-based circuit prototype, this approach calculates the element values from an extensive circuit net extracted by the CEMPIE method. Via inductances in a PCB power bus, including mutual inductances if multiple vias are present, are extracted in a systematic manner using this approach. A closed-form expression for via self inductance is further derived as a function of power plane dimensions, via diameter, power/ground layer separation, and via location. The expression can be used in practical designs for evaluating via inductance without the necessity of full-wave modeling, and, predicting power-bus impedance as well as effective frequency range of decoupling capacitors.
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.
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
Common mode current estimation for cable bundle inside a vehicle
- D Liu
Modal based BGA modeling in high-speed package
- S Jin