Multiconductor Transmission Line Networks Research Articles

Detection and Localization of Interference and Useful Signal Extreme Points in Closely Coupled Multiconductor Transmission Line Networks

This study highlights the importance of detecting and localizing useful and interference signal extreme points in multiconductor transmission lines (MCTL) by developing a new approach for detecting and localizing signal extreme points in MCTL networks of arbitrary complexity. A radio-electronic component is presented as a network consisting of a number of connected MCTL sections. Each MCTL section is divided into segments and the number of segments is set by the user. The approach is based on a quasi-static calculation of signal waveforms at any point (segment) along each conductor of an MCTL. The block diagrams of the developed algorithms are presented. Using the approach, a number of investigations have been done which include the following: the signal maximum detection and localization in the meander lines with one and two turns, the influence of ultrashort pulse duration on localization of its extreme points in the printed circuit board (PCB) bus of a spacecraft autonomous navigation system, the influence of ultrashort pulse duration on localization of crosstalk extreme points in the PCB bus, and the simulation of electrostatic discharge effects on the PCB bus. There are also some investigations with optimization methods presented. A genetic algorithm (GA) was used to optimize the influence of ultrashort pulse duration on localization of the pulse and crosstalk extreme points in the PCB bus. Furthermore, the GA was used to optimize the PCB bus loads by criteria of the peak voltage minimization. A similar investigation was carried out with the evolution strategy. The obtained results help us to argue that the signal extreme points can be detected both in structures with different configurations and applying different excitations.

Reduced Dimensional Chebyshev-Polynomial Chaos Approach for Fast Mixed Epistemic-Aleatory Uncertainty Quantification of Transmission Line Networks

This paper presents a hybrid Chebyshev-polynomial chaos (CPC) metamodel for the uncertainty quantification of multiconductor transmission line networks. The key feature of this metamodel is its capacity to account for two different types of uncertainty simultaneously present in a network—uncertainty arising from imprecise knowledge regarding the network parameters (epistemic uncertainty) and uncertainty arising from the random variability in the network parameters (aleatory uncertainty). Unfortunately, when investigating such mixed epistemic-aleatory problems, the CPU costs to construct the hybrid CPC metamodel becomes exorbitantly large. To address this issue, a new sensitivity sweeping-based dimension reduction algorithm especially tailored for mixed epistemic-aleatory problems has been developed in this paper. Numerical techniques based on iterative model enrichment and priority-based sampling have also been developed to further enhance the efficiency of the algorithm.

On the Design of Aircraft Electrical Structure Networks

As part of the technology research engaged in the EU Clean Sky 1 project, we present in this paper an electrical structure network (ESN) designed to prevent the impact on an electronic equipment of unwanted voltage drops appearing when nonmetal composite materials are used for grounding. An iterative process has been followed to reach an optimal tradeoff solution meeting all the aircraft requirements: structural, safety, low weight, electrical, etc. Guidelines on the design of a low-impedance metal ESN, to minimize the inductive behavior of the power distribution network, are outlined in this paper. To this end, we employ the UGRFDTD simulation tool, combining finite-difference time domain to analyze the general EM problem, and a multiconductor transmission-line network to handle internal coupling between cables running along coinciding routes. The capability of this tool to create time-domain snapshots of surface currents is shown to provide a useful way to optimize the ESN, thanks to the insight gained on the physics of the problem.

Comparison of High Frequency Detailed Generator Models for Partial Discharge Localization

This paper presents partial discharge localization in stator winding of generators using multi-conductor transmission line (MTL) and RLC ladder network models. The high-voltage (HV) winding of a 6kV/250kW generator has been modeled by MATLAB software. The simulation results of the MTL and the RLC ladder network models have been evaluated with the measurements results in the frequency domain by applying of the Pearson’s correlation coefficients. Two PD generated calibrator signals in kHz and MHz frequency range were injected into different points of generator winding and the signals simulated/measured at the both ends of the winding. For partial discharge localization in stator winding of generators is necessary to calculate the frequency spectrum of the PD current signals and then estimate the poles of the system from the calculated frequency spectrum. Finally, the location of PD can be estimated. This theory applied for the above generator and the simulation/measured results show the good correlation for PD Location for RLC ladder network and MTL models in the frequency range of kHz (10kHz<f<1MHz) and MHz (1MHz<f<5MHz) respectively.

An ME-PC Enhanced HDMR Method for Efficient Statistical Analysis of Multiconductor Transmission Line Networks

An efficient method for statistically characterizing multiconductor transmission line (MTL) networks subject to a large number of manufacturing uncertainties is presented. The proposed method achieves its efficiency by leveraging a high-dimensional model representation (HDMR) technique that approximates observables (quantities of interest in MTL networks, such as voltages/currents on mission-critical circuits) in terms of iteratively constructed component functions of only the most significant random variables (parameters that characterize the uncertainties in MTL networks, such as conductor locations and widths, and lumped element values). The efficiency of the proposed scheme is further increased using a multielement probabilistic collocation (ME-PC) method to compute the component functions of the HDMR. The ME-PC method makes use of generalized polynomial chaos (gPC) expansions to approximate the component functions, where the expansion coefficients are expressed in terms of integrals of the observable over the random domain. These integrals are numerically evaluated and the observable values at the quadrature/collocation points are computed using a fast deterministic simulator. The proposed method is capable of producing accurate statistical information pertinent to an observable that is rapidly varying across a high-dimensional random domain at a computational cost that is significantly lower than that of gPC or Monte Carlo methods. The applicability, efficiency, and accuracy of the method are demonstrated via statistical characterization of frequency-domain voltages in parallel wire, interconnect, and antenna corporate feed networks.

Multi-conductor transmission line networks in analysis of side-coupled metal–insulator–metal plasmonic structures

An approximate and accurate enough multi-conductor transmission line model is developed for analysis of side-coupled metal–insulator–metal (MIM) waveguides. MIM waveguides have been already modeled by single conductor transmission lines. Here, the side coupling effects that exist between neighboring plasmonic structures are taken into account by finding appropriate values for distributed mutual inductance and mutual capacitance between every two neighboring conductors in the conventional single-conductor transmission line models. In this manner, multi-conductor transmission line models are introduced. Closed-form expressions are given for the transmission and reflection of miscellaneous MIM plasmonic structures, e.g. dual-stop-band and band-pass filters. In all examples, the results of the proposed model are compared against the fully numerical finite-difference time-domain (FDTD) method. The results of the analytical model are in good agreement with the numerical results.

Characterization of Complex Aeronautic Harness—Numerical and Experimental Validations

This article describes the approach developed to model the topology of a complex harness. The modeling is based on the multi-conductor transmission line network theory. The topological model of the complex harness was validated using S-parameter simulations compared with measurements. The low-frequency results demonstrate the capability to correctly describe the topology of this type of wiring structure, including realistic and complex installation configurations. The results also show the importance of taking into account losses much larger than the usual skin effect wire loss models in order to reach good agreement with measurements.

Electromagnetic Interference Analysis of Multiconductor Transmission Line Networks Using Longitudinal Partitioning-Based Waveform Relaxation Algorithm

With the use of low powered devices, susceptibility of high-speed interconnects to electromagnetic interference (EMI) is becoming a critical aspect of signal integrity analysis. For modeling the EMI in time domain, commercial circuit simulators like SPICE typically use longitudinal segmentation methodologies to discretize the interconnect network. For long lines as found in printed circuit board or cables, a large number of longitudinal segments are required to capture the response of the network leading to inefficient simulations. In this study, a waveform relaxation (WR) algorithm for the efficient EMI analysis of multiconductor transmission line networks is presented. Techniques to compress the size of the subcircuits, reduce communication overheads, and accelerate the convergence of the WR iterations are provided. The overall algorithm is demonstrated to be highly parallelizable and exhibits good scaling with both the size of the network involved and the number of central processing units available.

TRAVELLING-WAVE MODELLING OF UNIFORM MULTI-CONDUCTOR TRANSMISSION LINE NETWORKS --- PART I: ANALYTICAL DERIVATION

In Part I of this work, analysis of uniform multi-conductor transmission line networks is performed on travelling-wave basis, via \quasi-TEM approach. Narrowband interpretation of the modal theory in the time domain and quantiflcation of the multiple re∞ections efiect are both included. Theoretical demonstration and analytical formulation are provided, along with guidelines towards computational implementation. Any network formed of lossy, diagonalisable uniform multi-conductor transmission lines of either distinct or degenerate eigenvalues is covered. This work applies especially in the fleld of Power-Line Communications, as High-Frequency transmission over the power electric network is dominated by multipath propagation.

TRAVELLING-WAVE MODELLING OF UNIFORM MULTI-CONDUCTOR TRANSMISSION LINE NETWORKS-PART II: EXPERIMENTAL VALIDATION-APPLICABILITY

In Part I of this work, travelling-wave modelling of uniform multi-conductor transmission line networks was analytically established with direct applicability to narrowband transmission, covering any network formed of lossy (in the general case), diagonalisable uniform multi-conductor transmission lines of either distinct or degenerate eigenvalues. As the whole work applies especially in the fleld of Power-Line Communications, in Part II, a validating experimental paradigm is flrst provided using a common cable type for indoor power electric networks. Then, direct applicability to narrowband transmission is addressed, along with potential expandability towards wideband signalling. A comparative evaluation with other existing methods of time-domain modelling is also included and relevant directions for future research are suggested.

An FFT-Accelerated Time-Domain Multiconductor Transmission Line Simulator

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A fast time-domain multiconductor transmission line (MTL) simulator for analyzing general MTL networks is presented. The simulator models the networks as homogeneous MTLs that are excited by external fields and driven/terminated/connected by potentially nonlinear lumped circuitry. It hybridizes an MTL solver derived from time-domain integral equations (TDIEs) in unknown wave coefficients for each MTL with a circuit solver rooted in modified nodal analysis equations in unknown node voltages and voltage-source currents for each circuit. These two solvers are rigorously interfaced at MTL and circuit terminals, and the resulting coupled system of equations is solved simultaneously for all MTL and circuit unknowns at each time step. The proposed simulator is amenable to hybridization, is fast Fourier transform (FFT)-accelerated, and is highly accurate: 1) It can easily be hybridized with TDIE-based field solvers (in a fully rigorous mathematical framework) for performing electromagnetic interference and compatibility analysis on electrically large and complex structures loaded with MTL networks. 2) It is accelerated by an FFT algorithm that calculates temporal convolutions of time-domain MTL Green functions in only <formula formulatype="inline"><tex Notation="TeX">$O({N_{\rm t} \log ^2 N_{\rm t} })$</tex></formula> rather than <formula formulatype="inline"><tex Notation="TeX">$O(N_{\rm t}^2)$</tex></formula> operations, where <formula formulatype="inline"> <tex Notation="TeX">$N_{\rm t} $</tex></formula> is the number of time steps of simulation. Moreover, the algorithm, which operates on temporal samples of MTL Green functions, is indifferent to the method used to obtain them. 3) It approximates MTL voltages, currents, and wave coefficients, using high-order temporal basis functions. Various numerical examples, including the crosstalk analysis of a (twisted) unshielded twisted-pair (UTP)-CAT5 cable and the analysis of field coupling into UTP-CAT5 and RG-58 cables located on an airplane, are presented to demonstrate the accuracy, efficiency, and versatility of the proposed simulator. </para>

Passivity Verification in Delay-Based Macromodels of Multiconductor Electrical Interconnects

This paper presents a generalized theory of passivity verification in delay-based macromodels for multiconductor transmission line networks generated using the method of characteristics (MoCs). We demonstrate that the passivity in an MoC macro-model is equivalent to the nonnegative definiteness in the admittance matrices of two submodels. We then provide the necessary and sufficient conditions for each submodel to have a nonnegative definite admittance matrix. The presented theory develops an algebraic test to verify the passivity in MoC macromodels. Numerical results demonstrate the validity of the proposed theory.

Electromagnetic topology quasisolutions for aperture interactions using transmission line matrix

A hybrid simulation technique that integrates transmission line matrix method with electromagnetic topology solutions has been employed to link a field scattering problem at an aperture in order to analyze the frequency and temporal characteristics of electromagnetic pulses. Using this same unified multiconductor transmission line network formulation any subsequent coupling with cables at the other side of the aperture can be integrated into the solution. The hybrid circuit can also be integrated to any existing topological simulation circuit for analyzing very large electrical systems. Incorporation of the compaction technique in the topological simulation reduces the number of simulation grids significantly, resulting in efficient computation without sacrificing accuracy. The simulation results for scattering fields at the aperture compare well with the finite-difference time domain method.

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

Susceptibility analysis of wiring in a complex system combining a 3-D solver and a transmission-line network simulation

This paper deals with the application of electromagnetic field-to-transmission-line coupling models for large cable systems analysis. It emphasizes the use of Agrawal's (1980) model applied here in a numerical simulation of an electromagnetic susceptibility problem up to 500 MHz. Based on the concepts of EM topology, the proposed methodology consists in calculating the incident fields with a three-dimensional (3-D) computer code and the coupling on cables with a multiconductor transmission-line network computer code. In order to validate the efficiency of this methodology in an industrial context, an experiment has been performed on a prototype wiring installed in a Renault Laguna car, stressed by an EM plane wave. Numerous validation configurations have been carried out. First, the prototype cable network under study has been tested on a ground plane to validate the coupling model but also, to validate the cable-network topology itself. Second, EM fields have been measured onto the structure and inside the structure. Then, they have been compared to 3-D calculations, performed with an FDTD code. Third, comparisons between measurements and calculations of bulk currents and voltages on 50 /spl Omega/ loads on the wiring have been achieved.

External field coupling to MTL networks with nonlinear junctions: numerical modeling and experimental validation

The problem of predicting the voltages and currents induced on a printed circuit multiconductor transmission line (MTL) network by an impinging transient plane wave electromagnetic field is considered. The MTL network contains nonlinear circuit elements and test cases with various dielectric substrates are examined. Numerical predictions based on quasi-TEM models of the MTL and modified nodal analysis (MNA) models of the lumped element junctions are compared to experimental results obtained in the time domain using a GTEM cell. As has been done in the past, the effect of the incident plane wave is introduced as forcing functions in the MTL equations. The primary goal of this paper is to quantify the accuracy of the various commonly used quasi-TEM mathematical time-domain models. It is shown that when modeling the forcing function terms, it is important to take into account the perturbation of the incident plane wave due to the dielectric substrate. (The experimental-numerical comparisons herein are shown for the case of end-fire illumination since it best demonstrates this point.) Neglecting the dielectric effect on the incident transient pulse, even for substrates with low dielectric constant, produces poor results.

Finite-difference model for computing the response of multiconductor transmission lines interconnected by load circuits

In this paper, we describe a time-domain technique to calculate the induced currents and voltages on multi-conductor transmission line (mtl) networks, which contain resistive circuits in the junctions. The network can be excited by an external plane wave or by voltage sources which are located at any circuit of the system. The method is based on a time-space centered finite-difference technique to solve the time-domain mtl coupled equations. This approach makes it possible to solve a linear matrix system which can be expressed under the AX = B form. We apply the method to mtl networks solved by a frequency analysis based on a state variable technique and to previously published examples solved by other numerical methods. The results correspond closely enough for the approach to be validated.

Theory of field-excited networks

The analysis of the transient response of multiconductor transmission line networks excited by electromagnetic (EM) fields can be performed either in the time- or in the frequency-domain. The transient analysis of field-excited networks having complex configurations and nonlinear loads is performed by using a combined frequency- and time-domain procedure. The simulation models of the line-sections are defined in the frequency-domain based on the exact formulation of Maxwell's equations. New expressions of the per-unit-length (p.u.l.) series impedances and shunt admittances are used in order to overcome the limitation of the Carson (1926) formulation in the case of a poorly conducting ground-plane and in the presence of very fast transients. An efficient procedure is applied for reducing the computation effort of the procedure in the case of complex large-dimension networks. Calculations are carried out to predict the overvoltages induced by an EMP-plane wave on a 20 kV-power network above a highly lossy ground and on a signal 18-port-multiconductor network.

The finite-difference time-domain solution of lossy MTL networks with nonlinear junctions

We describe a numerical technique to solve lossy multiconductor transmission line (MTL) networks, also known as tube/junction networks, which contain nonlinear lumped circuits in the junctions. The method is based on using a finite-difference technique to solve the time-domain MTL equations on the tubes, as well as the modified nodal analysis (MNA) formulation of the nonlinear lumped circuits in the junctions. The important consideration is the interface between the MTL and MNA regimes. This interface is accomplished via the first and last finite-difference current/voltage pair on each MTL of the network and, except for this, the two regimes are solved independently of each other. The advantage of the FDTD method is that the MTL equations may contain distributed source terms representing the coupling with an external field. We apply the method to previously published examples of multiconductor networks solved by other numerical methods, and the results agree exceptionally well. The case of an externally coupled field is also considered.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimization and sensitivity analysis of multiconductor transmission line networks

This paper describes a numerical approach and a design methodology of using a frequency domain technique for the optimization and sensitivity analysis of high speed multiconductor transmission line systems. To demonstrate the usefulness of this technique, the numerical frequency domain results have been validated by time domain simulations. The technique has also been used to demonstrate the superiority of closed loop topologies in terms of their electrical performance. Such topologies were thought to be troublesome and were generally avoided in most of the electronics industry. >