Multiconductor Transmission Lines Research Articles

Параметрическая оптимизация асимметричных многопроводных линий передачи с учетом комбинационных импульсов

Transmission lines are significant elements and play an important role in determining the performance, reliability and functionality of radio electronics. A number of factors appearing in the use of transmission lines can lead to problems in the field of electromagnetic compatibility. One such factor is the appearance of asymmetry due to inhomogeneities, PCB manufacturing errors, dense tracing, mismatch, etc. The paper considers the effect of asymmetry on the characteristics of transmission lines with inhomogeneous dielectric filling. It is found that asymmetry of cross section and/or boundary conditions leads to the appearance of combinational pulses. Combination pulses are of interest because their arrival times do not correspond to the per-unit-length delays of the modes propagating in the transmission lines, but consist of their combinations. Their level may be comparable to the level of information signals, which may result in distortion or loss of useful information. Meanwhile, asymmetry and the resulting combinational pulses represent a new resource for improving the performance of devices based on transmission lines, which can be used to protect radio electronics from electromagnetic interference of picosecond and nanosecond duration. For the first time the optimization of parameters taking into account combinational pulses is carried out on the example of three diagrams of symmetric multiconductor transmission lines with asymmetry of termination loads: reflection symmetric and with a reference conductor in the form of side polygons. Using the genetic algorithm, the optimal parameters are obtained, which allow to reduce the value of the maximum amplitude by 1.5 times, as well as the parameters allowing to increase in 2 times the minimum value of the time interval between the decomposition pulses, on which depends the possibility of complete decomposition of the interference pulse, compared to the value obtained in the initial diagram with optimized parameters, where there are no combinational pulses at the same device dimensions. The optimization results demonstrate the efficiency of using the resource of combinational pulses to improve protective structures based on transmission lines with inhomogeneous dielectric filling.

A new unsynchronized fault location approach based on sequence voltage profiles and a multiconductor line detailed model: Application to symmetrical transmission lines

This paper presents a new, improved approach to fault location in long and very long transmission lines, which uses measurements at both terminals of the line that do not need to be synchronized, using the satellite time-reference. The new method employs symmetrical component sequence voltage profiles that are computed using an innovative approach in which the detailed three-phase model of a multiconductor transmission line is represented as the series connection of several chain matrices. This allows the new method achieve the best performance, when compared to other 4 similar fault location approaches, requiring measurements at both terminals of a symmetrical line, considering all types of faults, under realistic variations in variables and parameters of the test system, including the effect of saturation of current transformers, and arc faults. The main advantage of this proposed technique is that it can be applied with no major changes in symmetrical and unsymmetrical transmission lines keeping its good performance. In addition, division of the line in chain matrices allows the new proposed approach to be applied in non-homogeneous lines. In this paper, for space reasons, the new approach is initially applied to symmetrical (ideally transposed) transmission lines only, with very successful and encouraging results.

Modeling and signal integrity analysis of silicon interposer channels based on MTL and KBNN

In this paper, the equivalent circuit model of interconnect channels in silicon interposer is developed for three-dimensional integrated circuit (3-D IC) based on the theory of multi-conductor transmission line (MTL). The deep neural network (DNN) is employed to learn the nonlinear mapping relationship between the geometric parameters and the distributed parameters, and it is demonstrated that the DNN has a high prediction accuracy. In the implementation, a coarse model is firstly developed by solving the scattering parameters of the model using the chain parameter matrix. The model is optimized using a knowledge-based neural network (KBNN), and a fine model is then established. The numerical examples demonstrate that the optimized model can achieve high accuracy. Finally, the inner contour of the worst-case eye diagrams of the channel is generated using the peak distortion algorithm (PDA), with the worst eye width and height obtained.

A light Darwin implementation of Maxwell’s equations to quantify resistive, inductive, and capacitive couplings in windings

High operating frequency is an enabler of high key performance indicators, such as increased power density, in electrical machines. The latter enhances the cross-coupling of resistive–inductive–capacitive phenomena in windings, which may lead to significant loss in performance and reliability. The full-wave Maxwell’s equations can be employed to characterize this coupling. To address the frequency instability that arises as a result, a simplification known as the Darwin formulation can be employed, where the wave propagation effects are neglected. Still, this modification is prone to ill-conditioned systems that necessitate intricate pre-conditioning and gauging steps. To overcome these limitations, a fast 2D formulation is derived, which preserves the current continuity conservation along the model depth. This implementation is validated experimentally on a laboratory-scale medium-frequency transformer. The computed impedances for the open- and short-circuit modes of the transformer are validated using measurements and compared with the multi-conductor transmission line model that is widely adopted for the analysis mentioned above. The developed formulation demonstrates a high accuracy and outstanding frequency stability in a wide frequency range, becoming an efficient and computationally light method to investigate the interconnected resistive, inductive, and capacitive effects in windings.

An Extended Asymptotic Model for Fast Evaluation of the Induced Current on Multiconductor Transmission Lines Excited by the High-Frequency Nonuniform Electromagnetic Field

An Extended Asymptotic Model for Fast Evaluation of the Induced Current on Multiconductor Transmission Lines Excited by the High-Frequency Nonuniform Electromagnetic Field

Analysis of the Radiation from a Complex Multi-Conductor Transmission Line

The Deployment of Power Line Transmission (PLT) and the development of new broadband services over the telephone network through technology like xDSL (x Digital Subscriber Line), requires higher data rates, consequently higher bandwidths, and operating frequencies. So it is generally accompanied with electromagnetic compatibility (EMC) phenomena, in particular the radiated emissions associated to the deployed system and used cables characteristics. In fact the electrical cable presents variations in their geometry, causing an increase in the electromagnetic radiation. This paper presents a theoretical approach to study a complex transmission line network over ground plane. This approach leads to an analytical expression for the evaluation of P.U.L. parameters of finite length twisted wires lines. These expressions give the capacitances and the inductances values in every point of the cable, the theoretical results are compared to measurements. The formalism is also derived to determine the distribution of the electromagnetic field radiated by Shielded or Unshielded Twisted Pair cables with discontinuity. The obtained results are compared to those provided by a code based on the antenna theory.

Automatic Determination of Set of Multivariate Basis Polynomials Based on Recursion and Application of LSPCR to High-Dimensional Uncertainty Quantification of Multi-Conductor Transmission Lines

Automatic Determination of Set of Multivariate Basis Polynomials Based on Recursion and Application of LSPCR to High-Dimensional Uncertainty Quantification of Multi-Conductor Transmission Lines

Analysis and Simulation Test of Electromagnetic Disturbance Mode Conversion in Secondary Circuit of Substation

Under ideal conditions, the electromagnetic interference experienced by the secondary circuit is manifested as a common mode. However, due to circuit imbalance, common mode disturbance is converted into differential mode disturbance, thereby presenting a danger to the normal functioning of secondary equipment. The investigation measured the distribution ratio of common mode voltages and differential mode voltages at the ports of secondary equipment during switching operations. A computational circuit model of the secondary circuit was established by using multi-conductor transmission line theory. The mechanisms and influencing factors of transformation from common mode to differential mode were analyzed, and a simulation test was carried out in a substation to explore the conversion law under impedance imbalance. The results showed that the differential mode voltage of the secondary equipment port was greater than the common mode voltage when the circuit breaker was in operation. Common-differential mode conversion in the secondary loop was predominantly caused by an imbalance in circuit structure and extraneous parameters. Differential mode disturbance generated by switch field side imbalance had a greater impact than that generated by protection chamber side imbalance. As the degree of imbalance increased, the differential mode voltage also increased.

Analytical equivalent circuit modeling and analysis of complex BGA for 3D silicon-interposer packaging

Through analyzing different cross-sections of the complex ball grid array (CBGA) sandwiched by silicon interposers, various distributed capacitances of the CBGA and the significance of the CBGA's coplanar capacitances are revealed. From the analyses, the composition of the CBGA's capacitance is found to have similarity with that of the coplanar waveguide's capacitance. Based on the electric-field coupling mechanism of the coplanar waveguide, geometrical analysis of the CBGA, and analysis of multiconductor transmission lines, analytical equations are derived to allow accurate modeling the equivalent circuit of the CBGA for 3D silicon-interposer packaging. The modeled equivalent circuit of the CBGA is validated with the full wave electromagnetic simulation, and it is demonstrated to have a good accuracy up to 40 GHz. Moreover, the CBGA structure can be further optimized for impedance matching with the guidance of the derived analytical equations.

Multiconductor transmission lines irradiated by plane wave: An EM‐reciprocity analysis methodology

AbstractThis paper extends previous work on electromagnetic (EM) reciprocity theorem analysis from the single‐conductor to the more general multiconductor transmission line (MTL) case. The focus is on the EM coupling problem of an ideal MTL above a perfectly electrically conducting ground when excited by a plane wave. The proposed methodology addresses mutual coupling effects and mismatched loads in the MTL. The expression for the current along the MTL in the test (radiation) state is derived, considering these factors. A novel calculation method for the induced voltage at the load is then introduced, assuming consistent coupling between different lines in both test and receiving states. Numerical examples validate the proposed EM‐reciprocity method, offering an alternative approach for analyzing the field‐to‐line coupling problem in MTL model.

Insulation design of -800 kV gas insulation transmission line for negative ion based neutral beam injector

The high-voltage transmission line carries electricity, water, and gas for the high-potential components in the NNBI system. High voltage transmission lines used in -800 kV acceleration grade NNBI systems require the transmission of multiple high voltages of different voltage levels. Its insulation design not only guarantees the reliability of insulation but also requires a small occupation volume. The FEA method is used for insulation design of multi-conductor transmission lines. In the design of -800 kV transmission line, coaxial and non-coaxial structures are mainly considered. In the case of SF6 filling space, conductor radius and conductor position are the main factors affecting insulation strength. Both structures can make its insulation strength meet the requirements. However, it is found that the coaxial transmission line is more compact and concise when it meets the insulation requirements, but it is difficult to install and maintain.

Rapid Analysis of Bent Cable Crosstalk Based on Numerical Calculation

In this paper, a fast prediction method of cable crosstalk is introduced, which can simulate the crosstalk problem more accurately in the actual cable situation. The traditional flexible cable model considers few factors to truly reflect the spatial pose of the cable. In this paper, constraints of the assembly space are considered to truly reflect the structural characteristics of the cable, providing a theoretical basis for cable bundle layout in the virtual environment. Based on the element method and the theory of multi-conductor transmission lines, the crosstalk coupling model of curved cable is established. In this model, the traditional multi-conductor transmission line theory is improved, and the bending cable bundle model is divided into several equivalent subsegments by using the element method. In the subsegment, the multi-conductor transmission line theory is used for modeling, and the chain parameter method is used for crosstalk coupling analysis. The accuracy of the model introduced in this paper is verified by MATLAB and CST Studio simulation.

Blind Separation of the Measured Mixed Cyclostationary Waveforms in Transmission Lines of the PCB

Crosstalk is an undesirable factor that degrades the quality of data transmission in printed circuit boards (PCBs). The signal integrity (SI) in multiconductor transmission lines is controlled by using a large number of multiport tests and measurements, which require a lot of time and expensive laboratory equipment. Proposed signal processing methods based on blind identification allow a reduction in the measurement burden. Contrary to the traditional approach requiring knowledge of sampling time offset, input pseudorandom bit sequence (PRBS), and time delay between received data and transmitted PRBS, the proposed alternative method performs blind separation of measured data for the linear fit pulse response (LFPR) procedure. The waveform identification of the partial pulse responses is evaluated for additively mixed cyclostationary sources of the data, intersymbol interference, and crosstalk. A mixed matrix model of composed random vectors is considered. The proposed estimation procedure is based on preprocessing of measured data using principal component analysis (PCA) and following independent component analysis (ICA). It is shown that the proposed component analysis allows diagnostics of signal integrity using eye-diagram patterns and the channel operating margin (COM).

An Asymptotic Model of Multiconductor Transmission Lines in a High-Frequency Region Considering the Lossy Ground

The classical transmission line (TL) theory may normally fail when analyzing the multiconductor TLs (MTLs) with high-frequency excitations, which is mainly due to the unsatisfactory quasi-TEM approximation. In comparison, the asymptotic method can be applied to address this problem efficiently and accurately. However, when taking into account the finitely conductive ground, Sommerfeld–Goubau (surface wave) propagation may appear in the high-frequency region, which may result in the degradation of the accuracy of the asymptotic method. This letter proposes a new asymptotic method with complete formulas to take into account the ground loss. The proposed method was validated with the case that MTLs are excited by the lumped source above the lossy ground. The validation examples show that the asymptotic method with the complete formulas could lower the attenuation in the propagation constant; thus, the solutions in the high-frequency region can be presented in a better way.

Uncertainty Quantification Method of Crosstalk Involving Braided-Shielded Cable

In this paper, in view of the uncertainty of geometric parameters of braided-shielded cable and structural parameters of the shield in practical problems, polynomial chaos expansions (PCE) is used to explore the uncertainty quantification of a crosstalk calculation model of braided-shielded cable. First, the model based on multi-conductor transmission line theory is expanded by PCE. Second, the truncation degrees of polynomials and sample size of PCE are determined by the leave-one-out method, and the statistical characteristic parameters of crosstalk are obtained by combining coefficients of polynomials. Compared with the calculation results of the Monte Carlo method, the mean value, standard deviation and probability density function obtained by the two methods are basically consistent, but the PCE method has obvious advantages in calculation efficiency. Finally, the influence of input variable parameters in the crosstalk calculation model of braided-shielded cable are calculated by combining the PCE and the Sobol’s global sensitivity analysis method, which provides theoretical guidance for the electromagnetic compatibility design of electrical and electronic equipment using braided-shielded cable.

Influence of the cross-sectional shape of conductors of multiconductor transmission lines on the accuracy of their parameters and characteristics calculation

Influence of the cross-sectional shape of conductors of multiconductor transmission lines on the accuracy of their parameters and characteristics calculation

Analytical Design of Compact Multiband Bandpass Filters with Multiconductor Transmission Lines and Shunt Open Stubs

A compact topology for implementing compact multiband bandpass filters is presented in this paper. To achieve the desired frequency response, two identical short-circuited multiconductor transmission lines (MTLs) and properly connected shunt open stubs are interconnected. Using this configuration, it is possible to design multiband bandpass filters effortlessly. As both the MTLs and the stubs are distributed elements, spur-line band-stop filters are added to mitigate the first replica of the structure’s frequency response. To assess the behavior of the developed filter design procedure, a prototype consisting of a six fingers-MTL and two shunt open stubs has been designed, manufactured, and analyzed, showing excellent agreement between analytical and measured results, considering that no simulation or optimization process has been performed during the design process, just for result verification. Furthermore, it is possible to establish a design criterion that allows the fast and reliable synthesis of multiband responses by varying just a small number of geometrical parameters of the MTLs and the corresponding stubs.

Time domain characteristics of lossy multiconductor transmission lines randomly excited by electromagnetic pulse

This paper provides a time domain method for solving the induced currents (and voltages) of frequency-dependent lossy multiconductor transmission lines (MTLs) model randomly excited by electromagnetic pulse (EMP) plane wave. The model is processed based on the generalized polynomial chaos expansion (gPCE) and improved finite difference time domain (FDTD). The improved FDTD method overcomes the shortcomings of the conventional method that oversimplifies the expression of conductor impedance. In addition, when quantifying the influence of uncertainty on induced values, general formula of the global sensitivity analysis is provided by defining the gPCE basis function sequence to solve the complicated search work. The verification shows that the improved FDTD method alone or combined with gPCE to solve the lossy MTLs model excited by EMP is superior to the conventional methods in solving time and accuracy. Finally, compared with the Monte Carlo method, the effectiveness of the sensitivity method is also verified.

Unified multiconductor transmission-line model of multiple-shields multiconductor cables: evaluation of shield connections performances

This paper presents a transmission-line model of a multiple-shields multiconductor cable. This unified model includes at the same time the propagation and cross-coupling characteristics of the electrical wires and of the cable-shields. It also includes the electromagnetic characteristics of the shields (in terms of transfer impedance and transfer admittance). It is derived in compliance with the multiconductor-transmission-line theory and it is valid whatever the connection configurations at the shield ends are. Therefore, it makes it possible the modelling of realistic connection problems ranging from ideal 360° shield connections to simple bonding wires. In addition, it is suitable for both electromagnetic susceptibility and emission problems. The paper proposes a physical explanation of the derived per-unit-length matrices. This unified model is also used to define the required conditions for being able to calculate the response of a shielded-cable in a two-steps model in which the shield problem and the inner shield problem are solved in sequence. Finally, the paper illustrates an application of the model in order to evaluate performances of a shielded-cable-link on crosstalk configurations with respect to various electrical bonding techniques of the shield.

An efficient modeling approach of 1D-planar metamaterials in the high-frequency regime

PurposeThe purpose of this paper is to present an alternative modeling approach in terms of the determination of a physically equivalent circuit model for one-dimensional (1D) planar metamaterials in the high-frequency regime, without a postprocessing optimization procedure. Thereby, an efficient implementation of physical relationships is aimed.Design/methodology/approachIn this paper, a method based on quasi-stationary simulations and mathematical conversions to derive the values for a physically equivalent circuit model is proposed. Because the electromagnetic coupling mechanisms are investigated in detail, a simplification for the considered multiconductor transmission line structure is achieved.FindingsThe results show that the proposed modeling approach is an efficient and physically meaningful alternative to classical full-wave simulation techniques for the investigated inhomogeneous transmission line structure in both the time domain as well as in the frequency domain. In the course of this, the effort is reduced while a comparable accuracy is maintained, whereby specific coupling mechanisms are considered in circuit simulations.Originality/valueThe process to obtain information about physically interpretable lumped element values for a given structure or to determine a layout for known ones is simplified with the aid of the proposed approach. An advantageous adaption of the presented procedure to other areas of application is well conceivable.