Finite-difference, time-domain analysis of lossy transmission lines

An active and efficient method of including frequency-dependent conductor losses into the time-domain solution of the multiconductor transmission line equations is presented. It is shown that the usual A+B√s representation of these frequency-dependent losses is not valid for some practical geometries. The reason for this the representation of the internal inductance the at lower frequencies. A computationally efficient method for improving this representation in the finite-difference time-domain (FDTD) solution method is given and is verified using the conventional time-domain to frequency-domain (TDFD) solution technique     

Coupled-mode formulation of multilayered and multiconductortransmission lines

A novel coupled-mode formulation for multilayered and multiconductor transmission lines is developed. In this formulation, the solutions to the original multiconductor system are approximated by a linear combination of eigenmode solutions associated with the isolated single conductor line located in an appropriate reference dielectric medium. The reciprocity theorem is used to derive the coupled-mode equations. The coupling coefficients are expressed in terms of the simple overlap integrals between the eigenmode fields and currents of the individual conductor lines. As a basic application, the dispersion characteristics of two identical coupled-microstrip lines are analyzed using the proposed coupled-mode theory. It is shown that the results are in very close agreement with those obtained by the direct Galerkin's moment method over a broad range of weak to strong coupling     

A configuration-oriented SPICE model for multiconductortransmission lines with homogeneous dielectrics

Using the SPICE circuit analysis computer program to simulate a lossless multiconductor transmission line is investigated. It is demonstrated that for the case of a homogeneous dielectric, the multiconductor line can be represented by a system of standard two-wire lines which is not based on modal decomposition. This system is readily modeled with SPICE. While restricted to situations where the dielectric constant can be assumed uniform, the present method has the advantage of an intuitive relationship to the conductor configuration, simpler SPICE input data requirements, and an improvement in computer run time over other methods     

Capacitance extraction for electrostatic multiconductor problems byon-surface MEI

In this paper, on-surface measured equation of invariance (OSMEI) method is implemented for capacitance extraction of electrostatic multiconductor interconnect problems. OSMEI uses the same mesh as that in method of moments (MoM), but generates highly sparse matrices rather than a full matrix. In comparison with “standard” MEI which contains a few finite difference (FD) or finite element (FE) mesh layers, the number of unknowns and the computation memory can be saved. For each OSMEI equation in the multiconductor interconnects, a given node on a given conductor is forced into coupling with the few adjacent nodes on conductor itself and the few sampled nodes on other conductors. Thus, the system sparse matrices can be generated. The convergent behavior of the capacitance with the number of the nodes in the OSMEI equations has been widely investigated, Numerical examples of the capacitance extraction for two-dimensional (2-D) and three-dimensional (3-D) multiconductor interconnects show that the computing errors are within 24%. The OSMEI method may become a powerful technique for the more complex interconnect problems     

Equivalent Transformations for Mixed-Lumped and Multiconductor Coupled Circuits

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

Time-domain solution of field-excited multiconductor transmissionline equations

Analytical solution of lossless field-excited multiconductor transmission lines is presented. The equivalent circuit of a multiconductor transmission line with distributed sources is reduced to a simple lumped parameter circuit with independent voltage sources at both the ends of the transmission line. The transient source waveforms are analytically estimated for exponential time dependence of the external field, as EMP, ESD, and lightning. The method is suitable for a direct implementation in computer-aided circuit analysis codes and enables a very fast analysis for any load condition. Some numerical results are presented for single conductor and multiconductor lines excited by all EMP plane-wave field     

Electromagnetic analysis of multiconductor losses and dispersion in high-speed interconnects

A self-consistent electromagnetic analysis of multiconductor transmission lines is presented for high-speed, high-density MMIC's and VLSI interconnects. In contrast to classical approach, this analysis handles the multiconductor as normal dielectric with high conductivity in electromagnetic simulation. Therefore, dispersion and loss effects can exactly be described in this model. Examples of interconnect circuits with up to four conductors are analyzed for dispersion and frequency-dependent losses. Propagation characteristics of multimode along symmetrical and asymmetrical multiconductor are obtained. Some inherent influences of losses on high-density interconnects and physical dependence of these effects are also discussed.     

一种分析微带交指滤波器的新思路

本文提出一种直接用耦合多导体多介质结构传输特性计算微波滤波器的方法，它不但考虑了相邻导体，也考虑了所有非相邻导体间的耦合，因此计算精度大大提高。此外，它还可以计算不对称耦合，适应面宽。分区均匀介质填充多导体结构有多个不同传播常数的本征模。这与均匀填充多导体结构有很大差别，即不但要考虑本征阻抗，而且要考虑不同的传播常数。本文用矩阵电报方程求出它们的本征值与本征矢量，从而求得传输特性，最后用网络等效方法优化求得滤波器特性。本文还介绍了由不同宽度谐振腔组成的滤波器的设计     

Evaluation of measured complex transfer impedances and transferadmittances for the characterization of shield inhomogeneities ofmulticonductor cables

Besides the knowledge of the primary line parameters per unit length, the determination of the complex transfer impedances and transfer admittances of shielded multiconductor cables is the prerequisite for the calculation of the propagation of disturbing currents on the inner wires of the cable. With a measurement procedure based on triaxial measurement setups using multiconductor transmission line theory for evaluation, it is possible to determine individual transfer impedances and admittances for each inner conductor of a shielded multiconductor cable over a broad frequency range. This paper shows the measurement procedure, the method of evaluation: and from measurement results, the determination of the location and the calculation of the area of single-shield inhomogeneities by the evaluation of measured transfer impedances and transfer admittances     

Perturbations impulsionnelles créées par un champ électromagnétique non uniforme sur des câbles multiconducteurs

The purpose of this paper is to show the effects of electromagnetic pulses (emp) on multiconductor transmission lines. The response of multiconductor transmission lines excited by an electromagnetic field, suspended over a reference conductor, in homogeneous and/or in-homogeneous medium is obtained. In quasi-tem assumption, we derive matrix expressions of the terminated voltages and currents. Experimental and numerical results, related to short lines, power lines, microstrip lines, shielded isdn bus illuminated by an electromagnetic field show how the perturbations can be reduced.     

Calculation of transverse waves in a shielded transmission line containing circular cylindrical conductors

A method is proposed for calculating a shielded homogeneous multiconductor transmission line containing conductors of circular cross section. Formulas are obtained for the matrix of the conductor capacitance per unit length and the electric parameters of transverse electromagnetic waves.     

“电磁场”课程中部分电容的实验方法讨论

部分电容实验是本科生＂电磁场＂课程静电场部分的主要实验之一。本文总结了部分电容实验中两种测量方法———直接法和间接法,并给出了部分参数的测量电路图;笔者分析了学生使用检流计测多导体静电独立系统中某一个导体上的电荷时易犯错误的原因,并给出正确的做法。     

Approximate solution for propagation modes on lossy multiconductor transmission lines in inhomogeneous media

The letter gives an approximate solution for wave propagation on a system of lossy multiconductor transmission lines with small losses. The solution leads to a general expression for the attenuation factor matrix. The expression gives a correct result for the cases of two and three conductors and can be used for any number of conductors.     

Echo-Free and Crosstalk-Free Transmission in Particular Interconnections

We explore several designs for implementing the special ZXtalk method for completely degenerate interconnections, capable of providing reduced echo and internal crosstalk in multiconductor interconnections. Transmission circuits comprising a MIMO series-series feedback amplifier are adequate to obtain a wide bandwidth. The external crosstalk may also be reduced, using an additional conductor to obtain a pseudo-differential scheme.     

Transposing conductors in signal buses to reduce nearest-neighborcrosstalk

A conductor layout technique is described that reduces nearest-neighbor crosstalk for multiconductor signal buses with applications in high-speed digital and microwave pulse integrated circuits. Periodic transposition of conductors in a bus increases the average spacing of formerly nearest neighbors and thus decreases their capacitive and inductive coupling compared with ordinary parallel conductors. A conductor transposition pattern is evaluated for crosstalk, propagation delay, and chip area. SPICE simulations demonstrate that conductor transposition reduces, in certain situations, near- and far-end nearest-neighbor crosstalk by roughly 40% compared with parallel conductors. Quantitative guidelines are developed for reducing nearest-neighbor crosstalk in a transposed five-conductor bus, including effects of signal rise time, source resistance, load capacitance, and bus length     

Analysis of the time response of multiconductor transmission lineswith frequency-dependent losses by the method ofconvolution-characteristics

A new method for analysis of the time response of multiconductor transmission lines with frequency-dependent losses is presented. This method can solve the time response of various kinds of transmission lines with arbitrary terminal networks. Particularly, it can analyze nonuniform lines with frequency-dependent losses, for which no effective method for analyzing their time response exists. This method starts from the frequency-domain telegrapher's equations. After decoupling and inversely Fourier transforming, then a set of decoupled time-domain equations including convolutions are given. These equations can be solved with the characteristic method. The results obtained with this method are stable and accurate. Two examples are given to illustrate the application of this method to various multiconductor transmission lines     

Skin Effect Modeling Based on a Differential Surface Admittance Operator

An important issue in high-frequency signal integrity prediction is the modeling of the skin effect of thick conductors. A new differential surface admittance concept is put forward allowing to replace the conductor by equivalent electric surface currents and to replace the material of the conductor by the material of the background medium the conductor is embedded in. This new concept is studied in detail for the two-dimensional TM case starting from the Dirichlet eigenfunctions of the cross section. Detailed expressions are derived for the important practical case of a rectangular cross section. Next, the differential surface admittance operator is exploited to determine the resistance and inductance matrices of a set of multiconductor lines. A first set of numerical results provides the reader with some insight into the behavior of the surface admittance matrix. A second set of results demonstrates the correctness and versatility of the new approach to determine inductance and resistance matrices.     

多导体传输线时域响应分析的卷积—特征法

本文提出了多导体传输线时域响应分析的卷积-特征法,其最大特点是能分析具有频变损耗和任意负载终端的非均匀传输线.     

Surface Interaction Matrices for Boundary Integral Analysis of Lossy Transmission Lines

A method intended to characterize enclosed computational electromagnetic domains in terms of interaction and response of a defined set of surface excitations is described. The finite-element method is used to compute a matrix relating surface current and tangential field in terms of an appropriate basis set such that a coupled solution with a boundary integral formulation is rendered seamless. The proposed method allows for a decoupled finite-element boundary-integral system through use of a discrete-frequency surface interaction matrix, computed in an alternative way, that is still independent of the properties of the background in which the enclosed region resides. The method is applied to per-unit-length resistance and inductance extraction of a variety of multiconductor lossy transmission lines. The primary advantage the proposed method presents for this particular application is reuse of matrices given recurrence of specific conductor cross sections.      

Accurate and efficient computation of dielectric losses inmulti-level, multi-conductor microstrip for CAD applications

An approach to accurate and efficient computation of dielectric losses in complex microstrip structures is proposed. It can be used in lieu of lossy, full-wave solutions to provide accurate and efficient data for the CAD of multilevel, multiconductor MIC and MMIC structures. Results that are as accurate as lossy full-wave techniques over a wide range of frequencies, including the dispersive region, are obtained. In addition to providing accurate results, the method is up to three times faster, depending on the number and type of substrates or superstrates. Results for various multiconductor, multilevel structures that compare well with the lossy, full-wave approach and require significantly less computer time to compute are shown