A generalized MoM-SPICE iterative technique for field coupling to multiconductor transmission lines in presence of complex structures

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.     

Time-domain analysis of lossy multiconductor transmission lines based on the Lax–Wendroff technique

Taking advantage of the hyperbolic characteristics of the telegrapher equations, this paper applies the Lax–Wendroff technique, usually used in fluid dynamics, to transmission line analysis. A second-order-accurate Lax–Wendroff difference scheme for the telegrapher equations for both uniform and nonuniform transmission lines is derived. Based on this scheme, a new method for analyzing lossy multiconductor transmission lines which do not need to be decoupled is presented by combining with matrix operations. Using numerical experiments, the proposed method is compared with the characteristic method, the fast Fourier transform (FFT) approach, and the Lax–Friedrichs technique. With the presented method, a circuit including lossy multiconductor transmission lines is analyzed and the results are consistent with those of PSPICE. The nonlinear circuit including nonuniform lossy multiconductor transmission lines is also computed and the results are verified by HSPICE. The proposed method can be conveniently applied to either linear or nonlinear circuits which include general transmission lines, and is proved to be efficient.     

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

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

圆柱腔内多导体传输线的瞬态电磁响应

为提高系统抗强电磁脉冲毁伤能力,采用时域有限差分法(Finite Difference Tim e Domain,FDTD)和通用电路仿真器(SPICE)相结合的协同仿真方法,以圆柱腔内由单导线、 双绞线、普通双线和同轴线组成的线束为研究对象,重点研究了导线类型、导线间距、捆扎 和RC滤波电路对耦合特性的影响。结果表明：耦合系数受腔体和传输线的双重影响,同轴线 耦合系数较其他两类线缆降低约40 dB;线间相互屏蔽是捆扎降低耦合系数的主要原因 ;随着导线间距增大,耦合系数幅值增大;RC滤波电路是降低电磁耦合的有效手段。所得结 论对电子系统进行抗电磁脉冲加固具有重要意义。     

Fast EMI Analysis via Transverse Partitioning and Waveform Relaxation

High-speed interconnects are increasingly becoming susceptible to electromagnetic interference (EMI). Hence, there is a growing need for fast simulation of interconnect lines in the presence of incident field coupling using circuit simulators such as SPICE. However, the presence of a large number of coupled lines in modern interconnect structures is a serious limiting factor in these simulations. In order to simultaneously address these difficulties, a new algorithm is presented in this paper for EMI analysis of large number of coupled interconnects. The new method exploits the recently developed waveform relaxation (WR) and transverse partitioning algorithms for fast EMI analysis. The same WR sources that are computed for multiconductor transmission line analysis are also employed for EMI analysis. The computational complexity of the proposed EMI analysis grows only linearly with the number of lines. In addition, the algorithm lends itself to parallel implementation leading to further reduction in CPU time.      

Frequency-domain upper bounds for signals on a multiconductor transmission line behind an aperture

This paper develops a technique for bounding the maximum voltages and currents at terminations of a muiticonductor transmission line (MTL) located behind an aperture-perforated conducting screen excited by an electromagnetic field in the frequency domain. The electromagnetic field is coupled through a small aperture as the excitation of a multiconductor transmission line behind the aperture. A model is presented in terms of external and internal sources which in turn create traveling waves on the multiconductor transmission line. These traveling waves transfer energy to the terminations. The energy at a termination is translated into voltages and currents from which the upper bounds are determined. These upper bounds are obtained using vector norms and associated matrix norms. The formulation is presented in the frequency domain to obtain useful upper bounds for analysis of multiconductor transmission line geometries with aperture excitation.     

Experimental Characterization of Multiconductor Transmission Lines in the Frequency Domain

Although a number of papers have been published on the experimental characterization of multiconductor transmission lines, they are limited to the time domain for lossless multiconductor lines in homogeneous media. This paper presents a method for the characterization of multiconductor transmission lines in inhomogeneous media. The experimental technique for the measurement of multiconductor line parameters is presented and the appropriate multiconductor line equations are solved to obtain these parameters. The experimental method involves only the short-and open-circuit impedance measurements for different configurations. The experimental results for a four-conductor line are found to be in good agreement with computed results and a low-frequency lumped model.     

Time-domain response of multiconductor transmission lines

Evaluation of the time-domain response of multiconductor transmission lines is of great importance in the analysis of the crosstalk in fast digital circuit interconnections, as well as in the analysis of power lines. Several techniques for the computation of the line response, starting from the known circuit-theory parameters, are presented and evaluated. These methods are: time-stepping solution of the telegrapher equations, modal analysis in the time domain, model analysis in the frequency domain, and a convolution technique which uses line Green's functions. The last method can treat the most general case of lossy transmission lines with nonlinear terminal networks. Numerical and experimental results are presented to illustrate these techniques and to give insight into the crosstalk problems in fast digital circuits.     

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.     

Sensitivity analysis of multiconductor transmission lines andoptimization for high-speed interconnect circuit design

Sensitivity analysis of multiconductor transmission lines is derived from a new, all-purpose multi-conductor transmission line model in both frequency domain and time domain. Computer implementation of this new model as well as the sensitivity analysis has been completed. It enables efficient, accurate simulations of interconnect circuit responses as well as sensitivity analysis with respect to both electrical and physical transmission line parameters. By applying sensitivity analysis to high-speed interconnect circuit design, design variables are optimized to achieve simultaneous minimization of crosstalk, delays and reflections at desired nodes in the circuit without violating any indispensable design rules. Numerical examples are presented to demonstrate the validity of the proposed sensitivity analysis and illustrate its application to the optimization of high-speed interconnect circuit design     

Distributed equivalent sources for the analysis of multiconductortransmission lines excited by an electromagnetic field

The interaction of multiconductor lines with electromagnetic radiation is commonly studied in terms of field-induced voltage and current sources distributed along the line. The author presents the relationships between these sources and the incident fields for the general case of a transmission line with its conductors embedded in different dielectric volumes of arbitrary shape. It is shown that the sources can be expressed directly in terms of the incident fields and some vector parameters which are determined from the solution of a series of electrostatic problems with appropriate boundary conditions independent of the incident electric fields. It is noted that the multiconductor lines are suitable for direct applications in microwave transmission lines with rather arbitrary configurations     

Efficient passive circuit models for distributed networks withfrequency-dependent parameters

This paper presents an efficient method for the analysis of multiconductor transmission lines with frequency-dependent parameters. The proposed technique generates positive-real representations for the frequency dependency of transmission line parameters as well as closed-form expressions based on exponential Pade approximants. The new model is suitable for inclusion in general purpose circuit simulators and overcomes the difficulty of mixed frequency/time simulation encountered during transient analysis. In addition, the proposed model can be easily incorporated with the recently developed passive model-reduction techniques. Numerical examples are presented to demonstrate the validity and efficiency of the proposed method     

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.     

Simplified Macromodel of MTLs With Incident Fields (SiMMIF)

Electromagnetic compatibility (EMC) analysis of high-speed designs has become imperative due to rapidly increasing radio-frequency interference and emerging technological trends such as higher operating frequencies, denser layouts, and multifunction convergent products. In this paper, a simplified macromodel of multiconductor transmission lines (MTLs) exposed to incident fields is presented. The proposed formulation can also handle frequency dependence of resistance, capacitance, conductance, and inductance (RLGC) line parameters. The method employs the recently developed delay-extraction-based compact and passive MTL macromodel, while developing closed-form expressions for incident field analysis. An error bound for the proposed macromodel is also presented. The macromodel is simulation program with integrated circuit emphasis (SPICE) compatible and overcomes the mixed frequency/time simulation difficulties usually encountered during transient analysis, while guaranteeing the stability of the global transient simulation. The algorithm provides higher accuracy as well as significant speed gains for EMC analysis of transmission line networks as compared to the existing techniques.     

A new approach for closed-form transient analysis of multiconductor transmission lines

A novel closed-form model for multiconductor transmission lines is presented. The proposed model is derived from the analytical characterization of half-T ladder networks, which using closed-form polynomials (named DFF and DFFz), allow one to exactly extract poles and residues of the two-port representation of multiconductor transmission lines, thus, generating a time domain macromodel that can be incorporated in a circuit simulator. Since the model is derived from a stable and passive equivalent network, its stability and passivity are strictly preserved. Simulation results for one, two, and three-conductor transmission lines with linear and nonlinear terminations are presented, confirming the validity of the proposed model.     

An equivalent circuit model for terminated hybrid-modemulticonductor transmission lines

An equivalent circuit for terminated hybrid-mode multiconductor transmission lines is presented. Existing CAD packages, such as SPICE, can be used for its implementation. Model parameters can be found from either a TEM or a full-wave analysis of the transmission lines. The equivalent circuit is used to simulate multiconductor microstrip for applications in high-speed integrated circuits. The accuracy of the TEM approximation is investigated for time-harmonic as well as pulse signal propagation. For some cases examined, the time-harmonic signal propagation data obtained using the TEM approximation become quite inaccurate at frequencies in excess of 20 GHz. The TEM approximation is adequate, however, for pulse propagation with 15-ps risetime and falltime pulses on the geometries investigated     

Propagation Modes, Equivalent Circuits, and Characteristic Terminations for Multiconductor Transmission Lines with Inhomogeneous Dielectrics

The theory of wave propagation on Iossless multiconductor transmission lines with inhomogeneous dielectrics is developed using matrix analysis. The treatment is concise and complete and has the advantage of identifying propagation modes in a way that permits straightforward physical interpretation. The equivalent circuit for the general line is derived and its application to the solution of wave problems with reflections is demonstrated. Special consideration is given to the problem of characteristically terminating a multiconductor line, i.e., terminating without reflections. The realizability of such a characteristic termination network is discussed, and proofs of realizability are given for the important cases of all lines with homogeneous dielectrics and all three-conductor lines, regardless of dielectric inhomogeneities. Symmetric three-conductor lines are discussed to exemplify the general theory, and an application to the problem of mode conversion on symmetric and asymmetric shielded strip lines is given.     

高速集成电路中多导体传输线的电磁参数提取与瞬态响应分析

本文在直线法中引入了一种新技术，将多层介质多导体结构的各层介质等效为级联的坪端口网络，介质层间导体等效为端口的电流源，从而大大简化了公式推导，方便了编程计算。     

TDSE方法用于多导体传输线端接动态元件的分析

利用时域空间扩展方法(TDSE)对多导体传输线端接动态元件的情况进行了分析，为电磁兼容分析提供了一种新的途径。利用该方法分别对由独立激励源和入射电磁波激励的传输线的终端感应电压和电流进行了分析。仿真结果表明：当传输线端接动态元件的时候，终端感应电压和电流的过渡过程时间将会变长。     

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