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     

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.     

A SPICE model for incident field coupling to lossy multiconductortransmission lines

An efficient time-domain macromodel for incident field coupling to lossy multiconductor transmission lines is presented. The model takes the form of ordinary differential equations and can be easily included in SPICE like simulators for transient analysis. The model is based on the closed-form matrix-rational approximation of the exponential matrix describing telegrapher's equations and semi-analytic rational approximation of forcing functions     

Efficient sensitivity analysis of lossy multiconductor transmissionlines with nonlinear terminations

An efficient approach for sensitivity analysis of lossy multiconductor transmission lines in the presence of nonlinear terminations is described. Sensitivity information is extracted using the recently developed closed-form matrix-rational approximation of the distributed transmission-line model. The method enables sensitivity analysis of interconnect structures with respect to both electrical and physical parameters. An important advantage of the proposed approach is that the derivatives of the modified nodal admittance matrices with respect to per-unit-length parameters are obtained analytically     

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 Green's Function-Based Sensitivity Analysis of Multiconductor Transmission Lines With Nonlinear Terminations

Time-domain sensitivity analysis of multiconductor transmission lines is derived from the dyadic Green's function of the 1-D wave propagation problem. The rational nature of the Green's function permits the generation of a time-domain macromodel for the computation of transient voltage sensitivities with respect to both electrical and physical parameters, completely avoiding similarity transformation. Through simulations of multiconductor transmission lines with linear and nonlinear terminations, comparisons are made with the perturbative approach and standard frequency-domain techniques for multiconductor transmission lines.      

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.     

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     

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.     

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     

Analysis of multiconductor transmission lines using the MacCormack method

I. Introduction With the increasing signal speed and decreasing feature size of modern high-speed integrated circuits, the effects of transmission lines, such as delay, crosstalk, and signal distortion, become very impor- tant[1?3]. Coupling between transmission lines must be considered in circuit analysis. When multicon- ductor transmission lines are studied, they are usu- ally decoupled first[4?9]. The decoupling processes are similar and all have the diagonalization of pa- rameter matrices…     

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 quasi-TEM analysis for curved and straight planar multiconductorsystems

A quasi-TEM (transverse electromagnetic) analysis for straight and weakly curved planar multiconductor transmission lines is presented. This transverse field of a weakly curved planar multiconductor system is described by the static electric and magnetic solutions of the corresponding axially symmetrical structure. The capacitance and inductance matrices of this system of concentric microstrip rings are calculated using the method of lines. A two-port network consisting of circularly curved transmission lines is calculated and the results are compared with measured values. It is concluded that the proposed method of approximation is suited for analysis of microwave components as well as for high-speed digital circuits with interconnections consisting of curved striplines instead of straight lines with discontinuities     

Closed-Form Expressions for the Total Power Radiated by an Electrically Long Multiconductor Line

Two analytical solutions based on transmission-line theory for the total power radiated by a multiconductor line above a ground plane are proposed. The line is not assumed to be electrically short or close to the ground plane, thus making the proposed model suitable for assessing the emission/immunity of actual transmission lines employed in industrial contexts such as in the automotive domain, railway lines, and power-distribution lines. The model allows an imperfect ground plane to be considered through the complex-image approximation together with propagation losses. Numerical and experimental results are provided as a validation, while an empirical rule to assess the accuracy of the results is proposed. The two expressions aim at allowing fast parametric analysis of radiation during the design phase of the electrical and geometrical configuration of an unshielded multiconductor transmission line.      

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.     

Analysis of Lossy Transmission Lines with Arbitrary Nonlinear Terminal Networks

A novel method for transient analysis of Iossy transmission lines with arbitrary nonlinear terminal networks is presented. The uniqueness of this approach is that we develop time-domain Green's functions for the multiport transmission-line systems by terminating the ports in quasi-matched loads. This ensures Green's functions of a short duration. Hence, the amount of frequency-domain data necessary to obtain time-domain Green's functions is modest. These Green's functions are then convolved with the line port voltages. With this technique one can analyze responses of multiconductor transmission lines with arbitrary nonlinear loads (even with memory) as we have at any instant of time Thévenin's equivalent of the linear portion of the system. An example is presented to illustrate the application of this technique to multiconductor nonlinearly loaded transmission lines.     

端接非线性负载的不等长传输线瞬态分析

对时域有限差分(FDTD)法应用于不等长多导体传输线端接非线性负载的情况进行了介绍.首先给出了多导体传输线电报方程和差分公式;然后介绍了不等长传输线的仿真模型;在此基础上,最后通过建立端接非线性负载的不等长多导体传输线模型,对该情况下传输线两端的电压响应进行了分析.数值仿真结果说明了FDTD法解决此类问题的正确性和有效性,为不等长传输线瞬态分析的进一步研究打下了基础.     

Efficient quasi-TEM frequency-dependent analysis of lossy multiconductor lines through a fast reduced-order FEM model

An efficient finite-element reduced-order quasi-TEM model for the frequency-dependent characteristics of lossy multiconductor transmission lines is presented. Conductor losses are evaluated as functions of frequency through a magneto-quasi-static model. Numerically generated problem-matched basis functions reduce the problem size and, therefore, the CPU time required by frequency sweeps without appreciable loss of accuracy. The proposed approach is applied to complex coplanar waveguides and to multiconductor interconnects; its results are compared with quasi-analytical techniques and with the full-wave finite-element method.     

Rules for robust generation of accurate reduced-order models forhigh-speed coupled interconnections

Recently, robust algorithms have been established fur passive order reduction of electrical models of complex interconnection networks. However, very little is known about the way the order of the reduced model should be chosen to ensure accuracy in subsequent transient simulation studies, in this paper, a rule is derived for the selection of the order of the reduced model for interconnections modeled as transmission lines. It is shown that pulse rise time, interconnection length, and physical properties impact the order of the reduced model. The proposed rule is validated through numerical studies involving both analytic and numerical results from the frequency- and time-domain response of multiconductor transmission line circuits     

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