一种多导体传输线瞬态响应时间步积分法

针对时域有限差分法分析非均匀有损耗多导体传输线瞬态响应的差分振荡问题,提出一种多导体传输线瞬态响应的时间步积分方法。该方法对不等长非均匀有损多导体传输线建模时,无需对耦合传输线进行解耦,能够较方便地求解耦合状态下的不等长非均匀有损多导体传输线系统。所提方法首先对电波方程中的空间微分算子进行差分离散,然后采用梯形积分法对时间微分算子进行积分,最终得到分析不等长非均匀有损多导体传输线瞬态响应的时间步积分算法。该算法不仅应用于不等长非均匀有损多导体传输线模型进行数值计算和理论分析,并对传输线终端端接线性负载和非线性负载的两种情况进行仿真验证。仿真结果表明该方法是有效的。     

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.     

多导体传输线瞬态响应研究

针对多导体传输线瞬态响应的无源性问题,提出了基于集总等效源模型的多导体传输线瞬态响应模型. 从外场激励下的多导体传输线的频域电报方程解出发,将外场在传输线上激励的分布电压源和电流源与传输线指数矩阵解耦,建立了集总等效电压源和电流源模型. 为避免复杂的傅里叶反变换及卷积运算,推导了集总源模型的时域递推方程. 在此基础上,采用时域有限差分法建立了端接线性负载、非线性负载和外场激励下的不等长多导体传输线瞬态响应离散递推方程. 通过对无损传输线的仿真对比,验证了方法的有效性. 最后,对端接线性负载、非线性负载和外场激励下的不等长多导体传输线瞬态响应进行了试验和仿真分析.     

多导体传输线瞬态响应研究

针对多导体传输线瞬态响应的无源性问题,提出了基于集总等效源模型的多导体传输线瞬态响应模型. 从外场激励下的多导体传输线的频域电报方程解出发,将外场在传输线上激励的分布电压源和电流源与传输线指数矩阵解耦,建立了集总等效电压源和电流源模型. 为避免复杂的傅里叶反变换及卷积运算,推导了集总源模型的时域递推方程. 在此基础上,采用时域有限差分法建立了端接线性负载、非线性负载和外场激励下的不等长多导体传输线瞬态响应离散递推方程. 通过对无损传输线的仿真对比,验证了方法的有效性. 最后,对端接线性负载、非线性负载和外场激励下的不等长多导体传输线瞬态响应进行了试验和仿真分析.       

多导体传输线瞬态响应研究

随着多导体传输线内各导体之间间距的减小, 导体之间的近邻效应对传输线的分布参数和传输特性的影响越来越大.为此, 我们针对三种典型的传输线结构, 分别建立了基于矢势有限元方法分析的多导体传输线的模型, 并分析了近邻效应对磁通密度和分布电感的影响.利用提出的方法计算了同轴传输线的单位长度分布电感, 并将它与采用解析方法得到的结果进行比较来证明该方法的正确性.计算双线传输线在不同间距时的单位长度电感, 与理论分析得到的结果相比较验证了导线间距越小, 近邻效应对单位长度电感的影响越大.最后, 计算考虑了近邻效应的耦合微带线的电感矩阵, 并将它与其他不考虑近邻效应的方法得到的结果相比较, 说明近邻效应对传输线电感矩阵的影响.     

Coupled mode analysis of forward and backward coupling in multiconductor transmission lines

The nonorthogonal coupled mode theory is extended to the analysis of multiconductor transmission lines by including backward coupling. Coupling coefficients are expressed as overlap integrals of the eigenfields and currents belonging to individual lines. These eigenmode solutions are calculated using the finite-difference time-domain method, which can provide a broadband solution through a single simulation. General termination conditions are given, and scattering parameters of a multiconductor transmission line can be obtained directly by solving the coupled mode equations subject to these termination conditions. As illustrative examples, several configurations of coupled microstrip lines are analyzed, and numerical results are presented. It is observed that both the forward and backward coupling results agree fairly well with results from Advanced Design System Momentum software.     

不均匀多导体传输线的瞬态分析

针对越来越严重的信号畸变和线间耦合问题,应用时域有限差分法（Finite Difference Time Domain,FDTD）建立了不均匀多导体传输线的仿真模型,并通过MATLAB编程对不均匀多导体传输线两端的电压响应进行了仿真分析.在此基础上,理论说明了各端口瞬态响应的波形特点.结果表明了时域有限差分法用于分析多导体传输系统电磁兼容问题的正确性和有效性,为电磁干扰的预测提供了有价值的参考信息.     

Adaptive transient solution of nonuniform multiconductor transmission lines using wavelets

This paper presents a highly adaptive algorithm for the transient simulation of nonuniform interconnects loaded with arbitrary nonlinear and dynamic terminations. The discretization of the governing equations is obtained through a weak formulation using biorthogonal wavelet bases as trial and test functions. It is shown how the multiresolution properties of wavelets lead to very sparse approximations of the voltages and currents in typical transient analyzes. A simple yet effective time-space adaptive algorithm capable of selecting the minimal number of unknowns at each time iteration is described. Numerical results show the high degree of adaptivity of the proposed scheme.     

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 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.     

A SPICE model for multiconductor transmission lines excited by anincident electromagnetic field

This paper describes a SPICE model that may be used for predicting the time-domain or frequency-domain voltages and currents induced at the terminations of a multiconductor transmission line (MTL) by an incident electromagnetic held. Explicit results for the entries in the SPICE circuit model are obtained for an incident uniform plane wave that may represent sources such as radio and television transmitters, radars, lightning, etc. The result relies on the transformation of the MTL equations into uncoupled modal lines by similarity transformations. The entries in the similarity transformations are provided for lossless lines. The model is implemented using controlled sources to implement the modal transformations and delay lines to implement the modal lines. If the model is implemented as a SPICE subcircuit model, the time-domain form of the incident field can be implemented as a source external to that subcircuit model so that changes in the line responses due to changes In the incident field waveform can be simulated without changing the subcircuit model. In order to avoid negative line delays, the result is restricted to incident waves having components of the propagation vector in the positive direction along the line. This restriction can be removed by simply reversing the line. The paramount advantages of the model are that both time-domain and frequency-domain results can be easily obtained with the existing SPICE code, and nonlinear loads, such as transistors and digital devices, as well as dynamic loads, such as inductors and capacitors, may be easily incorporated using the existing elements in the SPICE code. Predicted results for MTL's using the method are compared to those of the time-domain to frequency-domain transformation and finite difference-time-domain (FDTD) methods     

Quick quasi-TEM analysis of multiconductor transmission lines withrectangular cross section

This paper presents an efficient and accurate procedure for computing the quasi-static matrix parameters ([C], [L], [G], and [R]) of rectangular-shaped conductors embedded in a multilayered dielectric medium over an infinite ground plane. An additional top ground plane can also be considered., The problem is formulated in terms of the space-domain integral equation for the free-charge distribution on the slab conductor surfaces. The spatial Green's function is computed from its spectral counterpart using system identification techniques [Prony's method or matrix pencil method (MPM)]. The integral equation is solved by means of a Galerkin scheme employing entire domain basis functions. This results in a small matrix size. In addition, the quasi-analytical evaluation of the entries of the Galerkin matrix leads to a very efficient and accurate computer code. A detailed study on the convergence and accuracy of the method has been included     

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     

On eliminating crosstalk within multiconductor transmission lines

This letter presents a concept of total elimination of crosstalk between signals propagating in multiconductor transmission lines. It is sufficient to match the line on both ends with a proper net of resistances and assure a proper distribution of each exciting signal into some of the branches of the input net. The concept is verified using SPICE circuit simulator.     

Comments on "A SPICE model for multiconductor transmission lines excited by an incident electromagnetic field" [and reply]

In a recent paper, C.R. Paul (see ibid., vol.36, p.342, 1994) discusses the concept of using the SPICE circuit analysis code for simulating field-to-wire coupling. He may not be aware that similar work has already been undertaken. A paper by Broyde et al. (1991) appears to be the first published implementation of this idea. The present comments on Paul's mostly theoretical paper emphasize some practical aspects of the simulation of EMC problems using a SPICE simulation program when multiconductor transmission lines (MTL) models are implemented. C.R. Paul responds to the comments.     

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.     

A static study of multilayered multiconductor transmission lines

Accurate knowledge of passive MIES and MMIGS has become as important as knowledge of active components. A rather classical method of analysis of multi-dielectric multistrip transmission lines is presented. This analysis, restricted to the quasi-static approach, is based on a variational method in the discrete spectral domain, combined with the transverse transmission line method devoted to the calculation of Green’s functions. This work, devoted only to the study of the distributed parameters of the structures, i.e. in any transverse section, is followed by a complete modal analysis with respect to the direction of propagation and the possible boundary conditions at the terminals. These calculations consist actually mostly of an eigenvalue problem. They are carried out analytically as far as possible by means of a block matrix algebraic formalism particularly well suited to the problem. The mode impedances and the impedance matrix are obtained analytically in a general manner. All the parameters of new structures with four conductors are completely made explicit.     

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     

不等长非均匀有损耗传输线FDTD瞬态分析

以分析等长均匀无损耗多导体传输线的时域有限差分（FDTD）法为基础,在考虑传输线损耗的情况下,对不等长非均匀多导体传输线进行分析。首先,在考虑传输线损耗的情况下给出传输线上各点电压和电流的迭代计算公式;其次,利用该公式对不等长非均匀有损耗传输线模型进行数值计算和理论分析;最后,通过仿真实验,其结果表明所提计算方法是正确和有效的。该方法对不等长非均匀有损耗传输线的研究提供理论计算参考。