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.     

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。     

An efficient algorithm for sensitivity analysis of nonuniform transmission lines

This paper presents a new algorithm that addresses an important issue arising in computation of sensitivity for nonuniform transmission lines using the idea of model reduction through integrated congruence transform. This issue is related extending the concept of implicit basis construction, which was introduced earlier to simulate nonuniform transmission lines, to the task of sensitivity analysis. A new algorithm is presented to compute the orthogonal basis needed to obtain the reduced system used in sensitivity analysis. The proposed algorithm incorporates a new orthogonalization procedure which can be used to find an orthogonal basis for a set of moments derived from inhomogeneous differential equations, but without having to compute those moments explicitly. Numerical results demonstrate that reduced-order systems constructed by the proposed algorithm have improved numerical accuracy in sensitivity computation.     

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     

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.     

A Precise Time-Step Integration Method for Transient Analysis of Lossy Nonuniform Transmission Lines

This paper presents a novel time-domain integration method for transient analysis of nonuniform multiconductor transmission lines (MTLs). It can solve the time response of various kinds of transmission lines with arbitrary coupling status. The spatial discretization in this method is the same as the finite-difference time-domain (FDTD) algorithm. However, in order to eliminate the Courant-Friedrich-Levy condition constraint, a precise time-step integration method is utilized in time-domain calculation. It gives an analytical solution in the time domain for the spatial discretized Telegrapher's equations with linear boundary conditions. Large time steps can be adopted in the integration process to achieve accurate results efficiently. In the analysis of transmission lines with frequency-dependent parameters, a passive equivalent model is introduced, which leads to the similar semidiscrete model as that for the frequency-independent case. In addition, a rigorous proof of the passivity of the model is provided. Numerical examples are presented to demonstrate the accuracy and stability of the proposed method.     

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.     

Riccati matrix differential equation formulation for the analysisof nonuniform multiple coupled microstrip lines

A Riccati matrix differential equation (RMDE) is formulated for analyzing nonuniform coupled microstrip lines (NCML's) in the frequency domain. The formulation is based on a reciprocity-related definition in the theory of multiconductor transmission lines under quasi-TEM assumption. The hybrid-mode nature of modal phase velocities and strip characteristic impedances for multiconductor microstrip structure is included. The nonlinear RMDE is first transformed into a first-order linear differential matrix equation which can be efficiently solved using method of moments. A convergence study is performed to investigate the sufficient number of basis functions used in the method. The voltage-scattering parameters of a tapered microstrip and two three-line structures are presented. The frequency responses of a pair of nonuniform coupled lines are measured and compared with calculated results     

一种用于分析高速VLSI中频变互连线 瞬态响应的精细积分算法

本文利用精细积分法求解高速VLSI中频变参数互连线的瞬态响应.首先,从频域传输线方程出发,利用反拉氏变换将其转化为含有卷积项的时域方程,经过空间坐标离散后,再采用精细积分法进行求解.与以往的空间离散方法相比较,提出采用电压和电流空间间隔取点的方法,减小了截断误差.在计算常微分方程组中的非齐次项时,采用递归计算代替传统数值卷积大大提高了计算的效率.该方法对于耦合传输线无须进行解耦,在处理非均匀频变传输线时也非常方便.数值实验结果表明,该算法稳定性好,计算精度高.     

Analytical solutions in nonuniform multiconductor transmission linetheory

The theory of nonuniform multiconductor transmission lines (NMTLs) is characterized by generalized telegrapher equations. Formally, these are straightforwardly solved, but an explicit construction of the solution turns out to be mathematically demanding. This paper discusses and reports on recently proposed reduction schemes that simplify the structure of the solution and make it suitable for direct evaluation. Applications of these results are described, as well as field theoretical extensions of the existing formalism     

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.      

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     

Frequency Response of Multiconductor Transmission Lines Illuminated by an Electromagnetic Field

A well-known result [1], [2] for the response of a two-wire transmission line illuminated by a nonuniform electromagnetic field is extended to multiconductor lines. A simple matrix equation for the currents induced in arbitrary termination networks is obtained. Air Development Center.     

The Time Domain Propagator Method for Lossless Multiconductor Quasi-TEM Lines

A time domain propagator method is developed to solve telegraphers equations for coupled lossless multiconductor quasi-TEM transmission lines. The resulting expression is obtained in a form in which the propagator operates on the line voltage and current. Examples are presented showing that exceptionally accurate results are obtained for uniform and nonuniform coupled microstrip lines. The lack of numerical dispersion with the propagator method is demonstrated through an examination of two coupled microstrip lines.      

Electromagnetic Field-to-Wire Coupling in the SHF Frequency Range And Beyond

Methods have been developed for the treatment of field-to-wire coupling at superhigh frequencies (SHF's) and beyond. In this region, transmission-line lengths and wire separations become very large electrically, and field-to-wire coupling problems become intractable. Several types of transmission lines have been examined in the SHF range, including uniform and nonuniform transmission lines, coaxial transmission lines, and multiconductor transmission lines. Current distributions are found to be predominantly of a standing-wave or traveling-wave form. The higher order modes are not significant for those cases examined. Bounds may be obtained for induced currents in the field-to-wire problem by considering the transmission line as a receiving antenna. The maximum value of induced current under conditions of maximum susceptibility is shown to vary little with frequency.     

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.     

一种分析双层多导体微带传输线的有效方法

本文利用直线法结合周期边界条件,分析了双层多导体微带传输线的色散特性,与直线法结合吸收边界条件的常规方法相比,本文的做法可得到具有解析形式的特征值与特征矢,并且能够利用快速付里叶变换来计算阻抗元素,从而大大提高计算效率.计算实例证明了方法的正确性和有效性.最后给出了几种不同结构微带传输线的色散特性.     

分析多层介质多导体传输线的区域分解法

本文利用区域分解法 ,将直线法和有限差分法结合起来 ,用于计算多层介质中具有任意截面形状多导体传输线的电容和电感矩阵。通过在纯介质区域使用直线法 ,导体所在区域使用有限差分法分别进行求解 ,充分发挥两种方法各自的优越性。直线法中快速傅里叶变换的引入进一步提高了算法的计算效率。数值结果表明 :该方法是有效的 ,且计算时间与介质层的厚度无关。文中还研究了介质层分界面的不平整性对传输线电磁参数的影响。     

Efficient simulation of nonuniform transmission lines using integrated congruence transform

This paper presents a new algorithm based on integrated congruence transform for efficient simulation of nonuniform transmission lines. The proposed algorithm introduces the concept of model-order reduction (MOR) via implicit usage of the Hilbert-space moments in distributed networks. The key idea in the proposed algorithm is the development of an orthogonalization procedure that does not require the explicit computation of the Hilbert-space moments in order to find their spanning orthogonal basis. The proposed orthogonalization procedure can thus be used to compute an orthogonal basis for any set of elements that are related through a differential operator in a generalized Hilbert space, without the need to have these elements in an explicit form. The proposed algorithm also addresses the problem of MOR of nonuniform transmission lines, through defining a weighted inner product and norm mappings over the Hilbert space of the moments. Numerical examples demonstrate more accurate numerical approximation capabilities over using the moments explicitly.