Transient Response of Multiconductor Transmission Lines Excited by a Nonuniform Electromagnetic Field

The time-domain transmission-line equations for uniform multiconductor transmission lines in a conductive, homogeneous medium excited by a transient, nonuniform electromagnetic (EM) field, are derived from Maxwell's equations. Depending on how the line voltage is defined, two formulations are possible. One of these formulations is considerably more convenient to apply than the other. The assumptions made in the derivation of the transmission-line equations and the boundary conditions at the terminations are discussed. For numerical calculations, the transmission -line equations are represented by finite-difference techniques, and numerical examples are included.     

高速电路非均匀互连线间电磁干扰分析

根据高速电路中线宽发生变化的非均匀互连线结构特点,利用分段线性和等效电路摸型的方法,结合HSPICE电路分析软件,提出了适用于任意条数的非均匀互连线的多导体等效电路模型及仿真模型,从倾斜角度、非均匀互连线长度和信号上升时间几个特殊因素方面,对高速电路中非均匀互连线间的电磁干扰规律进行了分析和总结。     

Coupled-Mode Analysis of Nonuniform Coupled Transmission Lines

The transmission-line equations describing propagation along coupled transmission lines are cast in coupled-mode form so that the roles of the different coupling coefficients and the impedance variation are more directly observable. Restrictions on the various parameters for obtaining directional coupling with nonuniform lines are then discussed and exact solutions for the coupling response of two nonuniform coupled lines with particular variations of the coupling coefficients are presented. The results obtained from the exact closed-form solutions should aid in the design of tapered couplers.     

Closed-form Analysis of Lossy Cosine-Squared Tapered Nonuniform Transmission Lines

The rigorous analytical solutions and the ABCD matrix of the lossy Cosine-Squared tapered nonuniform transmission lines (CSTNTL) are presented in this paper. According to different boundary conditions, the unique solution is obtained mathematically. Through the numerical calculations based on analytical solutions, the distributed voltages and currents in different terminated cases are shown to explain the transmission characteristics of CSTNTL. Especially in the lossy case the distributed power values are simulated to show the attenuation phenomenon.     

Efficient Modeling of Transmission Lines With Electromagnetic Wave Coupling by Using the Finite Difference Quadrature Method

This paper proposes an efficient numerical technique, called the finite difference quadrature (FDQ) method, to model the transmission line with radiated electromagnetic (EM) wave noise coupling. A discrete modeling approach, the FDQ method adapts coarse grid points along the transmission line to compute the finite difference between adjacent grid points. A global approximation scheme is formulated in the form of a weighted sum of quantities beyond the local grid points. Unlike the Gaussian quadrature method that computes numerical integrals by using global approximation framework, the FDQ method uses a global quadrature method to construct the approximation schemes for the computation of, however, numerical finite differences. As a global approximation technique, the FDQ method has superior numerical dispersion to the finite difference (FD) method, and, therefore, needs much sparser grid points than the FD method to achieve comparable accuracy. Equivalent voltage and current sources are derived, exciting the transmission line at the grid points. Equivalent circuit models are consequently derived to represent the transmission line subject to radiated electromagnetic wave noise. The FDQ-based equivalent models can be integrated into a simulator like SPICE.     

Equivalent Representations of Lossy Nonuniform Transmission Lines

Equivalent transformations, which were recently derived for mixed lumped and distributed circuits, may be extended to circuits consisting of lumped reactance, resistors, and Iossy transmission lines. It is shown that circuits consisting of a cascade connection of lumped element sections and Iossy uniform transmission lines are equivalent to circuits consisting of a cascade connection of lossy nonuniform transmission lines, lumped elements, and ideal transformers. Furthermore, by considering the limiting case of these transformations, equivalent transformations for circuits consisting of a cascade connection of lumped reactance, resistors, and nonuniform transmission lines are obtained. Exact equivalent circuits of Iossy even-order binomial form transmission lines are derived from these equivalent transformations.     

Analysis of Microstrip-Like Transmission Lines by Nonuniform Discretization of Integral Equations

The nonuniform discretization of the integral equation on the tangential electromagnetic (EM) field on the boundary surface is proposed as a numerically efficient method to analyze the microstrip-like transmission lines. The calculated results of the propagation constant of the microstrip line based on this method are compared with other published analytical results. Various types of planar striplines are treated by the same formulas. The dominant and higher order modes of shielded microstrip line are discussed and compared with the longitudinal-section electric (LSE) and linear synchronous motor (LSM) modes of a two-medium waveguide.     

非均匀传输线特性重构中的噪声影响分析

利用时域反射技术(Time Domain Reflectometry,TDR),由测量得到的时域反射信号,可以重构出非均匀传输线的一些特征参数。当反射信号中混有噪声时,对非均匀传输线特性参数的重构会产生影响。采用Zakharov-Shabat类型逆散射问题的数值反演算法,以指数型非均匀传输线为例,对时域反射信号中混有高斯白噪声情况下的非均匀传输线特性参数重构问题进行了数值实验。数值计算结果表明,在噪声干扰下,算法本身是稳定的,在较宽的信噪比范围内,能有效地重构出非均匀传输线的特征参数。     

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.     

Tunable Filters With Nonuniform Microstrip Coupled Lines

A basic wideband tunable filter design based on combline topology is presented. At the presence of the parasitic effects, the structure of the filter must be modified by introducing additional degrees of freedom to the geometry of the coupled line segment. A design procedure involving iterative steps will be described. This procedure is used to design two bandpass filters with more than one octave tuning range in the UHF band. The experimental results are presented for the filter prototypes implemented using printed circuit boards and PIN diodes.     

非均匀有耗传输线ABCD参量的求解

传输线理论是射频与微波电路的重要基础理论,而其中ABCD参量特别适用于分析级联网络的传输性能.本文针对非均匀有耗传输线的ABCD参量求解问题,建立传输线的数学模型,给出了三种解法,即级联法、微分方程法和积分方程法,并对三种方法的准确性和效率进行了讨论.     

平面电磁波对双导线传输线终端瞬态响应的求解

随着传输线方法在电磁兼容和电磁干扰分析方面的广泛应用,人们对传输线方程的求解方法也越来越感兴趣.求解传输线方程的方法通常有时域差分方法和频域差分法.而对于平面电磁波对双导线传输线终端的响应,文章给出了其频域解析解,并且运用这个解析解和Fourier变换技术,可以很容易地给出传输线终端的瞬态响应分析.通过数值仿真实验研究三个角度参数φ、α和Ψ在电磁感应中的作用:当φ和α保持不变(或者Ψ和α保持不变),随着Ψ(或者φ)的增大,终端2的感应电流的响应时间缩短,第一阶段的感应时间延长;当φ和Ψ保持不变,随着α的增大,终端2处第一阶段的感应电流也随之减小.     

Equivalent Circuits of Binomial Form Nonuniform Coupled Transmission Lines

Equivalent circuits of nonuniform coupled transmission lines whose self and mutual characteristic admittance distributions obey binomial form are presented. Telegrapher's equations of these nonuniform coupled transmission lines can he solved exactly rising Bessel functions of fractional order. By decomposing the chain matrix, it is shown that equivalent circuits of these nonuniform conpled transmission lines consist of cascade connections of lumped reactance elements, uncoupled uniform transmission lines and ideal transformers.     

用波形迭代法分析非均匀多导体传输线的时域响应

本文从频域电报方程出发推出了一个描述传输线ABCD矩阵的微分方程,将传输线时域响应分析从微分方程的边值问题转化为数学上更易求解的初值问题。然后利用波形迭代法数值求解非均匀传输线的ABCD矩阵,证明了一个关于迭代收敛性的定理,并据此采取了旨在加快收敛速度的将传输线分割成许多相互级联的子网络的步骤。传输线的ABCD矩阵求得后,便可借用付里叶变换和卷积技术对具有线性、非线性负载的传输线时域响应进行分析。给出的应用实例表明,诙分析方法是有效而可靠的。     

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.     

Loop-Back AWG Router With Nonuniform Transmission Capacity

We have developed an arrayed-waveguide-grating-based wavelength router with a loop-back structure for a system with nonuniformly distributed traffic. We describe the design principle with particular regard to the loop-back waveguide connections, and discuss its optical routing functions with some experimental results.     

Coupling Model of Crossing Transmission Lines

The coupling between transmission lines crossing diagonally is described. The resulting equations are derived by neglecting the recoupling of the line under induction (acceptor line (AL)) to the exciter line (EL). The coupling coefficients of various models are also considered. Equivalent-circuit representations for finite-length lines are obtained in two different forms: one expressed in terms of ideal voltage and ideal current sources, and the other in terms of ideal transformers, mutual inductance, and mutual capacitance. The first expressions are useful for predicting coupling between various types of lines. The second shows the coupling mechanism. The validity of the theory is confirmed by the experimental studies.     

Application of Nonuniform Transmission Lines to Ultra Wideband Pulse Shaping

The work presented in this letter demonstrates that nonuniform transmission lines (NUTLs) can be used for pulse shaping applications in ultra wideband pulsed systems and presents an approach to their design for this application. The pulsed waveforms generated are modified Hermite polynomials and encoded pulse trains thereof and are characterised by a broad bandwidth ranging from near DC to over 10 GHz and relatively long temporal duration in the region of nanoseconds. These pulses are more mathematically complex and at least three times higher bandwidth than previously has been reported in the literature. It is also believed to be the first time that modified Hermite polynomial pulses have been generated in practice. The NUTL design approach is verified by test structures fabricated on FR4 circuit board. The results demonstrate that NUTLs, which are completely passive structures, allow generation of complex pulse shapes in applications requiring fast, transient waveforms.      

非均匀传输线ABCD参数的微分方程解法

随着集成电路工艺进入到深亚微米阶段,传输线特性分析对于集成电路设计和优化具有重要意义。针对非均匀传输线的ABCD参数,建立传输线数学模型,通过传输线电报方程推导出ABCD参数满足的微分方程组,并采用龙格-库塔法进行求解得到ABCD参数,最后通过数值算例验证了方法的有效性。     

用基于龙格-库塔迭代的NILT进行非均匀传输线的瞬态分析

通过龙格-库塔(Runge-Kutta)方法迭代求出非均匀传输线的广义ABCD矩阵，再解常微分方程求得整个系统的拉氏城响应，最后利用数字拉氏逆变换(NILT)获得电路的时域响应，从而使得传统的NILT法得以分析非均匀传输线，实例表明其具有较高的效率和精度。