Matched-termination network for multiple parallel transmission lines

A matched-termination network for multiple parallel transmission lines is capable of absorbing all the possible TEM propagation modes without reflection. A general expression is presented for such a network when the transmission lines are lossless. If, in addition, the propagation velocities are all equal, a network can be designed by inspection.     

Impulsive impedances in lossless circuits: Fourier and Laplacemethods

A proposal for adding impulsive components of impedance/admittance to the reactance/susceptance for lossless transmission lines is extended to all lossless resonant circuits. This new Fourier analysis yields a finite rate of energy transfer from a lossless source while the orthodox analysis would give an unbounded steady-state energy transfer. Laplace transforms help to resolve this paradox     

Nonconventional Transmission Zeros in Distributed Rectangular Structures

A lossless distributed rectangular structure, composed of a dielectric layer interposed between two perfectly conductive metallic layers, is considered. This structure is endowed with two ports, whose positions and widths are variable and is connected to the environment through uniform transmission lines. A procedure is exposed to obtain the impedance matrix at the terminals of the transmission lines. The existence of transmission zeros and of filtering properties is demonstrated.     

Application of Modal Analysis to the Transient Response of Multiconductor Transmission Lines with Branches

An effective method for computing the time-domain response of lossless multiconductor transmission lines with branches in cross-sectionally inhomogeneous dielectric media is presented. Lines of this type are characterized by multiple propagation modes having different velocities. The theory of wave propagation on lossless multiconductor transmission lines with inhomogeneous dielectrics is used to obtain the modal amplitudes on the uniform sections of the line. The scattering matrix for the junction is used to compute the transmitted and reflected waves in the different branches at the junction. Each mode arriving at the junction excites multiple modes in all branches. The method described in this paper identifies all propagation modes in all branches of the line, and leads to the direct physical interpretation of the results. The method is general and can be applied to either partially or completely nondegenerate cases. Experimental results for a six-conductor transmission line with a single branch are found to be in good agreement with the results computed using the described method.     

Equivalent representation of lossy transmission lines—Part II: Skin effect consideration

The frequency dependence of conductor and earth is considered in deriving an equivalent representation of lossy transmission lines, having their return path through the earth in terms of lossless lines with terminating time-varying resistance.     

Inversion of the telegraph equation and the synthesis of nonuniform lines

The synthesis of nonuniform Iossless transmission lines, an important problem arising in fields such as waveguide design, acoustics, electrical circuit design, and scattering theory, is discussed entirely in the time domain. It is shown that corresponding to every (impulse-response) function satisfying certain regularity conditions and the passivity condition there is a lossless line whose taper is simply related to the impulse response through an integral equation. In particular, this correspondence is unique for lines along which the velocity is constant. The proofs use only elementary results from functional analysis, the theory of partial differential equations, and some well-known physical aspects of lossless lines.     

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     

Measurement of Reflection Coefficients through a Lossless Network (Correspondence)

Often it is not convenient to measure a reflection coefficient directly. In some such cases, the following procedure may be used. The arrangement of components shown in Fig. 1 will be considered. It will be assumed that lines Nos. 1 and 2 are lossless. These lines may be transmission lines, waveguides, or one of each.     

A general method of transient analysis for lossless transmission lines and its analytical solution to time-varying resistive terminations

A general solution of the problem of transients on lossless transmission lines has been formulated that is based on the classical analysis of the forward and reflected waves on the line. The problem of transients on a lossless line with arbitrary boundary conditions at the end of the line is then investigated. Transients on a line terminated by a time-varying resistance with arbitrary time dependence are obtained analytically. In the special case where the time dependence is a ramp function, the problem is solved by the Laplace transform method and it is shown that the two solutions are identical.     

Cascade synthesis of a multivariable transfer matrix

The necessary and sufficient conditions are established under which a multivariable transfer matrix can be synthetised as a cascade connection of lossless noncommensurate transmission lines. It is proved that, for this particular structure, the transmittance defines a unique reflectance.     

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。     

Analysis of transients in nonuniform and uniform multiconductortransmission lines

The author presents an effective method for computation of the transient response of multiple nonuniform transmission lines. This time-domain analysis technique can predict reflections and crosstalk. The proposed spectral technique is used to transform partial differential equations describing a system of transmission lines into a set of linear ordinary differential equations, which can be solved with one of the many well-developed integration techniques. Numerical experiments performed with the prototype program showed that the method can solve specific problems (lossless, uniform lines) just as fast as less general methods based on modal analysis exploiting the particular properties of lines     

Comments on "Approximation for the Symmetrical Parallel-Strip Transmission Line" (etters)

In a recent article, Rochelle gave an approximation for the capacitance of both "wide" and "narrow" parallel-strip transmission lines in a homogeneous, lossless, dielectric medium. The author obtained a final, unique formula, which is an advantage.     

工艺参数随机扰动下的传输线建模与分析新方法

本文考虑集成电路制造过程中传输线制造工艺参数随机扰动对传输线传输性能的影响,建立了传输线的随机模型.结合精细积分算法与蒙特卡洛方法分析了该传输线随机模型的瞬态响应,通过对模型输出的正态性进行偏度-峰度检验给出了最差情况估计.对于正弦激励情况推导了无耗传输线相应随机微分方程解的一阶矩的解析形式,给出了二阶矩的数值计算方法,最后估计出输出信号振幅与相移的上下界.实验结果表明本文提出的传输线随机模型及其分析方法可以对传输线的性能进行有效的评估.     

Time-domain modeling of high-speed interconnects by modified methodof characteristics

In this paper, a new model of lossy transmission lines is presented for the time-domain simulation of high-speed interconnects. This model is based on the modified method of characteristics (MMC). The characteristic functions are first approximated by applying lower order Taylor series in the frequency domain, and then a set of simple recursive formulas are obtained in the time domain. The formulas, which involve tracking performances between two ends of a transmission line, are similar to those derived by the method of characteristics for lossless and undistorted lossy transmission lines. The algorithm, based on the proposed MMC model, can efficiently evaluate transient responses of high-speed interconnects. It only uses the quantities at two ends of the lines, requiring less computation time and less memory space than required by other methods. Examples indicate that the new method has high accuracy and is very efficient for the time-domain simulation of interconnects in high-speed integrated circuits     

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.      

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.     

Transient analysis of coupled, tapered transmission lines witharbitrary nonlinear terminations

A fast and efficient method of simulating the time-domain transient response of coupled, tapered transmission lines is presented. A time-domain scattering parameter formulation is used to derive the simple closed-form expression for the voltage variables for uniform lossless lines; this expression is applied to tapered lines by dividing the lines into many uniform section. Computational efficiency and stability are achieved using recursive time-domain algorithms. When a quasi-TEM propagation mode is assumed, the method is applicable to nonlinear terminations and inhomogeneous dielectric media. Memory requirements are minimized and are independent of the number of time steps. Simulation results showed good agreement with experimental results     

Sharp-Rejection Wideband Bandstop Filters

In this letter, a novel transmission line configuration has been proposed to design a sharp-rejection, bandstop filter (BSF) with wide rejection bandwidth. The rejection bandwidth and the level of rejection are controlled by the characteristic impedances of the transmission lines. Design equations are obtained by using a lossless transmission line model. The proposed design has been verified in microstrip line by fabricating a prototype BSF of -20 dB fractional bandwidth of 100% at a stopband center frequency f₀ = 1.5 GHz. The filter structure is simple and easy to fabricate.     

Time-domain model for power dissipation of CMOS buffers drivinglossy lines

The dynamic power consumption of a CMOS buffer driving lossless and lossy transmission lines is investigated. A time-domain model for power dissipation in both the line driver and the interconnect losses is also presented. The model fully agrees with HSPICE simulations and is particularly suitable for implementation in CAD tools for fast estimation of VLSI dissipation circuits