Transient analysis of lossy parabolic transmission lines withnonlinear loads

The exact analytical expressions of the time-domain step response matrix parameters for the lossy parabolic transmission line are developed, therefore extending the range of problems where Allen's method can be applied for the transient analysis of networks consisting of interconnections of linear distributed elements, lumped linear and/or nonlinear elements, and arbitrary sources. For completeness, similar expressions are derived for the lossless parabolic line. In order to demonstrate the versatility of the techniques presented in this paper, we study the transient response of a lossy parabolic line subjected to the following sets of boundary conditions: 1) a unit step input and a linear load, and 2) a trapezoidal pulse generator and a nonlinear load     

Analysis of crosstalk and field coupling to lossy MTLs in a SPICEenvironment

This paper proposes a circuit model for lossy multiconductor transmission lines (MTLs) suitable for implementation in modern SPICE simulators, as well as in any simulator supporting differential operators. The model includes the effects of a uniform or nonuniform disturbing field illuminating the line and is especially devised for the transient simulation of electrically long wideband interconnects with frequency dependent per-unit-length parameters. The MTL is characterized by its transient matched scattering responses, which are computed including both dc and skin losses by means of a specific algorithm for the inversion of the Laplace transform. The line characteristics are then represented in terms of differential operators and ideal delays to improve the numerical efficiency and to simplify the coding of the model in existing simulators. The model can be successfully applied to many kinds of interconnects ranging from micrometric high-resistivity metallizations to low-loss PCBs and cables, and can be considered a practical extension of the widely appreciated lossless MTL SPICE model, which maintains the simplicity and efficiency     

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     

Transient response of lossy transmission lines

Transient behaviour of lossy lines has been investigated and clarified. It has been shown that the lossy line terminated with a resistor ? (L/C) behaves similarly to a compensated resistive divider. Compensation occurs not only for distortionless lines, but also for so-called `quasidistortionless? lines.     

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     

Transient analysis of distortion and coupling in lossy coupledmicrostrips

The transient response of lossy coupled microstrips is studied using the spectral-domain approach (SDA) to rigorously compute the dielectric losses. The dielectric loss coefficient is computed using the SDA with a complex dielectric constant, and results are compared with those obtained by the formula advanced by M.V. Schneider (1969) using a finite-difference approximation for the partial derivative. Transient coupling is formulated in the frequency domain by an even/odd mode approach, showing how differences in either the modal loss coefficients or modal propagation constants can be responsible for coupling between lines. Results for pulse distortion on a semiconductor substrate are presented, showing how losses reduce the signal amplitude without significantly distorting the shape     

降低有损耦合微带线间串扰的方法分析

为降低和控制有损耦合微带线间的串扰,在强信号线两边各插入了一列用金属填充的、顶端用微带连接的接地孔.利用FDTD方法对该结构进行模拟并利用FEM法进行了验证.模拟结果表明串扰衰减程度与基底介质的损耗、接地孔参数有关.     

Plane wave coupling to multiple conductor transmission lines abovea lossy earth

The current induced on an infinite multiple conductor transmission line located above a lossy homogeneous medium due to a transient plane wave is discussed. An exact solution is formulated in the frequency domain using a spatial transform technique. The widely utilized quasi-TEM approximation is derived directly from the exact solution with emphasis on the physical consequences of the assumptions made. Both frequency domain and time domain numerical results are presented for typical transmission structures and documented electromagnetic pulse (EMP) excitations. Comparison of the quasi-TEM approximation to the exact solution is made in order to study the validity of its application in EMP coupling problems. The modeling of the EMP source as an incident plane wave is examined by comparing the induced current due to a dipole source with its steepest-descent contribution     

Transient plane wave coupling to bare and insulated cables buriedin a lossy half-space

The current induced on an infinite bare or insulated cable buried in a lossy earth medium due to a transient plane wave is presented. An exact solution is formulated in the frequency domain using a spatial transform under the thin-wire approximation. The widely used equivalent circuit transmission line model is derived from the exact solution. Results are presented for typical transmission structures under high frequency transient excitation and the exact solution is compared with the transmission line approximation. The transmission line approach provides good results for a wide range of cases. For accurate results in the high frequency situation it is necessary that the correct incident field expressions be used and that a complete representation of the earth's electrical properties (σ and ϵ) be retained     

端接非线性负载的非均匀传输线瞬态分析

在均匀多导体传输线的时域有限差分法(FDTD)基础上，对非均匀多导体传输线及端接非线性负载的情况进行了分析。结果表明：对于非均匀多导体传输线，采用FDTD法进行瞬态分析极为方便，并且可以处理端接非线性负载的情况；同时，还可获得线上各点的电压、电流波过程。通过实例验证了所提出的FDTD算法的有效性，可用于传输线波过程的研究。     

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。     

架空多导体传输线的时域阻抗分析

利用误差函数的拉普拉斯变换，对复深度法得出的频域阻抗直接进行拉普拉斯变换，获得了考虑土壤影响的架空多导体传输线时域自阻抗和互阻抗简单的表达式，通过Timotin公式和Pade变换的结果进行比较，验证了公式的正确性。     

Transient analysis of lossy transmission lines: an efficient approach based on the method of Characteristics

This paper is devoted to transient analysis of lossy transmission lines characterized by frequency-dependent parameters. A public dataset of parameters for three line examples (a module, a board, and a cable) is used, and a new example of on-chip interconnect is introduced. This dataset provides a well established and realistic benchmark for accuracy and timing analysis of interconnect analysis tools. Particular attention is devoted to the intrinsic consistency and causality of these parameters. Several implementations based on generalizations of the well-known method-of-characteristics are presented. The key feature of such techniques is the extraction of the line modal delays. Therefore, the method is highly optimized for long interconnects characterized by significant propagation delay. Nonetheless, the method is also successfully applied here to a short high/loss on-chip line, for which other approaches based on lumped matrix rational approximations can also be used with high efficiency. This paper shows that the efficiency of delay extraction techniques is strongly dependent on the particular circuit implementation and several practical issues including generation of rational approximations and time step control are discussed in detail.     

Transient analysis of radiated field from electric dipoles andmicrostrip lines

The transient response of the field radiated from electric dipole sources and microstrip lines with arbitrary time waveforms is analyzed. By using the three-dimensional Fourier transform of the spectral dyadic Green's function, relative to the integrated structure, an analytical closed-form solution is obtained and equivalent circuits for the analysis of the transient phenomena in the far-field region are derived. Numerical examples are provided to obtain noticeable insights to the behavior of planar circuits working under Gaussian pulsed excitation     

FDTD analysis of lossy, multiconductor transmission linesterminated in arbitrary loads

A hybrid method is presented for incorporating general terminations into the solution of lossy multiconductor transmission lines (MTLs). The terminations are characterized by a state-variable formulation which allows a general characterization of dynamic as well as nonlinear elements in the termination networks. The method combines the second-order accuracy of the finite difference-time domain (FDTD) algorithm for the MTL with the absolutely stable, backward Euler discretization of the state-variable representations of the termination networks. A compact matrix formulation of the recursion relations at the interface between the MTL and the termination networks allows a straightforward coding of the algorithm. Skin effect losses of the line conductors as well as the effect of an incident field are easily incorporated into the algorithm. Several numerical examples are given which contain dynamic and nonlinear elements in the terminations. These examples demonstrate the validity of the method and show that the temporal and spatial step sizes can be maximized, thereby minimizing the computational burden     

Finite-difference, time-domain analysis of lossy transmission lines

An active and efficient method of including frequency-dependent conductor losses into the time-domain solution of the multiconductor transmission line equations is presented. It is shown that the usual A+B√s representation of these frequency-dependent losses is not valid for some practical geometries. The reason for this the representation of the internal inductance the at lower frequencies. A computationally efficient method for improving this representation in the finite-difference time-domain (FDTD) solution method is given and is verified using the conventional time-domain to frequency-domain (TDFD) solution technique     

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.     

Condition of modal analysis in time domain of lossy coupled lines

Modal decomposition in the time domain is shown to be applicable to lossy coupled transmission lines of equal width. It is rigorous for two lines and is a good approximation for more than two lines. This allows a direct time-domain simulation of buses made of microstrip lossy lines on chip or on board in digital circuits     

Rigorous and approximate solutions for the three-conductor lossy transmission lines problem

The coupled first-order linear differential equations governing the voltage and the current on three-conductor lossy (identical) transmission lines are solved by two methods. One method is rigorous, and the other one is approximate and applies in the low- and high-frequency ranges. Although the rigorous solution is a numerical one, the approximate solution consists of explicit expressions that are easy to calculate and give physical insight into the coupling process. Experimental results that are available for two parallel identical lossy wires of finite length situated above a perfectly conducting ground (when only one of the wires is driven by a source) and previously published theoretical results compare satisfactorily with the results obtained by the two methods.<>     

Frequency-dependent characteristics of thick microstrip lines in lossy multilayered dielectric media

The Spectral Domain Approach (SDA) is used for a rigorous full-wave analysis of thick microstrip lines embedded in lossy multilayered dielectric media. The effects of the conductor thickness on the propagation constant and characteristic impedance are investigated.