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     

Explicit upwind schemes for lossy MTLs with linear terminations

The time domain multiconductor transmission line (MTL) equations are written as a general first order system of partial differential equations and a characteristic decomposition is used to obtain first order and second order accurate upwind differencing schemes. Linear boundary conditions in the form of generalized Thevenin equivalent sources are incorporated into the scheme. These schemes are compared with the standard time-space centered second order accurate leapfrog scheme where the current and voltage variables are interlaced in space and time. For any general explicit numerical scheme, for a given MTL, only the fastest propagating TEM mode can be solved for at the Courant limit of the scheme. This causes the other slower modes to disperse. The results of our comparisons, show that at the Courant number both upwind schemes produce less numerical dispersion for the slower propagating modes than the standard leapfrog scheme under the same conditions. In addition, the Courant number of the second order upwind scheme is twice that of the leapfrog scheme. These advantages make the upwind schemes better tools to model inhomogeneous MTLs with linear terminations     

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     

The finite-difference time-domain solution of lossy MTL networkswith nonlinear junctions

We describe a numerical technique to solve lossy multiconductor transmission line (MTL) networks, also known as tube/junction networks, which contain nonlinear lumped circuits in the junctions. The method is based on using a finite-difference technique to solve the time-domain MTL equations on the tubes, as well as the modified nodal analysis (MNA) formulation of the nonlinear lumped circuits in the junctions. The important consideration is the interface between the MTL and MNA regimes. This interface is accomplished via the first and last finite-difference current/voltage pair on each MTL of the network and, except for this, the two regimes are solved independently of each other. The advantage of the FDTD method is that the MTL equations may contain distributed source terms representing the coupling with an external field. We apply the method to previously published examples of multiconductor networks solved by other numerical methods, and the results agree exceptionally well. The case of an externally coupled field is also considered     

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。     

Transient analysis of nonuniform transmission lines with nonlinear terminal networks

A semi-analytical method in time domain is presented for analysis of the transient response of nonuniform transmission lines. In this method, the telegraph equations in time domain is differenced in space domain first, and is transformed into a set of first-order differential equations of voltage and current with respect to time. By integrating these differential equations with respect to time, and precise computation, the solution of these differential equations can be obtained. This method can solve the transient response of various kinds of transmission lines with arbitrary terminal networks. Particularly, it can analyze the nonuniform lines with initial conditions, for which there is no existing effective method to analyze the time response so far. The results obtained with this method are stable and accurate. Two examples are given to illustrate the application of this method.     

Accurate modeling of lossy nonuniform transmission lines by using differential quadrature methods

This paper discusses an efficient numerical approximation technique, called the differential quadrature method (DQM), which has been adapted to model lossy uniform and nonuniform transmission lines. The DQM can quickly compute the derivative of a function at any point within its bounded domain by estimating a weighted linear sum of values of the function at a small set of points belonging to the domain. Using the DQM, the frequency-domain Telegrapher's partial differential equations for transmission lines can be discretized into a set of easily solvable algebraic equations. DQM reduces interconnects into multiport models whose port voltages and currents are related by rational formulas in the frequency domain. Although the rationalization process in DQM is comparable with the Pade approximation of asymptotic waveform evaluation (AWE) applied to transmission lines, the derivation mechanisms in these two disparate methods are significantly different. Unlike AWE, which employs a complex moment-matching process to obtain rational approximation, the DQM requires no approximation of transcendental functions, thereby avoiding the process of moment generation and moment matching. Due to global sampling of points in the DQM approximation, it requires far fewer grid points in order to build accurate discrete models than other numerical methods do. The DQM-based time-domain model can be readily integrated in a circuit simulator like SPICE.     

The time-domain characteristics of a traveling-wave linear antenna with linear and nonlinear parallel loads

The time-domain characteristics of a traveling-wave linear antenna with linear and nonlinear parallel loads are discussed. The fast Fourier transform (FFT) is used to analyze the antenna with a linear parallel load. A numerical time-stepping finite-difference equation method is used to analyze the antenna with a nonlinear parallel load. The nonlinear effect is treated by the Newton-Raphson iteration technique. The effects of various linear and nonlinear parallel loads are examined. Physical insight into the nonlinear parallel loading of the antenna is also given in terms of detected time-domain sinusoidal electromagnetic (EM) waves.     

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。     

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     

Perfectly linear ramp generation with lossy capacitor

It is shown that a perfectly linear ramp voltage can be generated from a lossy capacitor using appropriate compensation current.     

Frequency- and time-domain Green's functions for a phasedsemi-infinite periodic line array of dipoles

We extend a previous prototype study of Felsen and Capolino (see ibid. vol.48, p.921-931, June 2000) of frequency-domain (FD) and time-domain (TD) Green's functions for an infinite periodic phased line array of dipoles to account for the effects of truncation, as modeled by a semi-infinite array. These canonical problems are to be used eventually for the systematic analysis and synthesis of actual rectangular TD plane phased arrays. In the presentation, we rely on the analytic results and phenomenologies pertaining to the infinite array, which are reviewed. Major emphasis is then placed on the modifications introduced by the truncation. Finite Poisson summation is used to convert the individual dipole radiations into collective truncated wavefields, the FD and TD Floquet waves (FW). In the TD, exact closed-form solutions are obtained, and are examined asymptotically to extract FD and TD periodicity-matched conical truncated FW fields (both propagating and nonpropagating), corresponding tip-diffracted periodicity-matched spherical waves, and uniform transition functions connecting both across the FD and TD-FW truncation boundaries. These new effects can again be incorporated in a FW-modulated geometrical theory of diffraction. A numerical example of radiation from a finite phased TD dipole array with band-limited excitation demonstrates the accuracy and efficiency of the FW-(diffracted field) asymptotic algorithm when compared with an element-by-element summation reference solution     

Frequency- and time-domain FEM models of EMG: capacitive effects and aspects of dispersion

Electromyography (EMG) simulations have traditionally been based on purely resistive models, in which capacitive effects are assumed to be negligible. Recent experimental studies suggest these assumptions may not be valid for muscle tissue. Furthermore, both muscle conductivity and permittivity are frequency-dependent (dispersive). In this paper, frequency-domain and time-domain finite-element models are used to examine the impact of capacitive effects and dispersion on the surface potential of a volume conductor. The results indicate that the effect of muscle capacitance and dispersion varies dramatically. Choosing low conductivity and high permittivity values in the range of experimentally reported data for muscle can cause displacement currents that are larger than conduction currents with corresponding reduction in surface potential of up to 50% at 100 Hz. Conductivity and permittivity values lying toward the middle of the reported range yield results which do not differ notably from purely resistive models. Also, excluding dispersion can also cause large error-up to 75% in the high frequency range of the EMG. It is clear that there is a need to establish accurate values of both conductivity and permittivity for human muscle tissue in vivo in order to quantify the influence of capacitance and dispersion on the EMG signal.     

Synthesis of nonuniform transmission lines with terminaldiscontinuities

An integral equation was previously derived by the authors (ibid., vol.AP-34, p.546-53, Apr. 1986) for the inverse problem associated with finite-length nonuniform lines having known impedance discontinuities at the input and output. A procedure for determining the characteristic impedance profile of the line from the solution of the integral equation was also presented. Here, the numerical aspects of this inverse problem are treated. This equation is solved using general expansions of both the kernel and unknown functions, thereby reducing the integral equation to a system of linear algebraic equations. This makes possible a numerical implementation of the theory by which the impedance profile of a nonuniform line may be reconstructed from given spectral data. The realizability aspects of the problem are treated and several examples of computer-assisted profile inversion are presented     

A time-domain technique for computation of noise-spectral density in linear and nonlinear time-varying circuits

This paper presents a new time-domain technique for computing the noise-spectral density. The power-spectral density (PSD) is interpreted as the asymptotic value of the expected energy-spectral density per unit time. The methodology of stochastic differential equations is used to derive a set of ordinary differential equations for the expected energy-spectral density. This set of equations can then be integrated in time until the steady-state value of the PSD is obtained. The method can be used to find the noise spectrum in any circuit in which noise can be treated as a perturbation. The general nature of this algorithm has been illustrated in this paper by using it to get the noise-spectral density in switched-capacitor circuits, externally linear circuits and oscillators. The results match well with published experimental/analytical data.     

Scattering parameter transient analysis of transmission linesloaded with nonlinear terminations

An approach for the time-domain simulation of transients on a dispersive and lossy transmission line terminated with active devices is presented. The method combines the scattering matrix of an arbitrary line and the nonlinear causal impedance functions at the loads to derive expressions for the signals at the near and far ends. The problems of line losses, dispersion, and nonlinearities are first investigated. A time-domain formulation is then proposed using the scattering-matrix representation. The algorithm assumes that dispersion and loss models for the transmission lines are available and that the frequency dependence is known. Large-signal equivalent circuits for the terminations are assumed to be given. Experimental and computer-simulated results are compared for the lossless dispersionless case, and the effects of losses and dispersion are predicted     

Practical problems in the time-domain probing of lossy dielectric media

Interest in time-domain probing of a lossy dielectric medium by means of optimization processes has been shown in former papers. Some problems related to the application of such techniques to realistic situations are envisaged. Screening effects due to losses are first investigated, and a setup (perturbed line) is presented to reduce them. The influence of a finite extent of the illumination, implied by classical wave applicators, is then discussed.     

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.     

Transients on lossy transmission lines with arbitrary boundary conditions

In this work the problem of transients on a lossy transmission line terminated by an arbitrary, including nonlinear, load is formulated. The tranmission line parameters are the constantsR, L, G, andC. The exact relation between the input and output voltages and currents in the form of two coupled integral equations is derived by the Laplace transform method. It is shown that the kernels of the integral equations may be represented in terms of either Lommel functions or integrals involving zeroth order modified Bessel functions. Simultaneous (numerical) solutions of these integral equations fulfilling the boundary conditions at the input and output of the line yields the input and output voltages and currents on the line. Finally the exact analytical relations in time domain of the voltage and current at an arbitrary point on the line (and the voltages and currents at the input and output terminals) are derived. In all parts, the problem has been formulated in such a way as to impose the causality condition explicitly.