A generalized MoM-SPICE iterative technique for field coupling to multiconductor transmission lines in presence of complex structures

A generalized method of moments (MoM)-SPICE iterative technique for field coupling analysis of multiconductor transmission lines (MTLs) in the vicinity of complex structures is presented. Telegrapher's coupling equations are modified with additional distributed voltage and current sources for more accurate analysis of the total current induced onto transmission line bundles in the presence of complex structures. These additional voltage and current sources are introduced to enforce the electric field boundary condition and continuity equation on MTLs beyond the quasi-static regime. The surrounding structure is modeled via the MoM and a SPICE-like simulator is used to simulate equivalent circuit model of the MTLs extracted via the partial element equivalent circuit method. The proposed technique is based on perturbation theory with the quasi-static current distributions on the transmission lines still assumed to be dominant. Validation examples for single and MTLs are given in the presence of complex structures.     

Shape sensitivities of capacitances of planar conducting surfacesusing the method of moments

In this contribution, a new method is presented to obtain the sensitivities of the capacitance or the charge with respect to a geometrical parameter of planar conducting surfaces. The charge density is found by an integral equation technique. By applying the flux-transport theorem, a new integral equation for the total derivative of the charge with respect to a geometrical parameter is derived from the original electrostatic integral equation for the charge distribution. This new integral equation is solved together with the original integral equation by the method of moments using the same set of basis and test functions. The method is also applied to obtain derivatives for the inductance, impedance and effective dielectric constant. Some simple electrostatic problems are presented, which illustrate the capabilities of our approach. In these examples we also discuss the difference between the geometrical derivatives obtained in this way with geometrical derivatives which are obtained by a central finite difference estimate. Next, some examples of the calculation of geometrical derivatives of capacitance and inductance matrices of multilayer, multiconductor thin microstrip lines are discussed     

Experimental Characterization of Multiconductor Transmission Lines in Inhomogeneous Media Using Time-Domain Techniques

An effective method for the time-domain characterization of lossless multiconductor transmission lines with cross-sectionally inhomogeneous dielectrics is presented. Lines of this type are characterized by multiple propagation modes having different velocities. Time-domain reflectometry is used to obtain the characteristics impedance and the modal velocities of the line. A pulse or step-function response of the line is used to obtain the modal amplitudes which, in turn, determine the velocity matrix. The appropriate multiconductor transmission-line equations are solved to obtain the per-unit-length inductance and capacitance matrices in terms of the measured characteristic-impedance and velocity matrices. The method is concise and complete and identifies the propagation modes in a way that permits direct physical interpretation of the results. The time-domain experimental results for a four-conductor transmission line are presented and are found to be in good agreement with independent frequency-domain measurements.     

Equivalent circuit of a dipole antenna using frequency-independentlumped elements

A four-element lumped-parameter equivalent circuit, consisting of a resistance, an inductance, and two capacitances, has been found to represent the feed-point impedance of a dipole antenna. The values of these elements are related only to the physical dimensions of the antenna, not the frequency of operation. Empirical formulas are given for all the elements. The equivalent circuit gives negligible errors in radiation resistance and reactance for dipole half-lengths less than 0.1λ, rising to 1% for resistance and 6% for reactance at 0.25λ. It can be readily used in standard computer software packages such as SPICE, PSPICE, and MICROCAP     

多导体传输线瞬态响应研究

针对多导体传输线瞬态响应的无源性问题,提出了基于集总等效源模型的多导体传输线瞬态响应模型. 从外场激励下的多导体传输线的频域电报方程解出发,将外场在传输线上激励的分布电压源和电流源与传输线指数矩阵解耦,建立了集总等效电压源和电流源模型. 为避免复杂的傅里叶反变换及卷积运算,推导了集总源模型的时域递推方程. 在此基础上,采用时域有限差分法建立了端接线性负载、非线性负载和外场激励下的不等长多导体传输线瞬态响应离散递推方程. 通过对无损传输线的仿真对比,验证了方法的有效性. 最后,对端接线性负载、非线性负载和外场激励下的不等长多导体传输线瞬态响应进行了试验和仿真分析.       

Asymptotically optimal design of congestion control for high speeddata networks

The basic mechanism of sliding windows for the congestion control of virtual circuits is examined. A problem concerning the optimal design of windows is formulated and formulas for basic quantities of interest, such as throughput, delay and moments of packet queues, in the optimal operating regime as well as in other regimes, are obtained. All results are asymptotic, in which the main parameter is λ, the delay-bandwidth product. It is shown that K*~λ+O(√λ), where K* is the optimum window size. Also, in the optimal operating regime, the steady-state mean and standard deviation of the queued packets at individual nodes O(√/λ). The design consequences are examined in the contexts of adaptive dynamic windowing, buffer sizing, and shared versus separate buffers in the case of multiple virtual circuits     

有损土壤上的多导体传输线的时域分析

将多导体传输线（ＭＴＬ）的土壤复数阻抗拓展为土壤运算阻抗,采用Ｐａｄｅ展开法,提出了计及土壤影响的多导体传输线的时域模型,建立了该模型的时域有限差分（ＦＤＴＤ）算法。通过对计及土壤影响的架空单导体和双导体传输线的波过程计算,表明本文方法的正确性,并可以应用于超高压变电站高压母线和超高压输电线路的瞬态电磁干扰计算。     

A new method for the calculation of the emission spectrum of DFBand DBR lasers

A method based on transmission matrices that allows the emission spectra of arbitrarily complicated semiconductor laser structures to be computed below and above threshold has been developed. These can include active and passive periodic or uniform sections. As examples, the authors compute the emission spectra of a normal distributed feedback (DFB) laser, a DFB laser with a λ/4 phase shifter, and a surface-emitting distributed Bragg reflector (DFB) laser. To do that, Petermann's method for calculating the spontaneous emission coupling coefficient has been extended to the case of a periodic waveguide. It is shown how the spontaneous emission, when treated correctly, can be used to measure the coupling coefficient of the grating in a DFB laser with a λ/4 phase shifter     

Estimation and testing in an imperfect-inspection model

An imperfect inspection model in which failures can only be detected with probability β is considered. The lifetimes of all the components are IID exponential with rate λ. Using the approximate likelihood filtering method, a first order binomial autoregressive model is obtained when 1-β is small. When λ is known, a locally most powerful test is proposed for testing the hypothesis that β=1 against the alternative that β<1. The asymptotic distribution of the test statistic is obtained under the null hypothesis as well as under the alternative. The test statistic is modified to handle the case of unknown λ. Its asymptotic distribution is also given. The bias of the maximum likelihood estimators of β and λ obtained from the approximated likelihood function is studied by simulation     

Equivalent circuits for multiconductor microstrip benddiscontinuities

The T-equivalent circuit previously used for single-line microstrip bends is extended to the variable-angle, multiconductor microstrip bend. A brief overview is given of the excess-charge and current approaches which are employed to obtain the capacitance and inductance matrices for the equivalent circuit. These techniques effectively avoid the majority of the numerical difficulties that occur in accounting for the infinite extent of the microstrip lines making up bends with arbitrary bend angles. In addition, to accurately accommodate the oblique bend angles without requiring many unknowns, the charge and current distributions are modeled with a combination of rectangular and triangular patches. Comparisons with previously published results from the technical literature and with experimental data are used to validate the excess capacitance and inductance computations. The excess capacitance and inductance matrices of several three-line bends are presented, and the three-line bend model is used in a simulation of a high-speed digital circuit to demonstrate the effect of the bend on digital pulse waveforms     

CW radio-frequency excited white-light He-Cd+ laser

We report on the design and performance of a continuous-wave transverse capacitively coupled radio-frequency excited He-Cd⁺ laser, which is capable of simultaneously delivering stable, tens-milliwatt power output at the three primary spectral lines blue: (λ=441.6 nm), green (λ=533.7 nm and λ=537.8 nm), and red (λ=635.5 nm and λ=636.0 nm). Mixing these lines can result in the laser beam featured by a wide band of colors, including white color. The radio-frequency discharge, that excited the He-Cd mixture inside an alumina ceramic tube (400 mm length and 4 mm inner diameter) inserted into the fused silica tubing, operated between 400 mm long and 4 mm wide outer electrodes. Transformation of the radio-frequency discharge impedance to the 50-Ω output resistance of the radiofrequency generator and symmetrization of the radio-frequency voltage were performed by a special matching circuit. Under single-line operation the He-Cd⁺ laser output powers of 60 mW, 38 mW and 14 mW were obtained for the blue, green and red lines, respectively, at an input radio-frequency power of 400 W. Owing to the power interaction between the laser oscillations at red and green higher laser output powers in red and green are possible under multi-line operation. At optimum conditions the white-light laser output power of about 60 mW is obtainable from the laser tube of 40 cm active length. The rms noise-to-signal ratio (lower than 0.4%) of the laser output power of the radio-frequency excited He-Cd⁺ laser was comparable to that of hollow cathode He-Cd⁺ lasers and much lower than that of conventional positive column He-Cd⁺ lasers. The presented laser has exhibited stable operation for more than 400 hours, showing ability to become a long life laser     

Current distribution, resistance, and inductance forsuperconducting strip transmission lines

A method for the calculation of the current distribution, resistance, and inductance matrices for a system of coupled superconducting transmission lines having finite rectangular cross-section is presented. These calculations allow accurate characterization of both high-T_c and low-T _c superconducting strip transmission lines. For a single stripline geometry with finite ground planes, the current distribution, resistance, inductance, and kinetic inductance are calculated as functions of the penetration depth for various film thicknesses. These calculations are then used to determine the penetration depth for Nb, NbN, and YBa₂Cu₃O_7-x superconducting thin films from the measured temperature dependence of the resonant frequency of a stripline resonator. The calculations are also used to convert measured temperature dependence of the quality factor to the intrinsic surface resistance as a function of temperature for an Nb stripline resonator     

Simulation of Electromagnetic Transients of the Bus Bar in Substation by the Time-Domain Finite-Element Method

In order to analyze the electromagnetic interference (EMI) generated from the aerial bus bars in substation, the transient electromagnetic wave process on the bus bars is calculated by using the time-domain finite-element (TDFE) method. The TDFE method is preferable to both the commonly used finite-difference time-domain (FDTD) method, which has difficulties in dealing with the multiconductor transmission lines (MTLs) with lumped parameter networks, and the universal software electromagnetic transient program (EMTP), which is not effective for the calculation of the whole electromagnetic wave processes along the MTLs. The feasibility and efficiency of the proposed TDFE method have been demonstrated by comparing the numerical results with experimental measurements. Furthermore, we have performed a successful case study on the numerical prediction of the EMI in the secondary cable in substation by using the TDFE method.      

Quasi-TEM analysis of multilayered, multiconductor coplanarstructures with dielectric and magnetic anisotropy including substratelosses

A quasi-TEM (transverse electromagnetic) analysis of multiconductor planar lines embedded in a layered structure involving lossy iso/anisotropic electric and/or magnetic materials is achieved. Conditions under which a quasi-TEM assumption is valid are theoretically determined. An efficient spectral-domain analysis is used to determine the complex capacitance and inductance matrices characterizing the transmission system. computation of the inductance matrix is reduced to the computation of an equivalent capacitance matrix when media characterized for a fully general permeability tensor are present. It is also shown that most actual monolithic microwave integrated circuit (MMIC) microstrip-type structures (where semiconductor substrates are present) and possible future applications including lossy magnetic materials can be analyzed by using the simple quasi-TEM model. The validity of the results has been verified by comparison with full-wave theoretical and experimental data on microstrip lines on magnetic substrates and slow-wave structures     

Simplified Macromodel of MTLs With Incident Fields (SiMMIF)

Electromagnetic compatibility (EMC) analysis of high-speed designs has become imperative due to rapidly increasing radio-frequency interference and emerging technological trends such as higher operating frequencies, denser layouts, and multifunction convergent products. In this paper, a simplified macromodel of multiconductor transmission lines (MTLs) exposed to incident fields is presented. The proposed formulation can also handle frequency dependence of resistance, capacitance, conductance, and inductance (RLGC) line parameters. The method employs the recently developed delay-extraction-based compact and passive MTL macromodel, while developing closed-form expressions for incident field analysis. An error bound for the proposed macromodel is also presented. The macromodel is simulation program with integrated circuit emphasis (SPICE) compatible and overcomes the mixed frequency/time simulation difficulties usually encountered during transient analysis, while guaranteeing the stability of the global transient simulation. The algorithm provides higher accuracy as well as significant speed gains for EMC analysis of transmission line networks as compared to the existing techniques.     

On the accuracy of the UTD for the scattering by a cylinder

The UTD formulation for the scattering by a cylinder is valid for antennas that are removed from the cylinder surface. The usual guideline is that reliable results can be obtained for antennas that are about λ/4 or more away from the surface. By exploring a few cases, we show that λ/4 is unnecessarily large for the lit region and sometimes too small for the shadow region. In addition, we find that with a simple heuristic modification to the UTD, heights as small as λ/20 can be accommodated, with an accuracy that is sufficient for most engineering applications     

The discrete Fourier transform method of solvingdifferential-integral equations in scattering theory

An accurate and efficient numerical method is presented for solving many differential-integral equations arising from electromagnetic scattering theory. It uses the discrete Fourier transform technique to treat both the derivatives and the convolution integrals which often appear in these equations. As a consequence, this method is extremely simple to implement, uses less computer memory than comparable methods, and yields accurate predictions. The differential-integral equation is recast into a periodic form conducive to application of the discrete Fourier convolution theorem. The differential operators are approximated by appropriate finite-difference and discrete-convolution operators. All these quantities are computed by using the fast Fourier transform. An approximate solution is obtained by using the conjugate gradient method. Results are compared to experimental data or analytical solutions for a 3λ×3λ metal plate (where λ is the wavelength), a homogeneous and a layered infinite circular dielectric cylinder, and a dielectric sphere. The accuracy of the method is further illustrated by comparing predictions with independent measurements by R.A. Ross (1966) on a 2λ×1λ metal plate at grazing incidence. In all cases, agreement is excellent     

Accurate solution of square scatterer as benchmark for validationof electromagnetic modeling of plate structures

An infinitesimally thin-square scatterer, of size λ×λ, excited normally by an incident plane wave, which is polarized along a scatterer edge, is analyzed. The accurate solution of its current distribution is found in the form of a double series of basis functions, which automatically satisfy the continuity equation at the plate edges and include the edge effect. The coefficients that multiply basis functions are determined starting from the electric field integral equation by using the Galerkin method. The solution obtained for the order of approximation n=8 is adopted as a benchmark. The corresponding coefficients are tabulated and graphs of such obtained current distribution are given. The solution adopted as a benchmark is applied for comparison of rooftop basis functions and polynomial entire-domain basis functions. The relative error of the mean absolute value of current deviation is used as an error metric     

A quasi-TEM analysis for curved and straight planar multiconductorsystems

A quasi-TEM (transverse electromagnetic) analysis for straight and weakly curved planar multiconductor transmission lines is presented. This transverse field of a weakly curved planar multiconductor system is described by the static electric and magnetic solutions of the corresponding axially symmetrical structure. The capacitance and inductance matrices of this system of concentric microstrip rings are calculated using the method of lines. A two-port network consisting of circularly curved transmission lines is calculated and the results are compared with measured values. It is concluded that the proposed method of approximation is suited for analysis of microwave components as well as for high-speed digital circuits with interconnections consisting of curved striplines instead of straight lines with discontinuities     

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.