Equivalent-circuit interconnect modeling based on the fifth-order differential quadrature methods

This paper introduces an efficient and passive discrete modeling technique for estimating signal propagation delays through on-chip long interconnects that are represented as distributed RLC transmission lines. The proposed delay model is based on a less frequently used numerical approximation technique, called the differential quadrature method (DQM). The DQM can compute the partial derivative of a function at any arbitrary point located within a prespecified closed domain of the function by quickly estimating the weighted linear sum of values of the function at a relatively small set of well-chosen grid points within the domain. By using the fifth-order DQM, a new approximation framework is constructed in this paper for discretizing the distributed RLC interconnect and thereafter modeling its delay. Due to high efficiency of DQM approximation, the proposed framework requires only few grid points to achieve good accuracy. The presented equivalent-circuit model appears like the ones derived by the finite difference (FD) method. However, it has higher accuracy and less internal nodes than generated by the FD-based modeling. The fifth-order DQM modeling technique is shown to preserve passivity. It has linear forms that are compatible with the passive order-reduction algorithm for linear network. Numerical experiments show that the proposed modeling approach leads to high accuracy as well as high efficiency.     

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.     

High-frequency electromagnetic field coupling to long terminatedlines

We present a theory for the EMC problem of electromagnetic field coupling to a long line with arbitrary terminations. The theory is applicable for the high-frequency plane wave electromagnetic field excitations, when the transmission line approximation is no longer valid. Analytical expressions are derived for the induced current along the line, and at the two-line terminals. The coefficients of these expressions are determined using a procedure based on the exact solutions of the integral equation for two similar line configurations, but having a significantly shorter length. The method is, therefore, particularly efficient when considering the electromagnetic field coupling to very long lines. The advantage of the proposed approach is that, in contrast with transmission line approximation, it takes into account high-frequency radiation effects. Furthermore, it allows a considerable reduction in computation time and storage requirements with respect to conventional numerical solutions based on the thin-wire approximation     

Electromagnetic field coupling to a line of finite length: theoryand fast iterative solutions in frequency and time domains

A system of integral-differential equations for evaluating currents and voltages induced by external electromagnetic fields on a finite-length horizontal wire above a perfectly conducting ground is derived under the thin wire approximation. Based on perturbation theory, an iterative procedure is proposed to solve the derived coupling equations, where the zeroth iteration term is determined by using the transmission line (TL) approximation. The method can be applied both in the frequency and in the time domains. The proposed iterative procedure converges rapidly to the exact analytical solution for the case of an infinite line, and to the NEC solution for a line of finite length. Moreover, with only one iteration, an excellent approximation to the exact solution can be obtained. The method is applied to assess the validity of the TL approximation for plane wave coupling to an overhead line of finite length. It is shown that the resulting errors for the early-time response are generally higher than those corresponding to infinite lines     

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     

Accurate determination of antenna directivity

The derivation of a formula for accurate estimation of the total radiated power from a transmitting antenna for which the radiated power density is known in a finite number of points on the far-field sphere is presented. The main application of the formula is determination of directivity from power-pattern measurements. The derivation is based on the theory of spherical wave expansion of electromagnetic fields, which also establishes a simple criterion for the required number of samples of the power density. An array antenna consisting of Hertzian dipoles is used to test the accuracy and rate of convergence of the derived formula. Its performance is compared to that of numerical integration using Simpson's formula     

Electromagnetic environmental impact of power electronics equipment

A dramatic increase in the number of line-powered electronic equipment (computers and other office equipment, electronic ballasts, variable-speed drives, and consumer electronics, e.g., color televisions) has taken place. These items of equipment draw distorted, and often fluctuating, line current; they also generate high-frequency conducted and radiated noise due to the sharp edges of the waveforms characteristic of the switching power processors employed in them. As a result of the finite grid impedance, the distorted line current increases the distribution losses and causes voltage distortion; also, the fluctuation leads to visible flicker of the emitted light of lamps. The conducted and radiated high-frequency noise interferes with radio and TV reception, communication via cellular telephones, and data transmission. The result is a gradually deteriorating electromagnetic environment. This paper presents the mechanisms that generate low-frequency and high-frequency electrical noise, lists the problems caused by the various noise types, provides an overview of the standards that establish noise limits, discusses and evaluates the various mitigation techniques, and raises concerns regarding the impact of the circuitry that has to be added to the equipment to meet the harmonic limits and the pitfalls and deficiencies of the line-harmonics regulation standards     

等离子体覆盖导体柱宽带散射特性分析

利用分段线性递归卷积频率相关时域有限差分（RLRC FD^2TD)方法研究了非均匀等离子体覆盖导体柱的散射特性，对TM波垂直入射时的双站、宽带仿真结果的分析表明，等离子体包层可以显著地减少雷达目标的电磁回波能量，衰减量与多种参数有关。     

Theoretical and experimental characterization of transientelectromagnetic fields radiated by electrostatic discharge (ESD)currents

The problem of the evaluation of the electromagnetic (EM) field radiated by an electrostatic discharge (ESD) current is examined, and an efficient numerical code for the evaluation of the radiated field is developed. The considered radiating structures, a monopole and a loop, are analyzed in the time domain using a modified electric field integral equation (EFIE). A modification of the integral equation was introduced in order to take into account the reflection of the incident pulse at the input terminals of the antenna, when fed by a transmission line. The reflected wave is very significant and its evaluation is fundamental for the comparison of theoretical and experimental data. The ESD current flowing along the wire is determined using the method of moments in time domain (MoMTD). From the knowledge of the transient current, the radiated EM field is evaluated by a standard technique. The developed model is the first stage of a project for the characterization of the measurement environment during an ESD test. All numerical results are validated by measurements and good agreement is shown     

用MEI—FD方法分析Chiral媒质的电磁散射问题

本文应用不变性测试分程和有限差分方法分析Ｃｈｉｒａｌ媒质的电磁散射问题。应用该方法时，要在所讨论的区域内建立起一组有关电场和磁场的耦合差分方程，并且要在截断边界上应用不变性测试方程建立起有关边界点系数的方程。文中给出了一些非均匀、有耗且具有电大尺寸任意横截面Ｃｈｉｒａｌ柱的雷达散射截面的数值结果     

Performance evaluation of FSK and CPFSK optical communicationsystems: a stable and accurate method

The modified moments method for evaluating the performance of coherent optical FSK and CPFSK systems is presented. Since the classical procedure becomes ill-conditioned as the order of the moments increases, we consider the construction of Gaussian quadrature rules (GQR) from the modified moments. The analysis accounts for the influences of IF bandwidth, transmitter and local oscillator laser phase noise, postdetection filters, and additive Gaussian noise. It is found that the proposed approach is a highly reliable and efficient method for calculating the error probability. A comparison with results obtained from the Gaussian quadrature rule, Gaussian approximation method, and analytical approximation formulas shows that this technique is very accurate. Analytical expressions are derived for FSK and CPFSK receivers which include polarization and phase diversity techniques. The use of numerical programming to avoid many unnecessary computations is discussed. This evaluation method can be used to account for the effects of crosstalk in multichannel systems and the influence of error-control codes     

Analysis of radiation characteristics of distribution line carrierswith the NEC code

The use of a medium-voltage (MV) transmission network as a physical medium for communications with the distribution line carrier (DLC) technique may lead to electromagnetic compatibility problems. Computed and experimental results concerning the undesired electromagnetic fields radiated by the DLC are discussed. The NEC-2 code is used to model a network considered as a radiating structure in the 10-100-kHz band and to estimate the average values of undesired radiated electromagnetic fields. An appropriate NEC user interface has been developed on a Macintosh computer in order to model a realistic complex network. Results obtained with NEC are validated through comparisons of simulated fields with measured ones, and satisfactory agreement is found. A numerical parametric study shows the effects of the network configuration on the undesired radiated fields     

射频电子设备的辐射电磁干扰诊断与抑制技术研究

射频电子设备产生的电磁干扰(EMI)噪声包括传导干扰噪声和辐射干扰噪声。其中,辐射EMI噪声是以空间电磁场形式影响其它电子设备的。针对射频电子设备产生的辐射EMI噪声,该文分别建立因传输线缆与芯片时钟信号引起的辐射EMI噪声理论模型与等效电路。同时,还针对上述辐射EMI噪声理论模型提出了相应的噪声抑制方法。实验结果表明,采用该文中方法,某型家用液晶显示器的EMI噪声得到了很好的抑制,从而验证了方法的有效性。     

Discretized Boundary Equation Method for Two-Dimensional Scattering Problems

A unified approach, named discretized boundary equation (DBE) method, is introduced for two-dimensional (2-D) scattering problems. It is based on the discretization of field expressions for one or two components of the scattered field. The DBEs can be used either on the object surface to obtain the solution directly or on the truncation boundary of a finite difference (FD) or finite element (FE) mesh as termination conditions. This paper describes the general theory of the DBE method and key points or limitations for its implementation. A new on-surface formulation for the solution of scattering by perfectly conducting cylinders is presented as an application of the two-component version of the DBE method and validated through numerical examples. Mesh termination conditions for the FD or FE method are derived based on the one-component formulation of the DBE method and their equivalence and difference to the measured equation of invariance are discussed. In particular, the DBE obtained with the minimum norm least squares solution is investigated thoroughly and its validity and features are demonstrated through numerical results, generated together with the FD method, for scattering by cylinders with various material properties.     

Analysis of Series-Connected Discrete Josephson Transmission Line

Employing a generalized resistive–capacitive shunted junction model for Josephson junctions (JJs), the nonlinear wave propagation in the series-connected discrete Josephson transmission line (DJTL) is investigated. A DJTL consists of a finite number of unit cells, each including a segment of superconducting transmission line with a single array stack, or generally a block including an $N$ identical lumped JJ element. As the governing nonlinear wave propagation is a system of nonlinear partial differential equations with mixed boundary conditions, the method of the finite difference time domain is used to solve the equations. By this numerical technique, the behavior of wave propagation along the DJTL can be monitored in time and space domains. Cutoff propagation, dispersive behavior, and shock-wave formation through the DJTL is addressed in this paper.      

Simulation of the High-Frequency Response of a Heterogeneous Ground through the Finite Difference Technique

To simulate the propagation of an electromagnetic plane wave in an inhomogeneous ground, the finite difference approach can be used. One of the main problems in using this method is imposing the boundary conditions near the ground surface, especially at high frequency. Indeed, for the E polarization, the upper top of the numerical grid must be sufficiently far away from the air-ground interface in order to neglect the field due to the heterogeneities and the discretization of the atmosphere is necessary. For magneto-telluric modeling, improved boundary conditions have already been proposed. This paper deals with a new condition, valid everywhere in air and which can be applied for E and H polarization. Thus even at high frequency, as for radar applications, only one line is added to the grid discretizing the ground.     

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。     

Closed-form transmission line model for radiated susceptibility in metallic enclosures

This work presents an approximate frequency domain mathematical model based on the transmission line (TL) theory for field-to-wire coupling in a rectangular metallic enclosure. The currents and voltages at the terminations of a TL induced by known electromagnetic (EM) field sources are expressed in closed form. Validity limits and applicability of the model are discussed by comparing the analytical TL-based predictions with the outputs of a full-wave numerical analysis of the overall structure using a three-dimensional finite integration technique. Deviations from the full-wave solution, due to the scattered field from the TL, have been identified, analyzed, and discussed. The proposed analytical model proves to be generally suited for accurate prediction of radiated susceptibility of single-ended interconnections in closed environments.     

Radiated emissions and immunity of microstrip transmission lines:theory and reverberation chamber measurements

The increasing complexity of electronic systems has introduced an increased potential for electromagnetic interference (EMI) between electronic systems. We analyze the radiation from a microstrip transmission line and calculate the total radiated power by numerical integration. Reverberation chamber methods for measuring radiated emissions and immunity are reviewed and applied to three microstrip configurations. Measurements from 200 to 2000 MHz are compared with theory, and excellent agreement is obtained for two configurations that minimize feed cable and finite ground plane effects. Emissions measurements are found to be more accurate than immunity measurements because the impedance mismatch of the receiving antenna cancels when the ratio of the microstrip and reference radiated power measurements is taken. The use of two different receiving antenna locations for emissions measurements illustrates good field uniformity within the chamber     

Analysis of Transmission Lines With Arrester Termination, Considering the Frequency-Dependence of Grounding Systems

The paper proposes a modeling technique to analyze the response of a transmission line terminated by a lightning arrester connected to a grounding system buried in a lossy ground. In this technique, the transmission line is modeled in the frequency domain with the aid of Baum–Liu–Tesche equations, while the grounding system to which the arrester is connected is treated using a general electromagnetic approach. The electromagnetic approach is based on the solutions to Maxwell's equations obtained by using the method of moment in the frequency domain. The arrester nonlinearity is included in the frequency-domain analysis using the arithmetic operator method. To examine the performance of the proposed modeling technique, numerical results are presented for a single-conductor transmission line connected to a typical lightning arrester. The results are first compared for a simple grounding configuration of a vertical rod with those obtained using the well-known electromagnetic transient program, showing the validity of the proposed technique. The generality of the technique is then demonstrated by studying the results of a more complex case of a typical grounding grid. It is shown that the early time responses of the lightning overvoltages are affected by the harmonic impedance of the grounding system.