Numerical Techniques in Electromagnetics is designed to show the reader how to pose, numerically analyze, and solve electromagnetic (EM) problems. It gives them the ability to expand their problem-solving skills using a variety of available numerical methods. Topics covered include fundamental concepts in EM; numerical methods; finite difference methods; variational methods, including moment methods and finite element methods; transmission-line matrix or modeling (TLM); and Monte Carlo methods. The simplicity of presentation of topics throughout the book makes this an ideal text for teaching or self-study by senior undergraduates, graduate students, and practicing engineers.

Numerical Techniques in Electromagnetics, Second Edition

With the rapid developments in very large-scale integration (VLSI) technology, design and computer-aided design (CAD) techniques, at both the chip and package level, the operating frequencies are fast reaching the vicinity of gigahertz and switching times are getting to the subnanosecond levels. The ever increasing quest for high-speed applications is placing higher demands on interconnect performance and highlighted the previously negligible effects of interconnects such as ringing, signal delay, distortion, reflections, and crosstalk. In this review paper various high-speed interconnect effects are briefly discussed. In addition, recent advances in transmission line macromodeling techniques are presented. Also, simulation of high-speed interconnects using model-reduction-based algorithms is discussed in detail.

/pdf/simulation-of-high-speed-interconnects-4k5dt3lsur.pdf

Simulation of high-speed interconnects

A comprehensive study on the effect of a lossy ground on the induced voltages on overhead power lines by a nearby lightning strike is presented The ground conductivity plays a role in both the evaluation of the lightning radiated fields and of the line parameters To be calculated by means of a rigorous theory, both fields and line constants need important computation time, which, for the problem of interest, is still prohibitive The aim of this paper is to discuss and analyze the various simplified approaches and techniques that have been proposed for the calculation of the fields and the line constants when the ground cannot be assumed as a perfectly conducting plane Regarding the radiated electromagnetic field, it is shown that the horizontal electric field, the component which is most affected by the ground finite conductivity, can be calculated in an accurate way using the Cooray-Rubinstein simplified formula The presence of an imperfectly conducting ground is included in the coupling equations by means of two additional terms: the longitudinal ground impedance and the transverse ground admittance, which are both frequency-dependent The latter can generally be neglected for typical overhead lines, due to its small contribution to the overall transverse admittance of the line Regarding the ground impedance, a comparison between several simplified expressions used in the literature is presented and the validity limits of these expressions are established It is also shown that for typical overhead lines the wire impedance can be neglected as regard to the ground impedance

Influence of a lossy ground on lightning-induced voltages on overhead lines

It is shown that radiated emissions due to common-mode currents on printed circuit board lands can greatly exceed those due to differential-mode currents. It is concluded that predictions of radiated emissions based solely on differential-mode (transmission line) currents can bear little, if any, resemblance to actual measured emissions. Therefore, radiated emission prediction models that use only differential-mode (transmission-line) currents and ignore common-mode (antenna) currents are not adequate for the prediction of radiated emissions from printed circuit boards (as well as cables). >

A comparison of the contributions of common-mode and differential-mode currents in radiated emissions

Presented here is a method for computing near- and far-field patterns of an antenna from its near-field measurements taken over an arbitrarily shaped geometry. This method utilizes near-field data to determine an equivalent electric current source over a fictitious surface which encompasses the antenna. This electric current, once determined, can be used to ascertain the near and the far field. This method demonstrates the concept of analytic continuity, i.e., once the value of the electric field is known for one region in space, from a theoretical perspective, its value for any other region can be extrapolated. It is shown that the equivalent electric current produces the correct fields in the regions in front of the antenna regardless of the geometry over which the near-field measurements are made. In this approach, the measured data need not satisfy the Nyquist sampling criteria. An electric field integral equation is developed to relate the near field to the equivalent electric current. A moment method procedure is employed to solve the integral equation by transforming it into a matrix equation. A least-squares solution via singular value decomposition is used to solve the matrix equation. Computations with both synthetic and experimental data, where the near field of several antenna configurations are measured over various geometrical surfaces, illustrate the accuracy of this method.

Near-field to near/far-field transformation for arbitrary near-field geometry utilizing an equivalent electric current and MoM

In modeling crosstalk on printed circuit boards, the distributed parameter transmission line model is applied to include the effects of electromagnetic coupling between tracks. Starting with a finite element approach, a computer model for predicting crosstalk voltages and currents in a general n+1 multiconductor configuration is outlined. After the currents on each track are calculated by using the finite element method and modal analysis, a simple radiation model is used to calculate the radiated field produced by the printed circuit boards for a frequency range of 30-1000 MHz. The algorithm presented was implemented in a series of Fortran programs, and the results obtained using this procedure compare very well with available theoretical and experimental data. >

Finite element method applied to modeling crosstalk problems on printed circuit boards

The electromagnetic pulse can cause degradation of modern digital and analog devices. Many analytical models have been used extensively to study the susceptibility of equipment related to EMI/EMC (electromagnetic interference/electromagnetic compatibility) engineering, but the emphasis has been mainly on lossless transmission lines. This work takes into account the transient skin-effect of a transmission line exposed to a time-varying electromagnetic field. Beginning with the classical transmission line theory, the transient skin-effect of a transmission line and the equivalent sources due to the external fields are incorporated. As a result, an integral-differential equation is derived. By using the finite-difference-time-domain (FD-TD) approach, the induced voltages onto the line are predicted. There is also a discussion of the numerical approach and the propagation of the predicted induced voltage. >

https://www.ruor.uottawa.ca/bitstream/10393/7627/1/MM68052.PDF

Skin-effect considerations on transient response of a transmission line excited by an electromagnetic pulse

In a printed circuit board environment, the solution domain is highly inhomogeneous, and analytic expressions for design parameters are very difficult to obtain, even for the simplest configuration. The finite element method (FEM) offers an attractive alternative for solving the problem in all its aspects including the determination of parasitic effects. A problem of practical interest, related to crosstalk, is formulated to be solved using the FEM. The technique is first applied to obtain the field distribution, and then the field is used to calculate transmission line parameters of conducting tracks on printed circuit boards. FEM is used to solve a radiation problem in three dimensions. The solution is used to predict far-field radiation levels of electronic equipment from near-field measurements. >

Finite-element method applied to EMC problems (PCB environment)

This paper presents a new approach to derive far-field data needed in antenna and EMI/EMC testing from near-field measurements. An exact integral equation solution to the wave propagation problem is used to transform the near-field data to the far field. The method requires near-field measurements on two closed surfaces enclosing all sources and inhomogeneities. The approach is validated with numerical simulation of measurements of fields radiated from a known antenna. >

Far-field predictions from near-field measurements using an exact integral equation solution

An optimum layout for minimizing the radiation from a printed circuit board (PCB) is sought. A pair of tracks on a PCB is modeled as a transmission line. The manner in which the characteristic impedance (Z/sub 0/) of this transmission line affects the vector potentials of the radiation fields is discussed. Numerical simulation results are presented. A guideline for choosing an optimum layout spacing is provided. >

G.I. Costache

Papers

Finite element method applied to modeling crosstalk problems on printed circuit boards

Skin-effect considerations on transient response of a transmission line excited by an electromagnetic pulse

Finite-element method applied to EMC problems (PCB environment)

Far-field predictions from near-field measurements using an exact integral equation solution

A note on the optimum layout of electronic circuits to minimize the radiated electromagnetic field strength