Electromagnetic fields in complex environments are the responsible for many challenging problems in EMC. Prediction of these fields is often very difficult, and full-wave solvers are often inapplicable for this task due to the excessive demand of computer resources. These difficulties can be overcome in some cases by improving full-wave solvers in order to reduce their computational cost. We have contributed in this respect through investigations of wavelets application for adaptivity in time-domain schemes, and through hybrid schemes allowing for inclusion of efficient models of nonlinear drivers/receivers into existing solvers. Another less recent research project involved radiation prediction for printed circuit boards via Green’s functions approaches.

Several efforts have been devoted to the characterization and modeling of nonuniform transmission lines. These structures are characterized by a dominant direction of propagation, but their cross-section is not translation-invariant. If the variations of the cross section are small, a good approximation of the physical behavior is provided by the Telegraphers Equations with space-dependent per-unit-length parameters. A few validations of this approach have been proposed. However, the main contribution by our group is focused on modeling and simulations. Several advanced algorithms have been proposed, including high-order finite-difference time-domain methods, time-domain space-expansion methods, and time-domain wavelet-based schemes allowing for time/space adaptivity of the discretization mesh.

One of the main reasons for the ubiquity of transmission-line structures in EMC studies is their susceptibility to unwanted interference. Crosstalk can be described as “internal interference” due to the intrinsic propagation properties of a multiconductor transmission line. Field coupling (EMI) leads instead to a behavior of the transmission line as a receiveing antenna, which captures any impinging electromagnetic field. Accurate predictions of these two effects are of paramount importance for EMC engeineers. Much of our research activity has been devoted to the development of modeling algorithms and tools for accurate and efficient simulations. These have been addressed both in stand-alone codes for algorithm prototyping and in macromodels to be employed in standard circuit simulation environments like SPICE.

The prediction of radiation from electronic systems is one of the most important problems in EMC. In fact, a good theoretical prediction before actual testing for compliance may allow quick and easy solutions and fixes in an early design stage. On the other hand, a good prediction is often very difficult due to the complexity of the typical systems under analysis. For this reason, the common approach is to simplify the analysis methods in order to provide quick answers to the designers. Unfortunately, models that are too simple do not allow to capture all the relevant physics and may lead to wrong conclusions. A typical example is the influence of the nonlinear characteristics of drivers and receivers. One of our research activities used several models of different complexity of these devices in order to assess the sensitivity of the radiation spectra. The results led to the conclusion that a simplified modeling approach which neglects nonlinearities is not sufficient. Other less recent activities concentrated on the radiation prediction for printed circuit boards in the post-layout phase using Green’s functions techniques.

Wavelets provide an excellent mathematical tool for adaptive representations. This feature has been exploited in several application areas, from image compression to adaptive filtering. When applied to the representation of an electromagnetic field within a given computational domain, a wavelet expansion may allow to describe the spatial variations of the field with few carefully selected basis functions These are localized where the fast or abrupt variations occur, whereas smooth regions require less coefficients. It is possible to use this wavelet expansion within full-wave field solvers in order to compute the evolution of the electromagnetic field by using less unknowns than for conventional schemes. This fact has led to much interest in so-called Multiresolution Time-Domain (MRTD) schemes. The contribution of our group for this application is the theoretical investigation of the numerical dispersion properties of such schemes.

This activity is focused on the design of efficient algorithms for the systematic characterization of electromagnetic fields interactions with sensitive electronic structures. This includes near and far field coupling to and radiation from electronic equipment. It is well known that this is a very challenging task due to the difficulties in combining complex geometry and material properties with nonlinear and/or dynamic behavior of electronic devices like drivers and receivers. One aspect that is often neglected is the sensitivity of signals and therefore radiation and coupling to the nonlinear characteristics of real components. Unfortunately, a direct system-level full-wave approach including all important effects for the EMC characterization of a given structure is not feasible. Therefore, our approach is to study hybrid methods for approximate characterizations. These methods try to combine the good features of different modeling techniques in order to reduce the computational cost of the simulations. One example that we developed is a combination of driver/receiver parametric macromodels with Finite-Difference Time-Domain solvers. This approach allowed us to investigate the field coupling to interconnected structures with realistic terminations, the latter characterized with an accuracy comparable to their transistor-level representation.