Fields, Radiation, and Numerical Techniques
Fields, Radiation, and Numerical Techniques

Hybrid Methods
This activity is focused on the design of efficient algorithm 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 systemlevel fullwave 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 FiniteDifference TimeDomain 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 transistorlevel representation. In the picture you can see a snapshot of the electric field within a twolayer printed circuit board excited by a pulse launched by a driver (red dot).

Waveletbased Methods
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 fullwave 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 socalled Multiresolution TimeDomain (MRTD) schemes. The contribution of our group for this application is the theoretical investigation of the numerical dispersion properties of such schemes.

Radiation Prediction
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. The picture represents the electric field spectrum up to 3GHz radiated from an interconnect terminated by real drivers and receivers characterized by accurate (top) and simplified bottom (models). Other less recent activities concentrated on the radiation prediction for printed circuit boards in the postlayout phase using Green’s functions techniques.