ETTC'2003 - SEE

What is the budget of the statistical approach? The main cost is induced by the construction of the data base, whether
this is done numerically, experimentally or by combining the two. In the case where numerical simulation is used, timeconsuming
methods such as finite differences, finite elements or integral representations are involved. On the other
hand, ANOVA, regression and kriging do not increase significantly the cost of the method. It must be noted that the
statistical approach does not replace any standard modeling method. Rather, it works in association with the latter,
enhancing its capabilities and making it possible to retrieve information that is otherwise difficult to obtain. As a final
remark here, this approach applies to a probability density function where the interpolation is done on the parameters of
this function.
To illustrate the statistical approach, it will now be applied to two EMC problems. The first one deals with the
determination of the probability density function of the coupling cross-sections of PCBs. The second problem addresses
the coupling of the field radiated by a randomly located dipole to a transmission line. This is a first order solution to the
coupling of mobile phone signals to transmission lines placed in a room. Other examples will be shown in the
presentation.
Case 1 : pdf of coupling cross-section to a PCB [5]
The canonical structure on figure I allows us to study the coupling probability distribution by processing, at a
reasonable cost, a large number of test configurations (typically by considering various incident waves) with all other
parameters under control.
Figure 1
We chose to study the coupling cross section (SEC : Section Efficace de Couplage) which is the ratio between the
collected power and the incident power density.
According to the Monte Carlo method, the angles q and j defining the direction of arrival of the incomming linearly
polarized plane wave, and the angle g which defines the orientation of its electric field, are random variables obeying
uniform distribution over the following ranges :
0 £ q £ 90°
0 £ j £ 360°
0 £ g £ 360°
The frequency follows a uniform distribution between 500 MHz and 6 GHz, the trace length L, follows a lognormal
distribution with a 0.7 mean and a 1.2 standard deviation (measurements on some PCB samples support this
hypothesis).We used the computer code CRIPTE (Calcul sur Réseaux des Interactions Perturbatrices en Topologie
Electromagnétique), which solves the B.L.T. (Baum-Liu-Tesche) equation, to obtain the collected power on the
terminal load (50 W) at different frequencies.
Results are presented on Figure 2 where the Beta distribution [1] was found to be the best fit to the histogram of the
SEC distribution.