**1. Introduction**

Facing to the increase of architecture complexity in the modern high-speed electronic equipments, the electromagnetic compatibility (EMC) characterization becomes a crucial step during the design process. This electromagnetic (EM) characterization can manifest with the unintentional conducting or radiating perturbations including, in particular, the near-field (NF) emissions. Accurate modelling method of this emission in NF zone becomes one of electronic engineer designers and researchers most concerns (Shi et al. 1989, Baudry et al. 2007, Vives-Gilabert et al. 2007, Vives-Gilabert et al. 2009, Song et al. 2010, Yang et al. 2010). This is why since the middle of 2000s; the NF modelling has been a novel speciality of the electronic design engineers. This modelling technique enables a considerable insurance of the reliability and the safety of the new electronic products. To avoid the doubtful issues related to the EM coupling, this analysis seems indispensable for the modern RF/digital electronic boards vis-à-vis the growth of the integration density and the operating numerical data-speed which achieves nowadays several Gbit/s (Barriere et al. 2009, Archambeault et al. 2010). In this scope, the influence of EM-NF-radiations in time-domain and in ultra-wide band (UWB) RF-/microwave-frequencies remains an open-question for numerous electronic researchers and engineer designers (Ravelo et al. 2011a & 2011b, Liu Y. et al. 2011a & 2011b). In the complex structures, the current and voltage commutations in the non-linear electronic devices such as diodes, MOSFETs and also the amplifiers can create critical undesired transient perturbations (Jauregui et al. 2010a, Vye 2011, Tröscher 2011, Kopp 2011). Such electrical perturbations are susceptible to generate transient EM-field radiations which need to be modelled and mastered by the electronic handset designers and manufacturers.

#### **1.1 Overview on the NF radiations characterization occurring in the RF/microwavedevice in time-domain**

It is noteworthy that the frequency-investigations on the EM-radiation of electronic devices are not sufficient for the representation of certain EM-transient phenomena notably when the sources of perturbations behave as a short duration pulse-wave. In fact, it does not enable to precise the probably instant times and the intensity peak of the EM-pulse. That is why the time-domain representation is particularly essential for the infrequent and ultra-

Computation of Transient Near-Field Radiated by Electronic Devices from Frequency Data 5

of the crucial steps before the implementation process. Therefore, the undesired EMC radiations should be investigated not only in frequency-domain but also in time-domain. For this reason, we propose in this chapter an extraction method enabling to determine the time-domain EM-NF maps from the frequency-dependent data by using the Fourier

To make this chapter better to understand, it is organized in three main sections. Section 2 describes the methodology of the time-frequency computation-method proposed. It details how to extract the transient EM-NF radiation from the given time-dependent excitation sampled signal and the frequency-dependent data. Then, more concrete validation of the computation-method investigated by considering the EM-NF radiated by an arbitrary set of magnetic dipoles is devoted in Section 3. The EM-NF reference data are calculated with the theoretical formulas introduced in (Baum 1971 & 1976, Singaraju & Baum 1976). As reviewed by certain research works (Hertz 1892, Chew & Kong 1981, Lakhtakiaa et al. 1987, Song & Chen 1993, Jun-Hong et al 1997, Schantz 2001, Selin 2001, Smagin & Mazalov 2005, Sten & Hujanen 2006, Ravelo 2010), the analytical calculation performed with the EM-wave emitted by elementary dipoles allows to realize more practical and more explicit mathematical analyses of the EM-field expressions in different physic areas. We point out that the EM-field emitted by electronic devices can be modelled by the radiations of the optimized combination of elementary EM-dipoles (Fernández-López et al. 2009). To confirm the feasibility of the method proposed, an application with another proof of concept with a concrete electronic device is also offered in Section 4. This practical verification will be made toward a microwave electronic design of low-pass planar microstrip filter operating up until

some GHz. Lastly; Section 5 draws the conclusion of this chapter.

case, the number *n* of time-dependent samples is logically, equal to:

*n*

**2. Methodology of the time-frequency computation method investigated** 

The present section is divided in two different parts. First, an explicit description illustrates how to examine the transient excitation signal for the UWB applications. Afterward, the development of the routine process indicating the algorithm of the computation method

Let us denote *i*(*t*) the transient current which is considered also as the excitation of the under test electronic structure. The sampled data corresponding to this test signal is supposed discretized from the starting time *tmin* to the stop time *tmax* with time step equal to *∆t*. In this

max min int *t t*

with int(*x*) expresses the lowest integer number greater than the real *x*. Accordingly, via the fast Fourier transform (fft), the equivalent frequency-dependent spectrum of *i*(*tk*) (with *tk* = *k.∆t* and *k* = {1…*n*}) can be determined. The frequency data emanated by this mathematical transform are generally as a complex number denoted by *I*( ) () *f ff k k* = *tit* [ ]. Therefore, the

Δ*t* ⎛ ⎞ <sup>−</sup> <sup>=</sup> ⎜ ⎟ ⎝ ⎠

, (1)

transform of the 2D data.

proposed is elaborated.

**2.1 Frequency coefficient extraction** 

**1.3 Outline of the presented chapter** 

short duration wave emission analysis. In order to investigate more concretely the unwanted time-domain perturbations, different EM-NF modelling and measurement techniques were recently introduced and published in the literature (Cicchetti 1991, Adada 2007, Liu L. et al. 2009, Winter & Herbrig 2009, Ordas et al. 2009, Braun et al. 2009, Rioult et al. 2009, Xie & Lei 2009, Edwards et al. 2010, Jauregui et al. 2010b, Ravelo 2010). Furthermore, several EM-solvers are also integrated in the commercial simulation tools for the determination of the EM-field radiations by the RF/microwave devices especially in frequency domain (ANSOFT 2006, AGILENT 2008, ANSYS 2009, NESA 2010).

Currently, the computation method of the EM-field becomes systematically more and more complicated when the electronic systems operate with baseband UWB signals. Despite the recent investigations conducted on the finite-difference time-domain method (FDTD) method (Liu et al. 2009, Jauregui et al. 2010b), the accuracy of the computation results with these time-domain commercial tools remains difficult to evaluate when the perturbation sources are induced from ultra-short duration transient NF. In addition, more practical techniques (Cicchetti 1991, Braun et al. 2009, Winter & Herbrig 2009, Ordas 2009, Rioult et al. 2009) have been also introduced for the measurement of the electric- and electronic- system electromagnetic interference (EMI). But compared to the existing frequency measurement techniques, they are much better because of the limitations either in terms of spaceresolution or electro-sensitivity or simply the calibration process. So, the evaluation of the accurate graphs of time-dependent EM-waves in NF is still an open challenge.

To cope with this limitation, in this chapter, an efficient computation methodology based on the transformation of wide bandwidth and baseband frequency-dependent data for the determination of the transient EM-NF mapping permitting is developed. In order to take into account the transient radiations specific to the expected use cases, an adequate excitation signal should be considered. This excitation is usually defined according to certain technical parameters (amplitude, temporal width, variation speed, time-duration…) which qualifies the undesired disturbing signal susceptible to propagate in the emitting circuits. Then, the fast Fourier transform (fft) mathematical treatment of the assumed disturbing signal synchronized with the given discrete frequency-dependent data in the adequate frequency range enables to determine the transient wave radiation mapping.
