**1.3 Outline of the presented chapter**

4 Fourier Transform Applications

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

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

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.

As aforementioned and discussed (Rammal et al. 2009, Jauregui et al. 2010a), the EM-transient analysis is actually important for the immunity predictions in the mixed or analogue-digital components constituting the high-speed electronic boards regarding the eventual radiations of high power electrical circuitry as the case of neighbouring hybrid electric vehicle propulsion systems. To assess such an EMC effect, as reported in (Adada 2007), the electronic circuit designers working on analogue/mixed signal (AMS) subsystems have preferred software tools such as SPICE, while those working on RF/microwave front-end components have tended to manipulate S-parameter frequency-domain design and simulation tools. By cons, currently, the fusion of the both approaches as AMS engineers are required to make further analysis on the critical components is needed by using the adequate EM simulation tools. In this case, we have to elaborate the context of ultra-wide band (UWB). Currently, this topic is one of improvement techniques in the area of EMC application. In this optic, the modelling of mixed component EM-NF emission becomes one

frequency domain (ANSOFT 2006, AGILENT 2008, ANSYS 2009, NESA 2010).

accurate graphs of time-dependent EM-waves in NF is still an open challenge.

**1.2 Background on the EMC application of the transient EM-NF** 

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.
