Portal de Periódicos da CAPES

Time domain inverse method based on the near field technique to solve electromagnetic interference problems: application to an AC/DC flyback converter

2018; Institution of Engineering and Technology; Volume: 11; Issue: 13 Linguagem: Inglês

10.1049/iet-pel.2018.5157

1755-4543

Bessem Zitouna, Jaleleddine Ben Hadj Slama,

Electrostatic Discharge in Electronics

IET Power ElectronicsVolume 11, Issue 13 p. 2133-2139 Research ArticleFree Access Time domain inverse method based on the near field technique to solve electromagnetic interference problems: application to an AC/DC flyback converter Bessem Zitouna, Corresponding Author Bessem Zitouna bessem.zitouna@yahoo.fr LATIS, Laboratory of Advanced Technology and Intelligent Systems, ENISo, National Engineering School of Sousse, University of Sousse, TunisiaSearch for more papers by this authorJaleleddine Ben Hadj Slama, Jaleleddine Ben Hadj Slama LATIS, Laboratory of Advanced Technology and Intelligent Systems, ENISo, National Engineering School of Sousse, University of Sousse, TunisiaSearch for more papers by this author Bessem Zitouna, Corresponding Author Bessem Zitouna bessem.zitouna@yahoo.fr LATIS, Laboratory of Advanced Technology and Intelligent Systems, ENISo, National Engineering School of Sousse, University of Sousse, TunisiaSearch for more papers by this authorJaleleddine Ben Hadj Slama, Jaleleddine Ben Hadj Slama LATIS, Laboratory of Advanced Technology and Intelligent Systems, ENISo, National Engineering School of Sousse, University of Sousse, TunisiaSearch for more papers by this author First published: 17 September 2018 https://doi.org/10.1049/iet-pel.2018.5157Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study presents a time domain modelling method for sources of electromagnetic disturbance. For the identification of an equivalent model, the proposed method is based on the synchronised temporal measurements of the magnetic near field above a power electronic system. To determine the parameters of the model, the proposed methodology is combined with an optimisation method based on the genetic algorithms. Unlike the classical approaches developed in the frequency domain, the proposed method allows finding a valid equivalent model for all radiation frequencies of measured time signals. It also enables knowing the phase shift in time between the radiating sources. The proposed method is applied in order to find the equivalent radiating sources of an AC/DC flyback converter. The accuracy and precision of the proposed method are validated by the good agreement between the measured cartography of the magnetic near field and that calculated using the parameters of the developed model. Finally, the latter's parameters are used to predict the cartography of other components of the magnetic field, which will be compared with the measured cartography. The superposition of the results confirms that the identified equivalent sources can represent real sources in the studied structure. 1 Introduction Due to the emergence of power electronics systems in all areas, the innovation of these devices has a notable development. Their integration and coexistence in the same box, as well as the increase in switching frequencies and carried powers, cause frequent and unwanted electromagnetic interferences in their vicinity. Thus, it is imperative to be treated with the electromagnetic compatibility before marketing of these electronic devices. Therefore, it is necessary to develop radiating models that will allow estimating the electromagnetic emissions of these systems. The creation of these models by the electromagnetic inverse method avoids the use of heavy measurements and very expensive equipment (anechoic chamber). To find solutions to the problems encountered in power electronics, the electromagnetic inverse method has emerged as an innovative and important solution technique. In the literature, a lot of work has been already achieved on the modelling of electronic components [1-3]. These approaches are based on the near field measurement of the magnetic field as a diagnostic tool of electromagnetic radiation [4, 5]. In [6-8], the inverse method based on the elementary dipoles was used to extract the equivalent model from printed circuit board circuits. The frequency inverse method was also applied in order to model electronic boards [4, 9, 10]. These various approaches have been developed in the frequency domain and have been utilised to characterise and model the radiation limited to only one frequency. In this frequency resolution, the identification of radiating sources is performed with the assumption that the emitting sources, in a power electronics board, are working simultaneously. It seems that the notion of time delay does not appear. This supposes that the studied systems have sinusoidal radiations; while in reality, this is not the case when considering power electronic systems where the electromagnetic disturbances are very important over a broad band of frequencies. Hence, in power electronics, there is a large phase shift in time at the source of radiation levels, which is not highlighted during the frequency domain resolution. So far, the study of the phase shift in time between the radiating sources has not been treated yet. Until now, few contributions have been proposed and published in the time domain inverse method. The authors of [11, 12] tried to combine the frequency inverse method with the time-frequency computation method. However, the developed modelling method was limited because it always depended on the parameters of the time intervals that mainly depended on the selected frequency band, the considered initial frequency, and the used computer performance. Other approaches have been performed [13-17]. These studies were dedicated to the development of new computational techniques and the analysis of the electromagnetic near field in the time domain. In [18], the time domain inverse method based on elementary dipoles was applied to identify the equivalent radiation model in a fairly simple structure, which was unfortunately not representative enough for all power electronic circuits. For this purpose, the added value of our approach is to put forward an efficient technique based on the inverse electromagnetic method in the time domain. This approach takes into account the time domain delay at the levels of the various radiated emissions of the circuit, which permits the identification of the contribution of each radiating source of the circuit over time. The proposed method is applied to complicated real cards composed of several bulky components, where the radiating sources are usually very close to each other. The proposed approach consists of modelling emissions of power electronics systems with a network of elementary dipoles using the measured signals of the magnetic near field in the time domain. These measured temporal signals are synchronised with respect to a repetitive control signal. This method utilises the time domain analytic equations that describe the radiation of elementary dipoles. Based on an optimisation method, the proposed approach seeks to identify the optimal parameters of an equivalent model which perfectly emits the same radiation as that emitted by the studied structure. In this study, the proposed method is tested on an AC–DC flyback converter. First, we will briefly show how the studied converter works. Then we explain how the suggested method is implemented and what their main advantages are. To do this, several tasks are performed. We firstly introduce the test bench of the near field in the time domain. Second, we present the measurement results of the vertical component of the radiated magnetic field (HZ) performed over an AC/DC converter, so as to model the radiation of this converter by the electromagnetic inverse method in the time domain. In particular, we give the analytical equations that describe the relationship between the induced voltage detected by the measurement probe and the electromagnetic field radiated by the studied converter. In the next section, the modelling methodology and its resolution by an optimisation method based on the genetic algorithms are explained in detail. To validate the reconstructed model using our proposed method, a comparison is made between the tangential components (HX) of the magnetic field, calculated using the identified model parameters and the one measured above the studied structure. Finally, we propose and validate the equivalent model of some power electronics components that are more useful and efficient in solving problems encountered in power electronics. 2 Flyback converter description The system studied is an AC–DC converter based on the principle of switched-mode power supplies (Fig. 1). Fig. 1Open in figure viewerPowerPoint Flyback AC/DC converter Switching power supplies are much smaller and lighter than linear power supplies, which explain their increasingly widespread use in various fields. In addition, switched-mode power supplies have a better efficiency, which varies between 65 and 90%. Contrarily, they have regulatory problems [19-21], which are more difficult to control. These power supplies produce a relatively large noise due to the rectangular signal to the switching frequency, which is rich in harmonics. This problem makes them unsuitable for certain applications. To this end, it is essential to characterise and control the electromagnetic interference behaviour of this type of converter. The converter studied is of a flyback type. The basic schema of a flyback converter is illustrated in Fig. 2. The choice of this structure type is due to the fact that it is very commonly used in low- and medium-power systems as those of battery chargers, voltage adapters or embedded systems. Fig. 2Open in figure viewerPowerPoint Schematic of AC/DC flyback converter This is the equivalent of a Buck-Boost converter in which the inductance is replaced by two coupled inductances acting as transformers. Therefore, the operating principles of these two converters are very close. In both cases, we distinguish a phase of storing the energy in the magnetic circuit and a phase of restituting this energy. Dimensioning the magnetic circuit defines the amount of energy that can be stored as well as the speed with which it is possible to carry out the storage and removal of energy. This is an important parameter that determines the power that can be provided by the flyback power supply. For our study, we consider the case of a low-power converter (5 W). The choice of low power is made to show that our method is efficient even for structures with very low powers where the search for the equivalent model can be difficult. From the electromagnetic compatibility point of view, the structure of the flyback is quite complex and it shows up different overvoltages and oscillations which allow having several modes of interference that cover a very wide frequency band that extends to several tens of MHz. This converter is supplied with a voltage of 220 V AC and it provides at its output a voltage of 5 V DC and a current of about 1 A. The switching is carried out at a frequency f = 60 kHz. The characteristics of the studied converter are summarised in Table 1. Table 1. Characteristics of the studied converter Type Input voltage Output voltage Maximum current Efficiency flyback 220 V AC 5 V DC 1 A 79% The analysis of an industrial scheme and the justification of adopted solutions, particularly in power electronics, are complex and require good technological knowledge of certain components. To this end, the proposed method consists of identifying and locating the radiating sources in the studied converter. This makes it possible to give the equivalent model to each radiant source. Thus, the proposed method based on the near field technique becomes an effective alternative that is very useful for designers of power electronics systems. Indeed, identifying all radiating sources in an electronic card and knowing its emissions at various distances facilitate the resolution of the problems of interferences encountered in power electronics. 3 Time domain test bench and measurement of near field emitted by studied converter To know the electromagnetic radiation at a well-defined surface above the studied converter in the time domain, we use a manual bench for measuring in the near field. In our application, the measurement of the radiation emitted by power electronic systems is performed in one single measurement for different radiation frequencies. This highlights the advantages of a near field test bench in the time domain compared with the test bench in the frequency domain. Fig. 3 shows the different parts of the test bench. Fig. 3Open in figure viewerPowerPoint Measurement test bench of near field in the time domain In frequency measurement, the spectrum analyser is characterised by input filtering, so the measurements are not influenced by the noise of the measuring devices. However, in temporal measurement, in our approach, the spectrum analyser is replaced by a high precision and high performance oscilloscope that presents a wide bandwidth for displaying and recording the signals detected by the probe. Thus, it is necessary to use a calibrated and shielded measuring probe. This can improve the obtained results and reduce the measurement time. To sweep the probe over the tested system, a plotting table is used. The displacement of the probe above the studied structure is manually performed. Each utilised probe is shielded. It consists of a loop connected to the central conductor on one side and to the external shield of a coaxial cable on the other side, as shown in Fig. 4. To create and validate a radiation model for our studied structure, we have performed two types of measurements: the normal component (HZ) and the tangential component (HX) cartographies of the magnetic field emitted by a power electronic structure. The use of these two components of the magnetic near field is sufficient to model the electromagnetic disturbance emitted by the studied equipment [10]. Indeed, this is good enough to make the recognition with the inverse method in the frequency domain [1, 4, 9]. Fig. 4Open in figure viewerPowerPoint Detailed structure of magnetic probes (a) Probe of tangential components HX and HY, (b) Probe of vertical component, (c) Measurement principle of electronic probe HZ To facilitate the access to the measurement oscilloscope, we opt for the use of different probes whose loops of measurement are oriented differently. Consequently, we utilise the probe in Fig. 4a to measure the normal field component (HZ), whereas, we use the probe in Fig. 4b to measure the tangential field components (HX, HY). It is worth noting that the used electronic probes are none other than small sensors or antennas as proposed and implemented in the IRSEEM NF test bench [22, 23]. To circumvent the limits of the measurements with these kinds of coils, the measuring probe is placed above the studied structure in a way that we can avoid the capacitive coupling between them and always keep a significant signal-to-noise ratio. Thus, the input and output cables are twisted and are far apart from the measurement plane and are oriented so as to direct the residual radiation of the cables away. In our study, before using the electronic probe, its calibration is performed and its ability to suppress unwanted field components is checked. The calibration which was performed as described in [24]. Extracting the magnetic field H(t) from the measured voltage at the probe terminals can be defined as follows: (1)where S = π × r2 is the probe surface (r = 1.6 mm) and μ0 = 4 × π × 10−7H/m is the permeability in the free space. This proposed method is based on measurements in the time domain of the near field over the device under test. The measurements are presented in the form of cartographies that describe the electromagnetic field distribution on the scanned surface. The cartography is a matrix representation of the amplitude and the phase of the measured near field at each point and at each instant over the studied system. The measurements of the time signals are carried out over an AC/DC converter arranged on the plane (XY). To create and validate a radiation model for our studied structure, two types of measurements are used. Indeed, the normal component (HZ) and the tangential component (HX) of the magnetic field cartography are measured. The measuring surface dimensions are 38 × 54 mm. It is constituted by 560 measurement points. The electronic probe is fixed at a height equal to 2 mm above the studied converter and the displacement step is 2 mm. To avoid the effect of radiation emitted by cables on measurement results, the following measuring conditions must be taken into account: first, the inputs and outputs cables are twisted. Second, the cables are far apart from the measurement plane and are oriented so as to direct the residual radiation of the cables away. Fig. 5b depicts the chosen face for the realisation of temporal reference measurements to identify the equivalent model. The chosen face permits being closer to the card by avoiding components that have cumbersome dimensions and also enables a better detection of the near magnetic field emitted by all elements of the studied converter. Fig. 5Open in figure viewerPowerPoint (a) AC/DC converter under test, (b)Selected converter face for measuring cartography used for modelidentification The equivalent radiating model can be identified on the basis of the electric or magnetic field. By analogy with the electromagnetic inverse method developed in the frequency domain, the search for the equivalent radiating model in this work is based on the measurements of the magnetic near field [10, 11, 25]. This shows its effectiveness to ensure the uniqueness of the equivalent radiation model [11]. On the other hand, to surpass the measurement complexities of the electrical field, we can exploit the magnetic field measurements to extract electrical field values [26, 27]. In our application, we work on all the studied structures with their control and power parts. Our objective is to find the radiating model for the whole converter. Historically, the radiation of the power part is very important compared to the radiation of the control one. Using the measured cartographies, we will try in the following section to identify the equivalent radiating sources of the studied converter utilising the electromagnetic inverse method developed in the time domain [18]. 4 Equivalent radiating model of studied flyback converter 4.1 Procedure, methodology section In this part, we apply the proposed temporal electromagnetic inverse method based on the genetic algorithms. Based on the near field measurements characterised by a very high signal-to-noise ratio, this approach consists of identifying an equivalent model that emits the same radiation of the AC–DC converter to be modelled. The suggested equivalent model is based on a network of elementary dipoles. An electric or magnetic dipole is characterised by a set of six parameters (Fig. 6). Fig. 6Open in figure viewerPowerPoint Presentation of the elementary dipoles The dipole may be represented by a d vector that comprises all the parameters: d = (Md, xd, yd, zd, θ, φ), where Md is the magnetic moment of the dipole which varies against time. The xd, yd, and zd represent the dipole's position, and their orientations are represented by θ and φ. In the time domain, the components of the magnetic field emitted by the elementary electric and magnetic dipoles in an observation point M(xo, yo, zo) can be deduced from the analytical expressions in the frequency domain using the frequency-time transformation operator. In the Cartesian coordinate system, the magnetic field components are expressed by the following equations [18]: For the electric dipole: (2)For the magnetic dipole: (3)where t′ = t − (R/c) is the delay time variable, is the distance between the measurement point and the radiating source, xd, yd, zd are the coordinates of the dipole centre, xo, yo, zo are the coordinates of the measurement point, r is the radius of the magnetic dipole, is the length of the electric dipole, θ, φ are the dipole orientations, and Ii is the intensity of the current in the dipole. Fig. 7 presents the methodology of the proposed method. The implementation of the proposed method starts with the synchronised measurement in the time domain of the magnetic near field cartography above the circuit to be modelled. To do this, it is necessary to measure the temporal signals with respect to a periodic and repetitive reference signal to stay in the same conditions during the passage from one measurement point to another (the slightest temporal difference modifies the result). Also, it is necessary that the functioning of the studied structure remains uniform (same current) during the temporal measurement of the magnetic near field cartography. Fig. 7Open in figure viewerPowerPoint Chart of the proposed method based on an optimisation algorithm The identification procedure of the equivalent sources begins with the search parameters of the radiating element that has the highest magnetic field and continues until identifying the source that has the lowest radiation. To identify the first dipole, it is necessary to search among all temporal signals in the measured cartography the signal that has the highest maximum value. Around the measurement point where the field is intense, we must perform a windowing of a limited part of the initial cartography. The studied structure emits electromagnetic disturbances on a broad frequency band ranging from the switching frequency up to tens of MHz. The measurements are performed for a sufficiently small distance to the studied structure. By analysing the analytical equations (2) and (3), the coefficients which multiply the terms of primary derivative dI/dt and second derivative d2I/dt2 are negligible compared with the coefficient which multiplies the term of current I(t). For this purpose, the magnetic field is approximately proportional to the current flowing in the elementary dipole. At this stage, during this identification, the excitation current shape will be chosen proportional to the measured field at the measurement point where the field has the highest magnitude. This simplifies the resolution by the optimisation method when identifying the parameters of the equivalent source. The optimisation method based on the genetic algorithms initially starts with the search for the parameters of a magnetic dipole. At each iteration, the genetic algorithms must modify all magnetic dipole parameters in order to minimise the error calculated by the fitness function. They will stop after a maximum number of iterations or when the error becomes less than a maximum error fixed in advance, which will guarantee a good coincidence between the estimated field and the reference one in all the measurement points of the window scan and at all times. After stopping the algorithm, even if the maximum number of iterations is not reached, the radiating dipole and its corresponding parameters will be identified. If the maximum number of iterations is reached and the optimisation method is not able to converge, we will restart the iterations for the search for an electric dipole. This can cause a very important overall computing time. Every time a dipole is identified, its radiation will be subtracted from the total cartography before proceeding to identify the rest of the dipoles. The identification of the equivalent sources will stop when the value of the magnetic field in the remaining cartography becomes less than or equal to the amplitude of the empty measurement noise (which is often known beforehand). Fig. 8 gives a further explanation of the proposed procedure that will be repeated until the extraction and identification of all radiating sources in the cartography of the measured magnetic fields. Fig. 8Open in figure viewerPowerPoint Methodology of the proposed electromagnetic inverse method in time domain In the literature, there are a variety of optimisation methods (simulated annealing, genetic algorithms, particle swarm optimisation etc.). In our work, the genetic algorithms method is used to resolve the time domain inverse method. Thus, the use of another optimisation method also remains possible [28, 29]. To guarantee and accelerate the convergence of the proposed temporal inverse method, we take into account the study of [30] to choose the optimal parameters of the genetic algorithms. These parameters are given in Table 2. Table 2. Optimum parameters of genetic algorithms fitness function population size (Np) Np = 20 × number of parameters of dipoles selection function Roulette crossover rate 0.8 In this table, M is the number of measurement points, T is the number of samples of the temporal signal, HZ(i,tK) is the measured magnetic field at time tK in the point i, and HZ(i,tK) is the calculated magnetic field with the equivalent model at the time tK in the point i. 4.2 Results In our work, the proposed method identifies an equivalent representation of a power electronic system according to their radiated field amplitudes. Thus, this identified equivalent model creates the same electromagnetic disturbances as those of the studied structure. By applying the suggested method to identify the radiating sources, we find seven magnetic dipoles as a number of sources. On the basis of the research work on the modelling of the radiation of electronic components and systems and the analysis of the radiations of the studied converter, we can identify the original components of the equivalent radiating dipoles. From the results obtained by the inverse method proposed in the time domain, we can see that the first two identified magnetic dipoles represent the equivalent models of two diodes. The third identified source represents the equivalent radiation of the transformer. Indeed, this last source (dipole no.3) has a centre located at the point (Xd = 0.10 cm/Yd = −0.21 cm/Zd = −1.21 cm) of the card. This position corresponds to the coordinates of the transformer in the studied converter (Fig. 9). In another component of the studied card, the seventh identified source is the equivalent model of a coil whose radiation is similar to that presented in [3]. Fig. 9Open in figure viewerPowerPoint Equivalent radiating source of transformer determined by the proposed method The parameters of the equivalent model obtained by the proposed method are shown in Table 3. Table 3. Model parameters obtained by the proposed method Identified dipoles Mdi, A m2 [Xdi Ydi Zdi], cm θi, ° φi, ° #1 3.12 × 10−7 1.46/−1.33/−0.645 0.57 7.45 #2 4.42 × 10−7 1.42/−0.32/−0.79 58.47 −132.99 #3 1.12 × 10−6 0.10/−0.21/−1.21 9.17 9.74 #4 2.96 × 10−7 −0.96/0.20/−0.61 −11.46 −17.77 #5 3.86 × 10−7 −1.34/1.19/−0.65 −43.56 128.98 #6 1.48 × 10−7 −0.35/−1.08/−0.37 72.80 179.42 #7 1.90 × 10−8 −1.36/−0.74/−0.62 83.12 8.85 In power electronics, the circuits are more and more integrated. Therefore, the volume of a card is more occupied by components rather than by tracks. By analysing Table 3, we observe that the identified dipoles are all above the printed circuit (Zd < 0). We quote the dipole equivalent to the transformer, which is located at the centre of the studied converter. It is co-ordinated along the vertical axis Zd equal to −12.1 mm. Hence, we identify an example case where the radiation of the components is very important compared to that of the tracks. Consequently, the majority of the radiation of the studied converter is due to the components of the power electronics card. Finally, we note that the identified sources correspond to true sources in the circuit, as depicted in Fig. 9. The quantity of information observed in the measured signals makes it possible to demonstrate the advantages of the measurements in the near field time domain emitted by power electronics circuits (Fig. 10). Fig. 10Open in figure viewerPowerPoint Internal structure of studied converter and radiations emitted by different radiating components To study these electromagnetic disturbances, we present in Fig. 11 the measured magnetic near field cartographies at different moments. Fig. 11Open in figure viewerPowerPoint Radiation above studied converter By analysing Fig. 11, we note that the radiating sources do not act at the same time; i.e. the evolution and the distribution of the electromagnetic emissions take place according to time. This is justified by the time lag observed at the level of the electrical quantities conveyed in the circuit and passing through the various elements of the converter. Thus, when an equivalent source appears at time t1, the other appertains at another instant. Contrarily, the information relating to temporal intervals is not available for frequency analysis. Indeed, in frequency cartographies, such as those presented in [10], we note that all radiating sources appear simultaneously as if they would contribute together to the radiation, which does not represent the real case of the radiation of the power electronics systems. Fig. 12 presents at various moments a comparison between the measured cartographies of the normal magnetic field component (HZ) and the calculated cartographies using the parameters of the equivalent model obtained by the electromagnetic inverse method proposed in the time domain. By examining the results obtained, we notice a good agreement between these cartographies. This demonstrates that the suggested method can identify with very good accuracy all radiating sources of the circuit. Fig. 12Open in figure viewerPowerPoint Measured magnetic field and estimated one (a) t = 9.95 µs, (b) t = 10.06 µs, (c) t = 10.56 µs 5 Validation of identified equivalent model To validate the reconstructed model, we propose in Fig. 13 to present a comparison between the estimated and measured cartographies. To do this, initially, we exploit the estimated parameters to calculate the cartography of the tangential component of the magnetic field (HX estimated). In the second step, over the studied structure, we perform an experimental measurement of the cartography of the tangential component of the magnetic field (HX estimated). In the second step, over the studied structure, we have performed an experimental measurement of the cartography of the tangential component of the magnetic field (HX measured). The validation of the model is presented in two different instants: t1 = 10.06 μs and t2 = 10.47 μs. Fig. 13Open in figure viewerPowerPoint Comparison of measured near field cartographies (HX) to those estimated at (a) t1 = 10.06 μs and (b) t2 = 10.47 μs In Figs. 12 and 13, we give the cartographies for various instants so as to be able to compare them correctly. This makes it possible to confirm the validity of the found equivalent model. This shows that there are no other models. As a consequence, the obtained equivalent model can represent the real sources. According to the results presented in Fig. 13, the magnetic near field calculated by using the parameters of the identified model is in good agreement with the measured magnetic near field. These results prove that the proposed method guarantees the uniqueness of the solution. Based on the measurements of the magnetic near field above a low-power (low radiation) electronic card, the proposed method has shown its effectiveness in finding the equivalent radiating sources. The proposed approach could be used for modelling the equivalent radiating sources of high-power structures where the radiated emissions will be very higher than those studied. The obtained equivalent model can be used to determine the distribution of the field at any point in the space around the studied system (by calculating the magnetic field at other distances in near field zone or to at the far field). This field distribution could be made in order to study the potential interaction between the studied system and other equipment located in the vicinity of this system (such as the study of the power board coupling with the rest of the embedded system). Finally, the knowledge of the radiating model of the power board can help the designer of the embedded system to place the power electronics circuits so as to minimise the effect of radiation of these circuits on the remaining components of the embedded system. 6 Conclusion The greatest effort has been made in this study to analyse in the time domain the radiation of the studied converter and subsequently to identify the equivalent model of each radiating source. To do this, the electromagnetic inverse method in the time domain has been put forward. This new approach is based on synchronised measurements of the near field above the studied converter. The parameters of the equivalent model based on a network of elementary dipoles are then determined through an optimisation method. Initially, the radiating sources are identified by using the measurements of the vertical component (HZ) of the magnetic field performed over the studied converter. Secondly, this equivalent model is validated by utilising the measurements of another component of the magnetic near field (the tangential component HX). The good agreement between the experimental results measured above the studied converter and the calculated results by exploiting the parameters of the obtained model highlights the robustness of the temporal electromagnetic inverse method when searching equivalent radiation models for actual industrial circuits having transient signals. Finally, we have exposed the operating possibilities of the inverse method in the time domain for the diagnosis and detection of faults in power electronics. 7 References 1Saidi S., and Ben Hadj Slama J.: 'Analysis and modeling of power MOSFET radiation', Prog. Electromagn. Res. M, 2013, 31, pp. 247– 262 2Labiedh W., and Ben Hadj Slama J.: ' Analysis and modeling of the magnetic near fields emitted by an IGBT and by a power diode generic radiating model for active components'. Int. Conf. on Electrical Sciences and Technologies in Maghreb (CISTEM), 2014, pp. 1– 6 3Levy P.-E., Gautier C., and Costa F. et al.: 'Accurate modeling of radiated electromagnetic field by a coil with a toroidal ferromagnetic core', IEEE Trans. Electromagn. Compat., 2013, 55, (5), pp. 825– 833 4Saidi S., and Ben Hadj Slama J.: 'A near-field technique based on PZMI, GA, and ANN: application to power electronics systems', IEEE Trans. Electromagn. Compat., 2014, 56, (4), pp. 784– 791 5Frikha A., Bensetti M., and Duval F. et al.: 'A new methodology to predict the magnetic shielding effectiveness of enclosures at low frequency in the near field', IEEE Trans. Magn., 2015, 51, (3), pp. 1– 4 6Shim H.W., and Hubing T.: 'A closed-form expression for estimating radiated emissions from the power planes in a populated printed circuit board', IEEE Trans. Electromagn. Compat., 2006, 48, (1), pp. 74– 81 7Tong X., Thomas D.W.P., and Nothofer A. et al.: 'Modeling electromagnetic emissions from printed circuit boards in closed environments using equivalent dipoles', IEEE Trans. Electromagn. Compat., 2010, 52, (2), pp. 462– 470 8Beghou L., Liu B., and Pichon L. et al.: 'Synthesis of equivalent 3-D models from near field measurements application to the EMC of power printed circuits boards', IEEE Trans. Magn., 2009, 45, (3), pp. 1650– 1653 9Beghou L., Costa F., and Pichon L.: 'Detection of electromagnetic radiations sources at the switching time scale using an inverse problem-based resolution method – application to power electronic circuits', IEEE Trans. Electromagn. Compat., 2015, 57, (1), pp. 52– 60 10Benyoubi F., Pichon L., and Bensetti M. et al.: 'An efficient method for modeling the magnetic field emissions of power electronic equipment from magnetic near field measurements', IEEE Trans. Electromagn. Compat., 2017, 59, (2), pp. 609– 617 11Liu Y., Ravelo B., and Fernandez-Lopez P.: 'Modeling of magnetic near-field radiated by electronic devices disturbed by transient signals with Complex form', Appl. Phys. Res., 2012, 4, (1), pp. 3– 18 12Liu Y., and Ravelo B.: 'Application of near-field emission processing for microwave circuits under ultra-short duration perturbations', Adv. Electromagn., 2012, 1, (3), pp. 24– 40 13Liu Y., and Ravelo B.: 'Fully time-domain scanning of EM near-field radiated by RF circuits', Prog. Electromagn. Res. B, 2014, 57, pp. 21– 46 14Rioult J., Seethramdoo D., and Heddebaut M.: ' Novel electromagnetic field measuring instrument with real-time visualization'. Proc. IEEE Int. Symp. on EMC, Austin, Texas, USA, August 2009, pp. 133– 138 15Ravelo B., Liu Y., and Ben Hadj Slama J.: 'Time-Domain planar near-field/near-field transform with PWS operations', Eur. Phys. J. Appl. Phys., 2011, 53, (03), pp. 1– 8 16Liu Y., Ravelo B., and Jastrzebski A.K. et al.: ' Calculation of the time domain z-component of the EM-near-field from the x- and y-components'. 41st European Microwave Conf., 2011, pp. 317– 320 17Ravelo B., Liu Y., and Louis A. et al.: 'Study of high frequency electromagnetic transients radiated by electric dipoles in near-field', IET Microw. Antennas Propag., 2011, 5, (6), pp. 692– 698 18Zitouna B., and Ben Hadj Slama J.: 'Enhancement of time-domain electromagnetic inverse method for modeling circuits radiations', IEEE Trans. Electromagn. Compat., 2016, 58, (2), pp. 534– 542 19Kim Y.-H., Jang J.-W., and Shin S.-C. et al.: 'Weighted-efficiency enhancement control for a photovoltaic AC module interleaved flyback inverter using a synchronous rectifier', IEEE Trans. Power Electron., 2014, 29, (12), pp. 6481– 6493 20Chen Y., Chang C., and Yang P.: 'A novel primary-side controlled universal-input AC–DC LED driver based on a source-driving control scheme', IEEE Trans. Power Electron., 2015, 30, (8), pp. 4327– 4335 21Zhu Z., Wu Q., and Wang Z.: 'Self-compensating OCP control scheme for primary-side controlled flyback AC/DC converters', IEEE Trans. Power Electron., 2017, 32, (5), pp. 3673– 3682 22Baudry D., Arcambal C., and Louis A. et al.: 'Applications of the near-field techniques in EMC investigations', IEEE Trans. Electromagn. Compat, 2007, 49, (3), pp. 485– 493 23Gilabert Y.V., Arcambal C., and Louis A. et al.: 'Modeling magnetic radiations of electronic circuits using near-field scanning method', IEEE Trans. ElectroMagn. Compat., 2007, 49, (2), pp. 391– 400 24Shall H., Riah Z., and Kadi M.: 'A 3-D near field modeling approach for electromagnetic interference prediction', IEEE Trans. Electromagn. Compat., 2014, 56, (1), pp. 102– 112 25Gao X., Fan J., and Zhang Y. et al.: 'Far-field prediction using only magnetic near-field scanning for EMI test', IEEE Trans. Electromagn. Compat., 2014, 56, (6), pp. 1335– 1343 26Ravelo B.: 'E-field extraction from H-near-field in time-domain by using PWS method', Prog. Electromagn. Res. B, 2010, 25, pp. 171– 189 27Liu Y., Ravelo B., and Jastrzebski A.K.: ' Calculation of time-domain near field Ex,y,z(t) from Hx,y(t) with PWS and FFT transforms'. Proc. Int. Symp. on Electromagnetic Compatibility, Roma, Italy, 17–20 September 2012, pp. 1– 6 28Kapsalis N.C., Kakarakis S.-D.J., and Capsalis C.N.: 'Prediction of multiple magnetic dipole model parameters from near field measurements employing stochastic algorithms', Prog. Electromagn. Res. Lett., 2012, 34, pp. 111– 122 29Tkadlec R., and Nováček Z.: 'Radiation pattern reconstruction from the near-field amplitude measurement on two planes using PSO', Radioengineering, 2005, 14, (4), pp. 63– 67 30Saidi S., and Ben Hadj Slama J.: ' Effect of genetic algorithm parameters on convergence of the electromagnetic inverse method'. Eighth SSD, Sousse, Tunisia, 22–25 March 2011, pp. 1– 5 Citing Literature Volume11, Issue13November 2018Pages 2133-2139 FiguresReferencesRelatedInformation