**1. Introduction**

In any electronic circuit, designers face serious challenges to ensure product efficiency and make it fit into a large community of electronic systems where harmful interferences can occur. Indeed, electromagnetic compatibility aims to achieve a peaceful coexistence of electronic equipment, especially when subjected to severe electromagnetic disturbances. In recent high-density PCBs (printed circuit boards), components are becoming increasingly sensitive to unwanted phenomena, such as radiated and conducted emissions characterized by sudden variations in voltage and current [1, 2]. Thus, EMC researchers and engineers have conducted multiple works using various relevant approaches to predict these emissions with a reasonable tradeoff between guaranteeing a good accuracy and a reduced computing time. For instance, to deal with radiated emissions, authors in [3–5] have proposed to use matrix inversion methods that have ended up with a need for a large set of measurements. As a solution, hybrid optimization methods based on artificial intelligence techniques such as genetic algorithms (GA) and artificial neural networks (ANN) have been progressively introduced [6, 7], and this has contributed considerably to speed up the algorithm convergence at a fixed operating frequency.

The common point in the research mentioned above has been using the frequency domain (FD) to model electromagnetic fields through a set of equivalent dipoles [2–8]. To obtain a behavioral model of the device under test (DUT), particularly in power circuits of a fast switching nature [2, 5], a direct alternative way of proceeding is to perform measurements in the time domain (TD), which can also recover the frequency spectrum using a further signal processing. Indeed, timedomain measurement has numerous advantages over frequency-domain measurements. On the one hand, TD devices provide faster and simpler measurements because they use high-speed time sampling techniques and offer the possibility of capturing the signal in TD and compute its different spectral components in a shorter period (e.g., spectrum analyzers, which are more expensive than oscilloscopes, usually have a narrow resolution bandwidth). On the other hand, better precision is obtained using TD measurements because all the frequencies are simultaneously measured, mainly in the case of a one-time transient where only a single frequency is captured and in the case of a periodic signal (with repetitive events) where the frequency step could limit the identification of all the events of interest. In the literature, few TD-based works have been presented to obtain the different equivalent parameters of radiating sources [9–15]. In [11–13], authors have evaluated the performance of TD methods to deal with EM transients using a microstrip device. More studies have been performed in [11–14].

Nevertheless, these approaches select the frequency band, and complex calculations require powerful machines with sufficient memory [11]. In [10], the temporal electromagnetic inverse method has been developed and implemented using GA, and thus, it depends on initial GA options. Therefore, researchers have developed alternative TD methods based on electromagnetic time reversal (EMTR) for radiating source identification in literature. Indeed, several studies have been achieved in the field of electromagnetics using the time-reversal (TR) technique for different purposes such as in source location identification [14, 15], acoustics [16–18], and recently power electronics [19–27]. Several studies have demonstrated TR's robustness and efficiency [14, 27, 28]. However, a handful of studies investigated the use of TR for EMC applications in the time domain until now. Rachidi et al. have presented using electromagnetic time reversal in lighting location and faults detection in power networks [14].

Most of the existing TR studies dedicated to sources characterization have been applied in the far-field region [17, 19, 20]. While in the case of power electronic EM radiation measurement, a nearfield (NF) scan has proven to be more advantageous because it is less dependent on different test conditions such as application range and equipment. Recent studies, as in [3] and [10], report that different issues in the converter circuits, basically linked to transient disturbances with a quite short duration, should be investigated in the TD using an NF test bench. In [22, 23], the proposed method has been applied to identify the equivalent model of radiation of simple structure, as an interesting basic study but not representative enough to deal *Study of Electromagnetic Radiation Sources Using Time Reversal: Application to a Power… DOI: http://dx.doi.org/10.5772/intechopen.100611*

with an advanced power circuit. Hence, this work applies the full time-domain method to a complicated board containing several bulky components with several radiating sources based on the electromagnetic time-reversal technique. Current and voltage high-speed commutations can create serious non-intentional transient disturbances covering a wide frequency band in structures such as power electronic converters. Knowing that in electromagnetic interferences (EMI) mitigation techniques (such as shielding), it is essential to predict radiating sources parameters at the early design stage to reduce emissions related to switching activities and parasitic interconnections. In this present work, we have studied the application of the EMTR technique based on time-domain analysis to reconstruct the radiation behavior and obtain an accurate equivalent model of the device under test (DUT), which emits critical non-sinusoidal signals. This methodology aims to help designers estimate radiated EM fields at different measurement distances and study the possible couplings between components.

Section 2 gives a detailed overview of the NF measurement test bench in the time domain. Moreover, the selected studied structure, which is an AC/DC flyback converter, is described. Section 3 discusses the theoretical investigations of the electromagnetic time-reversal technique and details the suggested implementation of the method for evaluating radiated emissions and sources reconstruction issues. Section 4 provides an application of the proposed EMTR-based method, and an adequate equivalent model that emits the same radiation behavior is studied.

Furthermore, a comparison study has been carried out for experimental validation purposes. The obtained results are presented in the form of time-dependent mappings of the magnetic nearfield. The last section outlines the main conclusions.

#### **2. Time-domain measurements test bench**

A TD test bench is employed to evaluate EM disturbances in the NF for power systems in this study. A single measurement (one scan) is carried out for multiples radiation frequencies at once.

#### **2.1 TD measurement technique**

TD measurement uses high precision measurement devices with a wide bandwidth, such as oscilloscopes, to capture temporal signals using a magnetic field probe. This measuring probe is nothing else than an academic small coil probe shielded sung copper [11] or a commercial magnetic loop of a radius equal to 1*:*6 mm generating a voltage from the varying magnetic flux. It scans the surface above the DUT, in the nearfield region, with a fixed displacement step, which prevents capacitive couplings and noise while measuring. The probe is connected to the scope using a shielded coaxial cable through an SMA connector, and it is calibrated as explained in [11, 29].

Indeed, based on the Faraday and Lenz laws and transformation equations, the variable magnetic field is obtained through the voltage measured at the terminals of the loop using the following equation:

$$\mathbf{H}(t) = -\frac{\mathbf{1}}{\mu\_0 \times \mathbf{S}} \int\_0^t \mathbf{V}(t)dt\tag{1}$$

Where *<sup>S</sup>* <sup>¼</sup> *<sup>π</sup>* � *<sup>r</sup>*2, is the loop surface and *<sup>μ</sup>*<sup>0</sup> <sup>¼</sup> <sup>4</sup> � *<sup>π</sup>* � <sup>10</sup>�<sup>7</sup> <sup>N</sup>*=*A2 is the permeability in the free space.

**Figure 1.** *Automated scanning test stands for NF measurement in the time domain.*

The studied test bench provides a three-dimensional field measurement, but according to our needs, we only consider measuring the normal component of the magnetic field Hð Þ<sup>z</sup> . Synchronous acquisitions are performed using a trigger, chosen to be a periodic and a repetitive reference signal. The following **Figure 1** presents the proposed nearfield test bench using a LeCroy WaveRunner 104XI oscilloscope.
