**2.2 Device under test: AC/DC flyback converter**

In this work, the studied structure is a flyback AC/DC converter based on the principle of switched-mode power supplies (SMPS), as in [30]. Indeed, despite the superior efficiency that they can offer, these switching converters generate a lot of noise and EMI because of their high changing dv/dt and di/dt events. These power supplies have a complex structure regarding EM emissions. It generates different types of EMI, such as harmonics of switching frequency and high-frequency noise due to phase voltage ringing or the reverse recovery. In industry, this converter topology is typically used in both low and medium power as in automotive, battery charging and avionics, etc.

In practice, the design of the SMPS circuit is of great importance because it has to meet the configuration specifications in terms of energy storage and losses and avoid transient oscillations that generate EM interference modes covering a wide frequency band of several tens of MHz.

In our study, the DUT is a low power converter of 5 W. The top and bottom faces of the studied flyback AC/DC converter are shown in **Figure 2**. Its corresponding configuration parameters are presented in **Table 1**, and the schematic is depicted in **Figure 3**. To guarantee a synchronous acquisition, transient radiation signals at the scan surface have been measured with respect to the input of the optocoupler of the converter as a reference signal, **Figure 3**.

The NF radiation distribution of the DUT is obtained through a rigorous scan of the bottom face of the board, which allows avoiding bulky components and having a better recoding of EM emissions at a reasonable measuring distance.

*Study of Electromagnetic Radiation Sources Using Time Reversal: Application to a Power… DOI: http://dx.doi.org/10.5772/intechopen.100611*

Measuring probe

Surface of interest

#### **Figure 2.**

*Studied flyback AC/DC converter: top and bottom faces.*


#### **Table 1.**

*Parameters of the studied configuration.*

#### **Figure 3.**

*Schematic of the studied flyback AC/DC converter.*


**Table 2.** *Measurement setup.*

**Figure 4.** *Control signal.*

**Table 2** provides the measurement setup adopted in the present work, and **Figure 4** shows the control signal that ensures the smooth running of the converter.

A measured radiated signal is depicted in **Figure 5**. As we can notice in **Figure 6**, sources are not radiating simultaneously to obtain an intense radiation area at one time step but not in another. The radiation behavior of EM signals changes over time, and it is not evident to capture these events using frequency analysis only.

#### **3. Basis of electromagnetic time-reversal technique**

#### **3.1 Theoretical principles**

The time-reversal technique has been known for a long with great success in acoustics and ultrasound applications [17]. This has encouraged researchers to investigate the use of this method in the vast field of electrical engineering, such as in power line communications, fault location, and EMC issues [14, 15, 18–27]. Time and space focusing of waves is the specific feature of time-reversal theory [28]. Indeed, when a random source is in a pulse mode, generated signals are propagated indefinitely in the environment until they vanish (forward propagation). To measure these emissions, a set of transceivers is placed in a defined configuration called a timereversal mirror (TRM). Then, recorded waves are time-reversed and injected into the same context (time reverse + back-propagation). After that, back-propagated waveforms will try to merge to form a maximum peak at a certain time step and position (focusing). In fact, the obtained location and parameters correspond to the actual source due to the reciprocity theorem and the reversibility in time of the wave equation. Hence, in an electromagnetic context, the performance of sources excited by high-frequency generators is easily evaluated or, more precisely, for an EMC

*Study of Electromagnetic Radiation Sources Using Time Reversal: Application to a Power… DOI: http://dx.doi.org/10.5772/intechopen.100611*

**Figure 5.** *Captured waveforms: (a) whole signal, (b) window.*

**Figure 6.** *Measured radiation field maps above the DUT at two different time steps:t*<sup>1</sup> ¼ 10*:*25 *μs and t*<sup>2</sup> ¼ 10*:*5 *μs.*

application. The EM emission behavior of a radiating source that exhibits high-level transients can be reconstructed in both space and time [14–27].

Based on the basic electromagnetic wave equations in a homogeneous medium, which is written as follows:

$$\frac{1}{\mathbf{c}^2} \frac{\partial^2 \Phi}{\partial t^2} = \nabla^2 \Phi \tag{2}$$

Where Φ stands for electric E or magnetic H field, and c is the speed of light in free space.

If *f t*ð Þ is a solution of Eq. (1), then *g t*ðÞ¼ *f*ð Þ �*t* is also a solution. In other words, theoretically, EM waves may propagate backward from the time step *t* ¼ T to *t* ¼ 0 s. In practice, the measured magnetic (or electric) field *H r*ð Þ , *t* at probe position *r* and for each time step *t*, *t*∈½ � 0; T where T is the time period and the back-propagated magnetic (or electric) field *H r*ð Þ , T � *t* are both solutions. However, it has been demonstrated that under the action of time inversion, the magnetic field *H* is of an odd parity [15, 31]. Accordingly, assuming that TR represents the time inversion operator, we have:

$$\text{TR } \{\mathbf{H}(r,t)\} = -\mathbf{H}(r,-t) \tag{3}$$

It is interesting to note that when a current *I t*ð Þ flows through a source, a magnetic field *H t*ð Þ is created. In the case of a conductive loop, the following relation gives the measured field:

$$\mathbf{H}\_i(\mathbf{t}) = h(r\_0 \to r\_i, \mathbf{t}) \otimes \mathbf{I}(\mathbf{t}) \tag{4}$$

Where ⊗ denotes a convolution product, 1≤*i* ≤ N number of receiving antennas, and *h r*<sup>0</sup> ! *ri* ð Þ , *t* is the impulse response of the system at a position *ri* and for a pulse generated by *r*0. Indeed, *h t*ð Þ represents the transfer matrix that rules the transmission and the reception procedures between the TRM transducers (area discretized into N positions) and a defined virtual set of point-like sources placed on the DUT surface and driven by a Dirac delta function. As a result, the focused signal is obtained as follows:

$$\mathbf{H}\_{\rm TR}(r\_0, t) = \sum\_{i=1}^{N} h(r\_i \to r\_0, t) \otimes \mathbf{H}\_{\rm x, y, z\_i}(-t) \tag{5}$$

Where, HTR ð Þ *r*0, *t* represents the focused signal at the position r0 and time step *t*. In the literature [14, 15], the excitation signal has commonly been identified as the reversed version of the extracted focusing signal at the source position *r*<sup>0</sup> using the following equation:

$$\mathbf{Max}(r\_0) = \mathbf{max}\_{t \in \mathbb{T}} \mathbf{(|H\text{tr}\, \mathbf{(}r\_0, t)|)} \tag{6}$$

#### **3.2 Equivalent model determination**

In power systems with high current levels, the magnetic field has a strong predominance effect. In the literature, particularly during the switching activity, disturbances resulting from high dI/dt and leading to a high-frequency current can occur. Thus, to model these transients, the inverse problem resolution has been proposed and applied to a nearfield scanning experiment. Indeed, an equivalent model in the nearfield region is defined as a set of equivalent dipoles that reproduce the same EM radiation behavior as the DUT. For an equivalent magnetic dipole, **Figure 1**, the main characteristics are the center position (*Xd*, *Yd*, *Zd*), orientation angles (θ, <sup>φ</sup>Þ, diameter (the loop surface *<sup>S</sup>* <sup>¼</sup> <sup>π</sup> � *<sup>r</sup>*2, where *<sup>r</sup>* is the radius), and the current *I* flowings in the loop [32]. The magnetic dipole moment *Md* is the following:

$$
\overrightarrow{\mathbf{M}\_d} = I \times \overrightarrow{\mathbf{S}} \tag{7}
$$

*Study of Electromagnetic Radiation Sources Using Time Reversal: Application to a Power… DOI: http://dx.doi.org/10.5772/intechopen.100611*

**Figure 7.** *Definition of an equivalent magnetic dipole.*

From the formula for the equivalent field radiated by a magnetic loop in the nearfield, expressed by (8), we can obtain the three-dimensional distribution map of the radiated field (*Hx*, *Hy* and *Hz*) in a defined height of measurement using a time-domain representation (**Figure 7**).

$$\mathbf{H}\_{\mathbf{x},\mathbf{y},\mathbf{z}} = A \left[ \left( B\_1 \mathbf{C}\_{\mathbf{x},\mathbf{y},\mathbf{z}} \right) - \left( B\_3 D\_{\mathbf{x},\mathbf{y},\mathbf{z}} E \right) \right] \tag{8}$$

Where:

$$A = \frac{1}{4\pi R} \tag{9}$$

$$B\_{m=1,3} = \left( \left(\frac{1}{c^2} \frac{\partial^2 \mathcal{M}\_d(t')}{\partial t^2} \right) + \left(\frac{m}{cR} \frac{\partial \mathcal{M}\_d(t')}{\partial t} \right) + \left(\frac{1}{R^2} \mathcal{M}\_d(t') \right) \right) \tag{10}$$

$$\mathcal{C}\_{\mathbf{x},\mathbf{y},\mathbf{z}} = (\sin\left(\theta\right)\cos\left(\rho\right), \sin\left(\theta\right)\sin\left(\rho\right), \cos\theta) \tag{11}$$

$$D\_{x,y,x} = \frac{1}{R^2} \left( (X\_d - X\_0), (Y\_d - Y\_0), (Z\_d - Z\_0) \right) \tag{12}$$

$$E = \begin{pmatrix} \cos\left(\theta\right)(Z\_d - Z\_0) + \\ \sin\left(\theta\right)\sin\left(\phi\right)(Y\_d - Y\_0) + \\ \sin\left(\theta\right)\cos\left(\phi\right)(X\_d - X\_0) \end{pmatrix} \tag{13}$$

$$\mathbf{R} = \sqrt{(X\_d - X\_0)^2 + (Y\_d - Y\_0)^2 + (Z\_d - Z\_0)^2} \tag{14}$$

$$t' = t - \frac{R}{\mathbf{c}}\tag{15}$$

#### **3.3 Applying EMTR to radiating source identification**

This work focuses on the characterization of EM emissions in the nearfield using an equivalent radiation model. An algorithm based on electromagnetic timereversal technique is applied to identify radiating sources parameters using the time-domain analysis. Indeed, in practice, active sources are not radiating

**Figure 8.** *Flowchart of the proposed method based on the EMTR technique.*

simultaneously and the emission distribution at each time step corresponds only to the contributions of the different sources at this specific time. In the proposed method, an elimination process is carried out over time, starting from the most radiating sources (a hot spot in the map where the radiation level is significantly greater than the neighboring regions in the scanning area), using (5) and (6). A reconstructed field distribution is obtained using the identified source parameters, Eq. (8). Then, the difference between the measured and the estimated scans is evaluated using an error distribution at each iteration. To guarantee the convergence of the method and obtain a physical meaning model, an error limit is defined as a threshold value. Ideally, the estimated scan corresponds to the measured one, and then, the error limit equals zero. Apart from that, as in an NF experiment, the threshold corresponds to the measurement errors magnitudes (can be estimated when making measurement tests without a load). The effect of the different configuration parameters involved in this method has been studied in [33]. The flowchart of the whole procedure is shown in **Figure 8**.
