**4.1 Modeling of the flyback converter**

An adequate equivalent radiation model has been identified by applying the proposed EMTR method to the measured emissions of the AC-DC converter

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


#### **Table 3.**

*THE Obtained equivalent model parameters.*

#### **Figure 9.**

*Magnetic nearfield maps of* z*-component in TD: (a) measured. (b) Estimated.*

obtained, as previously explained. Indeed, by comparing measured and estimated magnetic nearfield distribution *Hz*, using identified sources parameters given in **Table 3**, at a constant height of measurement and scan area, we can notice a good

**Figure 10.** *Cuts of measured and simulated Hz at Z* ¼ 0*.*

agreement between the two sets of results along time, as shown in **Figure 9**. Particularly, the obtained equivalent sources perform valid waveforms with less noise as if they have been captured when scanning the circuit without measurement errors (which is inevitable in practice).

In **Figure 10**, estimated radiated field cuts at *Z* ¼ 0 are compared to the reference signals along the x- and y-axis. Moreover, besides *Hz* reconstruction, the prediction of *Hx* and *Hy* is easy by including the obtained sources parameters in the analytical expressions of the magnetic field, as in (8).

It is worth noting that in order to the enhance the obtained results, it would be great to refine the mesh of the scanning area further and reduce even more the error limit (corresponding to the measurement errors including the test stand inaccuracies, spatial probe motion, and the coupling effects between the probe and the DUT, etc.). Nevertheless, both a large memory and a considerable computing time are needed.

#### **4.2 Validation of the obtained model**

In this study, we propose to confirm the efficiency of the obtained results using the EMTR-based method in TD with a standard inverse method performed in the frequency domain. Thus, we do not make measurements using an FD test bench, but we instead proceed by applying a fast Fourier transform to the measured magnetic field signals in TD. Indeed, in **Figure 11**, we notice the existence of several harmonics covering tens of megahertz in the frequency spectrum of the obtained FD magnetic field at different probe positions. This is among the major

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

**Figure 11.** *The spectrum of the measured magnetic field above DUT at different positions.*

disadvantages of FD measurements, especially in multisource structures with different characteristics and radiation patterns. We have implemented an optimization method based on genetic algorithms to apply the frequency inverse method and obtain an equivalent model for each studied frequency [8, 9]. In fact, the iterative process needed in this procedure can be reduced when choosing only significant frequencies; otherwise, it is time and memory-consuming. Moreover, to guarantee and accelerate the convergence of the method, a fine configuration has to be employed, particularly having a proper choice of the variable boundaries and population size. In **Figure 12**, mappings of the measured and estimated radiated field are depicted for different frequencies.

A good agreement is achieved between FD maps of measured fields and estimated using an optimization algorithm at different frequencies. Similar source positions have been obtained, which confirms the previous results. Looking at **Figures 9** and **12**, we notice that the proposed method based on EMTR matches the measurements better. Indeed, TD investigations provide rapid results, making modeling easier to use in critical test cases. It is worth noting that FD maps are only depicted at a single frequency for each measurement, and then, we cannot observe the behavior of all existing radiating sources without performing several measurement tests. However, a single temporal measurement is required for a TD method, as we have explained.

For further validation purposes, we propose to reconstruct the *x*-component of the EM field (*Hx*) using the obtained equivalent model and then compare the generated maps to the measured radiation distributions acquired with the magnetic probe dedicated for tangential components capturing. **Figure 13** shows an example of mappings at a defined time step. A good agreement is noticed between measured and estimated *Hx*. Hence, we conclude that the obtained equivalent magnetic dipoles are in good positions and that the proposed method is efficient in providing an equivalent method reproducing a three-dimensional reconstruction of the radiated field describing the overall behavior of the studied converter.

**Figure 12.** *Magnetic NF maps of* z*-component in FD: (a) measured. (b) Estimated.*

**Figure 13.** *Measured and estimated magnetic NF maps of* x*-component at t* ¼ 10*:*50 *μs.*

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