**5. Model for the polypropylene capacitor**

### **5.1 Model research**

After presenting the magnetic field cartography radiated by the capacitor in Section 3, we apply our approach to find a model that gives the same radiation as measured over the capacitor. To do this, we used the cartography of the vertical component Hz of the magnetic field at a frequency of 20 MHz. We chose the cartography of 20 MHz because it was the clearest one. **Figure 15** shows the position of the identified loop on the capacitor cartography. The modeling results for the obtained model are shown in **Table 1**.

**Figure 16** presents the measured and estimated cartographies of the magnetic field vertical component Hz. A reasonable agreement between the two cartographies is observed.

#### **5.2 Model validation**

Further validation of the model is performed on other faces of the capacitor or other components as proposed in [4, 23]. Hence, we measured the magnetic field cartography in the literal face and compared it to the one that has been calculated using the obtained model.

**Figure 15.** *Obtained loop position.*

*Development of Generic Radiating Model for Rectangular Capacitors: Magnetic Near Fields… DOI: http://dx.doi.org/10.5772/intechopen.98894*


#### **Table 1.**

*Parameters of the equivalent model of the polypropylene capacitor.*

#### **Figure 16.** *Measured and estimated cartographies.*

Accordingly, the capacitor is placed vertically, and measurements of the cartography are carried out on the other side of the capacitor. **Figure 17** depicts the layout of the measurements.

The validation of the model is made at 20 MHz and a measurement height of 3 mm. **Figure 18** shows the measured and calculated magnetic field cartography above the vertically placed capacitor.

According to the previous results, the magnetic field is reconstructed by the model shows good resembling with the measured one. These results confirm the existence of an equivalent rectangular current loop in the capacitor. To explain the obtained results, we present in **Figure 19** the internal structure of the capacitor. Film capacitors are made out of two pieces of plastic film covered with metallic electrodes wound into a cylindrical-shaped winding, with terminals attached, and then encapsulated.

The analysis of the internal structure of the film capacitor confirms the obtained equivalent model. Indeed, the surface of the capacitor appears as a rectangular loop.

The internal coupling phenomenon certainly causes this current distribution at the capacitor contour in the component. This current distribution in the capacitor film is consistent with that introduced in [12, 13].

**Figure 17.** *Measurement of the magnetic field over a vertically placed capacitor.*

**Figure 18.**

**Figure 19.** *Film capacitor's internal structure.*
