**Abstract**

This chapter deals with modeling the radiation from rectangular film capacitors as a power electronics component. The rectangular film capacitors are sources of electromagnetic radiation, where its characterization is crucial for electronic circuits EMC. Our study presents the analyses and modeling of the magnetic near field radiated by the plastic and the polyester capacitors. An electromagnetic inverse method is combined with an optimization method based on genetic algorithms to create a radiating equivalent model. A very good agreement is observed between the magnetic near field cartography measured above the studied structure and calculated using the developed model parameters. Finally, a generic radiating model is proposed for various types of rectangular film capacitors. The generic model is validated using the measurements on a rectangular capacitor. The obtained equivalent model can calculate the magnetic field at any near field zone and far field around the capacitors. Circuit designers can use the field distribution to optimize the placement of the capacitors on the printed circuit board to reduce their coupling and potential interaction with other equipment in the vicinity of the system.

**Keywords:** Electromagnetic compatibility (EMC), Film capacitors, electromagnetic radiation, near field, inverse problems, generic model, analysis and modeling

#### **1. Introduction**

In power electronics, the switching frequencies are increasingly high to reduce these systems' weight, volume, and cost. This rise in frequency is accompanied by an increase in conducted and radiated electromagnetic disturbances. It also has significant effects on the behavior of these components at high frequencies. The characterization of the electromagnetic behavior of the various components of power electronics systems is an important step to control these systems' electromagnetic compatibility that should start from the design phase [1–4].

Many researchers have proposed radiating models for components or systems. In [2], concerning systems, a radiating model of a DC-DC converter was put forward and referenced as TEN 40–2412. The suggested model was composed of a network of four magnetic dipoles. The study in [3] proposed two radiating models of a circuit based on a microcontroller. The first model was based on 53 magnetic dipoles, while the second one was based on 517 electric dipoles. In [4], a radiating model of the MOSFET was presented, constituted by a magnetic dipole. Two radiating models of toric self-inductance were suggested in [5]. The first developed model consisted of a large number of dipoles (676 dipoles). It was obtained by using a modeling approach based on the matrix inversion. The second model was composed of a network of 12 dipoles. Previously, researchers have already put forward a radiating model for an inductor [6, 7]. The proposed model by [6] consisted of a network of two simple magnetic dipoles. However, the one suggested by [7] was composed of a large number of magnetic and electric dipoles (520 dipoles). The measurements of the electromagnetic radiation were performed as described in [8].

On the other hand, several methods have been developed to model the radiated emissions of components and electrical systems. The study in [3] suggested two methods. The first one was based on magnetic dipoles, and the second one was based on electric dipoles. The two presented methods required both the field amplitude and phase. The study in [4] put forward an electromagnetic inverse method based on the Genetic Algorithms (GA). The method gave good results when the number of searched parameters is not very significant; otherwise, the method was inefficient considering calculation time and convergence. The same authors developed [2] a new approach based on image processing descriptor PZMI by processing only a scan window of the measured magnetic field cartography. Another approach was developed based on the matrix calculation [6, 7].

In this chapter, we are interested in the radiation of film capacitors. The film capacitors are widely used in the power electronics domain replacing electrolytic capacitors. They particularly permit the improvement of reliability and EMI suppression. Indeed, they are often used in new industrial applications, such as power converters for renewable energy and hybrid automotive systems. The film capacitors are mainly characterized by a high insulation resistance, large conduction currents, and good stability of its capacitance. These components are generally cumbersome, and their radiation certainly affects the overall radiation of the circuits. The electromagnetic field radiated by capacitors creates induced disturbances that may cause a dysfunction to the neighboring circuits. Therefore, the mastery of all the circuit's radiated fields is a requirement for the system's proper functionality. It will be worthwhile to dispose of the radiation model of capacitors.

The literature review of papers related to EMC analysis of discrete capacitors shows few studies dealing with conducted disturbances across these components and their coupling effects on other neighboring components. Particularly, in [9–12], the authors first studied the electromagnetic coupling between the components of an EMC filter. The filter was composed of two capacitors and two coils. Second, they proposed an automatic method to determine the optimal placement of components and the associated tracks' design. However, these studies treat the coupling only in EMC filter applications. They were not interested in the capacitor's radiation. In [12], methods for predicting the magnetic field distribution in the capacitors were presented. Although the existence of a magnetic field may seem anecdotal in capacitors whose functionality depends on the electric field, the magnetic field is precisely the cause of imperfections of the capacitors: the equivalent series inductance, the resonant frequencies, the associated losses, and the currents induced in metalized capacitors [13].

The present chapter aims to propose a radiation model for film capacitors, which has never been proposed before. In Section 2, the experimental techniques used to characterize the near field around the capacitors are presented. In Section 3, the magnetic near field above the capacitors is analyzed. The modeling method is explained in Section 4. In the following sections, the measured fields are used to

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

develop the radiating models of the studied capacitors. Finally, a generic model for all rectangular capacitors is presented.
