Spherical Equivalent Dipole Array Theory and Its Applications to Complex Electromagnetic System

The equivalent dipole array is an effective method for emission source modeling to solve practical electromagnetic engineering problems. In this paper, a spherical equivalent dipole array method (SEDAM) is proposed to model practical and complex electronic systems. Unlike the planar equivalent dipole array method (PEDAM), SEDAM is derived in the spherical coordinate system and is more suitable for large electromagnetic equipments. In addition, SEDAM can achieve accurate emission prediction around electronic systems of arbitrary structures, where PEDAM is not easy to be used. We first derived the analytical relationship between magnetic fields and magnetic dipole moments in the spherical coordinate system. To model the complex systems, several equivalent dipoles are properly placed on a spherical surface which encloses the equipment under test (EUT). By superposition of the fields generated by all the equivalent dipoles, the equivalent relational matrix is constructed and the weights for each dipole are solved. Then, the weighted dipole array can be used to predict the emission fields at desired locations. The proposed method is first verified through a numerical simulation. The results show that the proposed SEDAM outperforms the PEDAM in terms of accuracy. It is further validated through a measurement. The measurement results show that SEDAM can model the practical and complex electronic systems and predict their electromagnetic emission with acceptable accuracy.