Numerical Approaches for EMI Reduction of ICs and PCBs Inside Metallic Enclosures Sotirios Goudos Radiocommunications Laboratory Aristotle University of Thessaloniki GR-541 24 Thessaloniki, GREECE sgoudo@skiathos.physics.auth.gr Theodoros Samaras Radiocommunications Laboratory Aristotle University of Thessaloniki GR-541 24 Thessaloniki, GREECE theosama@auth.gr Elias Vafiadis Radiocommunications Laboratory Aristotle University of Thessaloniki GR-541 24 Thessaloniki, GREECE vafiadis@auth.gr John N. Sahalos Radiocommunications Laboratory Aristotle University of Thessaloniki GR-541 24 Thessaloniki, GREECE sahalos@auth.gr Abstract: This work presents a numerical approach to the reduction of Electromagnetic Interference (EMI) from the emissions of ICs and PCBs inside rectangular metallic enclosures. The ICs are modeled as small magnetic dipoles. Their interaction with the enclosures is studied with the dyadic Green’s functions. The Monte Carlo procedure in conjunction with optimization techniques is used in order to achieve optimal placement configurations for the ICs, by minimizing the electric current density on the metallic walls. The applications of the above approach in PCB design are discussed. Keywords : numerical techniques, EMI, Green’s functions, simulated annealing, genetic algorithms INTRODUCTION Electromagnetic interference (EMI) reduction inside metallic enclosures is a critical issue during the design stage of Printed Circuit Boards (PCBs). The placement of Integrated Circuits (ICs) on PCBs inside a shielded enclosure has an effect on the interference issue. Integrated circuits are modeled in the form of small magnetic dipoles. The validity of this modeling has been verified after suitable characterizations and measurements of several Personal Computers (PCs) and pieces of telecommunications equipment. The interaction between cavity walls and internal magnetic dipoles can be described by using the dyadic Green’s functions [1]. The mapping matrix approach is subsequently applied [2]. This approach outlines the interaction between the metallic walls inside the enclosure and the magnetic dipoles. It is noticed that the accurate prediction of electromagnetic emissions from PCBs, which are simulated as complex multiple dipole systems, is difficult or almost impossible. Due to the above, a stochastic procedure is proposed. In our work the current induced on the walls of a metallic rectangular cavity due to magnetic dipole sources for several positions and directions is presented. New probabilistic models of modern network equipment and ATX motherboards will be given. The placement of ICs on PCBs by using the Monte Carlo approach in conjunction with simulated annealing and/or genetic algorithms will be derived. The placement configurations are found by imposing a minimization criterion of the electric current density values on the walls. The minimization downgrades the emission capabilities, which are important in practice. FORMULATION For the rectangular cavity with dimensions a, b and c, along x, y and z-axis respectively (see Fig.1), the expressions for dyadic Green’s function of the magnetic and electric vector potential are given in [1], [2] and [3]. For a small magnetic dipole source the current density inside the cavity is given by: ˆ ˆ ˆ ( ) ( )( ) m x y z J r mx my mz r r δ ′ ′ = + + − (1) , , x y z m m m are the components of the magnetic dipole moments in the ˆˆ , x y and ˆ z directions respectively. The surface current density s J on the walls due to magnetic current moment z m has the following form: { } 2 sin( ) 1 sin( ) ˆ cos( )sin( )cos( )cos( ) ˆ sin( )cos( )cos( )cos( ) g z s m n m n g y x y x y x x y x y kz m J ee ab k kc k kx ky kx ky x k kx ky kx ky y     ′ = ×             ′ ′   −   ′ ′   +   ∑∑ (2) In (2) the coefficients are given as follows: 0 0 2 2 2 2 2 2 2 , , ( ) 1 0 2 0 x y z c x y g c i k m n l k k k a b c k k k k k k i e i π ω µε λ π π π = = = = = = + = − =  =  ≠  (3) If n possible cavity sources exist and m wall points of interest are taken into account then the amplitude mapping of every source to a specific point on the wall is represented by an n × m matrix A [2]. In A, a matrix element ρ ij represents the disturbance on j th -point caused by the i th -source. Disturbances caused by multiple sources at the same reference wall point can be summed using the principle of superposition. The deterministic values calculated in the mapping matrix are accurate enough only if all the source