EMC APPLICATIONS OF THE EMAPS HYBRID FEM/MOM CODE Yun Ji Univ. of Missouri-Rolla Mohammad W. Ali 3COM, Inc. Abstract-EMAPS is a numerical software package designed to model electromagnetic problems. It employs the finite element method (FEM) to analyze three- dimensional volumes, and the method of moments (MOM) to analyze the current distribution on the surface of these volumes. The two methods are coupled through the fields on the dielectric surface. This paper describes the formulation of the EMAPS code and demonstrates how it can be used to analyze simple printed circuit board configurations. I. INTRODUCTION €MAPS---ElectroMagnetic Analysis Program Version 5 is a 3D numerical electromagnetic modeling code developed at the University of Missouri-Rolla (UMR). The code can be freely downloaded from the world wide web at http://www.emclab.umr.edu/emap5. EMAPS is a hybrid FEM/MOM code designed primarily to simulate electromagnetic interference (EMI) sources at the printed circuit board level. Generally, printed circuit boards and their components are composed of many different materials with arbitrary shapes. Thus, the Method of Moments (MOM) does not model this kind of problem efficiently. A hybrid method combining FEM with MOM has been proposed by many researchers [1][2][3] as a means of modeling structures that are both open (i.e. unbounded) and complex. FEM is applied to model the fields within a fictitious boundary containing regions of high complexity, while MOM is used to model the fields on the fictitious boundary. The two methods are coupled by the fields at the dielectric boundary. Details of the hybrid formulation for EMAPS are presented in [4][5]. This paper demonstrates how EMAP5 can be used to model 3D microstrip configurations. II. FORMULATION The general structure of interest is shown in Figure 1. A dielectric volume V2 has electrical properties (EZ, p?). It is enclosed by a surface S2. A conductive volume V3 is enclosed by a conductive surface S,. The fields within V3 wnish. VI, which denotes the volume outside of VZand V3, is assumed to be free space, hence has electrical properties (Q, h). (El, H,) and (E2, H2) denote the electric and magnetic tields in VI and V2, respectively. The unit normal vectors for S2 and S, are defined pointing outward 0-7SO3-501j-4/SS/$10.00 0 1998 EEE 543 E' H' d Todd H. Hubing Univ. of Missouri-Rolla A n '2 )I? I .. , A n = 3 = conductive body sc U Fig. 1. A dielectric obect and a conductive object illuminated by E', Hi or Jint, Mint. toward VI. The structure is excited by an incident wave (E', H') or impressed sources (J'"', MInt). The scattered electric and magnetic fields are (E', H'). The dielectric surface sd, is defined as Sz if the conductive body is not adjacent to the dielectric body; Otherwise, sd= S2 - (S2 A S,). The objective is to solve for the scattered fields (E', H') or the surface electric current density on S,. A. Discretization of FEM From the double curl equation in terms of E, the weak form of FEM equation can be expressed as: where w(r) is a weighting function. Tetrahedral elements are used to discretize the volume Vz. Basis functions proposed by M. L. Barton and Z. J. Cendes [6] are chosen here. Each basis function is defined within a tetrahedron and is associated with one of the six edges. The electric field E within volume V, can be expanded as: