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An effective scheme allowing strong coupling of electronic circuits with three-dimensional electromagnetic fields is presented in this paper. The electromagnetic field is represented by means of an edge element method. The state space formulation is employed to describe the time variable topology of the electronic circuit. The whole system is solved with a time step procedure. The methodology is verified by comparing calculated and experimental results on a quasiresonant converter.Simultaneous solution of field and circuit equations is currently used in order to obtain the behavior of electromagnetic devices fed by static converters. Two and three-dimensional representations of the magnetic structure are employed [l], [2], [3], [4]. Concerning the electrical circuit, when the converter structure and its operation is simple, the electrical feeding circuit representation can be given by a set of configurations conresponding to the different operating sequences known 'a priori' [l].When the feeding circuit topology is more complex, its operation sequences are not easy to be identified 'a prior?.Thus, a more general method must be used. In a previous work [5], for two-dimensional representations of magnetic structures associated to static converters, the state space formulation has been successfuuy employed. In that case, a classical formulation based on nodal magnetic vector potential was used. The non-symmetric time dependent matrix system corresponding to the whole field-circuit equations was solved step by step with respect to time using a direct method.In this work, the state space representation of the electronic converter is also used for strong coupling between field and circuit equations. It can be more efficient than nodal GirGUit analyaia i n the (3a5e of cjamplex m v m e r structures [6]. For the three dimensional representation of the magnetic device, hexahedral edge elements are employed. Manuscript received November 3,1997. kC.Piuho email pinho@arUcad&.bs N.Sadowski email nelson@prucad.&.bc P.Ku0-Peng e " patrick@mcad&.bc J.PABastos e-mail; i paW,mu cad.&.br. Authors fau ($5) 48 234-37-90, phone (55) 48 23 1-96-49. The authors would like to express i%ek gratitude to "THORNTON Inpec Eleir6nic-a Ltda." fix furnishing the neceSSary fprrite cores to the experimental results presented in this paper. This work was supported in part by the CNPq LI. MATHEMATICAL FORMULAITON Using hexahedral edge elements for the field equations and state space formdation for the converter equations, the matrix system representing the coupled problem can be written as: d PA + N -A -CI = M dt d at F -A + (R -G, >I -G 4 X = GSE d -X-G1X-G3I=G2E dt In equation above the terms PA, NdA/ dt and M are obtained by assembling, respectively, the next elementary contributions [7]: Vm = 1,12 (2) Vkz = 1J2 (3) M e =JJlaVxwm .B,& Vm=1,12where , U is the magnetic permeability, o i s the electric conductivity, Qe is the volume of the element, w, and w, are hexahedral edge elements shape functions, B, is the permanent magnets remnant flux densi...