High frequency losses in multi-turn coils using a boundary element model

Skin and proximity effect problems in single and multiple conductors are formulated using an integro-differential expression and are solved using Boundary Element techniques. The formulation is in terms of the vector potential and its normal derivative together with an average potential A0to account for integral constraint conditions. The solution accuracy offered by simple constant and linear elements is examined, as is the effect of discretization. The losses in single and multiple turn, solid and hollow conductor coils are examined as a function of turn spacing and separation for values of a/δ as high as 40; a is a characteristic dimension of the coil conductor.