This is a generalization of Eq. (1) to a biphasic system with ellipsoidal inclusions of conductivity  into a matrix of conductivity . The fraction of inclusions is  and the system is  dimensional. For randomly oriented inclusions,
where the s denote the appropriate doublet/triplet of depolarization factors which is governed by the ratios between the axis of the ellipse/ellipsoid. For example: in the case of a circle (, ) and in the case of a sphere (, , ). (The sum over the  s is unity.)
The most general case to which the Bruggeman approach has been applied involves bianisotropic ellipsoidal inclusions.