Solution for the effective permittivity of mixtures with multilayer scatterers by transmission line approach

The effective permittivity of mixtures with N-layer spherical scatterers are shown to be a function of the permittivities of the constituent materials and their volume fractions. Essential in the solution is the unorthodox way of solving the field inside the piecewise homogeneous sphere. This is done by treating the scatterer as a transmission line in the radial direction, although the problem is quasistatic. Propagation and scattering matrices that relate the field components in adjacent layers are derived. The fields can be solved without having to invert the 2N*2N matrix. The case of a continuous radial permittivity profile is considered and a differential equation for this profile is derived.<>