Circuital modeling for cylinders with radial dependent conductivity and permittivity

For a cylinder with radially dependent permittivity and conductivity, we derive an equivalent circuit model whose elements are frequency independent resistances, inductances (self and mutual), and capacitances. The model is obtained by partitioning the system into shells which are thin enough so that the spatial variation of electric and magnetic fields is negligible over their cross section. In order to validate the model, the electromagnetic response of the cylinder is determined from the field equations. These are solved numerically and the results are compared with the response of the equivalent circuits. As the number of shells is increased, the equivalent circuit response for sinusoidal excitations approaches the exact electromagnetic response for all values of exciting frequency