Computational errors in application of impedance boundary conditions on a surface interior to a lossy medium

Impedance boundary conditions are often used to simplify the formulation of complex scattering problems involving lossy media, where the field penetration into the object is small. Its validity is examined when the impedance surface is inside a lossy medium. A lossy sphere coated by a spherical shell of different loss factor is studied. The plane wave scattering problem is formulated two different ways: by an exact analytic method using appropriate potential functions for the interior sphere, its lossy coating and the exterior region and by replacing the interior sphere with an impedance surface. The use of impedance boundary conditions over a surface inside a lossy medium is thus shown to be valid and to provide results with acceptable accuracies.<>