Surface impedance boundary conditions are usually used in combination with a numerical method. Therefore, both the formulation of the numerical method and the SIBC should be represented in terms of the same variables. It is rather natural that boundary conditions should not dictate the selection of the numerical technique. Instead, the numerical method is selected first and boundary conditions must then be derived in the state variables of the numerical method. Numerical methods used in practice frequently operate in terms other than the electric and=or magnetic fields (for example, the magnetic vector or scalar potential formalisms are commonly employed). The method may require quantities such as normal and tangential components of a function or the function and its normal derivative being related at the interface. These types of relationships are obtained in this chapter using the ‘‘surface impedance toolbox.’’ Since most electromagnetic quantities in conductors are governed by the

diffusion equation, it is natural to suppose they are mutually connected. Thus, another goal of this chapter is to derive general relations suitable for representation of various SIBCs in terms of different formalisms. In this sense, the discussion in this chapter forms the cornerstone of implementations that follow in Chapters 5 through 8.