On the surface impedance used to model the conductor losses of microstrip structures

In the numerical analysis of microstrip structures their finite conductivity is often modelled by using an equivalent surface impedance to relate the nonzero tangential electric field on the conductor surface to an equivalent electric surface current. The fields on top and below the patch are not necessarily the same and to account for this discontinuous tangential electric field a strict equivalence formulation should include magnetic surface currents. However, it is common practice to neglect them, presumably because they considerably complicate the surface integral equation and its numerical solution. Here it is shown that this practice leads to the use of an incorrect, although conservative, surface impedance. A basic assumption is that δ≪Δ≪λ with δ the skin depth, Δ the conductor thickness, and λ the free space wavelength