Principles of Electromagnetic Waves and Materials, 2nd Edition

Appendix 4A: Calculation of Losses in a Good Conductor at High Frequencies: Surface Resistance R_S

From Equation 2.14, the surface resistance R_S is written as

$$R_S=\sqrt{\frac{\mathrm{\omega }\mathrm{\mu }}{2\mathrm{\sigma }}=}\sqrt{\frac{\mathrm{\pi }f\mathrm{\mu }}{\mathrm{\sigma }}=}\frac{1}{\mathrm{\sigma }\mathrm{\delta }}.$$

The surface resistance is the AC resistance of a rectangular, good conductor material of 1 m long and 1 m wide, at high frequencies. In Figure 2.2, if l = 1 and b = 1, from Equation 2.38, R_AC = 1/σδ. R_S is given in the unit of Ω per square, but it increases with l and decreases as b increases. As l increases, the voltage increases ($\tilde{E}$ is in the z-direction). As b increases, the current $\tilde{I}$ increases. In computing fields in the dielectric medium at the interface of a dielectric–conductor medium, if we make the idealizing assumption that the conductor is a PEC, the current ...