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

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

From Equation 2.14, the surface resistance RS is written as

RS=ωμ2σ=πfμσ=1σδ.

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, RAC = 1/σδ. RS 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 (E˜ is in the z-direction). As b increases, the current 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 in the conductor is idealized as a surface current K˜ on the interface. Thus, if b = 1, the current is K and the power loss per meter square is

12I2RAC=12K2RS.

From the boundary condition at the PEC we obtain

K˜=H˜.

Thus, the power loss per meter square is

SR=12RSH˜2W/m2.

The total power loss over a surface S is given by

WL=S12RSH˜2ds.

This is the basis of Equation 4.14.

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