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Solved Problems-12

Problem-12
A uniform plane wave of frequency ‘f ’ is normally incident from air onto a thick conducting sheet with conductivity σ and ε = ε0, μ = μ0. Show that the proportion of power transmitted into the conductor (and then dissipated into heat) is given approximately by,
Description: 41143.png, Rs = Surface resistance

Calculate this quantity for f = 1 GHz and copper, σ = 5.8 ∞ 107 siemens/m.
Solution
For a good conductor, Description: 41135.png
 
So, Description: 41125.png
 
So, the complex characteristic impedance for a good conductor is,
 
or, Description: 41118.png

∴ transmission coefficient,
 
Description: 41111.png
 
∴ reflection coefficient,
 
Description: 41101.png
 
So, the power transmission coefficient is,
 
Description: 41094.png
 
Description: 41086.png
 
For copper at 1 GHz, the power transmission coefficient is,
 
Description: 41077.png
 





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