Topic: Electromagnetics
Skin depth at 2 GHz for a gold conductor with $\sigma=4.55\times10^{7}S/m$ is $1.5~\mu m$. Skin depth (in $\mu m$) at 8 GHz and 18 GHz is
- A. 3.00, 4.50
- B. 0.75, 0.50
- C. 0.375, 0.055
- D. 1.50, 1.00
Answer: B. 0.75, 0.50
Explanation: Here, $\delta=\frac{1}{\sqrt{\pi f\mu\sigma}}$. So, $\delta_{1}=1.5~\mu m$ for $f_{1}=2~GHz$. $\sigma=4.55\times10^{7}S/m$, $\mu=fixed$. $\delta\propto\frac{1}{\sqrt{f}}$. $f_{2}=8GHz$, $f_{3}=18~GHz$. $\frac{\delta_{1}}{\delta_{2}}=\sqrt{\frac{f_{2}}{f_{1}}} \Rightarrow \frac{1.5\times10^{-6}}{\delta_{2}}=\sqrt{\frac{8}{2}} \Rightarrow \delta_{2}=0.75~\mu m$. $\frac{\delta_{1}}{\delta_{3}}=\sqrt{\frac{f_{3}}{f_{1}}} \Rightarrow \frac{1.5\times10^{-6}}{\delta_{3}}=\sqrt{\frac{18}{2}} \Rightarrow \delta_{3}=0.50~\mu m$.