The skin depth delta in copper at 1,text GHz , given conductivity sigma = 5.8 times 10^7,text S/m and mu_0 = 4pi times 10^ -7 ,text H/m , is approximately:

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Electronics Engineering QUESTION #11713

Question 1

The skin depth $\delta$ in copper at $1\,\text{GHz}$, given conductivity $\sigma = 5.8 \times 10^7\,\text{S/m}$ and $\mu_0 = 4\pi \times 10^{-7}\,\text{H/m}$, is approximately:

$66\,\mu\text{m}$
$2.1\,\mu\text{m}$✔️
$0.066\,\mu\text{m}$
$210\,\text{nm}$

Correct Answer Explanation

$\delta = \sqrt{\dfrac{2}{\omega\mu\sigma}} = \sqrt{\dfrac{2}{2\pi \times 10^9 \times 4\pi\times10^{-7} \times 5.8\times10^7}} \approx \sqrt{\dfrac{2}{4.58\times10^{11}}} \approx \sqrt{4.37\times10^{-12}} \approx \mathbf{2.09\,\mu\text{m}}$. At GHz frequencies, current is confined to a very thin surface layer, making plating quality and surface finish critical for RF conductor loss.

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