Question

Skin depth at 2 GHz for a gold conductor with σ = 4.55 × 107 S/m is 1.5 μm. Skin depth (in μm) at 8 GHz & 18 GHz is:
1. 3.00, 4.50
2. 0.75, 0.50
3. 0.375, 0.055
4. 1.50, 1.00

Answer 1

Correct Answer - Option 2 : 0.75, 0.50

Concept:

The skin depth is that distance below the surface of a conductor where the current density has diminished to 1/e of its value at the surface.

The skin depth is represented by δ 

\(δ =\frac{1}{\sqrt{\piμνσ} }\)

Where 

μ = permeability

ν = frequency

σ = conductivity

Calculation:

Given:

δ₁ = 1.5 μm

f₁  = 2 GHz

f₂ = 8 GHz

f₃ = 18 GHz

μ is same at every frequency

So,

\(δ \propto\frac{1}{f}\)

\(\frac{δ_1}{δ_2}=\sqrt\frac{f_2}{f_1}\)

\(\frac{1.5 \ \times\ 10^{-6} }{δ_2}=\sqrt\frac{8}{2}\)

δ₂ = 0.75 μm.

Now,

\(\frac{δ_1}{δ_2}=\sqrt\frac{f_3}{f_1}\)

\(\frac{1.5 \ \times \ 10^{-6}}{δ_2}=\sqrt\frac{18}{2}\)

δ₂ = 0.50 μm.