The intrinsic impedance of copper at 3 GHz (with parameters: μ = 4π × 10^-7 H/m; ϵ = 10^-9/36π; and σ = 5.8 × 10⁷ mho/m) will be

Calculation:

μ  = 4π × 10^-7 H/m

\( = \frac{1}{{36\pi }} \times {10^{ - 9}}\)

σ = 5.8 × 10⁷ mho/m

f = 3 GHz

= 3 × 10⁹ Hz

\(\eta = \sqrt {\frac{{j\omega \mu }}{{\sigma + j\omega \epsilon }}} \)

\(\omega = 2\pi \times 3 \times {10^3} \times \frac{1}{{36\pi }} \times {10^{ - 9}}\)

ωϵ = 0.166

∵ ωϵ ≪ σ → it is a good conductor

\(\eta = \sqrt {\frac{{j\omega \upsilon }}{\sigma }} \)

\( = \sqrt j \sqrt {\frac{{\omega \upsilon }}{\sigma }} \)

\(\eta = \sqrt {\frac{{2\pi f\upsilon }}{\sigma }} \;{e^{j\frac{\pi }{4}}}\)

\(\eta = \sqrt {\frac{{2\pi \times 3 \times {{10}^3} \times 4\pi \times {{10}^{ - 7}}}}{{5.8 \times {{10}^7}}}} {e^{j\frac{\pi }{4}}}\)

\(\eta = 0.02\;{e^{j\frac{\pi }{4}}}{\rm{\Omega }}\)