\large{\alpha = \omega \sqrt{\frac{\mu\epsilon}{2} \left(\sqrt{1 + \left(\frac{\sigma}{\omega \epsilon}\right)^2} – 1 \right)}}
\large{\beta = \omega \sqrt{\frac{\mu\epsilon}{2} \left(\sqrt{1 + \left(\frac{\sigma}{\omega \epsilon}\right)^2} + 1 \right)}}
Calculando elementos a elementos do fator de atenuação e do fator de fase:
\omega = 2\pi f\omega = 2\pi 20*10^6\boxed{\omega = 12,566 . 10^7 rad/s}\boxed{\large{\frac{\mu.\epsilon}{2} = \frac{4\pi . 10^{-7} * 1,2*8,85 . 10^{-12}}{2}} = 6,673 . 10^{-18}}\boxed{\large{\sqrt{1 + \left(\frac{\sigma}{\omega \epsilon}\right)^2} = \sqrt{1 + \left(\frac{10^{-4}}{12,556.10^7 * 1,2 * 8,85.10^{-12}}\right)^2} = \sqrt{1 + \left(0,075\right)^2} = 1,00281}}Portanto voltando as equações do fator de atenuação e do fator de base temos:
\large{\alpha = 12,556.10^7 \sqrt{6,673.10^{-18} \left(1,00281 – 1 \right)} = 12,556.10^7 \sqrt{6,673.10^{-18} \left(0,00281 \right)} = 12,556.10^7 * 0,1369 * 10^{-9} }\boxed{\large{\therefore \alpha = 0,0172 Np/m}}
\large{\beta = 12,556.10^7 \sqrt{6,673.10^{-18} \left(1,00281 + 1 \right)} = 12,556.10^7 \sqrt{6,673.10^{-18} \left(2,00281 \right)} = 12,556.10^7 * 3,6558 * 10^{-9}}\boxed{\large{\therefore \beta = 0,459 rad/m}}