The power reduces by 1.5dB every 100[m] on a transmission line. Find
(a) attenuation constant, and
(b) fraction of power at a distance 1[Km] from the input end.
(a) From Eq. (9-32) we obtain
dB power loss = -20 \log _{10} \left[e^{- \alpha z}\right] = 8.69\alpha z (9-32)
\alpha = \frac{dB power loss}{8.69 z} = \frac{1.5 }{8.69 \times 100} = 0.0017 [Np / m] .
(b) From Eq. (9-30) we obtain
\boxed{ \left\langle\mathscr{P}(z)\right\rangle = \left\langle\mathscr{P}(0)\right\rangle = e^{-2 \alpha z} } [W] (9-30)
\frac{〈\mathscr{P}(1000)〉}{〈\mathscr{P}(0)〉} = e^{-2 \times 0.0017 \times 1000} = 0.033