free-space path-loss model

[logistic_guy]

Under the free-space path-loss model, find the transmit power required to obtain a received power of \(\displaystyle 1 \ \text{dBm}\) for a wireless system with isotropic antennas \(\displaystyle (G_l = 1)\) and a carrier frequency \(\displaystyle f = 5 \ \text{GHz}\), assuming a distance \(\displaystyle d = 100 \ \text{m}\). Repeat for \(\displaystyle d = 100 \ \text{m}\).

 

[logistic_guy]

\(\displaystyle d = \textcolor{red}{10 \ \text{m}}\)

The relation between transmit power and received power is:

\(\displaystyle P_r = P_t\left[\frac{\sqrt{G_l}\lambda}{4\pi d}\right]^2 = P_t\left[\frac{\sqrt{G_l}c}{4\pi df_c}\right]^2\)

Plug in numbers.

\(\displaystyle 0.00126 = P_t\left[\frac{\sqrt{1}300 \times 10^6}{4\pi 10(5 \times 10^9)}\right]^2\)

This gives:

\(\displaystyle P_t = 5527 \ \text{W} = \textcolor{blue}{5.527 \ \text{kW}}\)

 

[logistic_guy]

\(\displaystyle d = \textcolor{red}{100 \ \text{m}}\)

Plug in numbers.

\(\displaystyle 0.00126 = P_t\left[\frac{\sqrt{1}300 \times 10^6}{4\pi 100(5 \times 10^9)}\right]^2\)

This gives:

\(\displaystyle P_t = 5.527 \times 10^5 \ \text{W} = \textcolor{blue}{552.7 \ \text{kW}}\)