Answer:
gain = 353.3616
P_r = 1.742*10^-8 W
Step-by-step explanation:
Given:
- The output Power P_o = 0.1 W
- The diameter of the antennas d = 1.2 m
- The frequency of signal f = 2 GHz
Find:
a. What is the gain of each antenna?
b. If the receiving antenna is located 24 km from the transmitting antenna over a free space path, find the available signal power out of the receiving antenna.
Solution:
- The gain of the parabolic antenna is given by the following formula:
gain = 0.56 * 4 * pi^2 * r^2 / λ^2
Where, λ : The wavelength of signal
r: Radius of antenna = d / 2 = 1.2 / 2 = 0.6 m
- The wavelength can be determined by:
λ = c / f
λ = (3*10^8) / (2*10^9)
λ = 0.15 m
- Plug in the values in the gain formula:
gain = 0.56 * 4 * pi^2 * 0.6^2 / 0.15^2
gain = 353.3616
- The available signal power out from the receiving antenna is:
P_r = (gain^2 * λ^2 * W) / (16*pi^2 * 10^2 * 10^6)
P_r = (353.36^2 * 0.15^2 * 0.1) / (16*pi^2 * 10^2 * 10^6)
P_r = 1.742*10^-8 W