A microwave transmitter has an output of 0.1W at 2 GHz. Assume that this transmitter is used in a microwave communication system where the transmitting and receiving antennas are parabola, each 1.2m in diameter.

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.

gain = 353.3616

P_r = 1.742*10^-8 W

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