Question

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

Answer 1

Answer:

The gain of each antenna in decibels  is 353 .33 dB.

Explanation:

Given:

Frequency = 2 GHz

Diameter  =  1.2 m

To Find:

The gain of each antenna in decibels = ?

Solution:

Relationship between antenna gain and effective area

$= \frac{4 \pi f^2 A_e}{c^2}$-----------------------------------(1)

Where

f is frequency

$A_e$  is  effective area

c is the speed of light

$A_e$ = effective area of a parabolic antenna with a face area of A is 0.56A

$A_e = 0.56(\pi r^2)$

r  is the radius

r = $\frac{1.2}{2}$

r =  0.6

$A_e = 0.56(\pi (0.6)^2)$

$A_e = 0.56( 0.36 \pi)$

$A_e = 0.2016 \pi$

Substituting the values in eq(1)

$= \frac{4 \pi (2 \times 10^9)^2 \times 0.2016\pi}{(3 \times 10^8)^2}$

$= \frac{4 \pi (4 \times 10^{18} ) \times 0.2016\pi}{(9 \times 10^{16})}$

$= \frac{4 \pi (4 \times 10^{2} ) \times 0.2016\pi}{9}$

= $\frac{31.80 \times 10^{2}}{9}$

= 353 .33 dB