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

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

Step-by-step 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

`= (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 =
`(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)

`= (4 \pi (2 * 10^9)^2 * 0.2016\pi)/((3 * 10^8)^2)`

`= (4 \pi (4 * 10^(18) ) * 0.2016\pi)/((9 * 10^(16)))`

`= (4 \pi (4 * 10^(2) ) * 0.2016\pi)/(9)`

=
`(31.80 * 10^(2))/(9)`

= 353 .33 dB