# The gain of a parabolic dish antenna of 1 m diameter and 80% efficiency at 9.5 GHz is:

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The gain of a parabolic dish antenna of 1 m diameter and 80% efficiency at 9.5 GHz is:
1. 39 dB
2. 78 dB
3. 40 dB
4. 45 dB

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Correct Answer - Option 1 : 39 dB

Concept:

The efficiency of dish antenna is given by:

$Gain \ = \ \frac{η \ 4 \ \pi \ A_e}{λ^2}$ ---(1)

Where,

η = efficiency

Ae = Area of parabolic antenna

λ = Wavelength

Calculation:

η = 80 %

ν = 9.5 GHz

D = 1 m

As  c = νλ

$\lambda=\frac{3 \ \times \ 10^8}{9.5 \ \times \ 10^9}=0.0315$

$A_e=\frac{\pi \ D^2}{4}=\frac{\pi}{4}$

Putting all values in equation (1)

$Gain = \frac{0.80 \ \times 4\pi^2}{4 \ (0.0315)^2}=7912.62$

Gain in db = 10log10(7917.62) = 39 db.

1. The parabolic reflector antenna is also known as the satellite dish antenna.

2. They have very high gain, bandwidth, and low cross-polarization.

3. They operate in the VHF region of frequency range from 30 - 300 MHz