Correct Answer - Option 3 : Diameter is to be increased to 2 folds
Gain of parabolic reflector
\(G = 6{\left( {\frac{d}{\lambda }} \right)^2}\)
d → diameter
λ → wavelength
in dB G(dB) \( = 10\log \left[ {6{{\left( {\frac{D}{\lambda }} \right)}^2}} \right]\)
i.e. G(dB) ∝ 20 log (D)
To increase gain of the parabolic reflector
The diameter should be increased by 2 fold.
i.e. D’ = 2D
G’(dB) ∝ 20 log (2D)
G’(dB) 20 log 2 + 20 log D
G’(dB) 6.02 + G(dB)
G(dB) → initial gain
More information:
For parabolic reflector:
\(HPBW = \frac{{70\lambda }}{D},\;BWFN = \frac{{140\lambda }}{D}\)
λ → wavelength
D → diameter
Directivity \( = \frac{{41200}}{{\theta {^\circ _E} \times \theta {^\circ _H}}}\)
General formula for gain of Antenna
\(G = \frac{{4\pi {A_e}}}{{{\lambda ^2}}}\)
Ae → effective area
λ → wavelength