Question

The half - power beam width (HPBW) of an antenna in the two orthogonal planes are 120º and 40º respectively. The directivity of the antenna is approximately equals to
1. 10 dB
2. 6.5 dB
3. 12 dB
4. 8.5 dB

Answer 1

Correct Answer - Option 4 : 8.5 dB

Concept:

For large antennas:

Directivity is given by:

\(D ≈ \frac{{4 \pi}}{{\Omega_A}}\)

\(D ≈ \frac{{40000}}{{{\theta _E} \times {\theta _H}}}\)

For small antennas:

Directivity is given by:

\(D ≈ \frac{{41253}}{{{\theta _E} \times {\theta _H}}}\)

For electrically large antennas, the half-power beamwidths are small whereas for electrically small antennas, the half-power beamwidths large.

Calculations:

Given: θE = 20° and θH = 20°

Since half power beam widths are small.

Therefore, the approx. directivity will be:

\(D = \frac{{40000}}{{{\theta _E} \times {\theta _H}}} = \frac{{40000}}{{120 \times 40}} = 8.33\)

in dB,

D  = 10 log(8.33) ≈ 8.5 dB