Question 8.12: Find the HPBW of an infinitesimal dipole.

The normalized radiation intensity for the electric field of an infinitesimal dipole is given by I_{n} ( θ, \phi ) = \sin ^{2} θ , and it has a maximum value I_{n} = 1 for θ = π/2. The value I_{n} = 1/2 is found at the angles θ = π/4 and 3π/4. Therefore, the HPBW for the electric field is θ_{HP} = π/2. The normalized radiation intensity for the magnetic field of an infinitesimal dipole is I_{n} ( θ, \phi ) ≡ 1 . The HPBW for the magnetic field intensity is \phi_{HP} = π/2. From (8.45), we can approximate the directivity to be D ≈ 4/ π = 1.27 . The value that was computed in Example 8.11 was D = 1.5.

D \approx \frac{4\pi }{\theta _{HP} \phi _{HP}} (8.45)