antenna 3dB Beam Width and Antenna Gain

Is there a formula that related the 3dB beam width of a 1/2 wave dipole antenna with the gain of the antenna?

Since the a narrower beam on a E field radiation represents more directivity, more gain. I was hoping there is a convenient formula where if you determine the 3db beam width from a antenna directivity plot you can determine a good estimate of the antenna gain.

ARRL Antenna book has a formula:

41253
G = -----------------------------------------------
H(3dB beam width) * E(3dB beam width)

but I dont hink it works for 1/2 wavelength dipole antennas

Hello,

You can use the formula as a first guess as for a vertically oriented dipole, BWhor = 360 degrees, BWvert = 78 degrees. So this would result in Gi = 1.47 (versus 1.64 for the real thin half wave dipole), not a bad initial guess.

The reason why these formulas give bad result for large beam width, is because of the approximations in the illuminated surface of a sphere calculation, and by using sin(alpha) = alpha (use radians). In addition, it depends on how the field drops with inreasing off main beam angle.