Antenna Directivity

Directivity is the ratio of radiation intensity to the radiation intensity averaged over a sphere.It is different from gain although both terms are used interchangeably. Directivity is also different from beamwidth and is calculated using the beamwidth angles at half-power as follows,

D = 40,000 / (theta * phi)

where

theta = E-plane half-power beamwidth angle in degrees
phi = H-plane half-power beamwidth angle in degrees

Directivity can also be calculated if the aperture size and wavelength are known as follows,

D = 4* PI * A / lamda^2

where A = aperture area, lambda = wave length and PI=3.14

Beamwidth Calculations

Beamwidth is an important antenna parameter. Beamwidth is inversely proportional to antenna gain and hence inversely proportional to antenna size.

The beamwidth distance of a simple directional antenna at distance d from the antenna of a beamwidth angle of α, can be calculated using the following formula:

2dtan(α/2)

d = distance and α = angle

There is no formula that fits all types of antennae for beamwidth angle calculation, however a formula that can be used for parabolic antennae is:

Beamwidth = 70 * lambda / d

where lamba = the wavelength, d = the antennae diameter



Several online beamwidth calculators are available:

- Parabolic beamwidth calculator by Eric Johnston
- NOAA's beam property calculator

Poynting Vector

The Poynting vector is used to define power patterns in electromagnetic waves. It points in the direction of the wave propagation and its amplitude is calculated by multiplying the amplitudes of the electric and magnetic fields divided by the permeability of the medium in which the wave flows.

S = 1/u * EB

where

S is the Poynting vector amplitude

E = the electric field amplitude
B = the magnetic field amplitude
u = the permeability of the medium (4*PI* 10^-7 H/m for vacuum)