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)

Antenna Near-Field

Surrounding antennas are two spatial fields; the near field and far field. Near-field region contains reactive and oscillating electromagnetic field, while the far-field region contains only transverse-propagating electromagnetic fields.

The near-field is calculated by the formula on the right, where r is the furthest point in the near-field, D is the largest dimension of the antenna and lambda is the wavelength.

Reactive fields are formed by stationary charges or charges moving at uniform velocity. Examples are DC power sources as they cause a constant drift of charges resulting in a reactive field. AC sources also produce reactive fields in addition to radiating fields. Reactive fields store energy capacitively and/or inductively in the absence of a receiving circuit or antenna. If an antenna or receiving circuit is present, a reactive field will lead transfer energy through capacitive or inductive coupling.

Reactive fields characteristics are very dependent on the source of the energy, and is extinguished once the source is inactive. Reactive fields do not propagate and measuring these fields impacts the source voltage and currents. Reactive fields impedance and wave shape are dependent on the source and energy can be transported using transmission lines.
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Read more:
[1] Ron Schmitt, "Electromagnetics Explained: A Handbook for Wireless /RF, EMC and High Speed Electronics", Newnes, 2002.