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## The relationship between antenna size and frequency, aperture and wavelength

Release date：2021-12-28Author source：KinghelmViews：822

Antenna size and frequency

Generally, the relationship between the size of the designed antenna and the operating frequency of the antenna is:
Antenna length=C/(2f)
where C is the speed of light and f is the operating frequency of the antenna.
The antenna operating frequency refers to the resonant frequency, or center frequency, of the antenna. Each antenna has a certain frequency range, called bandwidth, within this range, the antenna impedance is the smallest and the efficiency is the highest.

"The relationship between the optimal length of the antenna and the wavelength is fixed"

Parabolic Antenna
Structurally, the parabolic antenna is composed of an illuminator and a reflector.
The illuminator is played by some weak directional antennas, such as short electric symmetrical dipole antennas and horn antennas.
Function: Convert high-frequency current into electromagnetic waves and project them onto a paraboloid.

The reflective surface is generally composed of an aluminum alloy plate with good electrical conductivity, with a thickness of 1.5-3mm, or the main paraboloid is composed of glass fiber reinforced plastic, and a metal mesh is attached to it.

Determination of half-power lobe width of parabolic antenna
The wider the main lobe of the illuminator pattern, the smaller the oral area.
Equation 1: Antenna Width Equation
k is a parameter, the value range is (65-80). k=70 under the best irradiation condition.

EQUATION 2: ANTENNA GAIN EQUATION

Formula 3: Antenna aperture size and area formula

Combining the two formulas, it is concluded that:
When the wavelength is determined, according to formula 2, the larger the effective area, the larger the gain.
According to formula 1, the larger the aperture (that is, the larger the effective area, according to formula 3), the narrower the beam.

Therefore, when the wavelength is determined, we can calculate the required aperture from the required gain (according to formulas 2 and 3). At this time, the beam width can be determined by formula 1.

For example calculation, take the L frequency band 1670MHz, the known wavelength is (c/1670MHz) = 0.03227m. The wavelength is determined!
From Equation 2, to obtain a gain of 14dBi, the effective area should be 0.065 square meters.
From formula 3, when the antenna efficiency is known to be 0.5, the aperture is obtained as 0.405m.
From formula 1, the known parameter k is 70, and the aperture and wavelength are substituted to obtain the antenna power lobe width (twice θ) as 31.027 degrees.

Going a step further, combining Equations 123, it is found that the beamwidth is uniquely determined by the gain! as follows:

Therefore, if the aperture is artificially increased, the beam width can be reduced, but at the same time, G will inevitably increase, which finally confirms the above formula: the gain is inversely proportional to the beam width.

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