Yagi-Uda
What is a parabolic antenna?
A parabolic antenna is used for microwave radio communications. It is often
referred to as a dish antenna. It consists of a parabolic reflector which collects and
concentrates an incoming parallel beam of radio waves and focuses them onto theactual antenna placed at its focal point or focus. The actual antenna at the focus is
sometimes referred to as the antenna feed. See Figure 1. In this paper, the term
antenna will refer to the actual antenna at the focal point of the the parabolic
reflector and parabolic antenna refers to its antenna together with its parabolic
reflector.
Satellite television dish antennas are an example of popular parabolic microwaveantennas. A parabolic antenna is similar to a reflecting telescope where a parabolic
concave mirror gathers incoming light and focuses it into the eyepiece. Another
optical example is the automobile headlight. A parallel beam of light is reflected off
the parabolic mirror behind the light bulb placed at its focus.
The following terminology is used in describing a parabolic reflector. The focus iswhere all the incoming radio waves are concentrated. The vertex is the innermost
point at the center of the parabolic reflector. The focal length of a parabola is the
distance from its focus to its vertex. The aperture of a parabolic reflector is its
opening and is described by its diameter. Also of interest is the depth of theparabolic reflector which is discussed below. See Figure 2.
The two dimensions that describe a parabolic reflector are the focal length f and the
diameter D of its aperture. The industry practice is to use the f/D ratio to specify
the shape of the parabolic reflector and the diameter D of its aperture. For a given
parabolic reflector, the focal length f is easily obtained by multiplying its f/D ratio
by its diameter D. ES100
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Design formulas for a parabolic reflector
The following formulas are useful for designing a parabolic reflector. The
derivation of the formulas are given in Appendix: Derivation of Equations and
Formulas.
Equation of a parabola
The general equation of a parabola in terms of its focal length f is
(1)
y =a x 2where
a=
1
4f
(2)
Equation (1) useful for laying out a parabola on large sheet of graph paper.
Depth of a parabolic reflector
In designing a parabolic reflector, it is often convenient to use its depth d instead of
its focal length. The formula for obtaining the depth is
D2
d=
16 f
(3)
Conversely, given a parabolic dish and its measurements for the diameter D and
the depth d, then its focal length f is obtained with
f=
ES100
D2
16 d
(4)
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Calculating f/D given the beamwidth of an antenna
An antenna placed at the focal point of a parabolic reflector is said to illuminate the
parabolic reflector. The antenna has a beamwidth which is the how wide an angle
the antenna would make if it were radiating a beam of radio waves. The
beamwidth is a property of the antenna itself and is the same regardless if the
antenna is used for receiving or transmitting. In designing a parabolic antenna,
the antenna needs to properly illuminate its parabolic reflector; that is, the
beamwidth of the antenna needs to match the f/D ratio of the parabolic reflector.
Otherwise, the antenna of an over illuminated parabolic reflector would receive a
noise from behind the parabolic reflector. Likewise, an under illuminated parabolic
reflector does not use its total surface area to focus a signal on its antenna.
The matching f/D ratio of a parabolic reflector is easily calculated using
f
1
=
D 4 tan / 4
(5)...
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