Antenna Theory - Parabolic Reflector

Parabolic Reflectors are Microwave antennas. For better understanding of these antennas, the concept of parabolic reflector has to be discussed.

Frequency Range

The frequency range used for the application of Parabolic reflector antennas is above 1MHz. These antennas are widely used for radio and wireless applications.

Principle of Operation

The standard definition of a parabola is - Locus of a point, which moves in such a way that its distance from the fixed point (called focus) plus its distance from a straight line (called directrix) is constant.

The following figure shows the geometry of parabolic reflector. The point F is the focus (feed is given) and V is the vertex. The line joining F and V is the axis of symmetry. PQ are the reflected rays where L represents the line directrix on which the reflected points lie (to say that they are being collinear). Hence, as per the above definition, the distance between F and L lie constant with respect to the waves being focussed.

The reflected wave forms a colllimated wave front, out of the parabolic shape. The ratio of focal length to aperture size (ie., f/D) known as “f over D ratio” is an important parameter of parabolic reflector. Its value varies from 0.25 to 0.50.

The law of reflection states that the angle of incidence and the angle of reflection are equal. This law when used along with a parabola, helps the beam focus. The shape of the

parabola when used for the purpose of reflection of waves, exhibits some properties of the parabola, which are helpful for building an antenna, using the waves reflected.

Properties of Parabola

• All the waves originating from focus, reflects back to the parabolic axis. Hence, all the waves reaching the aperture are in phase.

• As the waves are in phase, the beam of radiation along the parabolic axis will be strong and concentrated.

Following these points, the parabolic reflectors help in producing high directivity with narrower beam width.

Construction & Working of a Parabolic Reflector

If a Parabolic Reflector antenna is used for transmitting a signal, the signal from the feed, comes out of a dipole or a horn antenna, to focus the wave on to the parabola. It means that, the waves come out of the focal point and strike the Paraboloidal reflector. This wave now gets reflected as collimated wave front, as discussed previously, to get transmitted.

The same antenna is used as a receiver. When the electromagnetic wave hits the shape of the parabola, the wave gets reflected onto the feed point. The dipole or the horn antenna, which acts as the receiver antenna at its feed, receives this signal, to convert it into electric signal and forwards it to the receiver circuitry.

The following image shows a Parabolic Reflector Antenna.

The gain of the paraboloid is a function of aperture ratio (D/λ). The Effective Radiated Power (ERP) of an antenna is the multiplication of the input power fed to the antenna and its power gain.

Usually a wave guide horn antenna is used as a feed radiator for the paraboloid reflector antenna. Along with this technique, we have another type of feed given to the paraboloid reflector antenna, called as Cassegrain feed.

Cassegrain Feed

Casse grain is another type of feed given to the reflector antenna. In this type, the feed is located at the vertex of the paraboloid, unlike in the parabolic reflector. A convex shaped reflector, which acts as a hyperboloid is placed opposite to the feed of the antenna. It is also known as secondary hyperboloid reflector or sub-reflector. It is placed such that its one of the foci coincides with the focus of the paraboloid. Thus, the wave gets reflected twice.

The above figure shows the working model of cassegrain feed.

Working of a Cassegrain Antenna

When the antenna acts as a transmitting antenna, the energy from the feed radiates through a horn antenna onto the hyperboloid concave reflector, which again reflects back on to the parabolic reflector. The signal gets reflected into the space from there. Hence, wastage of power is controlled and the directivity gets improved.

When the same antenna is used for reception, the electromagnetic waves strike the reflector, gets reflected on to the concave hyperboloid and from there, it reaches to the feed. A wave guide horn antenna presents there to receive this signal and sends to the receiver circuitry for amplification.

Take a look at the following image. It shows a paraboloid reflector with cassegrain feed.

The following are the advantages of Parabolic reflector antenna −

• Reduction of minor lobes

• Wastage of power is reduced

• Equivalent focal length is achieved

• Feed can be placed in any location, according to our convenience

• Adjustment of beam (narrowing or widening) is done by adjusting the reflecting surfaces

The following is the disadvantage of a Parabolic reflector antenna −

• Some of the power that gets reflected from the parabolic reflector is obstructed. This becomes a problem with small dimension paraboloid.

Applications

The following are the applications of Parabolic reflector antenna −

• The cassegrain feed parabolic reflector is mainly used in satellite communications.

• Also used in wireless telecommunication systems.

Let us look at the other type of feed called as Gregorian feed for the parabolic reflectors.

Gregorian Feed

This is another type of feed used. A pair of certain configurations are there, where the feed beamwidth is progressively increased while antenna dimensions are held fixed. Such a type of feed is known as Gregorian feed. Here, the convex shaped hyperboloid of casssegrain is replaced with a concave shaped paraboloid reflector, which is of course, smaller in size

These Gregorian feed type reflectors can be used in four ways −

• Gregorian systems using reflector ellipsoidal sub-reflector at foci F1.

• Gregorian systems using reflector ellipsoidal sub-reflector at foci F2.

• Cassegrain systems using hyperboloid sub-reflector (convex).

• Cassegrain systems using hyperboloid sub-reflector (concave but the feed being very near to it.)

These are all just to mention because they are not popular and are not widely used. They have got their limitations.

The figure clearly depicts the working pattern of all the types of reflectors. There are other types of paraboloid Reflectors such as −

• Cut- paraboloid
• Parabolic cylinder
• Pill-box paraboloid

However, all of them are seldom used because of the limitations and disavantages they have in their working conditions.

Hence, of all the types of reflector antennas, the simple parabolic reflectors and the cassegrain feed parabolic reflectors are the most commonly used ones.