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Reflector Antennas

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Reflector Antennas

Since discovery of EM propagation in 1888 by Hertz, reflector antennas has been introduced.

Many various geometrical shapes are introduced at World War II by radar applications.

Its progress was in radio astronomy, microwave communication, and satellite tracking.

Most popular shapes are plane, corner, and curved reflectors (parabolic) as shown:

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Corner Reflectors

Plane Reflector:

Its simple type is a plane reflector introduced to direct energy in a desired direction.

Polarization of source and its position relative to surface can be used to control radiating properties (pattern, impedance, directivity) of overall system.

Image theory has been used to analyze radiating characteristics of such a system.

Perturbations by dimensions finite can be accounted for by method of GTD.

Corner Reflector:

To better collimate energy, corner reflector is introduced.

Because of its simplicity in construction, it has many unique applications.

In a radar, it can be used for deception of enemy used in EW systems when its included angle is 90◦ as shown:

Because of this unique feature, military ships and aircraft (stealth vehicles such as B-2, F117, F22, F35) are designed with minimum sharp corners to reduce their detection by enemy radar.

In most practical applications, included angle is 90o; however other angles are

sometimes used.

For reflectors with infinite sides, gain increases as included angle between planes decreases.

Corner reflectors are also widely used as receiving elements for home TV.

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For simplicity .

Feed element for a corner reflector is almost always a dipole or an array of collinear dipoles placed parallel to vertex a distance s as shown:

Greater bandwidth is obtained when feed elements are cylindrical or bi-conical dipoles instead of thin wires.

In many applications, especially large , surfaces are grid wires rather than solid sheet metal as shown: (g ≤ λ/10)

One of reasons for doing that is to reduce wind resistance and overall system weight.

Corner Reflectors

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Image theory to analyze field radiated by a source in presence of a corner reflector:

Corner Reflectors

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90o Corner Reflector:

Its radiation characteristics are most attractive.

Corner Reflectors

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Referring to figures, total field of system can be derived by summing contributions from feed and its images:

In far-zone, normalized scalar field can be written as:

Where for:

Corner Reflectors

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Corner Reflectors

It is evident that for small spacing, pattern consists of a single major lobe.

Whereas multiple lobes appear for larger spacing (s>0.7λ).

For s=λ pattern exhibits two lobes separated by a null along φ=0◦ axis.

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Other Corner Reflectors:

A similar procedure can be used to derive array factors and total fields for:

By using long filament wires as feeds, that azimuthal plane (θ=π/2) array factor is:

Multiple lobes begin to appear when:

Corner Reflectors

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Parabolic Reflector

Parabolic Reflector:

Overall radiation characteristics can be improved if configuration is upgraded.

In geometrical optic, a beam of parallel rays is focused at a focal point.

By principle of reciprocity, a point source is placed at focal point produces a parallel beam.

Disadvantage of front-fed is that T-line from feed must usually be long.

Long lines may not be tolerable in many applications such as low-noise receiving systems.

A arrangement for feeding in focal point is Cassegrain feed:

A parabolic reflector can take two different forms as:

Two techniques that can be used to analyze:

Aperture distribution method.

Current distribution method.

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Reflector Antennas

Example:

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Two-dimensional configuration of a paraboloidal reflector

Reflector Antennas

Surface Geometry:

Surface of a paraboloidal reflector is formed by rotating a parabola about its axis.

Design is based on optical techniques, and it does not take into account any deformations (diffractions) from edge of reflector.

Referring to figure and choosing a plane perpendicular to axis of reflector:

Since:

Terms of the rectangular coordinates:

A unit vector that is normal to local tangent at surface reflection point:

A gradient is taken to form a normal to surface:

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Reflector Antennas

A unit vector, normal to S:

To find angle between unit vector n and a vector directed from focus to reflection point:

In a similar manner, angle between unit vector n and z-axis:

Relating subtended angle θ0 to f/d ratio:

Induced Current Density:

If surface can be approximated by an infinite plane, by the method of image:

It is valid when curvature of reflecting object is large compared to a wavelength.

Using:

Another form is:

Hi and Hr are defined at surface of conductor

Physical-optics approximation

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Reflector Antennas

If reflecting surface is in far-field of source generating incident waves:

Two techniques that can be used to analyze:

Aperture distribution method.

Current distribution method.

Aperture Distribution Method:

Using GTD (ray Tracing), field reflected by surface of paraboloid is first found over a plane.

Plane is normal to axis of reflector as aperture plane:

Equivalent sources are then formed over this plane.

Usually it is assumed that equivalent sources are zero outside projected area.

These equivalent sources are then used to compute radiated fields.

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Reflector Antennas

Aperture Distribution Method (cont.):

Let us assume a y-polarized source with:

Incident field, with a direction perpendicular to radial distance:

Where:

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Reflector Antennas

Aperture Distribution Method (cont.):

It can be shown:

To find aperture field Eap at plane through focal point, first Er is found:

An equivalent is formed at aperture plane:

Where:

Where:

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Reflector Antennas

Aperture Distribution Method (cont.):

To demonstrate utility of technique, a 35GHz reflector, with an f/d=0.82, d=24.99cm.

Its feed is a conical dual-mode horn.

Since feed is symmetry, patterns do not possess any cross-polarized components.

Principal E- or H-plane pattern of a symmetrical front-fed paraboloidal reflector

Field point locations of constant amplitude contours in the aperture plane of a symmetrical front-fed paraboloidal reflector

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Reflector Antennas

Aperture Distribution Method (cont.):

Cross-Polarization:

Polarization components of the paraboloidal reflector is shown as:

The y-component is designated as the principal polarization.

The x-component as the cross-polarization.

It is evident that symmetrical cross-polarized components are 180o out of phase.

Direction of induced current determines far-field polarization of antenna.

By combination crossed electric and magnetic dipole feed, far-field radiation is free of cross-polarization.

Because of its ideal characteristics, it is usually referred to as a Huygens’ source.

Electric and magnetic dipole fields combined to form a Huygens’ source with ideal feed polarization for reflector

Co-polarization and cross-polarization components

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Reflector Antennas

Current Distribution Method:

By physical optics approximation, current on S1:

This current is then integrated over S1 to yield far-zone radiation fields.

Approximations are:

1. Current is zero on the shadow side (S2). 2. Discontinuity of current over the rim () of reflector is neglected. 3. Direct radiation from feed and aperture blockage by feed are neglected.

These approximations lead to accurate results for main beam and first or second minor lobes only.

To have accuracy in all regions, especially far minor lobes, GTD is used.

To analyze technique, we refer to radiation integrals CH3:

For far-field observations:

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Reflector Antennas

Aperture efficiency:

Spillover efficiency: fraction of total power that is radiated by feed and collimated by reflecting surface.

Taper efficiency: Uniformity of amplitude distribution of feed pattern over surface of reflector.

Phase efficiency: Phase uniformity of field over aperture plane.

Polarization efficiency: Polarization uniformity of field over aperture plane.

Blockage efficiency. Random error efficiency. Total efficiency:

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Gains of some worldwide large reflector antennas

Reflector Antennas

Gain:

Factors that reduces antenna gain are:

Asymmetrical patterns.

Phase center error.

Cross-polarized field components.

Blockage.

Random surface error.

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Example :

One of world's largest solar parabolic dishes at Ben-Gurion National Solar Energy Center in Israel.

Reflector Antennas

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Resolution: 0.05-700 Arcsec.

Reflector Antennas

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Reflector Antennas

The Very Large Array (VLA) at Socorro, New Mexico, United States.

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Reflector Antennas

Another Very Large Array (VLA):

On 12 May 2012, another Atacama Large Millimeter Array (ALMA) antenna was carried.

Atacama is a desert in northern of Chile.

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Very Large Array (VLA) dish details:

Reflector Antennas

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Green Bank Telescope which stands near Green Bank, West Virginia.

Reflector Antennas

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Cassegrain Antennas

Cassegrain Reflectors:

Cassegrain improves performance of large ground-based microwave reflector antennas for satellite tracking and communication.

Cassegrain is attractive for applications that require gains of 40dB or greater.

Both single- and double-reflector were designed to convert a spherical wave at source into a plane wave.

Magnification factor is ratio of main reflector diameter to sub reflector diameter.

For a high magnification:

Amplitude distribution is controlled largely by sub-reflector.

Phase distribution is controlled largely by curvature of main reflector.

Advantages of Cassegrain reflectors:

Ability to place feed in a convenient location.

Reduction of spillover and minor lobe radiation.

Ability to obtain an equivalent focal length much greater than physical length.

It introduces shadowing which is principal limitation of its use as a microwave antenna.

Shadowing can significantly degrade gain of system, unless main reflector is several of .

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Cassegrain Antennas

Geometrical optics for reshaping and synthesis of reflectors of a Cassegrain system.

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By technique of equivalent parabola, main dish and sub-reflector are replaced by an equivalent focusing surface at a certain distance from real focal point.

Cassegrain Antennas

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Cassegrain Forms:

In addition to classical Cassegrain forms, there are other configurations:

Cassegrain Antennas

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Gregorian Forms:

Cassegrain Antennas

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Spherical Reflector:

A paraboloid reflector is an ideal collimating device.

But in many applications, it is poor in angular scanning.

Although scanning can be accomplished by:

Mechanical rotation of entire structure.

Displacement of feed alone.

But it is used by large mechanical moment.

By contrast, spherical reflector can make an ideal wide-angle scanner.

This is obtained from its perfectly symmetrical geometrical configuration.

But spherical reflector are poor inherent collimating properties.

For example: a point source is placed at focus of sphere, does not produce plane waves.

Spherical Reflector

This departure of reflected wave front from a plane wave is known as spherical aberration.

It depends on diameter and focal length of sphere.

By reciprocity, plane waves incident on a spherical reflector do not converge at focal point.

However focusing of wave (at various angles) is performed by translating and orientating feed.

A spherical reflector has capability of focusing plane waves incident at various angles.

It is performed by translating and orientating feed and by illuminating different parts of geometry.

For three rays, focusing characteristics of a typical spherical reflector is illustrated in:

A caustic is a point, a line, or a surface through which all the rays in a bundle pass and where the intensity is infinite.

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Example:

Arecibo Observatory is a radio telescope near city of Arecibo in Puerto Rico.

Its spherical reflector has a 305m dish in diameter.

Surface is made of almost 40,000 perforated aluminum panels.

Its focal point is 150m above reflector.

Attached devices to antennas are very sensitive and highly complex radio receivers.

These devices operate immersed in a liquid helium, to maintain a very low receiver temperature.

At such cold temperatures electron noise in receivers is very small.

Therefore, incoming radio signals, which are very weak, are amplified.

Arecibo system operates at frequencies from 50MHz (λ=6m) up to 10GHz (λ=3cm).

1MW planetary radar transmitter located in a special room inside dome.

Spherical Reflector