Parabolic reflector operation and Cassegrain feed

Operation of parabolic reflector

A parabolic reflector antenna is a large conducting surface shaped as a paraboloid of revolution, with a small primary antenna (feed) placed at its focus. It converts the spherical wave of the feed into a plane wave and so produces a very narrow, high-gain pencil beam.

Geometry: a parabola is the locus of points equidistant from the focus F and a fixed line (directrix). The distance from vertex to focus is the focal length f; the opening (aperture) has diameter D; f/D is usually 0.25–0.5.

            )|
           ) |---->
   ray    )  |---->   all paths
  F o-->-)   |---->   F→P→Q equal
   feed   )  |---->   (plane wave)
           ) |---->
            )|
       <-f-> aperture plane, diameter D

Working

1. Equal path (phase) property: for every point P on the surface, FP + PQ = constant, where Q is on the aperture plane. Hence all rays from F arrive at the aperture in phase.
2. Parallel ray property: the tangent at P makes equal angles with FP and the axis, so every reflected ray is parallel to the axis.
3. The aperture therefore has a uniform phase distribution and radiates a plane wave: a narrow beam along the axis.
4. By reciprocity, an incoming plane wave along the axis is focused at F, where the receiving feed is placed.
5. The feed must radiate mostly towards the dish; energy spilling past the rim (spillover) and the shadow of the feed (aperture blocking) reduce efficiency.

Performance

Gain   G = η (πD/λ)²       η ≈ 0.55-0.7
HPBW   ≈ 70 λ/D degrees
FNBW   ≈ 140 λ/D degrees

E.g. D = 3 m at 6 GHz (λ = 5 cm): HPBW ≈ 1.17°, gain ≈ 43 dBi (η = 0.6).

Uses: satellite communication, radar, microwave links, radio astronomy.

Cassegrain feed system

The Cassegrain feed is a dual-reflector feed: a horn located at the vertex of the main paraboloid illuminates a small hyperboloidal subreflector placed near the focus, which reflects the waves back onto the main reflector.

        main paraboloid
          )
         )        hyperboloid
        )          subreflector
       )   <------- (
 [horn]o --------> (  F (focus of paraboloid
 at F' )   <------- (     = near focus of hyperbola)
        )
         )
          )
 horn at F' = far focus of hyperbola, near the vertex

• One focus of the hyperboloid coincides with the focus F of the paraboloid; the feed is at the other focus F′. Waves reflected from the subreflector appear to come from F, so the main dish produces a plane wave.
• Advantages: feed and receiver behind the dish (short waveguide, low loss, low noise), long effective focal length, easy maintenance.
• Disadvantage: subreflector blocks part of the aperture, so it is used with large dishes such as satellite earth stations.