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# Determining the focal length of a parabolic dish (axi-symmetric, circular)

Focal length = f

Depth = c

Diameter = D

f = ( D * D ) / ( 16 * c )

Measure the depth using a tight fishing line across the dish and a rule to measure depth c.

Parabolic dish showing measurements needed to determine focal length.

If the f/D ratio is low, say 0.25 to 0.35 then the feed will be close to the dish and needs to spread its power at a wide angle to efficiently illuminate the dish.  The feed therefore needs to be of small diameter.   If the f/D is 0.25 the feed is level with the dish aperture, which may make it difficult to make a satisfactory feed.

If the f/D is large like 0.5 to 0.75 then the feed will be further away from the dish and needs to project its power into a narrower angle.  The feed needs to be of larger diameter.

With a open circular waveguide antenna feed (scalar feed) the focal length will be the distance from the reflector to a phase centre point just inside the circular feed wave guide aperture.

If the feed is a horn,. the phase centre of the feed may be further back inside the horn.  The wider the angle of the horn, the deeper inside the phase centre moves. If it is unknown make four accurate signal quality measurements at carefully measured distances, say 10mm apart.  Then interpolate for the best focal distance.

The power at the edge of the dish should be about 10 dB lower than at the centre for best gain or about -16 dB lower for best discrimination against adjacent satellite interference.  The axially symmetric dish shown above suffers from beam blockage due to the LNB at the focal point blocking the beam.   This reduces gain and increases off-axis interference.

The rim of the dish above must be accurately flat.  For a receive only dish aim for maximum error of about 1/10th of a wavelength or about 6mm at C band and 2.5mm at Ku band.  You can use several fishing lines stretched across the dish to test the flatness of the rim of a parabolic dish. They should all just touch where they cross on another.

► Page created 15 March 2005,  amended 29 April 2014   Eric Johnston