Beamwidth, near/far field
18mar06
Near, far field
and
the sky ovverlap at 100 km. (top)
The illuminated area on the dish (and the edge
taper)
determine the half power beam width (HPBW) at a given frequency.The
relationship
is:
-
Diameter=(K*lambda)/hpbw (where k depends on the edge taper ..
typically
k=1.2)
In the far field, rays from
opposite
sides of the dish to a point in the far field are parallel. For points
in the near
field, the rays are not parallel. We can define parallel by the path
difference being less than a fraction of a wavelength.
The path difference for rays from the
opposite
edges of the dish to a point P is:
Using the hpbw to define the illuminated area (d=k*lambda/hpbw)
and solving for H gives:
-
H=(k*lambda/hpbw)^2/ (2.*dl)
-
Setting dl=lamba/2 gives: H=(k*lambda/hpbw)^2/lambda
-
Substituting back for hpbw gives the familiar= D^2/lambda relationship.
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