# Yet More on BBQ dish gain...

• Subject: [amsat-bb] Yet More on BBQ dish gain...
• From: Scott Townley <nx7u@xxxxxxxx>
• Date: Sun, 16 Mar 2003 13:30:34 -0700

```...I am not trying to re-ignite the "BBQ Debate" (oh that's a bad
pun).  Only providing information that some may find interesting.

In a previous note, I mentioned that I have modelled the K5GNA 38"x26" BBQ
dish in NEC-2.  It's an "exact" model in the sense that the grid spacing
and wire diameter are as-measured from an actual reflector.  Also, the feed
is the stock AIDC3733 dipole-plus-reflector plate.  The interesting bit
from the previous modelling was that the maximum gain was calculated to be
25.52dBi.

One difficulty in modelling this antenna outside of NEC is that it not a
circular aperture.  Often assumptions are made in equations etc. that the
antenna can be described by a single angle.  In the case of a
circular-section parabola, you can define the parabolic surface
intersection with a sphere with just the polar angle...in other words, the
angle subtended by the rim of the dish.  However, a rectangular-section
parabola requires two angles (both polar and azimuth), so all the math that
is normally reduced to a single variable of integration is out the window.
In short, using tools like those provided by W1GHZ don't necessarily apply,
or require special interpretation.  Not a fault of the tools, only their
application.

How can the BBQ calculate out to 25.5dBi?  That result requires a TOTAL
(illumination+spillover+blocking) efficiency of -1.6dB (69%).  As Jerry,
K5OE correctly points out on his website, the BBQ grid is overilluminated;
the edge-illumination is only 3dB down in the "long" plane (H-plane) and
5.3dB down in the "short" (E-plane) direction, based on modelling the
AIDC3733 feed by itself (my feed model matches Jerry's very closely).  Even
with space attenuation, nowhere near the "optimum" -10 to -12dB edge
illumination.  So this means (relatively) high spillover loss, but also
means (relatively) high illumination efficiency--remember that 0dB edge
taper (uniform reflector illumination) is 100% illumination efficiency.

With that in mind, I hand-integrated the modelled feed pattern of the
AIDC3733 against hand-calculated pairs of angles that describe the outline
of the BBQ dish.  The calculation of spillover is pretty
straightforward--count up all the energy that intercepts the reflector
against the total energy radiated (in all directions) by the feed.  For the
BBQ feed I come up with a spillover efficiency of 72.8% (-1.37dB).

That doesn't leave much for illumination efficiency, but remember that
"poor" spillover means "good" aperture.  Again, I hand-integrated the
radiation striking the reflector using an integral formulation for
illumination efficiency found in Balanis.  The calculated illumination
efficiency was 94.4% (-0.25dB), for a total (less blockage) efficiency of
68.7% (-1.63dB).  This is extremely close to the result implied by the
maximum gain calculation of 25.5dBi.  It would be expected that there is
very small feed blocking loss, because the reflector is only 0.45% of the
total antenna aperture.

So it would seem that the modelled result of 25.5dB is well founded.  NOTE
HOWEVER that modelling intrinsically assumes a mechanically perfect
implementation; perfect focus, perfect adherence to the double-curved
parabolic surface, etc.  In the field, focus errors or mechanical
distortion of the reflector will reduce the achieved maximum gain (aka YMMV).

Scott Townley NX7U
Gilbert, AZ  DM43di
http://members.cox.net/nx7u

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