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Yet More on BBQ dish gain...



...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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