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the nature of parabolic reflectors

Subject: the nature of parabolic reflectors
From: Bret <>
Date: Fri, 20 Feb 2004 10:28:11 -0800 (PST)
:
> From: Bret <>
> > Parabolic reflectors provide gain that has a slope rate of 6db per
> > octave (higher freq, higher gain, octave up =3D 6db more gain), down
> to
> > 0db gain where the wavelength of the signal equals pi times the
> > diameter of the parabola (assuming efficiency factor =3D 1).  Below
> that
> > freq. gain is 0db.

--- Walter Knapp <> wrote
> I'm not sure where you got this figure for the low end of the gain,
> but
> it's at considerable odds with Sten Wahlstrom's paper detailing the
> gain
> of parabolic systems. He clearly states the 0dB gain point as a
> diameter
> 1/64th the wavelength. How rapidly and how cleanly the gain rises
> between there and the wavelength and diameter being equal is highly
> dependent on the ratio of the focal length to dish depth. But, it
> does
> rise as long as your focal length to depth ratio stays above 1. If
> that's below 1 you get irregularities in the gain rise. Above the
> point
> where the wavelength and diameter being equal the rise is the 6dB per
> octave. At least in theory.

I would love to read Sten's paper, if you can provide a link.=20

As far as where I got the notion of low end of gain, it is from the
formula for gain for a parabolic reflector:
Gain =3D 10*log(k*(pi*Diameter/Wavelength)^2)

This seems to be commonly accepted:
http://www.qsl.net/n1bwt/chap4.pdf (page 4)
http://www.setileague.org/askdr/magnify.htm
http://www.setileague.org/askdr/efficien.htm

If we accept that formula for gain, then
Gain =3D 0 when
log(k*(pi*diameter/wavelength)^2) =3D 0
For that to equal 0, then
k*(pi*diameter/wavelength)^2 must =3D 1
because log (1) =3D 0

k is the efficiency factor of the reflector and feed system, to
simplify let's assume it is 1 (it will be less than 1 in reality, this
will shift the 0 db gain point to a higher frequency)

If we assume k =3D 1,
then gain =3D 0 when
(pi*diameter/wavelength)^2 =3D 1
Taking the square root of both sides of that equation,
pi*diameter/wavelength =3D square root(1)
pi*diameter/wavelength =3D 1
therefore
gain =3D 0 when pi*diameter=3Dwavelength (when efficiency factor =3D 1)

> The Telinga is not Sten Wahlstrom's optimal parabolic. That seems to
> go
> for one with a focal length to depth ratio of 4. The Telinga is
> something like 1.2 or so. But Sten also notes that most practical
> parabolas are of a ratio only slightly greater than 1. It's very
> clear
> from what he has that one should avoid parabolas with ratios less
> than 1.
>
> Walt
> 

The focal length to depth ration of the parabolic reflector will affect
rearward lobing of the polar pattern of gain:
http://www.cecer.army.mil/TechReports/pat_mike/pat_mike.post.pdf
(see parabolic reflector section under microphone systems pages 8,9).

Please tell me where I can find Sten's paper.=20

bret

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