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Re: the nature of parabolic reflectors

Subject: Re: the nature of parabolic reflectors
From:
Date: Fri, 20 Feb 2004 20:55:42 +0100 (MET)
Hi Bret,

The formula you got is obviously a simplified approximation that is only
valid when the size of the dish is significantly larger than the wavelength=
 of
the signals to be received (the links you provided refer to very short radi=
o
or light waves).

However, if the wavelengths of the signals are in the range of the diameter
of the reflector, then a more precise (and more complicated) formula is
required. Sten Wahlstr=F6m's paper in the Journal of the Audio Engineering =
Society
describes the theory of parabolic reflectors for acoustic applications:

Wahlstr=F6m, S. (1985): The Parabolic Reflector as an Acoustic Amplifier. J=
.
Audio Eng. Soc., Vol. 33, No. 6, pp 418.

I guess that this paper is not available on the internet.

Regards,
Raimund=20



> :
> > 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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>
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>
>
>
>=20
>

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