Or maybe we can talk Randy into posting his work. An electrical
engineer and one of our very active nature recordists who wrote a
definitive mathematical analysis of parabolas some time back.
Rich
--- In wrote:
> 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 radio
> 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).=20
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
> >
> > __________________________________
> > Do you Yahoo!?
> > Yahoo! Mail SpamGuard - Read only the mail you want.
> > http://antispam.yahoo.com/tools
> >
> >
> >
> > "Microphones are not ears,
> > Loudspeakers are not birds,
> > A listening room is not nature."
> > Klas Strandberg
> > Yahoo! Groups Links
> >
> >
> >
> >=20
> >
>
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