Thanks to one and all. A summary of what I've understood by this and other
replies is:
The formula for the Rayleigh criterion is based on solving a right triangle
for the distance to the center of the antenna element as described below by
Dr Turnbull and neglecting a small lambda term in the result, thus the
formula dist > 2*(Ant dimension)^2/lambda is a slight over estimate for a
given wavelength.
Ken Javor's derivation gave Lamda/16 as "an accepted path length difference
at the far field..." That is, the difference in distance between the line
(from the center of the antenna) to a point and a line from that same point
(hypotenuse) to the edge of the antenna element.
The phenomena I was curious about, what happens when you hold the antenna
dimension constant and vary the frequency does work the way I thought it
did. It just seemed odd because it goes against my intuition that shorter
wavelengths should have a shorter focal length for a given aperture or
antenna. But the right triangle geometry says otherwise.
One last thought, there is another far field distance criterion based on
wave impedance (Maxwell's)
dist > Lambda /(2*PI )
For a given antenna size and wave length Maxwell's criterion could give a
longer or shorter required distance, so it looks like one should check both
and choose the greater.
Best,
George Stults
-----Original Message-----
From: Luke Turnbull [mailto:[email protected]]
Sent: Friday, November 22, 2002 1:53 AM
To: '[email protected]'; George Stults
Subject: Re: rayleigh criterion and farfield
The derivation of this formula involves considering a position in front of
the antenna, on the line in the direction of radiation. The distance from
this point to the edge of the antenna will be slightly more than the
distance to the centre. If this distance is a significant fraction of a
wavelength, the the far field pattern is not realised because of phase error
/ cancellation. Hence at higher frequencies (shorter wavelengths), the same
position in front of the antenna will have phase errors where there were no
problems at lower frequencies.
Hope this helps,
Dr Luke Turnbull
Principal EMC Engineer
TRW Conekt
Statford Road
Solihull
B90 4GW
Tel: +44 (0)121.627.3966
Fax: +44 (0)121.627.4353
email: [email protected]
web: www.trw.com/conekt/
>>> George Stults <[email protected]> 11/21/02 05:59pm >>>
Hello Group,
A book I've been reading gives the Rayleigh criterion for farfield
conditions based on antenna (or EUT max dimension) size as
dist for farfield conditions > 2*(max antenna dimension)^2/lambda
When I look at this, it says that the required distance for far field
conditions increases as the square of the dimensions of the antenna, which
seems intuitive.
What I found strange is that if you hold the antenna dimension constant, (ie
for a given fixed antenna dimension) it predicts that the distance for
farfield conditions will increase linearly with the frequency. That does
not seem intuitive.
Does anyone have a thought about how this works?
Regards,
George Stults
WatchGuard Technologies Inc
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