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Definition help

 
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W4BSG
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Joined: 15 Jun 2009
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PostPosted: Mon Jun 15, 2009 1:26 am    Post subject: Definition help Reply with quote

Hello-
I have a question, based on several articles I have reviewed today. I have seen "Effective Aperture" related to the expression:

Ae=(lambda)^2/(4 Pi)

But I thought it should be:

Ae=Pi (lambda)^2 /4

(Both equations should have efficiency terms applied)
I am questioning this because Kraus has the second, but Wikipedia and another web reference haves at least two places where the first is given.
Have I lost my marbles?
Thanks-Bill
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admin
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PostPosted: Mon Jun 15, 2009 9:45 pm    Post subject: Effective Aperture Reply with quote

I have only seen the effective aperture defined as:

Ae = (lambda^2)*Gain/(4*pi)

Note that the effective aperture is defined as the amount of power delivered to the load for a plane wave incident upon the antenna:

Ae = [Power Delivered - watts]/[Incident Power Density from a plane Wave - watts/meter^2]

See:
http://www.antenna-theory.com/basics/aperture.php

I'm not sure where Kraus's definition comes from. If he defines things differently it could very well show up as he has it....however, I believe the definition above is now standard.
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W4BSG
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PostPosted: Tue Jun 16, 2009 3:13 pm    Post subject: Definition help Reply with quote

I am still confused. I was of the opinion that Aperture had units of Area, but your words give the units as power. As I was using it, Power density * aperture = power. For a circular aperture of diameter=Lambda, the area would be:
A=(Pi/4)*lambda^2 with units of M^2.
Then power,W from a wave of power density with units W/M^2 would be as I had it before, with Pi in the numerator.
Well, back to the refereces. Where do I find IEEE definitions?
Bill
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admin
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PostPosted: Tue Jun 16, 2009 5:09 pm    Post subject: units of area Reply with quote

The ratio of power [in watts] to power density [in watts/meter^2] does give the units of area [meter^2]. This is how I was defining it.

Remember that the physical area of an antenna (Ap) is not equal to the effective aperture (Ae) or how much power the antenna captures.
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W4BSG
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PostPosted: Tue Jun 16, 2009 5:55 pm    Post subject: Reply with quote

I realize that physical and effective areas are different, but they ARE related. Over a fair range of sizes, the relationship is scalable. However, in most circular functions, Pi has a fixed function, and the expressions I am puzzled by are not familiar.
What is the path of derivation in this area that carries Pi from the numerator to the denominator?
Bill- Puzzled.
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