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W4BSG AntennaTheory.com Newbie
Joined: 15 Jun 2009 Posts: 3 Location: Alabama

Posted: Mon Jun 15, 2009 1:26 am Post subject: Definition help 


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?
ThanksBill 

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admin Site Admin
Joined: 03 Jan 2007 Posts: 197

Posted: Mon Jun 15, 2009 9:45 pm Post subject: Effective Aperture 


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.antennatheory.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 AntennaTheory.com Newbie
Joined: 15 Jun 2009 Posts: 3 Location: Alabama

Posted: Tue Jun 16, 2009 3:13 pm Post subject: Definition help 


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 Site Admin
Joined: 03 Jan 2007 Posts: 197

Posted: Tue Jun 16, 2009 5:09 pm Post subject: units of area 


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 AntennaTheory.com Newbie
Joined: 15 Jun 2009 Posts: 3 Location: Alabama

Posted: Tue Jun 16, 2009 5:55 pm Post subject: 


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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