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Aperture antenna directivity calculation

  1. Nov 29, 2015 #1
    Hello
    Here is an uniform E filed distribution aperture antenna E and H far filed euations
    2204887800_1448824658.png

    and here is directivity calculation approach
    6234799200_1448824658.png
    my problem is why don't we calculate D with both E(theta) and E(phi)? My mean is:
    instead of using
    .latex?U%3Dr%5E2.P_%7Bave%7D%3Dr%5E2%28%5Cfrac%7B%7CE%28%5Ctheta%29%7C%5E2%7D%7B2%5Ceta%20%7D%29.gif
    we should use
    3Dr%5E2%28%5Cfrac%7B%7CE%28%5Ctheta%29%7C%5E2+%7CE%28%5Cphi%29%7C%5E2%7D%7B2%5Ceta%20%7D%29.gif
    because both of them are not zero in far-filed zone and not zero at theta=pi/2
     
  2. jcsd
  3. Nov 29, 2015 #2

    marcusl

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    [itex]E_0[/itex] is the magnitude of the electric field vector E. If you were to compute the sum of the magnitude squared of the components as you suggest, it should come out as [itex]E_0^2[/itex] as written in the text.

    BTW, you have written something different. I assume that you mean [itex] E_\theta^2 + E_\phi^2[/itex] rather than [itex]E^2(\theta)+E^2(\phi)[/itex]? The latter is valid but means something else.
     
  4. Nov 29, 2015 #3
    Dear marcusl
    you are right I wanted to write %3Dr%5E2%28%5Cfrac%7B%7CE_%7B%5Ctheta%7D%7C%5E2+E_%7B%5Cphi%7D%7C%5E2%7D%7B2%5Ceta%20%7D%29.gif
    As the writer wrote we have
    Bab%7D%7B%5Clambda%20%7D%29%5E2*%20%5Cfrac%7BE_%7B0%7D%5E2Sin%28%5Cphi%29%5E2%7D%7B2%5Ceta%20%7D.gif
    and we assume phi=pi/2 that maximizes U.
    and with my approach:
    2%29%3D%28%5Cfrac%7Bab%7D%7B%5Clambda%20%7D%29%5E2*%20%5Cfrac%7BE_%7B0%7D%5E2%7D%7B2%5Ceta%20%7D.gif
    and I didn't know why we assume only gif.gif to calculate power intensity ( U) ( as in the book mentioned)?
     
    Last edited: Nov 30, 2015
  5. Nov 30, 2015 #4

    marcusl

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    Gold Member

    The book didn't say to use [itex]E_\theta[/itex], it said that the field is maximum at [itex]\theta=0[/itex]. Putting that angle into the equations and finding the sum of the squares of the components, as you did, gives the answer.
     
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