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Need help with some antenna maths

Discussion in 'Hobby Electronics' started by PèéJäy, Oct 23, 2003.

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  1. PèéJäy

    PèéJäy Guest

    Hi all,

    Could some kind soul point me in the right direction to solve or simplify
    the following:

    S = a ( cos(3pi/2 cos(x)) / sinx )^2

    Need to solve for x. We never learnt this in maths and none of my books seem
    to cover it either. It's in relation to finding the direction of maximum
    radiation from a dipole antenna.

  2. budgie

    budgie Guest

    geez, it's so long since I did that sort of trig that I'd get a sore
    head. But surely you know which way the maxrad is?
  3. PèéJäy

    PèéJäy Guest

    Yes, it's one of those flower shaped patterns, but unfortunately I need to
    be able to prove that it's at exactly 42 and 137 degrees. I've never had to
    deal with embedded trig functions yet!
  4. Gee, I thought I was real stupid after seeing that calculus test, but
    surprisingly, I do remember this stuff. I would give the answer too, but I
    am afraid I would be doing someone elses homework. I suggest heading to the
    local tech bookstore and investigating schaum!! Gee he musta' been smart...
  5. If you like, you can use a spreadsheet. Fill a column with angles from 0 to
    90 degrees in one degree steps. Copy the formula into the cells all the way
    down the next row.

    Now insert a graph into the spreadsheet which plots your two columns X,Y.
    You can even make it a polar plot to get a nice radiation pattern.

    This isn't "real" maths, but it tells you what you want to know.

  6. Phil Allison

    Phil Allison Guest


    ** Seems you have your function in its simplest form - now you just
    evaluate it.

    To find maxima one uses differentiation - that is not solving.

    ............. Phil
  7. Vermin

    Vermin Guest

    I managed to stumble through the EW quiz you posted Phil, but this has
    me stymied. It would take me an afternoon to work it out even if I
    could be bothered dragging out my old maths text books.

    But... just from looking at it, isn't it going to be maximum as x
    approaches 0?

    As sin(0)=0 so as x and therefore the denominator in the above
    equation approaches 0 the expression approaches infinity.
  8. Peter Martin

    Peter Martin Guest

    One way is to use Excel.

    Type the function in a cell. Define x as another cell. Make a guess for x.

    Then use "Goal Seek" to solve for x. If there's more than one solution
    you'll need to have different starting guesses.
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