speed of a radio wave in a medium

Discussion in 'Wireless & RF Design' started by mentaaal, May 2, 2009.

  1. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    Hey guys, I have a telecomms exam next and I am bit confused on one of the formulae we have. The formula is: C = Co / √εr which is used to calculate the speed of the wave in a coaxial cable for example. Where C is the speed in the desired medium, Co is the speed of light in a vacuum and εr is the relative permittivity in a medium

    Whats bothering me is shouldnt there be a relative permeability term in there as well? Like we have been shown in another subject that the speed of light in a vacuum is equal to 1/ √(εoεrμoμr) [i think]
     
  2. studiot

    AAC Fanatic!

    Nov 9, 2007
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    Yes you are correct, strictly there should be a relative permeability term in there as well.

    However the thinking runs like this to get to your first equation:

    As an electromagnetic wave moves from free space into a medium it is attenuated by that medium. This is in addition to moving more slowly.

    We acount for this by attributing the attenuation to the relative permittivity, which now becomes a complex quantity.

    εr = ε_{1} - jε_{2}

    thus √(εoεrμoμr) = √(εo(ε_{1} - jε_{2})μoμr)

    = (n-j\eta)√(εoμoμr)

    where n = √ε_{1}

    and \eta = ε_{2}/2√ε_{1}

    Now here is the bit they probably haven't told you

    Assume ε_{1} >> ε_{2}

    and that μr = 1

    The electromagentic wave equation is

    E = E_{0}exp{jω(t-z/v)} exp(-ω\etaz/c)

    this reduces to

    v = c/√εr as required for the large real term.
     
  3. steveb

    Senior Member

    Jul 3, 2008
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    You and studiot are correct. In simpler terms we can say that waves usually do not propagate well in magnetic materials, so as a practical matter, we just forget about the relative permeability which is very close to 1 in most cases of interest to engineers.
     
  4. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    Ah yes well the absolute main thing was if i was going going to use the corect formula in the exam. Obviously its important for me as an engineer but we are starting fields and waves next year which i am guessing will be dealt with in detail then. (the entire class in my course last year failed this module... shudder shudder shudder)

    Thanks very much for that though and you are quite right we have only been mildly introduced to this material so I had no way of knowing where that came from .


    Thanks!
     
  5. studiot

    AAC Fanatic!

    Nov 9, 2007
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    The luck of the green in the exam!
     
  6. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    Thanks I am going to need it!
     
  7. KL7AJ

    AAC Fanatic!

    Nov 4, 2008
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    We might add that in PRACTICAL transmission lines, such as dielectric fillled coax, the velocity factor can be reduced to as little as .66! Air filled coax, however (HELIAX and such) have velocity factors approaching 1. For all practical purposes, air is about the same permeability as a vacuum. :)

    Eric
     
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