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antenna length vs. dielectric constant?

Discussion in 'Electronic Design' started by Guest, Mar 10, 2005.

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  1. Guest

    Guest Guest

    Most antenna length formulas assume the antenna will be operating in either
    air or a vacuum where the dielectric constant of "space" is equal to 1.

    What happens to the length of a half-wave dipole when it is operated in a
    space with a dielectric constant of 80?

    Since the end-to-end capacitance increases with an increased dielectric constant
    for the medium surrounding an antenna, I'm guessing that an antenna designed
    for operation in air must be shortened to reduce both its incuctance and
    end-to-end capacitance to regain the resonance it used to have in air. I
    just don't know *how much* shorter.

    Can somebody "do the math" for me?

    Jim
     
  2. Don Pearce

    Don Pearce Guest

    You just scale the whole thing in inverse ratio to the dielectric
    constant; air = 1. Dielectric constant describes the relative velocity
    of the wave in the medium. Seen this way, the scaling is clear.

    But presumably at some point the wave must emerge from the Er80 medium
    into Er1 of air. Have you given any thought to that transition, which
    will be highly reflective?

    d

    Pearce Consulting
    http://www.pearce.uk.com
     
  3. The velocity of wave propagation in space is predicted
    by 1/sqrt(u * e) where 'u' and 'e' are the permability
    and permittivity of free space. In your medium, the
    wavelength will be reduced by a factor sqrt(80).
    Just scale it according to the wavelength reduction.
    It's simple enough that you can do it.
     
  4. Don Pearce

    Don Pearce Guest

    Oops - forgot the square root in my post.

    d

    Pearce Consulting
    http://www.pearce.uk.com
     
  5. James Meyer

    James Meyer Guest

    Actually, I'm working on a system to use a radio to link a submarine to
    a transmitter. Both TX and RX antennas will be under water. Fresh water. I
    know things get much more complicated in salt water.

    Jim
     
  6. Reg Edwards

    Reg Edwards Guest

    Propagation velocity, in metres per second, along a thin wire is
    proportional to 1/Sqrt(L*C) where L is the inductance and C is the
    capacitance per metre.

    Encasing the wire with a VERY LARGE, theoretically infinite, volume of a
    dielectric material, including off the ends, will increase the capacitance
    per metre by K, where K is the dielectric constant of the material.

    The material will have NO effect on inductance.

    Therefore, the velocity for a very large volume will be reduced by the
    factor Sqrt(K).

    But take the practical case of a wire encased with polyethylene only up to a
    diameter of 25mm, 1" inch. Polyethylene has K = 2.6.

    Because of the very small diameter of the dielectric relative to infinity,
    the velocity along the wire will decrease by only a few percent. To maintain
    the same resonant frequency, as on an antenna, the wire must be pruned to a
    shorter length by the same percentage.

    Calculations to find the exact percent reduction are complicated. The wire
    diameter must also be taken into account.

    Incidentally, for pure water, K=80. But who will want to encase a radio
    antenna in many gallons of water just to reduce its length by a few more
    percent. It is obvious that even a heavy tropical downpour will not have
    the slightest effect. ;o)
     
  7. James Meyer

    James Meyer Guest

    Suppose you needed to communicate with a submarine and could put both
    antennas underwater?

    Jim
     
  8. Mac

    Mac Guest

    You mean a full size submarine? In the ocean? Are you familiar with the
    expression "lossy dielectric?"

    Just wondering.

    (yes I know they CAN communicate with subs, but they use low frequencies,
    and the subs trail very long antennas to do it.)

    --Mac
     
  9. Reg Edwards

    Reg Edwards Guest

    ============================

    There is only a very remote probability that anyone beside myself who is
    reading this can produce the math. Then there's the problem of writing the
    formulae involved in HTML. You will be wasting your time hunting through
    Google and books. And I havn't the many hours to spare to sort out your
    problem and write out the solution. In any case, to avoid errors, it would
    be necessary to write it all on paper with a pencil and post it to you via
    snail mail in the hope you could understand it. You can see my predicament.
    Sorry!

    By the way, why do you wish to know?
     
  10. Don Pearce

    Don Pearce Guest

    No, salt water is really easy. It doesn't work, so you don't try. (Yes
    I know about those ELF systems)

    d

    Pearce Consulting
    http://www.pearce.uk.com
     
  11. James Meyer

    James Meyer Guest

    It's for a small model of a submarine that will be used to test a
    prototype propulsion system and it will be deployed in a large fresh water
    flooded stone quarry. A few hundred feet of range is all we need. That's all
    I'm allowed say right now.

    Jim
     
  12. Reg Edwards

    Reg Edwards Guest

    By the way, why do you wish to know?

    ===============================
    If you had a capacitance formula what would you do with it?

    Whatever radio frequency you have in mind for your dipole - forget it.

    Try doing what whales do. Use a very low audio frequency, a loudspeaker and
    a microphone. Or borrow a trained whale to read the meters. ;o)
     
  13. James Meyer

    James Meyer Guest

    Both your earlier post and the one from Larry Brasfield gave me a good
    starting point. The rest I can extract empirically.
    Just what I've recently posted. If I went into more detail, we'd both
    "dissappear".

    Jim
     
  14. Rich Grise

    Rich Grise Guest

    This sounds like a job for ultrasonic, if you can filter out bottom
    clutter.

    Good Luck!
    Rich
     
  15. Mac

    Mac Guest

    Wow. Cool. It really does seem that ultrasonics would work better. But I
    have never tried to transmit RF underwater, so I guess I should keep my
    opinion to myself. ;-)

    Anyway, as for your original question, it seems to me that,
    theoretically at least, you can just use any typical land-based
    antenna, but scale the dimensions by sqrt(80). So if you are planning
    on using ~70 MHz, you could design a land antenna for ~630 MHz. I get
    630 by pretending that sqrt(80) = 9. Then I multiply 70 MHz by 9 to
    get 630 MHz.

    If you are thinking of using frequencies in this range, maybe you could
    just try a UHF TV antenna in the water.

    An interesting question is what is the input impedance?

    Best of luck to you.

    --Mac
     
  16. Andy

    Andy Guest

    Andy replies,

    Screw the math...... Get an SWR meter and go to a river....
    The empirical evidence will tell you a lot more than an academic
    exercise
    will.

    In this case, there is no substitute for field measurements....

    If, after you find the answer, you can get it to agree with some
    theoritical treatment, you have a good basis for an article, which
    at $50 a page will pay you for your efforts....

    Andy in Fink, Texas
     
  17. Reg Edwards

    Reg Edwards Guest

    Andy, you first have to get the equipments working before thinking about an
    SWR meter, the most time-wasting instrument ever invented.

    HF antennas submerged in sea water just don't work at all. In the absence
    of anything else they may be very good as ground electrodes.

    Stop trying to be clever and wasting the questioners's time. He already
    knows more about it than you do - and even he doesn't know very much.
     
  18. Barry Lennox

    Barry Lennox Guest

    Bear in mind that the model RC submarine crowd just use off-the-shelf
    commercial RC transmitters to control model subs 2-300 hundred metres
    away and to a few metres depth. Despite some saying it won't work, it
    does. So maybe you won't have have to re-invent the wheel. Do a Google
    search for model RC subs, there is a lot of info out there.

    Barry Lennox.
     
  19. Mark

    Mark Guest

    read what the op said


    he needs to transmit a few hundred feet

    if he has to transmit only a few hundred feet, the antenna doesn't
    have to "work very well"

    even if it works poorly. it will work well enough

    Mark
     
  20. James Meyer

    James Meyer Guest

    Thanks Barry. We've already used a standard RC setup to do the few
    meters depth thing. With Larry and Reg's help, I have enough info to begin the
    next stage of the project. I looked at the web pages for model subs almost a
    year ago and their experiences matched our own at the time. Perhaps it's time
    to take another look to see if there has been any progress since then.

    Jim
     
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