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Resonant Frequency of a Sphere

Discussion in 'Electronic Design' started by S. S., Feb 18, 2004.

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  1. S. S.

    S. S. Guest

    Could anyone tell me the formula to calculate the electrical resonance
    frequency of a metal sphere?
    e.g. - a 1mtr diameter, hollow metal 'ball'?
    I understand how to calculate a simple resonant circuit from fr = 1/(6.28 x
    sqrLC), and that a Cavity Resonator (Hi-Q filter in radio equipment -
    etc) is like a sealed cylinder where the ends are equiv to the capacitor
    and the cylinder is equiv to the coil.
  2. First you have to find the field inside the sphere,
    the so called eigenmodes.
    Meaning you have to solve Maxwell, likely in spherical
    coordinates. There are various packages
    doing that for you. Beside a terribly expensive one,
    microwave studio, I'm unable tell you one.

  3. S. S.

    S. S. Guest

    thanks rene, i'll try to find a copy. if you think of any other programs,
    please drop me a line.
  4. James Meyer

    James Meyer Guest

    It would be more practical to measure the resonance. You have to assume
    to many variables when you calculate it.

    In other words, knowing the calculated resonance is an interesting
    mental exercise. Making use of the resonance means devising some method to
    couple energy into the sphere. If your method of coupling doesn't match your
    assumptions for the calculations, then the results of the calculation are

    Do you have a sphere? Do you need help measuring its resonant
    frequency? Is your question homework/quiz related?

  5. Depending on the way you couple in, there might be a multitude of
    available modes.

  6. S. S.

    S. S. Guest

    thanks jim,
    it's part of an experiment that i want to try - my work / hobby is in the rf
    field, so to speak. :)
    it's to see the effects of various sizes of 'spheres' ranging from approx
    150mm up to a max of 1 mtr in a given situation.
    the objective being to find a more efficient way of doing a job.
    approximate figures or a graph would be ideal. i just need to find a
    starting point and an idea of the physical size variables.
    i'm not wanting to take into account specifics like material composition,
    permeabilty, etc yet.



  7. James Meyer

    James Meyer Guest

    Take my word for it, a sphere as a resonant cavity offers no practical
    advantages over a cylinder.

  8. S. S.

    S. S. Guest

  9. Jim Meyer

    Jim Meyer Guest

    Here's a page with a JAVA calculator for frequency vs. size for
    Helmholtz (spherical) resonators. Be sure to use the speed of light
    instead of the speed of sound if you want RF cavities.

  10. R.Legg

    R.Legg Guest

    it's to see the effects of various sizes of 'spheres' ranging from approx
    To 'see' you have to physically model. Is the efficiency improvement
    required in the application of the sphere, or in the design method?
    How is this efficiency measured?

    In order to take material composition, permeability etc out of the
    results, you'd have to select specifics and keep them constant. If you
    are improving hardware, then the invariables have been preselected.

  11. Soundwaves are longitudinal while EM waves are not. It may
    not work as expected then.
    You need the eigenmodes for a conducting sphere with
    some boundary conditions. The coupling certainly matters
    as well. You can couple with a dipole or with a loop.

  12. S. S.

    S. S. Guest

    that's a very useful site, thanks heaps.
    but as Rene mentions, the readings appeared to vary considerably and i can't
    seem to get a ball-park figure.
    i might have to start on a maths degree, or use the old fashioned method for
    the 'mathematically illiterate' - start building a sphere with some wire
    gauze and attach test equipment.
  13. S. S.

    S. S. Guest

    if the use of a sphere enhances the performance very slightly in an
    experiment, that would be all that's required for now.
    i think you're right, i need to build it. i'm not good enough at maths to
    design it on paper with the number of variables involved.
    Rene mentioned a modelling programme call microwave studio - that's the
    other option if i can justify the $$$.
  14. If you don't have it, let it calculate for you. You'd spend another
    few months just to become familiar with the tool. To start with, there
    is a 3D editor to input the geometry.
    Just ask some of these guys, eg at microwave studio or similar, who
    offers the services. A daily user should be able to do these
    calculations within a day or two.

  15. S. S.

    S. S. Guest

    a much better idea!
  16. The Phantom

    The Phantom Guest

    The book, "Fields and Waves in Communication Electronics", by Ramo,
    Whinnery and Van Duzer, 1965 edition, on page 556 has the solution
    you're looking for. Given a hollow metal sphere of inside radius a,
    the wavelength of the lowest order TM mode is 2.29a. The wavelength
    of the lowest order TE mode is 1.395a
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