# Resonant Frequency of a Sphere

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

1. ### 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 -
diplexers
etc) is like a sealed cylinder where the ends are equiv to the capacitor
plates
and the cylinder is equiv to the coil.
Thanks.

2. ### Rene TschaggelarGuest

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.

Rene

3. ### 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 MeyerGuest

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
invalid.

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

Jim

5. ### Rene TschaggelarGuest

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

Rene

6. ### 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.

cheers,

scott

7. ### James MeyerGuest

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

Jim

9. ### Jim MeyerGuest

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.

Jim

http://www.vk2zay.net/calculators/helmholtz.php

10. ### R.LeggGuest

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.

RL

11. ### Rene TschaggelarGuest

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.

Rene

12. ### 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.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. ### Rene TschaggelarGuest

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.

Rene

15. ### S. S.Guest

a much better idea!
thanks

16. ### The PhantomGuest

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