Re: Help with difficulty finding overtones or nodes?

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: jdwarshui-at-emich.edu 

Hi Phil:

The difference between lumped and distributed L.C. are directly
analogous to the differences found between simple harmonic motion of a
mass and spring and the standing wave resonance found in ropes. In the
mechanical world when a rope is at the correct frequency to produce
stationary nodes we will find the same exchange between kinetic and
potential energy that is found in a lumped mass spring system.

When an inductor's wire length is just a tiny fraction of its
wavelength we can consider this to be lumped, no standing wave can be
produced within this inductor as it is too short at this wavelength to
produce the conditions where waves can superimpose to produce
stationary nodes. An inductor used this way behaves analogously to a
fixed mass in a mass spring system.

When the wire length of an inductor matches the frequency we can no
longer treat this inductor as a lumped system. Waves traveling (both
directions) through the uniform medium of a cylindrical inductor can
now superimpose to form stationary nodes. Mathematically we now need
to examine this medium as a distributed inductance per length directly
analogous to a rope's mass per length.

The upshot is that we can no longer look at an inductor the same way
as we are accustomed. So for example if we wanted to see two voltage
nodes on a given inductor we would no longer use the inductance value
of the full length of the inductor but would instead substitute the
inductance value of one fourth of the inductors length. For a coil
with 1000 turns we would use the inductance (and self capacitance)
value of only 250 turns to get a full wave coil (and the entire coils
length would need to match the wave length).

You can find the formulae to describe L.C. node formation at:
http://people.emich.edu/jdwarshui/correspondence.html