Re: How do you measure couplin

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

Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Tesla list wrote:
 >
 > Original poster: Peter Lawrence <Peter.Lawrence-at-Sun.COM>
 >
 > Antonio,
 >          this is great and helps a lot, but I am also looking for the
 > differential equations of a "losely coupled oscillators" and the
 > derivation of the equations of its voltage verses time, whereas you
 > seem to have assumed from the beginning the sum of two sin waves.

Really, my deduction assumed a lossless circuit, and also assumed
perfect tuning.
The general case of two lossy LC circuits coupled is solvable too,
but the analytical expressions are quite complicated. They involve
complex roots of a 4th-order polynomial, for example.
I have everything implemented in the program Teslasim. In the
documentation of the program you can find the Laplace transforms of
the waveforms.
The program computes the time-domain waveforms from the transforms
numerically, and lists and plots the results.
The Teslasim program is available at (I revised it today, making
small changes):
http://www.coe.ufrj.br/~acmq/programs

 > One of the reasons is that most descriptions of the frequency splitting
 > phenomena of "losely coupled oscillators" shows a fourier transform 
(spectrum
 > analysis) with two smooth "humps", whereas the fourier transform of two sin
 > waves is two infinitessimally thin "spikes", and I'm trying to figure out
 > which is correct...

This depends on how the spectrum is calculated, and on if the
circuit is lossy or lossless.
The exact Fourier transform would show impulses in the lossless case
and smooth curves in the lossy case.
A fast Fourier transform, or any kind of discrete Fourier transform,
would show impulses only if the circuit is lossless and if the time
interval considered is an exact number of periods of the two resonance
frequencies. All other cases would show several frequencies, forming
humps around the resonance frequencies. They are real only if the
circuit is lossy.

You can verify this by calculating Fourier transforms using as input
the tables that the Teslasim program can compute and save.

Antonio Carlos M. de Queiroz