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Re: This phase shift stuff... - Plane Wave



Tesla List wrote:

> So it did what I thought it would.  From my other work, I suspected this
> would be the case but I had never actually checked for the effect in this
> detailed way.  The voltage along the secondary seems to rise and fall in
> unison, just like a vibrating guitar string.  Even the harmonic seems to
> act just like a vibrating string.  No phase shift effects.  Computer models
> and calculations tell me there is a "little" phase shift (1.6 degrees) but
> that is to small for me to measure.

Why this phase shift? Losses? (see below...)
 
> Antonio and I seem to have completely different results!  I did not see ANY
> phase shift let alone a 90 degree shift.  Obviously, there is a little
> correlation problem here!  :-) "Real science" may be needed to find what
> the discrepancy is.  The effects are not subtle at all.  Anyone else who
> would care to try, please do!  Antonio, if you have any ideas of what might
> be wrong please let me know and we can work to resolve this.

We were effectively thinking about different things. The -amplitude- of
the
voltage along a coil without top load at resonance follows (ideally) a
90 degrees sinusoid, while the -amplitude- of the current follows a
90 degrees cosinusoid.
If you look at the phase relationship between the voltage at any point
along the coil and the driving voltage, really there is -no- phase shift
at resonance, and (in the lossless case) at any other frequency (there
are 180 degrees phase changes at the voltage nodes at the high-order
resonances). This happens in any lossless system, and as you could see,
is what nature shows that really happens.
The system behaves exactly as the rope analog.
If there is a top load in the coil, the system continues to show no
phase shift along the coil, but the amplitudes of voltage or current 
along the coil, that continue to vary as a sinusoid and a cosinusoid, 
don't reach anymore the 90 degrees variation.
The difference between this model and the lumped LC model is that
in the lumped model the voltage amplitude rises linearly along the 
coil, and the current is constant along the coil.
About what happens in a coil that is not small compared the the
vawelength in air of the signal, I think that the behavior, at least
in steady state, would be different only due to irradiation, that
would be significant in this case.

Antonio Carlos M. de Queiroz