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Phase shift
Terry and all:
This is getting to be an old thread, about phase shift along a Tesla coil,
but I would like to do a little rambling about it. Let me start with a
matched transmission line. A lossless line will have only a forward
travelling wave, for which the variation is sin(wt - Bz) where w = 2(pi)f
and B is sometimes called the phase shift factor. In the lossless case, B
is numerically equal to the propagation factor. This forward travelling
wave has the feature that two points separated by 90 degrees in space (a
change in z of one quarter wavelength) will have a phase shift in time of 90
degrees. Put your scope probes a quarter wavelength apart and your scope
will show two waves shifted in time by 90 degrees.
Suppose now we cut the transmission line so it is an open circuit. A
forward travelling wave produces a reflected wave of the same amplitude.
The variation of voltage with time and space now has the form (ignoring
factors of two) sin(wt)sin(Bz). Time and space have been decoupled. If we
are at the open end, voltage will be a maximum. If we put one scope probe
at the open end and the other probe, say, 45 degrees away (Bz = 45 degrees),
the scope will show two waves in time phase, no phase shift at all. The
probe 45 degrees away will show a voltage smaller than the one at the end by
square root of 2.
Next we think of the transmission line as a parallel line (like 300 ohm TV
twin lead), split it for a quarter wavelength, and pull the two ends apart
into a half wave dipole. With a moderate amount of arm waving and
imagination, we note that the current has to be zero at the ends of the
dipole just like at the ends of the open circuited transmission line. This
leads us to assume that the current on the dipole is similar in shape and
character to that in the same portion of the wire when it was still part of
the open circuited transmission line. Jordan and Balmain in their book
"Electromagnetic Waves and Radiating Systems" write the formula for current
as having the term sin(B)(H - z) where H is the half length of the dipole
and z is measured from the feed point. Current is maximum at the feed point
and zero at the end of the antenna. Time is not involved. There is no
phase shift in time. If one could measure the current at the feed point and
another current part way along the dipole, both currents would pass through
zero at the same time. The peak amplitude of the current further out the
dipole would be smaller, according to the sin function.
If I understand Terry's experiment with a base fed coil, this is exactly
what he showed. It was an excellent piece of experimental work. Dare I say
that Maxwell was validated once more? Unless I am missing something, there
will not be a rush to rewrite the textbooks.
Gary Johnson