On Apr 26, 4:59 pm, Jim Kelley wrote:
Cecil Moore wrote:
The standing wave current phasor has the "same rotational speed
as its components"???

It has to. Thankfully, rotational speed is the one thing that does
not change between the radio and the antenna.

How can that be when the forward current
phasor and the reflected current phasor are rotating in opposite
directions?

Rotational speed has nothing to do with direction of travel. It has
only to do with the source. Rotational speed is simply omega;
2pi*c/wavelength, or 2pi*f. When waves of equal frequency are
traveling in opposite directions, the RF waveform which comprises the
standing wave (the latter being simply the amplitude envelope of the
superposed traveling waves) has the same wavelength, and thus the same
rotational speed as the traveling waves. Although the position of the
peaks does not vary with time, their amplitude is still a time varying
function. This rudimentary effect is illustrated in the movie he

http://www.kettering.edu/~drussell/D.../superposition....

Mixing on the other hand is the product (rather than the sum) of two
or more waveforms and does in fact yield different rotational speeds.

73, Jim AC6XG


Hey, are you guys using a non-standard definition for "phasor"? I'm
really confused by Jim's posting here. To me, a phasor simply
indicates the amplitude and phase of a sinusoidal component, relative
to some reference phase. I'd be comfortable with a "local definition"
that said the amplitude was relative to a reference amplitude, or was
in dB or dBm or dBuV or the like. But I am NOT comfortable with the
idea that a phasor at a particular point in space rotates in time
unless there is some time-varying thing that causes it to rotate,
maybe like a "trombone" section of line that someone is sliding in and
out. I do expect the phasor that represents a sinusoid propagating on
a transmission line to be a function of distance along the line and of
the frequency of the signal, in that it must rotate 360 degrees for
every one wavelength along the line. (More detail on this below.)

For "phasor" to be a useful concept, you'd better be talking about a
system in which there is a single sinusoidal excitation frequency --
or you better be verrrry careful to define what you mean by your
phasor diagrams.

See, for example, the page in Wikipedia on phasors.

Or else please give me enough info or references so I can straighten
out my thinking about them.

If I'm not mistaken, on a lossless line excited by a source at one end
with a reflective load at the far end such that the amplitude of the
forward wave is a1 and the amplitude of the reflected is a2, then the
phasor representing the forward wave, relative to the source end, will
be
forward phasor = a1*exp(-jx/lambda)
and for the reverse, assuming for convenience that the line is just
the right length so that the reverse is in phase with the generator at
the generator end,
reverse phasor = a2*exp(+jx/lambda)
where x is the distance along the line from the generator, lambda is
the wavelenth in the line, and exp() is e to the power(). Then the
phasor of the whole signal, fwd plus refl, at any point x is
net phasor = a1*exp(-jx/lambda)+a2*exp(+jx/lambda)
exp(jy) can be expanded as cos(y)+j*sin(y), so
net phasor = (a1+a2)*cos(x/lambda)+j*(a2-a1)*sin(x/lambda)

This makes is VERY clear that the phasor changes angle along any line
where a2 does not equal a1; in the special case where a2=a1, then the
phase can only be 0 or 180 degrees all along the line. If you pick a
different reference point (e.g. change the load or line lenght or
frequency in a way that moves the generator away from a point where
the return is in phase with the generator at the generator), then that
just adds a constant phase offset. But also notice that if a2 does
not equal a1, the phasor angle along the line goes through all
possible values, zero to 360 degrees. If a2 is almost equal to a1,
that phase shift occurs relatively quickly along the line, centered on
points where cos(x/lambda) goes to zero. I expect the same to be true
on a resonant antenna; the reflected wave is NOT the same amplitude as
the forward, but is similar, so you'll find places where the phase
change is quick but continuous as you move along the wire--this
assumes that the antenna is long enough that you can find such places.

Cheers,
Tom