Keith Dysart wrote:
Cecil Moore wrote:

Keith Dysart wrote:
Except that V(x,t) and I(x,t) are not, in general, related by Z0.

From "Fields and Waves ..." by Ramo & Whinnery, 2nd edition:

V(x,t) = V*e^j(wt-kx) + V'*e^j(wt+kx)

I(x,t) = [V*e^j(wt-kx) - V'*e^j(wt+kx)]/Z0

You are quite unfair to Ramo & Whnnery when you quote them
out of context. It makes them look like they do not have a
clue.

It's not out of context. Those are their equations for
standing wave voltage and standing wave current. It is
net voltage and net current because each equation is
the sum of two component values.

Just because you find the same string ["V(x,t)"]

Actually, it wasn't the same string. R&W used 'z'
instead of 'x' for the length of the wire as was
common a half-century ago when I had their textbook
for both undergraduate and graduate level courses.

in their text does not mean that they are talking about
the same thing. (It better not in this case, or you should
throw their book away.)

But they *are* talking about the same thing. The first equation
above is the total (standing wave) voltage. The second equation
is the total (standing wave) current. The only term difference
between the two equations is the Z0 term. There is a sign difference
in the current equation that shifts the reflected current by 180
degrees putting the net voltage and net current in quadrature.

Methinks suggesting that Ramo & Whinnery should be thrown away
is "delusions of grandeur".

You, yourself, have made the point in other posts that
the current and voltage on an open circuited line are
in quadrature, so they can not be in the ratio of Z0.

Nobody said they are "in the ratio of Z0" and that's not
what you said before either. You said they are "not related
by Z0" and they are related by Z0 just as the above equations
demonstrate. You didn't say "ratio", you said "related".

The ratio of standing wave voltage to standing wave current
above is:

V(x,t) V*e^j(wt-kx) + V'*e^j(wt+kx)
------ = --------------------------------- = Z
I(x,t) [V*e^j(wt-kx) - V'*e^j(wt+kx)]/Z0

This is the old familiar SWR circle on the Smith Chart.
Smith Charts are normalized to Z0 = 1.0. The impedance
on the Smith Chart must be multiplied by Z0 to get the
actual impedance. Those impedances are indeed
"related to Z0". The s-parameter signals are normalized
to the square root of Z0. Vfor/Ifor = Vref/Iref = Z0.
Virtually everything about a transmission line is "related"
to Z0 including the standing wave voltage and current.

Methinks you are confusing cause and effect. The standing
wave is not the cause of the two traveling waves.

Of course not. "Standing wave" is just a short hand description
of the distribution of voltage and current on the line.

Yes, a "short hand description" that exists only in the human
mind and gets some folks into trouble - like trying to use
the illusion of moving standing wave current to "measure"
the delay through a coil. There is no standing wave current
movement through a coil or a wire. Standing wave current
doesn't move - it just stands there, oscillating in place.
EM current that doesn't move is obviously an illusion (and
a violation of the laws of physics).

Here's what Eugene Hecht said about standing waves in "Optics".

"It [the standing wave phasor] doesn't rotate at all, and
the resultant wave it represents doesn't progress through
space - it's a standing wave."

Applied to a wire or a loading coil, we can paraphrase -
standing wave current "doesn't progress through" a wire or
a loading coil - "it's a standing wave". EZNEC supports this
concept. Take a look at the current phase for a 1/2WL wire
dipole. From one end of the dipole to the other, the total
current phase varies by only a couple of degrees. Kraus agrees:

http://www.w5dxp.com/krausdip.jpg

Sorry Cecil. The observed voltage and current on the line
are the reality.

The net voltage and net current are real but their independent
existence apart from the underlying traveling waves is just
an illusion. They are not independent. They are the *result*
of superposition of the forward and reverse waves. They are
merely an *effect* and not the cause of anything.

There are lots of real illusions. That beautiful Texas
"sunrise" this morning was just an illusion, an effect of
the rotation of the earth.
--
73, Cecil http://www.w5dxp.com