Cecil wrote,
"The forward current is equal at both ends of the coil. The reflected
current is equal at both ends of the coil."

If that's really true, then the net current is precisely equal at both
ends of the coil. I thought you had been claiming that the current is
different at each end. Which way is it going to be? If they are
different phases, then they are NOT equal. If they are different
phases, where does the phase shift COME FROM? If I allow a wave in one
direction ONLY and the currents at the two ends are DIFFERENT in phase,
WHAT HAPPENS inside the coil to make them different? Where does the
extra charge come from, or go to?

It's all very simple. Yawn.

Hint: Replace the coil with a piece of coaxial transmission line,
formed into a loop so the input and output ends are adjacent. Short
the outer conductors together and notice that nothing changes in terms
of the voltages across each end of the line and currents in the center
conductors at each end. Note the difference in current at the two ends
of the line, and note the current in the single outer conductor
terminal of this three-terminal system. Notice that the sum of all
three currents at every instant in time is essentially zero (current
direction taken as positive going into each terminal). Got it yet? Do
you understand WHAT it is, besides the inductance, that allows a coil
to look like a transmission line? Do you understand that the mode is
not quite TEM, so some of the usual TEM transmission line behaviour is
not going to hold?

Cheers,
Tom

K7ITM wrote:

Cecil wrote,
"The forward current is equal at both ends of the coil. The reflected
current is equal at both ends of the coil."

If that's really true, then the net current is precisely equal at both
ends of the coil.

I was speaking above about the magnitudes only, not the phases.
It was clear from the rest of my posting that was the assumption.
The fact that you attempted to change the meaning by trimming is
noted.

So to be perfectly clear, here is my statement re-worded using
a 45 degree phase shift through the coil.

The forward current magnitude is equal at both ends of the coil.
The reflected current magnitude is equal at both ends of the coil.

At the bottom of the coil, the forward current is 1 amp at zero deg.
At the bottom of the coil, the reflected current is 1 amp at zero deg.
At the bottom of the coil, the standing wave current is 2 amps at
zero deg.

At the top of the coil, the forward current is 1 amp at -45 deg.
At the top of the coil, the reflected current is 1 amp at +45 deg.
At the bottom of the coil, the standing wave current is 1.4 amp at
zero deg.

I asked if you knew how to do phasor math but you trimmed out that
phasor math part of my posting.
--
73, Cecil http://www.qsl.net/w5dxp

No, Cecil, I did not try to change the meaning by trimming. I was
simply pointing out a basic flaw in your whole development. You use
the differing phase to establish that a travelling wave in each
direction results in a difference in the standing wave current at each
end, but then you try to use amplitude only to show no net current into
the coil. Now use the SAME phase difference you used to develop the
standing wave, and use it to determine the net AC current into the
coil, AT SOME PHASE. Now use the same phase difference in the other
direction to see that it also results in a net AC current AT SOME
PHASE. AND for the case where there is a standing-wave current
difference between the two ends of the coil, the net coil current is
EXACTLY as predicted by the vector sum of the two travelling wave net
currents.

Now you decide. Can I do phasor math? Do you need a specific example
with numbers, or can YOU work that out yourself? Suggest you use the
example from your previous posting. If that causes any difficulty, try
it with 180 degrees phase shift through the component. I've done it,
and it keeps giving me precisely the same answer as a full cycle of
instantaneous currents.

It appears that Cecil is back with many postings, but he seems to be
ignoring answering my question. Perhaps he's unable to do so. Just so
the lurkers understand that indeed it is possible to work through the
phasor math, here goes. Here's exactly the scenario Cecil set up,
quoted from his posting:

==========

"So to be perfectly clear, here is my statement re-worded using
a 45 degree phase shift through the coil.

The forward current magnitude is equal at both ends of the coil.
The reflected current magnitude is equal at both ends of the coil.

At the bottom of the coil, the forward current is 1 amp at zero deg.
At the bottom of the coil, the reflected current is 1 amp at zero deg.
At the bottom of the coil, the standing wave current is 2 amps at
zero deg.

At the top of the coil, the forward current is 1 amp at -45 deg.
At the top of the coil, the reflected current is 1 amp at +45 deg.
At the bottom of the coil, the standing wave current is 1.4 amp at
zero deg."

==========

OK, so the difference in "FORWARD" current from the bottom to the top
is:
fwd.bottom.current - fwd.top.current
= 1A at 0 degrees - 1 amp at -45 degrees
= 1+j0 - sqrt(.5)-j*sqrt(.5)
= 1-sqrt(.5) + j*sqrt(.5)
(about 0.765 at 67.5 degrees)


The difference in "REFLECTED" current from the bottom to the top is:
refl.bottom.current - refl.top.current
= 1A at 0 degrees - 1 amp at +45 degrees
= 1+j0 - sqrt(.5)-j*sqrt(.5)
= 1-sqrt(.5) - j*sqrt(.5)

The SUM of these two differences is:
[1-sqrt(.5) + j*sqrt(.5)] + [1-sqrt(.5) - j*sqrt(.5)]
= 2 - 2*sqrt(.5) + j0
= 2 - sqrt(2) + j0
= 2 - sqrt(2) at zero degrees

The standing wave current at the bottom of the coil is 2 amps just as
Cecil suggests at one point: It's the sum of the "forward" and
"reflected":
net current at the bottom = sw.bottom.current
= 1+j0 + 1+j0
= 2+j0
= 2 at zero degrees

Presumably Cecil meant that the standing wave current at the TOP
(not the BOTTOM) of the coil is 1.4 amps at 0 degrees. That's close,
but more exactly, it's
net current at the top = sw.top.current
= sqrt(.5)-j*sqrt(.5) = sqrt(.5)+j*sqrt(.5)
= 2*sqrt(.5)
= sqrt(2)
= sqrt(2) at zero degrees.

So the difference in net current (that is, the difference in the
standing wave current) between the top and the bottom of the coil
in this example is exactly:

sw.bottom.current - sw.top.current
= 2 at zero degrees - sqrt(2) at zero degrees
= 2 - sqrt(2) at zero degrees

So, we see that the difference in current between the bottom and
the top is exactly the same, independent of whether we just use
the standing-wave currents, or the currents in the "forward"
travelling wave plus the currents in the "reflected" wave. That it's
also
exactly the same answer you get by looking at a full cycle of
instantaneous currents is left as an exercise (fairly simple) for the
reader.

Either way, there is a difference, and that current must go
somewhere. It should be pretty easy to account for it. In
fact, it's not even very hard to predict fairly accurately in
the case of a loading coil in an antenna perpendicular to a ground
plane or equivalently in a symmetrical doublet.

Cheers,
Tom

K7ITM wrote:
OK, so the difference in "FORWARD" current from the bottom to the top
is:
fwd.bottom.current - fwd.top.current
= 1A at 0 degrees - 1 amp at -45 degrees
= 1+j0 - sqrt(.5)-j*sqrt(.5)
= 1-sqrt(.5) + j*sqrt(.5)
(about 0.765 at 67.5 degrees)

That is truly magic. Someone must have slept through class that
day.

Good grief! You can't subtract two currents that are a foot apart
from each other. Currents superpose at a point. Currents from
each end of the coil a foot apart don't superpose. They don't
even know each other exist. Good Grief!

Ifor=1A at 0 deg Ifor=1A at -45 deg
-----------------X-/////////-Y------------------
Iref=1A at 0 deg Iref=1A at +45 deg

The forward current superposes with the reflected current at the
bottom of the coil to get 2 amps at zero degrees. The forward
current superposes with the reflected current at the top of the
coil to get 1.4 amps at zero degrees. The delay through the coil
is 45 degrees.

Neglecting losses:
The energy in the forward wave is the same at the top and bottom
of the coil. The energy in the reflected wave is the same at
the top and bottom of the coil. There is zero net steady-state
energy storage between the top and bottom of the coil. There's
no RF battery there.
--
73, Cecil http://www.qsl.net/w5dxp

Sorry you've missed the point, Cecil. I can only hope the lurkers get
it.

(Aside: I'm not exactly sure what you mean by "no net steady-state
energy storage." If that's true, then there's never ANY current in the
inductor, because the energy stored in an inductor's magnetic field is
i^2*L/2, and that's always positive for non-zero i.)

Cheers,
Tom

K7ITM wrote:
Sorry you've missed the point, Cecil. I can only hope the lurkers get
it.

If the lurkers think one can add or subtract the forward current
at both ends of the coils, as you did, I feel sorry for them.
--
73, Cecil http://www.qsl.net/w5dxp

A bit more on this...

I trust it's an accurate summary to say that Cecil gave us the
"forward" and "reflected" currents at both ends of a coil, and
correctly deduced the standing-wave currents at each end from those.
But given that information, Cecil is unable (and believes it is
impossible) to determine the net charge in the volume containing the
coil as a function of time (to within a constant, at least), even
though the the wires in which we know the currents are the only way for
charge to get in and out of that volume. I do hope we can at least
agree that current is the rate at which charge passes a point...

And I do hope most folk tuned in here don't have so much trouble with
it.

Farewell, goodbye, auf wiedersehen, adieu...

Tom

Cecil wrote:
"K7ITM wrote:
OK, so the difference in "FORWARD" current from the bottom to the top
is:
fwd.bottom.current - fwd.top.current
= 1A at 0 degrees - 1 amp at -45 degrees
= 1+j0 - sqrt(.5)-j*sqrt(.5)
= 1-sqrt(.5) + j*sqrt(.5)
(about 0.765 at 67.5 degrees)

That is truly magic. Someone must have slept through class that
day.

Good grief! You can't subtract two currents that are a foot apart
from each other. Currents superpose at a point. Currents from
each end of the coil a foot apart don't superpose. They don't
even know each other exist. Good Grief!

Ifor=1A at 0 deg Ifor=1A at -45 deg
-----------------X-/////////-Y------------------
Iref=1A at 0 deg Iref=1A at +45 deg

The forward current superposes with the reflected current at the
bottom of the coil to get 2 amps at zero degrees. The forward
current superposes with the reflected current at the top of the
coil to get 1.4 amps at zero degrees. The delay through the coil
is 45 degrees.

Neglecting losses:
The energy in the forward wave is the same at the top and bottom
of the coil. The energy in the reflected wave is the same at
the top and bottom of the coil. There is zero net steady-state
energy storage between the top and bottom of the coil. There's
no RF battery there.
--
73, Cecil http://www.qsl.net/w5dxp "

K7ITM wrote:
Cecil is unable (and believes it is
impossible) to determine the net charge in the volume containing the
coil as a function of time (to within a constant, at least), even
though the the wires in which we know the currents are the only way for
charge to get in and out of that volume.

THERE IS NO RF BATTERY STORING ENERGY! THERE IS ZERO LONG TERM
ACCUMULATION OF CHARGE! Neglecting losses, energy in exactly equals
energy out over the long term.

The fact that 2 amps of standing wave current exists at the bottom of
the coil and 1.4 amps of standing wave current exists at the top of
the coil doesn't imply any long term accumulation of charge. Long
term accumulation of charge in a coil is impossible.
--
73, Cecil http://www.qsl.net/w5dxp

Thanks, Tom, for taking the trouble to go through the numbers. As I said
earlier, most of us know, and all engineers certainly should know,
superposition requires that results from an analysis using the total
current must be the same as the sum of the results from separate
analyses using forward and reflected currents (or any other components
whose sum is the total current). Your analysis shows this, as it should.

Roy Lewallen, W7EL