Cecil Moore wrote:
John Popelish wrote:

When you talk about current flowing, you seem to be thinking of
current waves traveling along a conductor. Others seem to be saying
"current" and thinking of charge movement. I think that only the
second is technically correct ...


John, many thanks for some rationality from a cool head.

Conventions aside, that sounds about right. So would you agree
that if there's a forward current of one amp and a reflected
current of one amp, the net charge movement is zero and therefore
the standing wave current is not "going" anywhere? How can something
with a constant fixed phase angle of zero degrees "go" anywhere?

Standing waves involve no net wave travel in either direction, though
anywhere except at the current nodes, charge is certainly moving back
and forth along the conductor, during a cycle.


That's unclear to me. Why can't the E-field and H-field simply be
exchanging energy at a point rather than any net charge moving
laterally?

Cecil,

I think I said all of that before the fun and games started. In any case
I agree 100% with John.

Let me try again to answer your question. This is all very basic
textbook stuff. I claim not the slightest bit of credit for any of this.

First, I hope we can agree that current is defined as the movement of
charge. In this case the charge moves only in the direction of the wire,
let's call it the z-direction.

The generic equation for a forward traveling wave is simply:

y = A cos (kz-wt)

The generic equation for a reverse traveling wave is:

y = B cos (kz+wt)

One can add constant phase offsets to the cosine arguments, but it does
not make any difference here. It just makes things look messy,
especially in ASCII. The parameters k and w are not independent either,
but again that does not really matter here.

In the case of current we can say:

If = Io cos (kz-wt)
Ir = Io cos (kz+wt)

I have set the "A" and "B" coefficients to the same value, Io, for
simplicity. If the currents are not the same the math gets a little
messier, but there is no fundamental difference. Keep in mind that the
If and Ir refer to the current that moves along the z-direction, i.e.,
charge moving in the back-and-forth direction along the wire. The "f"
refers to the forward "wave", and the "r" refers to the reverse "wave".
The current in both cases is not "forward" or "reverse" but simply
back-and-forth as in any AC condition. It is essential to separate the
concepts of wave and current. They may be connected, but they are not
the same, and they are not interchangeable.

OK, now lets add these two traveling waves together to make a standing
wave. This is a linear system, and superposition applies. We can simply
add the components. The basic equation is:

Isw = If + Ir = Io { cos (kz-wt) + cos (kz+wt) }

Through the use of a standard trigonometric identity this can be reduced to:

Isw = 2Io cos (kz) cos (wt)

What can be seen immediately is that the standing wave current still has
exactly the same time dependence that the traveling waves had. The
magnitude of the current is now a function of z, unlike the constant
magnitude in the traveling waves. The "current" is still defined as
above, namely the charge that moves back-and-forth in the z-direction.

The current oscillation factor (wt) is now decoupled from "z", unlike
the traveling wave case. The "wave" is stationary. The current itself,
however, behaves exactly the same as in the case of the traveling waves.

Of course there are important differences in radiation patterns for
traveling waves and standing waves. The magnitude of the current is
different along the wire. However, except at the standing wave nodes,
the standing wave current is very real and non-zero.


I am almost embarrassed to write this, since surely you and most readers
know all of this quite thoroughly. However, it appears you may have
overlooked something. I hope this helps.

73,
Gene
W4SZ