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W5DXP wrote:
You will never understand the present topic unless you understand that
EM wave interference doesn't affect the flow of energy in the individual
waves. That is true for light and RF.

I should have added: "in the absence of a physical impedance discontinuity."
If a physical impedance discontinuity exists, then of course, the flow of
energy in the individual waves is affected by reflections.
--
73, Cecil http://www.qsl.net/w5dxp

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I wrote:
"As energy can`t be destroyed it had to be reflected by a hard short or
open." Keith replied:
"Or just stopped and stored."

Wave energy is energy in motion. No motion, no waves.

Keith also wrote:
"All of this is easily visualized by observing the amplitude of the P(t)
function at various points along the line."

Power as a function of time has the same amplitude in the forward wave
everywhere along the line. Same is true of the reflected wave.
Interference as demonstrated by standing waves has no effect on this.

Keith wrote:
"I would strongly suggest that no energy crosses these points in the
line where the voltage and current are always zero since p(t) is always
zero."

See my comment above on power as a function of time. Keith erred in
saying "points in the line where the voltage and current are always
zero", as where SWR volts are zero, amps are max, and vice versa.

I wrote:
"If energy were turned around before it reached the end of the line,
nulls more distant from the source than the turnaround point would not
exist."

Keith wrote:
"Not so,---."

There is no argument that can make wave interference where there are no
waves. In a lossless line, pre-existing waves could circulate forever.
But, our discussion relates to effects on actual lines.

Keith wrote:
"Try visualizing how a step function charges the line."

Totally irrelevant. SWR nulls are the result of phase opposition at
specific points produced by alternating waves. A step function changes
only when it starts or stops. Only during the changes does Zo apply
unless a line is terminated in its Zo. In this case there`s no reflected
wave to make a null. As Reg once said, "If your line were infinite in
length, you could measure Zo with your ohmmeter.

Best regards, Richard Harrison, KB5WZI

Keith wrote:
"I do not find that step 7) is in error."

Step 7) declares power is zero at quarter wave points where volts or
amps are zero in the standing wave pattern.

Power flow does not stop at an actual short or open in a line. It merely
changes direction. At zero volt or amp points, where there is no actual
short or open, no reversal of direction occurs. Power flow is affected
in no way by standing wave nulls or maxima where no impedance
discontinuity exists.

Energy exists in every SWR null. It is in the two waves which produce
the null as these experience no change in energy due to standing waves.

Best regards, Richard Harrison, KB5WZI

What is missing here, IMO, is that the physics of energy flow has not
been adequately explained. Cecil provided a reference to it but did not
elaborate for the general readership.

The energy in forward and reflected waves has been well documented for
many years. From Kraus, Electromagnetics, McGraw Hill, 1953, Chapter 9,
Section 9-13, "Energy Relations in a Standing Wave":

EQ 9-145 We = 2eEo^2[cos^2wt*sin^2Bx]

EQ 9-147 Wm = 2uHo^2[sin^2wt*cos^2Bx]

Note: The energy in the E field [We] is a function of the sin^2(Bx).
The energy in the H field [Wm] is a function of the cos^2(Bx).

You will remember from trigonometry the the maxima [or minima] of a sin
and cos are displaced by 90 degrees. Conclusion: when the E field is
zero the H field is maximum; when the H field is zero the E field is
maximum. Ergo! Energy is conserved and propagates through the zero E
field as an H field; also, when the H field is zero the energy is in the
E field. This is what Cecil is referring to when he refers to the
Poynting vector.

It is analogous to a parallel tuned circuit. When the instantaneous
voltage across the capacitor is zero we don't claim there is no energy
in the circuit. We know that the energy is stored in the inductor.
Conversely, when the instantaneous current in the inductor is zero we
don't claim there is no energy in the circuit. We know the energy is
stored in the capacitor.

In a TEM wave the energy cycles between the E field and the H field and
the energy components are 90 degrees out of phase.

Deacon Dave, W1MCE

Keith wrote:
"Basic electricity, a dash of circuit theory, a bit of knowledge of
trigonometry, some basic calculus, and the ability to think is all that
is required."

An electrical education limited to d-c familiarity leads to mistaken
assumptions when dealing with a-c in Keith`s case it seems.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:

Keith wrote:
"I do not find that step 7) is in error."

Step 7) declares power is zero at quarter wave points where volts or
amps are zero in the standing wave pattern.

Unfortunately, probably due to my poor description, you have missed
the point I was trying to make.

You are, I think, disagreeing with the RESULT of step 7.

Even though the result may be wrong, step 7) can be correct.

Step 7) again:
"7) From 6), the energy crossing quarter wave points is 0"

This is saying that if the result of step 6) is correct, then
the result of step 7) is correct. The transformation from 6)
to 7) merely integrated power to get energy; a common and
correct thing to do.

So if you disagree with the result of step 7), it is in step 6)
which you must search for the error since step 7) is correct.

If step 6) is correct, then search in step 2) and step 5) for
the error.

I suspect that like Cecil, you will end up at step 2) as the
source of what you perceive to be an error.

Then, when we resolve whether 2) is in error, we will know
whether the result of 7) is in error.

....Keith

Richard Harrison wrote:

Keith wrote:
"Are there other signals which would produce this result?"

A short-circuit produces a voltage inversion. The plus volts and the
minus volts make a zero in a short.

Imagine a couple of identical positive pulses separated by some distance
and traveling in the same direction along a long transmission line which
has a short approached by the pulses. When the first pulse hits the
short it is inverted and reflected to travel back toward its source as a
minus voltage pulse.

When the first pulse encounters the second pulse they disappear at the
instant of coincidence, but otherwise, travel on their merry ways. What
happens at coincidence is transfer of the energy associated with volts
to the energy wave associated with amps as energy can`t be obliterated
while the volts disappear.

I do like pulses. Thinking about pulses on the line certainly helped
clarify my understanding of how lines worked.

So what happens when two pulses collide? I don't think you will like
this answer either, but here goes.

First, remember that power and energy are not the same. Power can
become zero while the energy remains. It simply means that the
energy is now stored in the capacitance or inductance (or equally,
the E field or H field) but is not moving. So no energy is lost
or destroyed when the power goes to zero.

So what happens to these two pulses? They bounce off of each other
and return whence they came. This must happen since the voltage on
the region of the line where the two pulses collide remains zero
and since p(t) = v(t) * i(t) there is no power in this region
so there must be no energy flowing. You would observe exactly
the same result were you to short the line at the point of
collision just before the collision occurred. Two pulses colliding
is just like a reflection.

As a simple analogue, consider two identical elastic balls rolling
towards each other. They bounce back after the collision.

On a line this is easier to visualize with two negative pulses
colliding. Each pulse consists of a clump of charge. When these
clumps of charge collide, remembering that like charge repels,
they bounce back.

What actually happens during the collision? With balls, the
energy is stored in the deformation of the ball and then
released as the balls separate. With pulses, the power stops
(current is zero), and the energy is stored in the capacitance
of the line in the region of the collision. After all the
energy has stopped flowing (no power, zero current, all energy
in the E field), the energy is released into the reflected
pulses and once again, there is energy moving (power) on the
line.

....Keith