Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
It is worth doing to convince yourself. Then examine
P(t) to understand how the instaneous energy transfer
varies with time.

Oh, I know how to integrate P(t). But I don't
comprehend the utility of the following:

The instantaneous value of voltage is 10 volts.
The instantaneous value of current is 1 amp.
The voltage and current are in phase.

The instantaneous power is 10 joules per 0 sec?
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Dave Heil wrote:
You keep writing, over
and over, that the Sun just sits there in space. We both know that
isn't actually correct either. The Sun rotates and is moving through
space quite rapidly.

Of course, the sun's rotation and movement through
space have nothing to do with the sun rising, traveling
across the sky, and then setting.

I've asked a number of times how you refer to the
phenomena of what most of us call "Sunrise" and "Sunset."

I have responded four or five times now. If you are
too dense to get it this time, I will probably not reply
again. The sun does NOT "rise", does NOT travel across
the sky, and does NOT "set".
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Roy Lewallen wrote:
Roger wrote:
. . .

This does raise the question of the description of the traveling wave
used in an earlier posting.

The example was the open ended 1/2 wavelength transmission line, Zo = 50
ohms, with 1v p-p applied at the source end. The term wt is the phase
reference. At the center of the line, (using the source end as a
reference), you gave vr(t) =-.05*sin(wt-90 deg.) and ir(t) =
0.01*sin(wt-90 deg.)

By using the time (wt-90), I think you mean that the peak occurs 90
degrees behind the leading edge.

The leading edge and peak of what? The function sin(wt -90) looks
exactly like the function sin(wt) except that it's delayed 90 degrees in
phase. So the forward voltage wave is delayed by 90 degrees relative to
the source voltage. This is due to the propagation time down 90
electrical degrees of transmission line.

I think we are in sync here, but something is missing. When I think of
a traveling sine wave, it must have a beginning as a point of beginning
discussion. I pick a point which is the zero voltage point between wave
halves. It follows that the maximum voltage point will be 90 degrees
later. I think you are doing the same thing, but maybe not.

Next I imagine the whole wave moving down the transmission line as an
intact physical object, with the peak always 90 degrees behind the
leading edge. In our example 1/2 wave line, the leading edge would
reach the open end 180 degrees in time after entering the example. We
can see then, that the current peak will be at the center of the
transmission line when the leading edge reaches the end.


This posting was certainly correct if we consider only the first
reflected wave. However, I think we should consider that TWO reflected
waves may exist on the line under final stable conditions. This might
happen because the leading edge of the reflected wave will not reach the
source until the entire second half of the initial exciting wave has
been delivered. Thus we have a full wave delivered to the 1/2
wavelength line before the source ever "knows" that the transmission
line is not infinitely long. We need to consider the entire wave period
from (wt-0) to (wt-360.

If these things occur, then at the center of the line, final stable
vr(t) and ir(t) are composed of two parts, vr(wt-90) and vr(wt-270) and
corresponding ir(wt-90) and ir(wt-270). We should be describing vr(t)
as vrt(t) where vrt is the summed voltage of the two reflected waves.

Sorry, it's much worse than this.

Unless you have a perfect termination at the source or the load, there
will be an *infinite number*, not just one or two, sets of forward and
reflected waves beginning from the time the source is first turned on.
You can try to keep track of them separately if you want, but you'll
have an infinite number to deal with. After the first reflected wave
reaches the source, its reflection becomes a new forward wave and it
adds to the already present forward and reflected waves. The general
approach to dealing with the infinity of following waves is to note that
exactly the same fraction of the new forward wave will be reflected as
of the first forward wave. So the second set of forward and reflected
waves have exactly the same relationship as the first set. This is true
of each set in turn. Superposition holds, so we can sum the forward and
reverse waves into any number of groups we want and solve problems
separately for each group. Commonly, all the forward waves are added
together into a total forward wave, and the reverse waves into a total
reverse wave. These total waves have exactly the same relationship to
each other that the first forward and reflected waves did -- the only
result of all the reflections which followed the first is that the
magnitude and phase of the total forward and total reverse waves are
different from the first pair. But they've been changed by exactly the
same factor.

It's not terribly difficult to do a fundamental analysis of what happens
at each reflection, then sum the infinite series to get the total
forward and total reverse waves. When you do, you'll get the values used
in transmission line equations. I've gone through this exercise a number
of times, and I recommend it to anyone wanting a deeper understanding of
wave phenomena. Again, the results using this analysis method are
identical to a direct steady state solution assuming that all
reflections have already occurred.

The infinite number of waves could, of course, be combined into two or
more sets instead of just one, with analysis done on each. If done
correctly, you should get exactly the same result but with considerably
more work.

I do want to add one caution, however. The analysis of a line from
startup and including all reflections doesn't work well in some
theoretical but physically unrealizable cases. One such case happens to
be the one recently under discussion, where a line has a zero loss
termination at both ends (in that case, a perfect voltage source at one
end and an open circuit at the other. In those situations, infinite
currents or voltages occur during runup, and the re-reflections continue
to occur forever, so convergence is never reached. Other approaches are
more productive to solving that class of theoretical circuits.

Again, we seem to be in complete agreement except for the statement "In
those situations, infinite currents or voltages occur during runup".
For many years I thought that "initial current into a transmission line
at startup" would be very high, limited only by the inductive
characteristics of the line. With this understanding, I thought that
voltage would lead current at runup. It was not until I saw the formula
Zo = 1/cC that I realized that a transmission line presents a true
resistive load at startup. Current and voltage are always in phase at
startup.

If we agree that voltage and current are always in phase in the
traveling wave, then we should find that in our example, the system
comes to complete stability after one whole wave (two half cycles) is
applied to the system.
. . .

which is the total power (rate of energy delivery) contained in the
standing wave at the points 45 degrees each side of center. If we want
to find the total energy contained in the standing wave, we would
integrate over the entire time period of 180 degrees.

So think I.

I haven't gone through your analysis, because it doesn't look like
you're including the infinity of forward and reverse waves into your two.

. . .

Roy Lewallen, W7EL

73, Roger, W7WKB

Standing-Wave Current vs Traveling-Wave Current
 

Roger wrote:
If we agree that voltage and current are always in phase in the
traveling wave, then we should find that in our example, the system
comes to complete stability after one whole wave (two half cycles) is
applied to the system.

Assume a constant power source and you will get the results
that Roy is talking about.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:
Roger wrote:
If we agree that voltage and current are always in phase in the
traveling wave, then we should find that in our example, the system
comes to complete stability after one whole wave (two half cycles) is
applied to the system.

Assume a constant power source and you will get the results
that Roy is talking about.
No, because you would find two waves of equal voltage and current
traveling in opposite directions, always arriving at exactly out of
phase, at the source.

Now the question here is "Do the waves bounce off one another?" which
would result in a doubling of observed voltage, or "Do the wave pass
through one another?" which would allow a condition of energy entering
the system equal to energy leaving the system.

73, Roger, W7WKB

Standing-Wave Current vs Traveling-Wave Current
 

Roger wrote:
Cecil Moore wrote:
Assume a constant power source and you will get the results
that Roy is talking about.

No, because you would find two waves of equal voltage and current
traveling in opposite directions, always arriving at exactly out of
phase, at the source.

No, because a *constant power source* is pumping joules/second
into the system no matter what voltage or current it requires
to move those joules/second into the system. It's like the
power source in "Forbidden Planet".

Now the question here is "Do the waves bounce off one another?"

Waves do NOT "bounce" off one another. At a physical
impedance discontinuity, the component waves can
superpose in such a way as to redistribute their energy
contents in a different direction. (Redistribution of energy
in a different direction in a transmission line implies
reflections.) In the absence of a physical impedance
discontinuity, waves just pass through each other.

www.mellesgriot.com/products/optics/oc_2_1.htm

micro.magnet.fsu.edu/primer/java/scienceopticsu/interference/waveinteractions/index.html
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:
How can the current in the middle of the line be 0.4 amps
when the current at both points '+' is zero? Does that
0.4 amps survive a cut at point '+'?

This should have been: Does that 0.4 amps survive a cut
at both points '+' where the current is zero?
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:
Roger wrote:
Cecil Moore wrote:
Assume a constant power source and you will get the results
that Roy is talking about.

No, because you would find two waves of equal voltage and current
traveling in opposite directions, always arriving at exactly out of
phase, at the source.

No, because a *constant power source* is pumping joules/second
into the system no matter what voltage or current it requires
to move those joules/second into the system. It's like the
power source in "Forbidden Planet".

Now the question here is "Do the waves bounce off one another?"

Waves do NOT "bounce" off one another. At a physical
impedance discontinuity, the component waves can
superpose in such a way as to redistribute their energy
contents in a different direction. (Redistribution of energy
in a different direction in a transmission line implies
reflections.) In the absence of a physical impedance
discontinuity, waves just pass through each other.

www.mellesgriot.com/products/optics/oc_2_1.htm

micro.magnet.fsu.edu/primer/java/scienceopticsu/interference/waveinteractions/index.html

There is a third possibility. The interaction of the two waves can
establish a very high resistance, so high that no current flows-zero.

Does this place us at a logical impasse, with current reversing and
voltage doubling at in one argument (at the open end), but not doubling
at the source end? No, the voltage will double at the source end when
stability is reached after one full cycle (in the 1/2 wave example).

Logically then, we must recognize that our source voltage WILL NOT
remain constant following the arrival of the reflected wave. Certainly
this is what we find when we retune our transmitters after changing
frequency.

What would be the logic of insisting that the input voltage be held
constant to the 1/2 wave example after it is shown that the reflected
wave must interact with the incoming wave give a very high impedance at
the source?

73, Roger, W7WKB

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:
Dave Heil wrote:
You keep writing, over and over, that the Sun just sits there in
space. We both know that isn't actually correct either. The Sun
rotates and is moving through space quite rapidly.

Of course, the sun's rotation and movement through
space have nothing to do with the sun rising, traveling
across the sky, and then setting.

I've asked a number of times how you refer to the phenomena of what
most of us call "Sunrise" and "Sunset."

I have responded four or five times now.

You certainly have. Each of the times I've asked the questions of what
you call Sunrise and Sunset, you've not provided an answer.

If you are
too dense to get it this time, I will probably not reply
again.

I'm not at all dense, Cecil, as you know from previous exchanges through
the years. I've asked questions. What I get from you in response, does
not contain answers. If you choose not to answer, just say so. A
threat not to reply isn't really much of a threat.

The sun does NOT "rise", does NOT travel across
the sky, and does NOT "set".

Let me ask you once again: If you awaken before dawn and observe the
sun when it first becomes visible, what do *you*, Cecil Moore, call the
phenomenon you are seeing? Please note that I now say and have
previously written that I do not believe that the Sun rises, sets or
travels across the sky. I've stated that the terms Sunrise and Sunset
are commonly used to describe the Sun's first appearance and last
appearance of each day.

Dave K8MN

Standing-Wave Current vs Traveling-Wave Current
 

Roger wrote:

I think we are in sync here, but something is missing. When I think of
a traveling sine wave, it must have a beginning as a point of beginning
discussion. I pick a point which is the zero voltage point between wave
halves. It follows that the maximum voltage point will be 90 degrees
later. I think you are doing the same thing, but maybe not.

Next I imagine the whole wave moving down the transmission line as an
intact physical object, with the peak always 90 degrees behind the
leading edge. In our example 1/2 wave line, the leading edge would
reach the open end 180 degrees in time after entering the example. We
can see then, that the current peak will be at the center of the
transmission line when the leading edge reaches the end.

Yes, you're describing some of the properties of a sinusoidal traveling
wave. I generally describe them mathematically.

Again, we seem to be in complete agreement except for the statement "In
those situations, infinite currents or voltages occur during runup". For
many years I thought that "initial current into a transmission line at
startup" would be very high, limited only by the inductive
characteristics of the line. With this understanding, I thought that
voltage would lead current at runup. It was not until I saw the formula
Zo = 1/cC that I realized that a transmission line presents a true
resistive load at startup. Current and voltage are always in phase at
startup.

They are provided that Z0 is purely resistive. That follows from the
simplifying assumption that loss is zero or in the special case of a
distortionless line, and it's often a reasonable approximation. But it's
generally not strictly true.

But that doesn't have anything to do with my statement, which deals with
theoretical cases where neither end of the line has loss. For example,
look at a half wavelength short circuited line driven by a voltage
source. Everything is fine until the initial traveling wave reaches the
end and returns to the source end.

If we agree that voltage and current are always in phase in the
traveling wave, then we should find that in our example, the system
comes to complete stability after one whole wave (two half cycles) is
applied to the system.

Assuming you're talking about the half wavelength open circuited line
driven by a voltage source -- please do the math and show the magnitude
and phase of the initial forward wave, the reflected wave, the wave
re-reflected from the source, and so forth for a few cycles, to show
that what you say is true. My calculations show it is not. I'd do it,
but I find that the effort of showing anything mathematically is pretty
much a waste of effort here, since it's generally ignored. It appears
that the general reader isn't comfortable with high school level
trigonometry and basic complex arithmetic, which is a good explanation
of why this is such fertile ground for pseudo-science. But I promise
I'll read your mathematical analysis of the transmission line run-up.

Roy Lewallen, W7EL