Standing-Wave Current vs Traveling-Wave Current
 

Roger wrote:

I agree that we would have the same problem with a perfect current
source which had an infinite impedance.

How about using a perfect POWER source, that could not absorb power.
Output power would be limited by the external impedance. Mathematically,
the perfect POWER source would be described by

Ps = (Vp^2)/Zvp = Zip * Ip^2 where Ps = maximum power output, Vp =
voltage from perfect voltage source, Zvp = 0, Zip = infinity, and Ip =
current from a perfect current source.

The power output could be infinite, but power could never be absorbed by
the source.

Just as for both perfect voltage and perfect current sources, the actual
power output would be limited by external loads.

The impedance of the perfect POWER source would be Vp/Ip, both
controlled by external loads. To me that means that the output power
from the perfect POWER source would follow the impedance presented by
the load, but power going into the source would be defined as being zero.

Would the "perfect power source" be acceptable to you?

No. As I mentioned on another thread, this is a nonlinear device, which
would not permit using the linear circuit analysis I used. It would
require reverting to fundamental differential equations, which I'm not
willing to do. I'll be willing to use absolutely any linear source
(which doesn't change during the analysis period) you can devise. Any
linear source can be reduced to a Thevenin or Norton equivalent to
produce identical results.

Can't your concept of transmission lines deal with linear sources? If
not, why not?

Roy Lewallen, W7EL

Standing-Wave Current vs Traveling-Wave Current
 

Roy Lewallen wrote:
Roger wrote:

I agree that we would have the same problem with a perfect current
source which had an infinite impedance.

How about using a perfect POWER source, that could not absorb power.
Output power would be limited by the external impedance.
Mathematically, the perfect POWER source would be described by

Ps = (Vp^2)/Zvp = Zip * Ip^2 where Ps = maximum power output, Vp =
voltage from perfect voltage source, Zvp = 0, Zip = infinity, and Ip =
current from a perfect current source.

The power output could be infinite, but power could never be absorbed
by the source.

Just as for both perfect voltage and perfect current sources, the
actual power output would be limited by external loads.

The impedance of the perfect POWER source would be Vp/Ip, both
controlled by external loads. To me that means that the output power
from the perfect POWER source would follow the impedance presented by
the load, but power going into the source would be defined as being zero.

Would the "perfect power source" be acceptable to you?

No. As I mentioned on another thread, this is a nonlinear device, which
would not permit using the linear circuit analysis I used. It would
require reverting to fundamental differential equations, which I'm not
willing to do. I'll be willing to use absolutely any linear source
(which doesn't change during the analysis period) you can devise. Any
linear source can be reduced to a Thevenin or Norton equivalent to
produce identical results.

Can't your concept of transmission lines deal with linear sources? If
not, why not?

Roy Lewallen, W7EL

No, my concept of transmission lines deals fine with linear sources, it
is the non-linear constant voltage source and constant current source
that can not handle a second source of power arriving at a time later
than the original pulse.

Thank you for much thoughtful discussion. I have learned a lot, and
sharpened my skills. I won't drop the topic, because it can bear great
fruit, but let's you and I drop it for a while.

You may be right about differential equations needed for an perfect
POWER source, but so far, I don't think so. I am being honest that I
think your analysis applies up to the point of using the -1 reflection
factor at the source. In fact, I will probably use it in the future,
with an attribute to you.

Following Keith's post discussing zero voltage as a current source, I
can see why you might insist on using the -1 reflection factor. As time
passes, I will try to improve the concept of the perfect POWER source to
see if that can bridge the conceptual differences, but retain the
relative simplicity of sine waves adding.

73, Roger, W7WKB

Standing-Wave Current vs Traveling-Wave Current
 

Roy Lewallen wrote:
Roger wrote:

I agree that we would have the same problem with a perfect current
source which had an infinite impedance.

How about using a perfect POWER source, that could not absorb power.
Output power would be limited by the external impedance.
Mathematically, the perfect POWER source would be described by

Ps = (Vp^2)/Zvp = Zip * Ip^2 where Ps = maximum power output, Vp =
voltage from perfect voltage source, Zvp = 0, Zip = infinity, and Ip =
current from a perfect current source.

The power output could be infinite, but power could never be absorbed
by the source.

Just as for both perfect voltage and perfect current sources, the
actual power output would be limited by external loads.

The impedance of the perfect POWER source would be Vp/Ip, both
controlled by external loads. To me that means that the output power
from the perfect POWER source would follow the impedance presented by
the load, but power going into the source would be defined as being zero.

Would the "perfect power source" be acceptable to you?

No. As I mentioned on another thread, this is a nonlinear device, which
would not permit using the linear circuit analysis I used. It would
require reverting to fundamental differential equations, which I'm not
willing to do. I'll be willing to use absolutely any linear source
(which doesn't change during the analysis period) you can devise. Any
linear source can be reduced to a Thevenin or Norton equivalent to
produce identical results.

Can't your concept of transmission lines deal with linear sources? If
not, why not?

Roy Lewallen, W7EL

No, my concept of transmission lines deals fine with linear sources, it
is the non-linear constant voltage source and constant current source
that can not handle a second source of power arriving at a time later
than the original pulse.

Thank you for much thoughtful discussion. I have learned a lot, and
sharpened my skills. I won't drop the topic, because it can bear great
fruit, but let's you and I drop it for a while.

You may be right about differential equations needed for an perfect
POWER source, but so far, I don't think so. I am being honest that I
think your analysis applies up to the point of using the -1 reflection
factor at the source. In fact, I will probably use it in the future,
with an attribute to you.

Following Keith's post discussing zero voltage as a current source, I
can see why you might insist on using the -1 reflection factor. As time
passes, I will try to improve the concept of the perfect POWER source to
see if that can bridge the conceptual differences, but retain the
relative simplicity of sine waves adding.

73, Roger, W7WKB

Standing-Wave Current vs Traveling-Wave Current
 

I was afraid that a mathematical treatment wouldn't be appropriate for
this forum -- it is, after all, an amateur newsgroup -- and it looks
like I was right. It's taken a considerable amount of time to develop
and present the analysis and answer questions as completely as I can,
but it appears from the responses that the time was largely wasted. It's
been my hope that at least a few "lurkers" have gained some insight from
it. If so, please drop me an email letting me know one way or the other
-- don't worry, I'll keep your email confidential. I'd been considering
making up an analytical and quantitative analysis of where the energy
goes in a transmission line. But it's certainly pointless if my analysis
of even the most basic development of line voltage can't be understood
or believed, as seems to be the case.

Roy Lewallen, W7EL

Standing-Wave Current vs Traveling-Wave Current
 

On Sun, 30 Dec 2007 19:08:44 -0800, Roger wrote:

No, my concept of transmission lines deals fine with linear sources, it
is the non-linear constant voltage source and constant current source
that can not handle a second source of power arriving at a time later
than the original pulse.

Hi Roger,

That is not the problem of the sources, it is your problem alone in
coming to terms with the network. Any reference that reaches deep
into the fundamentals of lines and networks begins with the Thevenin
source (and at least one off of my shelf delves into two Thevenin
sources facing each other).
"There are waves of identical frequency traveling
in both directions on the line, but their amplitudes
and phases are independently variable,
and neither can be called "incident" or "reflected"
waves."

It is notable that the author expressly offers only one set of
equations for the distributed voltage and current along a line and
distinctly says:
"It is worth noting that (8.1) and (8.2) [those equations]
are also applicable to Fig. 8-2 below [showing the dual
source configuration with deliberate matches], a
distinctly different transmission line circuit."

What makes it "a distinctly different transmission line circuit" is
that it is in fact one source feeding both ends. It settles the hash
about frequency, phase, coherence, amplitude, matching, and all the
other folderol that attends many of Cecil's jejune postings:
"Here a single source supplies signals to both ends
of a transmission line section, through networks that terminate
the section in its characteristic impedance at each end."

As time
passes, I will try to improve the concept of the perfect POWER source to
see if that can bridge the conceptual differences, but retain the
relative simplicity of sine waves adding.

The two equations, needing no reference to a constant power source:
V(z) = V1· e^-y·z + V2· e^+y·z
I(z) = (V1· e^-y·z - V2· e^+y·z) / Zo
where
z: the distance along a line
y = a + jB
a: nepers per unit length of line
B = 2 · pi / wavelength
V1 & V2 are arbitrary voltage phasors to be determined by
boundary conditions at the ends of the line.

It took very little effort to then proceed to the obvious:
"Whenever two waves of identical frequency travel
in opposite directions on a transmission line ...
the fundamental phenomenon of interference or
'standing waves' occurs. ... exhibits periodic maxima
and minima ... in its most striking form when
the two oppositely directed waves have equal
amplitude and the transmission line system has
zero attenuation."

Elaborations of stepped pulses of energy had better resolve to
identical analysis using the math above, or the strain of elaboration
has led to sterile inventions.

73's
Richard Clark, KB7QHC

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
Cecil Moore wrote:
They engaged in typical author-speak.

I think not.

You are welcome to your opinion. Authors always
couch their assertions in probabilities by
never uttering an absolute lest they be proved
wrong by one esoteric example.

Well, there is no energy flowing through the '+' points.

I proved that energy is flowing through the '+' points
before the line is cut. Superposition proves that there
is energy flowing through those points.

And I have no issue if you wish to claim that there
are reflections at these points, though I might use
'bouncing' to differentiate from reflections occuring
at points with non-zero reflection coefficients.

So bouncing is what happens at points with zero reflection
coefficients. You seem to have invented a new religion.

No energy is flowing (q.v. IEEE definition of
instantaneous power), and yet you want energy
to be flowing.

Lots of energy is flowing in both directions.
Only the *NET* energy flow is zero.

Although many have tried to prove that the output (source)
impedance is the impedance encountered by the reflected waves,
all of those numerous experiments have failed.

You, Cecil, are the only one who believes this. Any good
book on transmission lines will tell you otherwise.

I am not surprised that you are ignorant of the raging
arguments that have been going on primarily between
Bruene and Maxwell and their respective supporters.
I believe it continued to rage in the 2007 letters to
the QEX editors.

Web references and Spice models which agree that "the
output (source) impedance is the impedance encountered
by the reflected waves" have been previously provided,
but you refused to explore them.

No, I asked you to measure the reflection coefficients
and report the results. You refused to do so. If the issue
had ever been resolved, it would be common knowledge and
we wouldn't be arguing about it.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
Cecil Moore wrote:

The impedance of a perfect voltage source IS zero.

Please measure it and report your results.

The fact that 0 can not be achieved does not detract

If the goal is to confuse, confound, and promote
ignorance, be my guest.

A voltage source has two sides? Explain!

All of my references illustrate that voltage source
with two leads. Please pass a TV signal through it
to prove it is a zero impedance.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Roger wrote:
However, I can see the dilemma faced by a purist who sees 2v from a
reflected wave (because the reflected wave has returned to the source
and reflected as if it were an open end) and the 1v from the source at
exactly the same location. Something must be wrong.

It can happen at a Z0-match point where destructive
interference exists on the source side and constructive
interference exists on the load side.

Here's an example:

Source-+---1/2WL 300 ohm line---50 ohm load

Assume the source voltage is 1 volt
The reflected voltage is ~2.5v
The forward voltage is ~3.5v
The load voltage is 1 volt

I don't recall any examples using perfect CURRENT sources.

A Norton equivalent circuit is a perfect current source.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Richard Clark wrote:
Given this equivalency, the forced power presumption collapses. Power
in the black box (if in fact that is the intent of this coy
"perfection") cannot be known.

Every reference I have on Thevenin and Norton equivalent
circuits say essentially that same thing.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Roger wrote:
My suggested perfect current source would supply only as
much current as could be absorbed by the load, so no power would be used
by the source, and current would be limited by the load.

That would be a Norton equivalent source with the
parallel source resistor set to infinity.
--
73, Cecil http://www.w5dxp.com