On Sun, 17 Aug 2003 18:16:42 -0700, Roy Lewallen
wrote:

Interesting stuff snipped

Magid has the most rigorous derivation of power and energy flow on
transmission lines I've seen, as well as other extensive transmission
line information. One conclusion that pricked my ears was that on a line
with a pure standing wave (e.g., a lossless line terminated with an open
or short circuit), ". . . power (and therefore, energy) is completely
trapped within each [lambda]/4 section of this lossless line, never able
to cross the zero-power points and thus constrained forever to rattle to
and fro within each quarter-wave section of this line." I had reached
this same conclusion some time ago, but realized I hadn't properly
evaluated the constant term when integrating power to find the energy.
But I didn't want to get into the endless shouting match going on in the
newsgroup, and dropped it before going back and fixing my derivation.
Hopefully some of the participants in power and energy discussions will
read Magid's analysis before resuming. I found this book used at a very
modest price.


Roy:

Interesting point and I don't recall reading or hearing it elsewhere.

The following is dashed off without fully thinking it through, so no
warranty on its accuracy.

If you think of a sound wave (longitudinal transmission, of course) in
a lossless acoustic transmission line terminated with a short, the
individual air molecules within each 1/4 wave section are likewise
trapped since at the 1/4 wave points there is zero sound pressure.
This may be a useful analogy for the electromagnetic transverse
propagating T-line.

Jack K8ZOA

W5DXP wrote:

Roy Lewallen wrote:
Magid has the most rigorous derivation of power and energy flow on
transmission lines I've seen, as well as other extensive transmission
line information. One conclusion that pricked my ears was that on a line
with a pure standing wave (e.g., a lossless line terminated with an open
or short circuit), ". . . power (and therefore, energy) is completely
trapped within each [lambda]/4 section of this lossless line, never able
to cross the zero-power points and thus constrained forever to rattle to
and fro within each quarter-wave section of this line."

He's obviously talking about net energy.

Not obvious at all.

There is no impedance discontinuity
in a continuous piece of transmission line so there is nothing to cause
reflections at the zero-power points.

A mechanical analogue may help. Consider that executive toy: five steel
balls attached by string to a frame. Pull back the ball on one side and
let it go, when it strikes the second ball, the fifth ball swings up.
Reduce this toy to just two balls.

Pull one back, when it strikes the second, it swings out, then swings
back striking the first which then swings out. It is clear that there
is energy transfer between the balls.

Redo the experiment by pulling both balls back and letting them go at
the same time. After colliding, both balls bounce back. Were you to
place a very thin sheet of steel between the balls at the collision
point it would not move. Since Work is Force x Distance and the Distance
is zero there is no Work being done on the sheet so no energy can be
crossing it.

In the shorted or open transmission line (from Magid, above), the
analogue is two clumps of charge rushing towards each other and meeting
at a voltage maximum (current zero). No charge crosses this point
(obvious because the current is zero), but the charge coming from each
direction builds to a voltage maximum and bounces away again (since
like charge repels).

Net energy doesn't cross the zero-
power points but equal forward energy and reflected energy must cross the
zero-power points.

Not possible since NO energy crosses the zero voltage and zero current
points (unless you want to reject Pinst = Vist x Iinst).

That is easy to prove by observing ghosting on a TV set
being fed by 1000 feet of ladder-line. If energy is completely trapped
within each 1/4WL section, ghosting would be impossible.

This ghosting argument appears quite powerful along with the somewhat
similar observation that information can be sent in both directions
simultaneously on a phone line.

The difficulty I encountered, while trying to understand, is that
simultaneously holding the views that:
1) ghosting is caused by reflected energy flowing back along the line;
and
2) Pinst = Vinst x Iinst
required too much double think.

Item 2) seemed to be too universally applicable to let go, so a better
understanding of 1) was required.

Although it seems unrelated, it is worthwhile to consider how to send
information along a line without sending energy in the same direction.

For simplicity, consider an ideal transmission line of useful length
with
a matched Thevenin DC source on the left and a matched load connected
through a switch on the right. Initially, the switch is open and the
line is charged to V: the voltage of the voltage source. Observe that
there is no current flowing anywhere, hence no energy flowing and
therefore no power. This is entirely consistent with 2), above.

Close the switch. Charge starts flowing from the line through the load.
A negative voltage step begins to propagate backwards along
the line at the velocity of the line. When this voltage step reaches
the source, the line has entered a new energy state with constant
voltage V/2 across its length, a current of V/2/R flowing and
energy is flowing from the left to the right at V**2/R/4 Watts. This
power is dissipated in the load at the right.

Opening the switch will cause a positive voltage step to propagate to
the left and when it reaches the source, the line will have been
restored to its initial conditions with no energy flowing.

A detector at the source (monitoring voltage or current) can determine
if the switch is open or closed (after the voltage steps have finished
propagating), thus information can be transferred from right to left
while energy only flows from left to right.

This information is transferred by doing something that changes the
energy state on the line and waiting for the new energy state to
propagate along the line. It is important to note that the
propagation of the change in energy state is not the same as the
propagation of energy. They can, and often do, occur in different
directions at the same time.

And to return to the original question, this is the cause of ghosting;
it is the propagation of the change in energy state on the line that
results in ghosting. If the source was matched, then the line settles
to its final state in one round trip and no ghosting is observed.
When the source is not matched, it takes several round trips for the
line to settle and ghosting is what you see.

By the way, this is not quite Magid's situation since he was saying
the energy completely bounced back and forth only when the line was
open or shorted. In other situations with standing waves, some of the
energy is bouncing within the 1/4 wave sections, while other energy
is flowing forward.

....Keith

wrote:
W5DXP wrote:
I forgot to add. At the "zero-power points", either voltage or current is
zero. All that means is that all the energy is contained in the opposite
field.

Not quite all. It also means that there is NO power since P = V x I.

It means there is no NET power transfer. There are power flow vectors
in both directions that are equal in magnitude. Reference: _Fields_
and_Waves_in_Communications_Electronics_ by Ramo, Whinnery, & Van Duzer,
section 6.10, page 350, where they describe Pz-, the reflected wave
Poynting vector and Pz+, the forward wave Poynting vector.

There can be lots of energy present but none of it is flowing past
the zero voltage or zero current point; hence no power.

There is a forward power flow vector and a reflected power flow vector.
There is no net power flowing past any point. There are, however, equal
magnitude component constant power flow vectors flowing in both directions.

To believe that energy is flowing across a zero voltage or zero current
point requires the rejection of the view that instantaneous power is
equal to instantaneous voltage multiplied by instantaneous current.

No, it doesn't. It only requires acceptance of Ramo, Whinnery, & Van Duzer.

However, to reject energy flow across a zero voltage or zero current
point requires a confusion of cause and effect. Energy flow in both
directions is the *CAUSE* of the standing waves. You simply cannot
turn around and say that standing waves eliminate their own cause
but continue to exist anyway.

Rejection of
P = V x I would have wide impacts on our understanding of electrical
power and energy flows.

Nobody is rejecting it. If the lossless stub is one second long, it takes
two seconds of *POWER* to bring it to steady-state. If the stub contains
no moving energy, where did all those joules go? They cannot disappear or
stand still. If they are moving, power exists.
--
73, Cecil http://www.qsl.net/w5dxp



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Magid has the most rigorous derivation of power and energy flow on
transmission lines,
==========================
The following short question is adressed to all contributors to this
newsgroup who feel impelled to bolster their lack of self-confidence by
dragging in the chapter and verse of their favourite worshipped authors and
Gurus, most of whom nobody has ever heard of and highly unlikely ever to get
their hands on.

How do you know that?

W5DXP wrote:

wrote:
W5DXP wrote:
I forgot to add. At the "zero-power points", either voltage or current is
zero. All that means is that all the energy is contained in the opposite
field.

Not quite all. It also means that there is NO power since P = V x I.

It means there is no NET power transfer.

Do not be afraid to admit that you have changed the definition of P = V
x I
and therefore do not accept the standard definition.

When I learned Pinst = Vinst x Iinst there were no caveats about how
Pinst meant Pnet. Instantaneous energy is flowing or it is not. When
Pinst
is 0 for all time, then there is no energy flowing.

To satisfy your theory (and minimize double think), you have had to
change
this to Pnet is zero to allow these cancelling powers to flow. So be it.

There are power flow vectors
in both directions that are equal in magnitude. Reference: _Fields_
and_Waves_in_Communications_Electronics_ by Ramo, Whinnery, & Van Duzer,
section 6.10, page 350, where they describe Pz-, the reflected wave
Poynting vector and Pz+, the forward wave Poynting vector.

There can be lots of energy present but none of it is flowing past
the zero voltage or zero current point; hence no power.

There is a forward power flow vector and a reflected power flow vector.
There is no net power flowing past any point.

True, sort of. At the quarter wave points where voltage or current are
always
zero, there is no energy flowing. Period.

At other points, energy flows in one direction for a quarter cycle and
then in the other direction for the next quarter cycle, producing a net
of zero. A true instantenouse power meter (one which measures V and I
and
displays V x I) will easily demonstrate this. As a thought experiment,
move such a true power meter along a shorted or open line and think if
its indications in the time domain, then do the averages. It will be
quite instructive. Repeat for a line terminated in other than its
characteristic impedance.

By the way, since energy flows forward for a quarter cycle and backwards
for the next, the maximum distance travelled by this energy is one
quarter
wavelength on the line. It is not flowing all the way to the end of the
line and then back. There is not enough time for this to happen (on a
multi-wavelength line) since it changes direction every quarter cycle.

There are, however, equal
magnitude component constant power flow vectors flowing in both directions.

To believe that energy is flowing across a zero voltage or zero current
point requires the rejection of the view that instantaneous power is
equal to instantaneous voltage multiplied by instantaneous current.

No, it doesn't. It only requires acceptance of Ramo, Whinnery, & Van Duzer.

However, to reject energy flow across a zero voltage or zero current
point requires a confusion of cause and effect. Energy flow in both
directions is the *CAUSE* of the standing waves. You simply cannot
turn around and say that standing waves eliminate their own cause
but continue to exist anyway.

Not quite. Standing voltage and current waves (which are not waves in
the normal sense) can be observed on the line. They can be measured with
real voltage and current instruments; as can real energy flows with
a real (V x I) power meter (but not a 'Bird watt' meter which
is doing something quite different). It happens that if you assume the
existence of forward and reverse voltage and current waves, mathematical
functions can be derived that will produce the same distribution of
voltage and current as observed on the line. This is extraordinarily
convenient some analysis but does not mean that these assumed waves are
real.

A mechanical analogue would be to look at a guy wire on a pole. You can
analyze the forces as two vectors at 90 degrees (or any other angle of
convenience!), but never make the mistake of assuming that there are
actually two guy wires present. Just because it is mathematically
convenient to assume the existence of two vectors does not mean they
exist.

Rejection of
P = V x I would have wide impacts on our understanding of electrical
power and energy flows.

Nobody is rejecting it. If the lossless stub is one second long, it takes
two seconds of *POWER* to bring it to steady-state. If the stub contains
no moving energy, where did all those joules go?

This energy is indeed stored in the stub. None of it moves across zero
voltage
or current boundaries. Between these boundaries, it is indeed moving as
it changes from being stored in the capacitance and inductance of the
line.
This time variation of the location of the stored energy produces the
observed
voltages and currents on the line.

They cannot disappear

Absolutely. They do not disappear.

or stand still.

With AC excitation they do not stand still, but when similar analysis is
done
for a line excited with a DC source, the energy does indeed stand still.
An
open line stores the energy in the capacitance and a shorted line stores
it
in the inductance.

If they are moving, power exists.

Yes, but it never moves more than a quarter wavelength.

....Keith

W5DXP wrote in message ...

The transmission coefficient can certainly be greater than unity,
being (2*Z2)/(Z1+Z2).

From Pozar's Microwave Engineering (Pg. 606):

Reflection Coefficient looking into load = (Zl-Zo)/(Zl+Zo)

Where Zl is the load impedance, and Zo is the characteristic
impedance reference.

The reflection coefficient cannot be greater than unit.

How can you have an S21 that is greater than unity with a passive
network?


Slick

Keith wrote:
"At the quarter wave points where voltage and current are always zero,
there is no energy flowing. Period."

Yes there is energy flowing, and it is flowing in both directions if it
is flowing in one direction. Otherwise there would be no standing wave.

The waves flow right through each other so long as the impedance is
uniform. Energy flow is unabated at those points of illusory zeros.
Those zeros are not zeros at all in the forward and reverse waves. They
only appear as zeros when your sensor can`t separate the forward from
the reverse. Get a proper directional sensor and the forward wave is
sensed as full amplitude as is the reverse wave.

Best regards, Richard Harrison, KB5WZI

"Reg Edwards" wrote in message ...
Magid has the most rigorous derivation of power and energy flow on
transmission lines,
==========================
The following short question is adressed to all contributors to this
newsgroup who feel impelled to bolster their lack of self-confidence by
dragging in the chapter and verse of their favourite worshipped authors and
Gurus, most of whom nobody has ever heard of and highly unlikely ever to get
their hands on.

How do you know that?

Gee, Reg, since you took that out of context, it seems a bit unfair.
Roy wrote it, and after the comma was, "I've seen." I don't know it,
but I'm willing to take Roy at his word on the matter.

Cheers,
Tom

wrote:
In the shorted or open transmission line (from Magid, above), the
analogue is two clumps of charge rushing towards each other and meeting
at a voltage maximum (current zero). No charge crosses this point
(obvious because the current is zero), but the charge coming from each
direction builds to a voltage maximum and bounces away again (since
like charge repels).

Unfortunately, the analogy is not a good one. In a transmission line,
there must exist a discontinuity to cause a reversal of momentum of
the waves. No such discontinuity exists so there is nothing to reverse
the momentum of the forward and reflected waves.

Not possible since NO energy crosses the zero voltage and zero current
points (unless you want to reject Pinst = Vist x Iinst).

Ramo, Whinnery, and Van Duzer disagree. They say that the power
reflection coefficient is equal to the reflected Poynting vector
divided by the forward Poynting vector which in this case would
be unity.

The difficulty I encountered, while trying to understand, is that
simultaneously holding the views that:
1) ghosting is caused by reflected energy flowing back along the line;
and 2) Pinst = Vinst x Iinst required too much double think.

Life is tough all over. :-) What I am saying doesn't require double
think. :-)

Although it seems unrelated, it is worthwhile to consider how to send
information along a line without sending energy in the same direction.

Information transfer doesn't require energy? Methinks you are confusing
the carriers of the wave with the waves themselves. Zero carriers may
indeed cross the zero power point, but that does not prevent energy
from crossing the boundary. It just means that the energy crossing the
boundary must be equal in both directions.

One point. The power is not Vavg * Iavg. The power is Vavg*Iave*cos(theta)
All up and down a shorted lossless transmission line, theta is equal to
90 degrees. Around a voltage zero point, on one side the voltage is equal
to 0.00000001 volts and is 90 degrees out of phase with the current, i.e.
zero power. On the other side of the voltage zero point, the voltage is
equal to -0.00000001 volts and is 90 degrees out of phase with the current.
There are an infinite number of points where the voltage is 90 degrees out
of phase with the current. That's why the average power is always zero, not
because the average voltage is zero, but because the voltage is *ALWAYS* 90
degrees out of phase with the current in a lossless shorted feedline.

When the source is not matched, it takes several round trips for the
line to settle and ghosting is what you see.

Put an amplifier between the TV set and the feedline. Let the amplifier
have as high an impedance as possible (insulated gate FET). That will
cause reflections. Those reflections will still be there during steady-
state and observing the ghosting will prove that, during steady-state,
the ghosts have made one or more round trips back to the source where
they are re-reflected (assuming a mismatched source or a Z0-match
provided by a network).
--
73, Cecil http://www.qsl.net/w5dxp
"One thing I have learned in a long life: that all our science, measured
against reality, is primitive and childlike ..." Albert Einstein



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Reg Edwards wrote:
The following short question is adressed to all contributors to this
newsgroup who feel impelled to bolster their lack of self-confidence by
dragging in the chapter and verse of their favourite worshipped authors and
Gurus, most of whom nobody has ever heard of and highly unlikely ever to get
their hands on.

You never heard of Ramo, the 'R' in TRW? :-)
--
73, Cecil http://www.qsl.net/w5dxp



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