Rotational speed
 

Cecil Moore wrote:

The standing wave current phasor has the "same rotational speed
as its components"???

It has to. Thankfully, rotational speed is the one thing that does
not change between the radio and the antenna.

How can that be when the forward current
phasor and the reflected current phasor are rotating in opposite
directions?

Rotational speed has nothing to do with direction of travel. It has
only to do with the source. Rotational speed is simply omega;
2pi*c/wavelength, or 2pi*f. When waves of equal frequency are
traveling in opposite directions, the RF waveform which comprises the
standing wave (the latter being simply the amplitude envelope of the
superposed traveling waves) has the same wavelength, and thus the same
rotational speed as the traveling waves. Although the position of the
peaks does not vary with time, their amplitude is still a time varying
function. This rudimentary effect is illustrated in the movie he

http://www.kettering.edu/~drussell/D...rposition.html

Mixing on the other hand is the product (rather than the sum) of two
or more waveforms and does in fact yield different rotational speeds.

73, Jim AC6XG

Analyzing Stub Matching with Reflection Coefficients
 

On 26 Apr 2007 16:39:41 -0700, Keith Dysart wrote:

Is there some
other fault in the model that makes it sufficiently incorrect
to be unusable?

The story of the Princess and the Pea. How many mattresses before the
Princess will be satisfied?

73's
Richard Clark, KB7QHC

Rotational speed
 

Jim Kelley wrote:
. . .
Mixing on the other hand is the product (rather than the sum) of two or
more waveforms and does in fact yield different rotational speeds.

And multiplying voltage and current waveforms, or squaring a voltage or
current waveform to get power gives a wave with double the rotational
speed and, unless V and I are in quadrature, a DC offset.

Roy Lewallen, W7EL

Analyzing Stub Matching with Reflection Coefficients
 

Keith Dysart wrote:
Certainly the model I described is linear. Is there some
other fault in the model that makes it sufficiently incorrect
to be unusable?

Yes, it doesn't model a class-C amplifier.
--
73, Cecil http://www.w5dxp.com

Rotational speed
 

Jim Kelley wrote:
Rotational speed has nothing to do with direction of travel.

I assumed that the "same rotational speed" implies
the same direction.
--
73, Cecil http://www.w5dxp.com

Rotational speed
 

Cecil Moore wrote:
Jim Kelley wrote:
Rotational speed has nothing to do with direction of travel.

I assumed that the "same rotational speed" implies
the same direction.

The reason I assumed that is this assertion by W7EL.
"This is the total current. It has magnitude and phase
like any other phasor, and the same rotational speed
as its components."

The total current, as graphed by Kraus and displayed
by EZNEC *DOES NOT* have the same rotational speed as
its components. It is obvious that Roy meant the
same direction when he said "same rotational speed".
--
73, Cecil http://www.w5dxp.com

Analyzing Stub Matching with Reflection Coefficients
 

On Apr 26, 9:12 pm, Cecil Moore wrote:
Keith Dysart wrote:
Certainly the model I described is linear. Is there some
other fault in the model that makes it sufficiently incorrect
to be unusable?

Yes, it doesn't model a class-C amplifier.

Ah yes. At first there was a reason. But then that was taken
care of, so now we have well...

welll...

well...

It just does NOT model it.

Rather lame, methinks.

....Keith

Analyzing Stub Matching with Reflection Coefficients
 

Keith Dysart wrote:
It just does NOT model it.

You got it. Einstein said an explanation should be as
simple as possible, but not too simple. There is too
much evidence gathered over decades of arguments for
simple-minded models to work anywhere except in your
dreams.

Your earlier example proved it. In a source with
absolute zero power, you claimed that all the
reflected power was being dissipated in that
source. Maybe you should fix your trivial model
before tackling anything more complicated.
--
73, Cecil http://www.w5dxp.com

Analyzing Stub Matching with Reflection Coefficients
 

On Apr 26, 9:48 pm, Cecil Moore wrote:
Keith Dysart wrote:
It just does NOT model it.

You got it. Einstein said an explanation should be as
simple as possible, but not too simple. There is too
much evidence gathered over decades of arguments for
simple-minded models to work anywhere except in your
dreams.

Okay, so you can't find anything to point at that is wrong
with the model. You could always ask. I could point to a
few things that are arguably weak with the model.

Your earlier example proved it. In a source with
absolute zero power, you claimed that all the
reflected power was being dissipated in that
source.

Of course I claimed no such thing; you do need to read
more carefully. And you have conveniently neglected the
other example which was presented right beside for
which 4 times the "reflected power" was dissipated by
the source. These two copmletely different results
call into question the nature of "reflected power".

....Keith

Analyzing Stub Matching with Reflection Coefficients
 

Keith Dysart wrote:
Okay, so you can't find anything to point at that is wrong
with the model.

What is wrong with the model is that it doesn't work
in reality. Neither does the 6000 year old model of
the age of the earth.

Of course I claimed no such thing; you do need to read
more carefully. And you have conveniently neglected the
other example which was presented right beside for
which 4 times the "reflected power" was dissipated by
the source. These two copmletely different results
call into question the nature of "reflected power".

No, they call into question the validity of the model.
The reflected energy is there and can be dissipated
by a circulator load. That the model gets it wrong is
proof of an invalid model, not proof that photons
contain zero energy. Photons contain energy that obeys
the conservation of energy principle.

The fact that zero energy is dissipated in a source
is prima facie evidence of destructive interference
and a "redistribution of energy in a direction that
allows constructive interference". Understanding
interference is the key and your model doesn't even
mention interference.
--
73, Cecil http://www.w5dxp.com

Analyzing Stub Matching with Reflection Coefficients
 

On Apr 27, 7:28 am, Cecil Moore wrote:
Keith Dysart wrote:
Okay, so you can't find anything to point at that is wrong
with the model.

What is wrong with the model is that it doesn't work
in reality.

Hmmm. Having a complete inability to articulate any issues
with the model, you are, none-the-less, convinced that it does
not work in 'reality'. Hmmm.

Of course I claimed no such thing; you do need to read
more carefully. And you have conveniently neglected the
other example which was presented right beside for
which 4 times the "reflected power" was dissipated by
the source. These two completely different results
call into question the nature of "reflected power".

No, they call into question the validity of the model.
The reflected energy is there and can be dissipated
by a circulator load.

The fact that zero energy is dissipated in a source
is prima facie evidence of destructive interference
and a "redistribution of energy in a direction that
allows constructive interference".

But then what is the fact that 4 times the energy is
dissipated in the source prime facie evidence of?

Good explanations explain all the observations, not
just the supporting ones.

....Keith

Analyzing Stub Matching with Reflection Coefficients
 

Keith Dysart wrote:
Hmmm. Having a complete inability to articulate any issues
with the model, you are, none-the-less, convinced that it does
not work in 'reality'. Hmmm.

I have been articulating issues with the model for weeks
now and I am just about articulated out. We are repeating
the same things over and over and unless you take time
out to comprehend interference, there's no reason to
continue.

The fact that zero energy is dissipated in a source
is prima facie evidence of destructive interference
and a "redistribution of energy in a direction that
allows constructive interference".

But then what is the fact that 4 times the energy is
dissipated in the source prime facie evidence of?

Of *total constructive interference* in the source, of
course. I already answered that question days ago. It
is futile to try to communicate with someone who refuses
to listen. Here are the power intensity equations
governing the power dissipated in the two sources in
the previous two examples.

Thevenin equivalent if P1 = P2:
Pdis = P1 + P2 - 2*SQRT(P1*P2) = 0
*Total Destructive Interference* as defined by Hecht in
"Optics", 4th edition, page 388.

Norton equivalent if P1 = P2:
Pdis = P1 + P2 + 2*SQRT(P1*P2) = 4*P1
*Total Constructive Interference* as defined by Hecht in
"Optics", 4th edition, page 388.

Until you learn to recognize interference when it is staring
you in the face, you are going to continue to make the same
mistakes over and over. Forward and reflected energy is alive
and well and obeys the conservation of energy principle. That
you cannot figure out where the photonic energy goes during
a wave interference event is not my problem. Hints about
destructive interference:

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

"Clearly, if the wavelength of the incident light and the thickness
of the film are such that a phase difference exists between reflections
of p, then reflected wavefronts interfere destructively, and overall
reflected intensity is a minimum. If the two reflections are of equal
amplitude, then this amplitude (and hence intensity) minimum will be
zero."

Note that "intensity" is *power density* in watts/unit-area.

"In the absence of absorption or scatter, the principle of conservation
of energy indicates all 'lost' reflected intensity will appear as
enhanced intensity in the transmitted beam. The sum of the reflected and
transmitted beam intensities is always equal to the incident intensity.
This important fact has been confirmed experimentally."

http://micro.magnet.fsu.edu/primer/j...ons/index.html

"... when two waves of equal amplitude and wavelength that are 180-
degrees out of phase with each other meet, they are not actually
annihilated. All of the photon energy present in these waves must
somehow be recovered or *redistributed in a new direction*, according to
the *law of energy conservation* ... Instead, upon meeting, the photons
are *redistributed to regions that permit constructive interference*, so
the effect should be considered as a *redistribution* of light waves and
photon energy rather than the spontaneous construction or destruction
of light."

emphasis mine
--
73, Cecil http://www.w5dxp.com

Analyzing Stub Matching with Reflection Coefficients
 

Cecil Moore wrote:
Keith Dysart wrote:
Certainly the model I described is linear. Is there some
other fault in the model that makes it sufficiently incorrect
to be unusable?

Yes, it doesn't model a class-C amplifier.


Cecil,

I heard a rumor that the FCC does not like people to inject class-C type
pulses directly into an antenna from the output of an amateur transmitter.

Perhaps that rumor is just an urban legend, however, and non-linear
outputs are welcome.


8-)

73,
Gene
W4SZ

Analyzing Stub Matching with Reflection Coefficients
 

Gene Fuller wrote:
I heard a rumor that the FCC does not like people to inject class-C type
pulses directly into an antenna from the output of an amateur transmitter.

Perhaps that rumor is just an urban legend, however, and non-linear
outputs are welcome.

The subject is modeling a class-C source, Gene,
not filtering a class-C source. We all know how
to filter a class-C source. Do you have a model
for a class-C source?
--
73, Cecil http://www.w5dxp.com

Analyzing Stub Matching with Reflection Coefficients
 

Cecil Moore wrote:
Gene Fuller wrote:
I heard a rumor that the FCC does not like people to inject class-C
type pulses directly into an antenna from the output of an amateur
transmitter.

Perhaps that rumor is just an urban legend, however, and non-linear
outputs are welcome.

The subject is modeling a class-C source, Gene,
not filtering a class-C source. We all know how
to filter a class-C source. Do you have a model
for a class-C source?


Cecil,

The original topic was the *output* of an amateur transceiver, e.g., as
seen by a transmission line.

Sorry I did not catch the thread redefinition toward the inner workings
of such a device. That move could open up infinite opportunity for more
arguments.

8-)

73,
Gene
W4SZ

Analyzing Stub Matching with Reflection Coefficients
 

Gene Fuller wrote:
Sorry I did not catch the thread redefinition toward the inner workings
of such a device.

Apology accepted. The crux of what we have been discussing
for days, if not weeks, is what does a model of the active,
dynamic volcano of energy, i.e. the source, look like?
--
73, Cecil http://www.w5dxp.com

Rotational speed
 

Cecil Moore wrote:

Cecil Moore wrote:

Jim Kelley wrote:

Rotational speed has nothing to do with direction of travel.


I assumed that the "same rotational speed" implies
the same direction.

The reason I assumed that is this assertion by W7EL.
"This is the total current. It has magnitude and phase
like any other phasor, and the same rotational speed
as its components."

The total current, as graphed by Kraus and displayed
by EZNEC *DOES NOT* have the same rotational speed as
its components. It is obvious that Roy meant the
same direction when he said "same rotational speed".

I'm sure you're in a better position to know that than Roy is.

ac6xg

Rotational speed
 

Jim Kelley wrote:

Cecil Moore wrote:
Cecil Moore wrote:

Jim Kelley wrote:

Rotational speed has nothing to do with direction of travel.

I assumed that the "same rotational speed" implies
the same direction.

The reason I assumed that is this assertion by W7EL.
"This is the total current. It has magnitude and phase
like any other phasor, and the same rotational speed
as its components."

The total current, as graphed by Kraus and displayed
by EZNEC *DOES NOT* have the same rotational speed as
its components. It is obvious that Roy meant the
same direction when he said "same rotational speed".

I'm sure you're in a better position to know that than Roy is.

It's a matter of logic, Jim. We know that the forward
current and reflected current phasors are rotating in
opposite directions. Kraus and EZNEC say that the
phase angle of the current on a 1/2WL dipole changes
by only 2 degrees, end to end. Therefore, contrary to
what Roy asserted, the total current does NOT have the
same rotational speed as its components.

That was Roy's mistake in using total current to try
to measure phase shift through a coil. One cannot
use total current phase on a standing wave antenna
to determine any valid measurement concerning phase
shift through a coil. But since the phase information
is preserved in the total current amplitude, it can
be used to estimate phase shift through the coil.

Roy said, "What I measured was a 3.1% reduction in
magnitude from input to output, with no discernible
phase shift."

From this, for a base-loaded coil we can estimate the
phase shift through the coil to be

arccos(.969) = 14.3 degrees

With no discernible phase shift we can estimate that
there was no decrease in current from end to end for
either the forward current or reflected current.
--
73, Cecil http://www.w5dxp.com

Rotational speed
 

Cecil Moore wrote:


We know that the forward
current and reflected current phasors are rotating in
opposite directions. Kraus and EZNEC say that the
phase angle of the current on a 1/2WL dipole changes
by only 2 degrees, end to end. Therefore, contrary to
what Roy asserted, the total current does NOT have the
same rotational speed as its components.

Due to the shape of the North American elk's esophagus, even if it
could speak, it could not pronounce the word lasagna.

Cliff Claven

Rotational speed
 

Jim Kelley wrote:

Cecil Moore wrote:
We know that the forward
current and reflected current phasors are rotating in
opposite directions. Kraus and EZNEC say that the
phase angle of the current on a 1/2WL dipole changes
by only 2 degrees, end to end. Therefore, contrary to
what Roy asserted, the total current does NOT have the
same rotational speed as its components.

Due to the shape of the North American elk's esophagus, even if it could
speak, it could not pronounce the word lasagna.

The technical content of your posting is noted. Roy can
easily verify that EZNEC disagrees with his assertion
that "the total current has the same rotational speed
as its components". The total current has hardly any
rotational speed at all, i.e. 2 degrees of rotation
end-to-end in 180 degrees of a 1/2WL dipole.
--
73, Cecil http://www.w5dxp.com

Rotational speed
 

Cecil Moore wrote:

The reason I assumed that is this assertion by W7EL.
"This is the total current. It has magnitude and phase
like any other phasor, and the same rotational speed
as its components."

The total current, as graphed by Kraus and displayed
by EZNEC *DOES NOT* have the same rotational speed as
its components. It is obvious that Roy meant the
same direction when he said "same rotational speed".

EZNEC does not display "rotational speed". The user sets the rotational
speed of all voltage, current, and field phasors by choosing the
frequency, and it remains constant at that rate for all voltages,
currents, and E and H fields. The "direction" of the rotation is always
forward in time; it does not stop in time nor reverse and go backward in
time. This should be obvious to anyone who has taken a beginning course
in circuit analysis.

Roy Lewallen, W7EL

Rotational speed
 

Cecil Moore wrote:


We know that the forward
current and reflected current phasors are rotating in
opposite directions. Kraus and EZNEC say that the
phase angle of the current on a 1/2WL dipole changes
by only 2 degrees, end to end. Therefore, contrary to
what Roy asserted, the total current does NOT have the
same rotational speed as its components.

I'm bothering to respond to Cecil's rantings and diversions only because
he's using EZNEC to support his junk science.

All voltages, currents, E and H fields reported by EZNEC have the same
(phasor) "rotational speed", which is 2 * pi * f radians/second where f
is the frequency chosen by the user. Nothing which EZNEC reports alters
this. The fact that the phase angle of the current is nearly constant
over the length of a dipole indicates that the phase angles of the
elements of current along the wire are nearly the same. This means only
that at any instant, the phasors representing currents along the line
are all pointing in nearly the same direction. All are rotating at
exactly the speed given above.

If one wants to break the current into "components", that is, any number
of currents which linearly sum to produce the total current, the phasors
representing all those components will also rotate at the same rate.

I'd suggest that Cecil go back and review basic phasor theory, but I
know that learning isn't the objective here. It's to sustain the
argument at all costs and any level of banality until everyone else
tires and leaves.

Roy Lewallen, W7EL

Rotational speed
 

Cecil Moore wrote:

The technical content of your posting is noted.

Likewise. Hence the quote.

73 ac6xg

Rotational speed
 

On Apr 26, 4:59 pm, Jim Kelley wrote:
Cecil Moore wrote:
The standing wave current phasor has the "same rotational speed
as its components"???

It has to. Thankfully, rotational speed is the one thing that does
not change between the radio and the antenna.

How can that be when the forward current
phasor and the reflected current phasor are rotating in opposite
directions?

Rotational speed has nothing to do with direction of travel. It has
only to do with the source. Rotational speed is simply omega;
2pi*c/wavelength, or 2pi*f. When waves of equal frequency are
traveling in opposite directions, the RF waveform which comprises the
standing wave (the latter being simply the amplitude envelope of the
superposed traveling waves) has the same wavelength, and thus the same
rotational speed as the traveling waves. Although the position of the
peaks does not vary with time, their amplitude is still a time varying
function. This rudimentary effect is illustrated in the movie he

http://www.kettering.edu/~drussell/D.../superposition....

Mixing on the other hand is the product (rather than the sum) of two
or more waveforms and does in fact yield different rotational speeds.

73, Jim AC6XG


Hey, are you guys using a non-standard definition for "phasor"? I'm
really confused by Jim's posting here. To me, a phasor simply
indicates the amplitude and phase of a sinusoidal component, relative
to some reference phase. I'd be comfortable with a "local definition"
that said the amplitude was relative to a reference amplitude, or was
in dB or dBm or dBuV or the like. But I am NOT comfortable with the
idea that a phasor at a particular point in space rotates in time
unless there is some time-varying thing that causes it to rotate,
maybe like a "trombone" section of line that someone is sliding in and
out. I do expect the phasor that represents a sinusoid propagating on
a transmission line to be a function of distance along the line and of
the frequency of the signal, in that it must rotate 360 degrees for
every one wavelength along the line. (More detail on this below.)

For "phasor" to be a useful concept, you'd better be talking about a
system in which there is a single sinusoidal excitation frequency --
or you better be verrrry careful to define what you mean by your
phasor diagrams.

See, for example, the page in Wikipedia on phasors.

Or else please give me enough info or references so I can straighten
out my thinking about them.

If I'm not mistaken, on a lossless line excited by a source at one end
with a reflective load at the far end such that the amplitude of the
forward wave is a1 and the amplitude of the reflected is a2, then the
phasor representing the forward wave, relative to the source end, will
be
forward phasor = a1*exp(-jx/lambda)
and for the reverse, assuming for convenience that the line is just
the right length so that the reverse is in phase with the generator at
the generator end,
reverse phasor = a2*exp(+jx/lambda)
where x is the distance along the line from the generator, lambda is
the wavelenth in the line, and exp() is e to the power(). Then the
phasor of the whole signal, fwd plus refl, at any point x is
net phasor = a1*exp(-jx/lambda)+a2*exp(+jx/lambda)
exp(jy) can be expanded as cos(y)+j*sin(y), so
net phasor = (a1+a2)*cos(x/lambda)+j*(a2-a1)*sin(x/lambda)

This makes is VERY clear that the phasor changes angle along any line
where a2 does not equal a1; in the special case where a2=a1, then the
phase can only be 0 or 180 degrees all along the line. If you pick a
different reference point (e.g. change the load or line lenght or
frequency in a way that moves the generator away from a point where
the return is in phase with the generator at the generator), then that
just adds a constant phase offset. But also notice that if a2 does
not equal a1, the phasor angle along the line goes through all
possible values, zero to 360 degrees. If a2 is almost equal to a1,
that phase shift occurs relatively quickly along the line, centered on
points where cos(x/lambda) goes to zero. I expect the same to be true
on a resonant antenna; the reflected wave is NOT the same amplitude as
the forward, but is similar, so you'll find places where the phase
change is quick but continuous as you move along the wire--this
assumes that the antenna is long enough that you can find such places.

Cheers,
Tom

Analyzing Stub Matching with Reflection Coefficients
 

Cecil Moore wrote:
Gene Fuller wrote:
Sorry I did not catch the thread redefinition toward the inner
workings of such a device.

Apology accepted. The crux of what we have been discussing
for days, if not weeks, is what does a model of the active,
dynamic volcano of energy, i.e. the source, look like?

Cecil,

In the context of antenna and transmission line matters you have an
interesting definition of "source" for an amateur transmitter. Why
consider the source to be some place after the output conditioning, such
as the output connector, when you can go all the way back to the wall plug?

73,
Gene
W4SZ

Analyzing Stub Matching with Reflection Coefficients
 

Gene, W4SZ wrote:
"Why consider the source to be some place after the output conditioning,
such as the output connector, when one can go all the way back to the
wall plug?"

The wall plug can scarcely be responsible for harmonics on the
trabsmission line and antenna, but the output conditionimg can be
inadequate.

A tank circuit of reasonable Q can be adequate to remove enough
harmonics to make the transmitter a linear source in many cases.

A linear source makes King, Mimno, and Wing`s statement on page 44 of
"Transmission lines, Antennas, and Wave Guides" operative:
"When impedances are conjugately-matched for transmission of power in
one direction, they are conjugately-matched for rower transmission in
the reverse direction, if no power loss occurs in the matching devices."

Best regards, Richard Harrison, KB5WZI

Rotational speed
 

A phasor is a replacement of cos(omega * t + phi) with cos(omega * t +
phi) + j * sin(omega * t + phi) = exp(j * (omega * t + phi)) = exp(j *
omega * t) * exp(j * phi). The first of those quantities is understood
but not generally written in phasor analysis, but is nonetheless an
essential part of the definition of a phasor. This shows that a phasor
is a vector which rotates in the complex plane, with a rotational speed
of omega * t radians/sec. The reason the time-dependent rotational term
is left out when speaking of phasors is that phasor analysis is used
only for systems in which only one frequency is present, as you said.
Therefore, all have the identical multiplying term exp(j * omega * t)
and, basically, they all cancel out in phasor equations. Omega is, of
course, 2 * pi * f.

Cecil regularly confuses the change in phase angle of the phasor with
position, with the rotation of the phasor with time.

A proof of the validity of the replacement of the real cos function with
the complex phasor function, as well as a good description of phasors in
general, is given in Pearson and Maler, _Introductory Circuit Analysis_.
A good graphical illustration and description of a phasor as a rotating
vector can be found in Van Valkenburg, _Network Analysis_. Those are the
only two basic circuit analysis texts I have, but I'm sure the topic is
covered well in just about any other one.

Roy Lewallen, W7EL

K7ITM wrote:

Hey, are you guys using a non-standard definition for "phasor"? I'm
really confused by Jim's posting here. To me, a phasor simply
indicates the amplitude and phase of a sinusoidal component, relative
to some reference phase. I'd be comfortable with a "local definition"
that said the amplitude was relative to a reference amplitude, or was
in dB or dBm or dBuV or the like. But I am NOT comfortable with the
idea that a phasor at a particular point in space rotates in time
unless there is some time-varying thing that causes it to rotate,
maybe like a "trombone" section of line that someone is sliding in and
out. I do expect the phasor that represents a sinusoid propagating on
a transmission line to be a function of distance along the line and of
the frequency of the signal, in that it must rotate 360 degrees for
every one wavelength along the line. (More detail on this below.)

For "phasor" to be a useful concept, you'd better be talking about a
system in which there is a single sinusoidal excitation frequency --
or you better be verrrry careful to define what you mean by your
phasor diagrams.

See, for example, the page in Wikipedia on phasors.

Or else please give me enough info or references so I can straighten
out my thinking about them.

If I'm not mistaken, on a lossless line excited by a source at one end
with a reflective load at the far end such that the amplitude of the
forward wave is a1 and the amplitude of the reflected is a2, then the
phasor representing the forward wave, relative to the source end, will
be
forward phasor = a1*exp(-jx/lambda)
and for the reverse, assuming for convenience that the line is just
the right length so that the reverse is in phase with the generator at
the generator end,
reverse phasor = a2*exp(+jx/lambda)
where x is the distance along the line from the generator, lambda is
the wavelenth in the line, and exp() is e to the power(). Then the
phasor of the whole signal, fwd plus refl, at any point x is
net phasor = a1*exp(-jx/lambda)+a2*exp(+jx/lambda)
exp(jy) can be expanded as cos(y)+j*sin(y), so
net phasor = (a1+a2)*cos(x/lambda)+j*(a2-a1)*sin(x/lambda)

This makes is VERY clear that the phasor changes angle along any line
where a2 does not equal a1; in the special case where a2=a1, then the
phase can only be 0 or 180 degrees all along the line. If you pick a
different reference point (e.g. change the load or line lenght or
frequency in a way that moves the generator away from a point where
the return is in phase with the generator at the generator), then that
just adds a constant phase offset. But also notice that if a2 does
not equal a1, the phasor angle along the line goes through all
possible values, zero to 360 degrees. If a2 is almost equal to a1,
that phase shift occurs relatively quickly along the line, centered on
points where cos(x/lambda) goes to zero. I expect the same to be true
on a resonant antenna; the reflected wave is NOT the same amplitude as
the forward, but is similar, so you'll find places where the phase
change is quick but continuous as you move along the wire--this
assumes that the antenna is long enough that you can find such places.

Cheers,
Tom

Rotational speed
 

Roy Lewallen wrote:
EZNEC does not display "rotational speed". The user sets the rotational
speed of all voltage, current, and field phasors by choosing the
frequency, and it remains constant at that rate for all voltages,
currents, ...

Sorry, that is not true for *total* current. Check it out
yourself. EZNEC says the phase of the total current only
varies ~3 degrees from end to end for a 1/2WL dipole.
Kraus agrees with that.

Here's what you said: "This is the total current. It has
magnitude and phase like any other phasor, and the same
rotational speed as its components."

That is simply a false statement. And because it is
false, your current phase measurements through a loading
coil were invalid. Here's what you said:

"What I measured was a 3.1% reduction in magnitude from input to output,
with no discernible phase shift."

Of course you measured no discernible phase shift since
you were using a current that doesn't change phase. The
current that you used gives us no clue as to the phase
delay through a loading coil.

The phase of the total current is naturally related to
the rotational speed and it is almost unchanging, i.e.
the total current doesn't rotate by more than ~3 degrees.
It certainly does NOT rotate at omega*t.

That is one thing that makes standing-wave current quite
different from traveling wave current. You used standing
wave current to try to measure the phase shift through
a loading coil. Since standing wave current doesn't change
phase by more than ~3 degrees along the entire length of
a 1/2WL dipole, using it to "measure" the phase shift
through a loading coil is invalid.

The reason that the total current phasor doesn't have the
same rotational speed as the forward and reflected currents
is that it is the sum of the forward and reflected currents
which are rotating in opposite directions. The two phase angles
add up to almost zero all along a 1/2WL dipole.
--
73, Cecil http://www.w5dxp.com

Rotational speed
 

On Apr 27, 3:37 pm, Roy Lewallen wrote:
A phasor is a replacement of cos(omega * t + phi) with cos(omega * t +
phi) + j * sin(omega * t + phi) = exp(j * (omega * t + phi)) = exp(j *
omega * t) * exp(j * phi). The first of those quantities is understood
but not generally written in phasor analysis, but is nonetheless an
essential part of the definition of a phasor. This shows that a phasor
is a vector which rotates in the complex plane, with a rotational speed
of omega * t radians/sec. The reason the time-dependent rotational term
is left out when speaking of phasors is that phasor analysis is used
only for systems in which only one frequency is present, as you said.
Therefore, all have the identical multiplying term exp(j * omega * t)
and, basically, they all cancel out in phasor equations. Omega is, of
course, 2 * pi * f.

Cecil regularly confuses the change in phase angle of the phasor with
position, with the rotation of the phasor with time.

A proof of the validity of the replacement of the real cos function with
the complex phasor function, as well as a good description of phasors in
general, is given in Pearson and Maler, _Introductory Circuit Analysis_.
A good graphical illustration and description of a phasor as a rotating
vector can be found in Van Valkenburg, _Network Analysis_. Those are the
only two basic circuit analysis texts I have, but I'm sure the topic is
covered well in just about any other one.

Roy Lewallen, W7EL

OK, noted, but your definition doesn't match what I was taught and
what is in the Wikipedia definition at http://en.wikipedia.org/wiki/Phasor_(electronics).
What I was taught, and what I see at that URL, is that the PHASOR is
ONLY the representation of phase and amplitude--that is, ONLY the
A*exp(j*phi). To me, what you guys are calling a phasor is just a
rotating vector describing the whole signal. To me, the value of
using a phasor representation is that it takes time out of the
picture. See also http://people.clarkson.edu/~svoboda/.../Phasor10.html,
which defines the phasor very clearly as NOT being a function of time
(assuming things are in steady-state). But in my online search, I
also find other sites that, although they don't bother to actually
define the phasor, show it as a rotating vector. Grrrr. I'll try to
remember to check the couple of books I have that would talk about
phasors to see if I'm misrepresenting them, but I'm pretty sure they
are equally explicit in defining a phasor as a representation of ONLY
the phase and magnitude of the sinusoidal signal, and NOT as a vector
that rotates synchronously with the sinewave.

Cheers,
Tom

Rotational speed
 

Roy Lewallen wrote:
All voltages, currents, E and H fields reported by EZNEC have the same
(phasor) "rotational speed", which is 2 * pi * f radians/second where f
is the frequency chosen by the user.

This is false!!! Set a zero load anywhere along a 1/2WL dipole
and check the phase. It will everywhere be within 3 degrees of
zero.

Nothing which EZNEC reports alters
this. The fact that the phase angle of the current is nearly constant
over the length of a dipole indicates that the phase angles of the
elements of current along the wire are nearly the same. This means only
that at any instant, the phasors representing currents along the line
are all pointing in nearly the same direction. All are rotating at
exactly the speed given above.

This contradicts what you said before. You said the *total current*
phasor is rotating. Both Kraus and EZNEC disagree with you. Here's
what you said:

Roy wrote:
"This is the total current. It has magnitude and phase
like any other phasor, and the same rotational speed
as its components."

This is a false statement! And since it is false, it renders
your loading coil phase measurements invalid. The total current
does NOT have the same rotational speed as its components.
The phase of the total current does NOT change through a
loading coil or through a 1/2WL wire.
--
73, Cecil http://www.w5dxp.com

Rotational speed
 

Roy Lewallen wrote in
:

A phasor is a replacement of cos(omega * t + phi) with cos(omega * t +
phi) + j * sin(omega * t + phi) = exp(j * (omega * t + phi)) = exp(j *
omega * t) * exp(j * phi). The first of those quantities is understood
but not generally written in phasor analysis, but is nonetheless an
essential part of the definition of a phasor. This shows that a phasor
is a vector which rotates in the complex plane, with a rotational speed
of omega * t radians/sec. The reason the time-dependent rotational term

Should that be ...of omega radians/sec..., omega*t is the phase
displacement, omega is the phase velocity?

Owen

Rotational speed
 

K7ITM wrote:

OK, noted, but your definition doesn't match what I was taught and
what is in the Wikipedia definition at http://en.wikipedia.org/wiki/Phasor_(electronics).
What I was taught, and what I see at that URL, is that the PHASOR is
ONLY the representation of phase and amplitude--that is, ONLY the
A*exp(j*phi). To me, what you guys are calling a phasor is just a
rotating vector describing the whole signal. To me, the value of
using a phasor representation is that it takes time out of the
picture. See also http://people.clarkson.edu/~svoboda/.../Phasor10.html,
which defines the phasor very clearly as NOT being a function of time
(assuming things are in steady-state). But in my online search, I
also find other sites that, although they don't bother to actually
define the phasor, show it as a rotating vector. Grrrr. I'll try to
remember to check the couple of books I have that would talk about
phasors to see if I'm misrepresenting them, but I'm pretty sure they
are equally explicit in defining a phasor as a representation of ONLY
the phase and magnitude of the sinusoidal signal, and NOT as a vector
that rotates synchronously with the sinewave.

Tom,

I'm sure a lot of people forget the derivation of a phasor after using
it for a while, just as they do so many other things.

Again, a phasor is a complex representation of a real sinusoidal
function and, as such, definitely has a time varying component. That the
component isn't written doesn't mean it's not there. By all means, check
your texts. I'm sure that any decent circuit analysis text has a
serviceable development of the subject.

I always cringe when I see wikipedia quoted as a reference -- I was
referred to an entry regarding transmission lines some time ago, and it
contained some pretty major misconceptions. That leads me to mistrust it
when looking up a topic which I don't have a good grasp of. I don't have
a full understanding of the process by which it's written, but it seems
that all participants in this newsgroup are equally qualified to create
or modify a wikipedia entry. How could that result in a reliable reference?

Roy Lewallen, W7EL

Rotational speed
 

Owen Duffy wrote:
Roy Lewallen wrote in
:

A phasor is a replacement of cos(omega * t + phi) with cos(omega * t +
phi) + j * sin(omega * t + phi) = exp(j * (omega * t + phi)) = exp(j *
omega * t) * exp(j * phi). The first of those quantities is understood
but not generally written in phasor analysis, but is nonetheless an
essential part of the definition of a phasor. This shows that a phasor
is a vector which rotates in the complex plane, with a rotational speed
of omega * t radians/sec. The reason the time-dependent rotational term

Should that be ...of omega radians/sec..., omega*t is the phase
displacement, omega is the phase velocity?

You're right. Thank you for the correction. My apology for the error.

Roy Lewallen, W7EL

Rotational speed
 

K7ITM wrote:
I expect the same to be true
on a resonant antenna; the reflected wave is NOT the same amplitude as
the forward, but is similar, so you'll find places where the phase
change is quick but continuous as you move along the wire--this
assumes that the antenna is long enough that you can find such places.

On a 1/2WL standing wave antenna, the reflected current is
within about 10% of the forward current. I think you will
find that under those conditions, the phase change is NOT
continuous.

The total antenna current reported by EZNEC is the sum of
the forward current and reflected current all up and down
a 1/2WL dipole. With the feedpoint as the 0 deg reference,
EZNEC reports only ~3 degree change between the feedpoint
and the end segment of the dipole. The phase change is
NOT quick and never exceeds ~3 degrees.

A typical forward current at the feedpoint might be
1A @ 0 deg while the reflected current might be
0.9A @ 0 deg. That phase angle is obviously zero.

45 degrees out from the feedpoint, the forward current
might be 0.975A @ -45 deg. The reflected current might
be 0.925A @ 45 deg. Adding those two phasors gives a
phase angle very close to zero. The phase angle does
NOT change quickly - it changes hardly at all.

Kraus agrees. On page 464 of "Antennas for all Applications",
3rd edition, Figure 14-2, he graphs the amplitude and phase
of the current in a 1/2WL dipole. The current phase never
exceeds ~3 degrees over the entire length of the dipole.
The phase change is NOT quick. It is exceedingly slow.

This has to do with how the forward current phasor and the
reflected current phasor adding together to obtain a *constant*
zero degrees of phase in a thin-wire dipole. Kraus shows
both a thin-wire dipole and a dipole where the length to
diameter ratio is 75. The length to diameter ratio of a
75m dipole is in the many thousands, closer to a thin
wire than to 75.
--
73, Cecil http://www.w5dxp.com

Analyzing Stub Matching with Reflection Coefficients
 

Gene Fuller wrote:
In the context of antenna and transmission line matters you have an
interesting definition of "source" for an amateur transmitter. Why
consider the source to be some place after the output conditioning, such
as the output connector, when you can go all the way back to the wall plug?

The RF source is obviously the point where
DC is converted to RF. That's the point
under discussion.
--
73, Cecil http://www.w5dxp.com

Rotational speed
 

On Apr 27, 7:36 pm, K7ITM wrote:
Grrrr. I'll try to
remember to check the couple of books I have that would talk about
phasors to see if I'm misrepresenting them, but I'm pretty sure they
are equally explicit in defining a phasor as a representation of ONLY
the phase and magnitude of the sinusoidal signal, and NOT as a vector
that rotates synchronously with the sinewave.

My recollection is of being introduced to phasors with the study of
electric machines which have real rotating magnetic fields. By
jumping onto the rotor and rotating with those magnetic fields,
solutions became trivial by allowing vector arithmetic on the now
stationary phasors.

....Keith

Rotational speed
 

Roy Lewallen wrote:
Cecil regularly confuses the change in phase angle of the phasor with
position, with the rotation of the phasor with time.

Everyone is wrong except you, huh? The fact still remains
that your following assertion was wrong:

Roy said:
"This is the total current. It has magnitude and phase
like any other phasor, and the same rotational speed
as its components."

Total current on a standing-wave antenna does NOT have
the same rotational speed as its components. It hardly
rotates at all up and down the entire 1/2WL dipole.
EZNEC and Kraus agree with me on that fact. All you
have to do is fire up EZNEC and prove it to yourself.

That means that your and Tom's phase measurements
through a loading coil were invalid. One cannot
use a current with unchanging phase to measure
a phase shift.
--
73, Cecil http://www.w5dxp.com

Rotational speed
 

K7ITM wrote:
I'll try to
remember to check the couple of books I have that would talk about
phasors to see if I'm misrepresenting them, but I'm pretty sure they
are equally explicit in defining a phasor as a representation of ONLY
the phase and magnitude of the sinusoidal signal, and NOT as a vector
that rotates synchronously with the sinewave.

This brings up a point that I need to clarify. All my phasors
are referenced to a phase angle of zero at the feedpoint. Take
a snapshot when the feedpoint phasor is at zero degrees and
then look at all the other phasors up and down the antenna.
I hope that clears up any confusion I may have generated by
not explaining my reference point earlier.
--
73, Cecil http://www.w5dxp.com

Rotational speed
 

Keith Dysart wrote:

My recollection is of being introduced to phasors with the study of
electric machines which have real rotating magnetic fields. By
jumping onto the rotor and rotating with those magnetic fields,
solutions became trivial by allowing vector arithmetic on the now
stationary phasors.

A most excellent description! Thanks for sharing it.

Now if we could just get a certain individual to either stay on the
rotor or the stator and not keep jumping back and forth without telling
anyone or even realizing it himself. . .

Roy Lewallen, W7EL

Rotational speed
 

Cecil Moore wrote:
Total current on a standing-wave antenna does NOT have
the same rotational speed as its components. It hardly
rotates at all up and down the entire 1/2WL dipole.

This is, of course, referenced to the feedpoint signal
at zero degrees. The phase of a traveling wave changes
45 degrees in 45 degrees of wire. The phase of the
standing wave changes no more than a couple of degrees
in 45 degrees of wire. Sorry for any confusion that
might have occurred because I neglected to explain my
reference phasor.
--
73, Cecil http://www.w5dxp.com