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

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

Cecil Moore wrote:

The technical content of your posting is noted.

Likewise. Hence the quote.

73 ac6xg

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

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

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

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

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

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

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