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

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

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

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

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

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

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

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

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

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