On Apr 27, 6:39 pm, K7ITM wrote:
On Apr 27, 4:01 pm, Roy Lewallen wrote:



K7ITM wrote:

OK, noted, but your definition doesn't match what I was taught and
what is in the Wikipedia definition athttp://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 alsohttp://people.clarkson.edu/~svoboda/eta/phasors/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

Hi Roy,

Well, I did not forget the derivation. In Balabanian, "Fundamentals
of Circuit Theory," (a book I have but didn't actually study from) he
uses "sinor" instead of "phasor" but says they are the same, then in a
convoluted way gets around to saying that it's just the phase and
magnitude, and not the real(exp(jwt)) part. Smith, "Circuits,
Devices, and Systems," (most likely the book from which I learned
about phasors) is much clearer about it. Under "Phasor
Representation" in my edition,

"If an instantaneous voltage is described by a sinusoidal function of
time such as
v(t) = V cos (wt + theta)
then v(t) can be interpreted as the "real part of" a complex function
or
v(t) = Re {V exp[j*(wt + theta)]} = Re
{[V*exp(j*theta)]*[exp(j*wt)]} (eqn 3-18)
In the second form of eqn 3-18, the complex function in braces is
separated into two parts; the first is a complex constant, the second
is a function of tiem which implies rotation in the complex plane.
The FIRST PART we DEFINE [Tom's emphasis...] as the phasor (bold) V (/
bold), where
(bold) V (/bold) = V*exp(j*theta)
...
The phasor V is called a "transform" of the voltage v(t); it is
obtained by transforming a function fo time into a complex constant
which retains the essential information. ... "

OK, so your definition is different from mine. So far, I've found two
actual definitions of the phasor on-line, and both agree with my books
and my own useage. But if it's common useage to consider a phasor to
be a rotating vector, I'll defer to that at least in this discussion.
So far, though, I haven't found a reason to give up my definition of a
phasor. ;-)

Cheers,
Tom

More on this:

First, I agree with Mike's usage; if your phase reference is at one
frequency and you're looking at a signal at a different frequency with
respect to your reference, the phasor representing that different
frequency will rotate at a rate equal to the difference in the
frequencies: counterclockwise if the second frequency is higher, I
suppose, since the second frequency's phase gets further and further
ahead of the reference as time goes on.

Second, I did a google search for "phasor definition" and investigated
a whole bunch of sites. Some didn't have anything worth noting. I
made notes of 18 sites. Nine of them had strict mathematical
definitions. Every one of the mathematical definitions agreed that a
phasor contains only amplitude, and phase relative to a reference, and
has the exp(wt) part stripped out. Some had a full development of the
concept, and some only stated the end result, but in the result they
all agreed. In the nine narrative definitions/descriptions, five were
clear that a phasor contains only phase and amplitued and not time
information--not a rotating vector with respect to time (unless it's
representing a second frequency, presumably). Two of the narratives
specifically said that a phasor is a time-rotating vector. The others
were at best ambiguous, or simply didn't say.

To me, the whole idea of using phasors is to remove the time-varying
quantity from discussion, so you can concentrate on phase and
magnitude. As I showed in my first posting in this "subthread,"
phasors (as phase and magnitude only) very quickly lead you to an
accurate description of what happens with forward and reflected waves
on a transmission line, with respect to the amplitude and phase of the
net signal at any point along the line. The phasor representation
clearly shows that with waves of the same frequency of nearly equal
amplitude in each direction, you get relatively long stretches along
the line where the phase changes only slightly, and then a region
where it changes very quickly. That's not something I can easily see
in just thinking about the waves as time-varying quantites, but as
phasors, the result is immediately obvious to me. There are plenty of
other similar examples.

I'm very curious now to see exactly what Pearson & Maler and Van
Valkenburg say in their texts. Are they clear with a mathematical
definition, or do they end up just using words that can be interpreted
in different ways? So far, I have investigated eleven references that
define a phasor mathematically (the nine mentioned here plus the two
college texts mentioned before), and all agree that it doesn't contain
the exp(wt) component: in a linear system at steady-state excited by
a single frequency, a phasor representing a quantity at a single point
in space does not rotate.

I suppose I get a little carried away on things like this, but to me
it's important that we're communicating with words for which we share
a single definition, not words that mean distinctly different things
to different people.

Cheers,
Tom