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