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#451
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Rotational speed
On Apr 27, 9:22 pm, Cecil Moore wrote:
Owen Duffy wrote: Isn't hopping onto the rotor (assuming synchronous speed) to make your observations called moving from the time domain to the frequency domain, and all the mathematical shortcuts are only valid if all quantities share the same angular velocity (or frequency), implying sinusoidal waveform. Ever wonder which direction, clockwise or counter-clockwise, a standing-wave phasor is rotating? Clockwise, of course, by convention. Always look at the end of the machine that lets you draw your phasor diagram clockwise. This way, when a first phasor is clockwise from a second, the first phasor occurs first when you convert back to time. ....Keith |
#452
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Rotational speed
Mike Monett wrote:
So a phasor can be stationary or rotating depending on its relation to something else in the discussion. This is the way I have been assuming that everyone was thinking. I'm amazed at all the different concepts. -- 73, Cecil http://www.w5dxp.com |
#453
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Rotational speed
Keith Dysart wrote:
Which suggests that if there are two directions of rotation, phasors don't help much with the solution. By conventional definition, coherent phasors traveling in opposite directions are rotating in different directions, one clockwise and one counter-clockwise. Adding a forward wave and a reflected wave of equal amplitude results in: E = Eot[sin(kx+wt) + sin(kx-wt)] By convention, the forward +wt wave rotates counter- clockwise as the angle increases in the + direction. By convention, the reflected -wt wave rotates clockwise as the angle increases in the - direction. The standing wave equation becomes: E(x,t) = 2*Eot*sin(kx)*cos(wt) Which direction is the standing-wave phasor rotating? -- 73, Cecil http://www.w5dxp.com |
#454
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Rotational speed
Keith Dysart wrote:
On Apr 27, 9:22 pm, Cecil Moore wrote: Owen Duffy wrote: Isn't hopping onto the rotor (assuming synchronous speed) to make your observations called moving from the time domain to the frequency domain, and all the mathematical shortcuts are only valid if all quantities share the same angular velocity (or frequency), implying sinusoidal waveform. Ever wonder which direction, clockwise or counter-clockwise, a standing-wave phasor is rotating? Clockwise, of course, by convention. Always look at the end of the machine that lets you draw your phasor diagram clockwise. The equation for a standing wave, E(x,t) = 2*Eot*sin(kx)*cos(wt) would have an identical value if it were written, E(x,t) = 2*Eot*sin(kx)*cos(-wt) Thus, a standing wave phasor can be considered to be rotating either clockwise or counter-clockwise. -- 73, Cecil http://www.w5dxp.com |
#455
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Rotational speed
On Apr 27, 10:25 pm, Cecil Moore wrote:
Keith Dysart wrote: Which suggests that if there are two directions of rotation, phasors don't help much with the solution. By conventional definition, coherent phasors traveling in opposite directions are rotating in different directions, one clockwise and one counter-clockwise. It would, I think, be more precise to say that the vectors are rotating. When you change your point of view by rotating the frame of reference along with the vectors, those vectors become phasors which do not rotate. Although a little looseness in the language easily leads to saying that they do. Adding a forward wave and a reflected wave of equal amplitude results in: E = Eot[sin(kx+wt) + sin(kx-wt)] By convention, the forward +wt wave rotates counter- clockwise as the angle increases in the + direction. I agree. I should have said counter-clockwise in my other post. Once you jump on the rotor to rotate counter- clockwise with the vectors, the rest of the world (e.g. the stator) appears to be going clockwise around you. By convention, the reflected -wt wave rotates clockwise as the angle increases in the - direction. The standing wave equation becomes: E(x,t) = 2*Eot*sin(kx)*cos(wt) Which direction is the standing-wave phasor rotating? Which I will try to answer in a response to your next post. ....Keith |
#456
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Rotational speed
On Apr 27, 10:32 pm, Cecil Moore wrote:
Keith Dysart wrote: On Apr 27, 9:22 pm, Cecil Moore wrote: Owen Duffy wrote: Isn't hopping onto the rotor (assuming synchronous speed) to make your observations called moving from the time domain to the frequency domain, and all the mathematical shortcuts are only valid if all quantities share the same angular velocity (or frequency), implying sinusoidal waveform. Ever wonder which direction, clockwise or counter-clockwise, a standing-wave phasor is rotating? Clockwise, of course, by convention. Always look at the end of the machine that lets you draw your phasor diagram clockwise. The equation for a standing wave, E(x,t) = 2*Eot*sin(kx)*cos(wt) would have an identical value if it were written, E(x,t) = 2*Eot*sin(kx)*cos(-wt) Thus, a standing wave phasor can be considered to be rotating either clockwise or counter-clockwise. I suggest that the solution to this ambiguity is to do the same analysis for the current, which should be found to be 90 degrees shifted from the voltage. The real current is either leading or lagging the voltage. Rotate the frame of reference in the direction that will cause a lagging current to appear counter-clockwise from the voltage and a leading current to appear clockwise from the voltage. This is all convention, of course. You can rotate the frame of reference in either direction, you just need to remember which direction on the graph represents earlier time and which represents later. Physically, it is just a question of which end of the rotor you climb on to. ....Keith |
#457
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Rotational speed
Keith Dysart wrote:
I suggest that the solution to this ambiguity is to do the same analysis for the current, which should be found to be 90 degrees shifted from the voltage. The real current is either leading or lagging the voltage. Rotate the frame of reference in the direction that will cause a lagging current to appear counter-clockwise from the voltage and a leading current to appear clockwise from the voltage. This just illustrates how artificial standing waves are. For 1/4WL the standing-wave current leads the standing- wave voltage by 90 degrees then suddenly undergoes a step function to lag the standing-wave voltage by 90 degrees for the next 1/4WL. In any case, the point is whether standing-wave current can be used to measure the phase shift through a loading coil. EZNEC indicates that it cannot. Kraus indicates that it cannot. Yet the people who did exactly that continue to report the results as valid. -- 73, Cecil http://www.w5dxp.com |
#458
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Rotational speed
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 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 |
#459
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Rotational speed
K7ITM wrote:
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. Yes, that was what I was doing. I think that is what EZNEC does. I think that is what Kraus does. It seems to be the key in determining what phase shift occurs through a 75m loading coil. Incidentally, one of the best treatments of this subject, IMO, is in "Optics", by Hecht. 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. Apparently, someone needs to get carried away in order to get this problem resolved. A measured zero phase shift through a loading coil using a current that doesn't change phase is meaningless and misleading. -- 73, Cecil http://www.w5dxp.com |
#460
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Rotational speed
On Apr 28, 8:54 am, Cecil Moore wrote:
This just illustrates how artificial standing waves are. You have hit the nail on the head here. In another post you provided two expressions for the spatial and temporal distribution of voltage on the line... A) E(x,t) = Eot[sin(kx+wt) + sin(kx-wt)] B) E(x,t) = 2*Eot*sin(kx)*cos(wt) There are an infinite number. Three immediately come to mind... C) E(x,t) = expressed as an exponental D) E(x,t) = expressed as a differential equation E) expression A) can be re-expressed as an infinite sum keeping track of all the individual reflections. All of these accurately yield the correct E(x,t) and there are similar expressions which correctly yield I(x,t). In the same sense that B) (called by you the standing wave expression) is artificial, they are all equally artificial. And yet they each have their place for solving problems since they all, in the end, yield the correct E(x,t), the only thing that actually exists. For reasons hard to fathom, you have latched on to A) as being THE TRUTH, though it really lacks any features to distinguish it from the rest. D) is arguably a much better choice for truth since it will handle signals other than sinusoidal. As said before, you would find it valuable to let go of A) as THE TRUTH, since it would permit you to solve real world problems that you currently refuse to solve because you believe the technique for solution conflicts with A) as TRUTH. ....Keith |
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