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rattus

Senior Member
Who can provide the rest of us a good definition of a "phasor"? I think I know, but I want to hear what others think.
 

iwire

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Location
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ryan_618 said:
Isn't that what the cops hit you with when you have drank too much?

8)

No I think thats a tazer. :wink:

A phasor is what Spock and Kirk carry.

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Rattus

A phasor is a vector drawn to represent a wave, such that the vector sum of several phasors can be used to determine the intensity and phase of the several waves after interference. Phasors are used directly in optics, radio engineering and acoustics. The constant length of the phasor gives the amplitude and the angle it makes with the x-axis gives the phase angle. Because the mathematics of waves frequently carries over to electronics, phasors can be used there in rudimentary circuit analysis of AC circuits. Finally, phasors can be used to describe the motion of an oscillator, with its various properties including projections onto the x and y axes having different physical meanings.

Simple 12th grade physics.

But if your refering to Harmonics then A phasor can be used to model the behavior of a particle in simple harmonic motion, in which case, the y value of the phasor corresponds to the particle's current displacement, and one should imagine the phasor rotating around the origin as the object oscillates. The maximum displacement is given by the phasor's length. If we are provided with the period of rotation (i.e oscillation), and we call the length of the phasor A, then the end of the phasor travels a distance 2πA in time T, so the end of the phasor travels with velocity 2πA / T, which is the maximum speed of the oscillator. Since the maximum velocity occurs when there is no displacement (and so zero phase) so the phasor is completely in the x direction, we can see that the current velocity is given by 2πx / T, where x is the current x value.

But as you probably already know Phasors are most commonly used to visually solve problems of the type "several waves of similar frequency but different phases and amplitudes are interfered at a point, what is the resulting intensity?" To solve this problem, draw one phasor for each of the waves, and then simply perform vector addition on them. The length of the resulting vector is the amplitude of the resulting wave, and its length can be squared to find the intensity. Note that, while the sum of several sine waves is not necessarily another sine wave, the sum of several sine waves of the same frequency is, allowing the resultant phase to be read as the angle of the resultant phasor.

Pretty simple huh?
 

rattus

Senior Member
Ron and 77401,

Thanks for your serious replys. What I am lloking for is a discussion of phasors as used in electric power work.

For example:

How many ways can a phasor be represented?

Provide examples of fixed and rotating phasors.

Provide a phasor diagram of a 120/208 wye system. This confuses a lot of people.

Provide examples of phasor analysis, that is, Ohm's law with impedance instead of resistance.
 

iwire

Moderator
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Location
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rattus said:
Thanks for your serious replys. What I am lloking for is a discussion of phasors as used in electric power work.

Life's to short not to have some fun. I won't interrupt your serious discussion anymore. :)
 

eric stromberg

Senior Member
Location
Texas
Complex numbers are a combination of "real" numbers and "imaginary" numbers. Personally, i'd like to go back in time and have "imaginary" changed to a more meaningful name. I mean, how are you supposed to stand in front of a group of students and say "Today, we are going to learn about 'imaginary' numbers." How is the class supposed to take you seriously?

In any event, "imaginary" numbers are very useful. With them, we can represent time as a distance. Consider the three phases in an electrical circuit. All the phases are sinusoids, but they are displaced in time from one another. This comes from the position of the windings in the generator. Let's say that it takes 1/60 of a second for the generator rotor to make one rotation. Let's imagine phase A winding starting at the top of the generator, phase B winding starting 1/3 the way round and phase C winding starting 2/3 the way round. Phase A sinusoid starts, then 1/180th of a second later phase B sinusoid starts, then 1/180th of a second later phase C sinusoid starts.

The timing relationships can not be handled adequately by simply using real numbers. The 'imaginary' numbers, however, allow us to show these phase displacements as simple distances on paper. Because they show relative phasing, they are called 'phasors.' 8)

Eric Stromberg, P.E.
 

rattus

Senior Member
Zog,

The word "vector" is often used instead of "phasor". The angle of a vector indicates a direction in space. The angle of a phasor indicates time. At 60hz, 360 degrees represents 16.7milliseconds. So phasors are not true vectors; let's call them pseudovectors. The math is the same though.
 

charlie b

Moderator
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Location
Lockport, IL
Occupation
Retired Electrical Engineer
A vector is a line segment that has both length and direction (i.e., the direction is indicated by an arrow head). You can use a vector to model anything that has both of those characteristics. For example, you can use a vector to model the distance and direction you would have to walk, to get from your house to the bus stop.

A phasor is a vector that has been used to model a physical parameter that varies like a sine wave. All phasors are vectors, just like all cats are animals, and the reverse is not true in either case.

For example, we use phasors to model currents and voltages. The length of the phasor can represent the peak value of a voltage, though we usually have it represent the RMS value. The direction (i.e., angle with respect to the horizontal) can represent the phase angle of one voltage, as compared to another. For example, in a balanced 3-phase system, I would draw three rays of equal length, with 120 degrees between any two. I would lay the first one out horizontally on the paper, pointing to the right, and call it "Voltage of Phase A." The ray pointing down and to the left would be the "Voltage of Phase B," and the one pointing up and to the left would be "Voltage of Phase C." The sequence can be visualized by imagining the three rays spinning in a circle around the center point. The spin is counter-clockwise. So if you stand off to the right of the diagram, you will see the three rays pass by you in the sequence A, then B, then C, then A, and so forth.

You can model an unbalanced 3-phase system by having different lengths for the three phasors, and by having the angles between them be something other than 120 degrees. However, you cannot use phasor diagrams to model something that is not a sine wave, or for which all parameters do not have the same, constant frequency. You can't model harmonics with phasors, except by having each harmonic (i.e., the fundamental frequency, the second harmonic, the third harmonic, etc.) in its own diagram.
 
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