crossman
Senior Member
- Location
- Southeast Texas
I am just now realizing it, but there is a difference between a vector and a phasor. Would someone give me the "idiot's guide" view of this?
Thanks!
Thanks!
Vectors vs Phasors
- Thread starter crossman
- Start date
- Status
ron
Senior Member
- Location
- New York, 40.7514,-73.9925
Re: Vectors vs Phasors
When I've used the term "phaser", it could have been substituted with the word "vector". There maybe some specific instances for non-steady state, or multiple frequency applications where the words take on different definitions, but I understand both to contain a magnitude and direction.
What is the application is which you're hearing the term used?
[ January 31, 2005, 12:21 PM: Message edited by: ron ]
When I've used the term "phaser", it could have been substituted with the word "vector". There maybe some specific instances for non-steady state, or multiple frequency applications where the words take on different definitions, but I understand both to contain a magnitude and direction.
What is the application is which you're hearing the term used?
[ January 31, 2005, 12:21 PM: Message edited by: ron ]
- Location
- Mission Viejo, CA
- Occupation
- Professional Electrical Engineer
Re: Vectors vs Phasors
According to IEEE Dictionary a ?phasor is: A complex number expressing the magnitude and phase of a time-varying quantity. Unless otherwise specified, it is used only within the context of steady-state alternating linear systems.
(Read this as the mathematical representation of a rotating vector)
According to the Star Trek dictionary a ?phaser? is a device for zapping Klingons.
Edited to correct spelling "Star Trek"
[ January 31, 2005, 12:46 PM: Message edited by: rbalex ]
According to IEEE Dictionary a ?phasor is: A complex number expressing the magnitude and phase of a time-varying quantity. Unless otherwise specified, it is used only within the context of steady-state alternating linear systems.
(Read this as the mathematical representation of a rotating vector)
According to the Star Trek dictionary a ?phaser? is a device for zapping Klingons.
Edited to correct spelling "Star Trek"
[ January 31, 2005, 12:46 PM: Message edited by: rbalex ]
Ed MacLaren
Senior Member
Re: Vectors vs Phasors
The majority of the sources that I checked seem to refer to "phasor diagrams" and "vector calculations", while some use the terms interchangably. (Is that a word? )
Ed
The majority of the sources that I checked seem to refer to "phasor diagrams" and "vector calculations", while some use the terms interchangably. (Is that a word?
)Ed
jtester
Senior Member
- Location
- Las Cruces N.M.
Re: Vectors vs Phasors
While they are often usually used interchangeably, I always understood that a vector was a line with a magnitude and a direction, where a phasor was a rotating vector, one with a magnitude and a changing direction.
Jim T
While they are often usually used interchangeably, I always understood that a vector was a line with a magnitude and a direction, where a phasor was a rotating vector, one with a magnitude and a changing direction.
Jim T
Re: Vectors vs Phasors
Vectors have a direction - north, south, up, etc. But I would refrain from using the term "direction" with phasors. Most phasors are considered to be rotating with time. So they don't have a "direction". When we draw them, we are drawing them for one instant in time. But we don't really care if they point northwest, or southeast. What we do care about is that they lead or lag our reference phasor by x number of degrees.
I can't think of any case where the math would be different for vectors or phasors (as long as all the phasors are the same frequency). In fact, I think we could always use a vector to represent a phasor at one instant in time.
Another small difference, vectors are drawn in a real coordinate system, where phasors are drawn in the complex plane.
Steve
Vectors have a direction - north, south, up, etc. But I would refrain from using the term "direction" with phasors. Most phasors are considered to be rotating with time. So they don't have a "direction". When we draw them, we are drawing them for one instant in time. But we don't really care if they point northwest, or southeast. What we do care about is that they lead or lag our reference phasor by x number of degrees.
I can't think of any case where the math would be different for vectors or phasors (as long as all the phasors are the same frequency). In fact, I think we could always use a vector to represent a phasor at one instant in time.
Another small difference, vectors are drawn in a real coordinate system, where phasors are drawn in the complex plane.
Steve
- Location
- Lockport, IL
- Occupation
- Semi-Retired Electrical Engineer
Re: Vectors vs Phasors
Think of a vector as being an arrow. It has a beginning point, and heads out in some direction. It does not end in a point, but rather in an arrow head. To describe the vector, you need two things: its length and its direction. The exact location of the beginning point is not important. But once you have the beginning point, you have to go in the given direction for the given distance to find the arrow head.
For example, draw an arrow on a sheet of paper, making it exactly one inch long, and having it point exactly towards the right hand edge of the sheet. Now draw another arrow on the same sheet, also making it exactly one inch long, and having it point exactly towards the right hand edge of the sheet. How many vectors do you see? Here?s a hint: the answer is not ?two.? There exists only one vector that meets the description I gave above. What you see on your paper are two representations of that one and only vector. Thus, a vector is really an abstract concept, but then so are the numbers 1, 2, 3, and any others you care to name. You can point to ?one apple,? but you cannot point to ?one? itself. It is the same with vectors.
A phasor is an engineering tool (actually, a mathematical tool, but we engineers have stolen it for our own purposes). All such phasors are vectors; each has a length and a direction. We chose the length to represent a physical quantity (such as the number of volts from line to line). We chose a direction to represent an angle (such as the angle between voltage and current). This tool allows us to perform calculations in a far, far simpler way than would be possible using trigonometry.
One of the benefits of this tool comes from our ability to represent differences between two voltages (like Phase A to Ground versus Phase B to Ground), and the differences between a voltage and a current. If you look at a phasor diagram (basically a collection of arrows representing a bunch of voltages and a bunch of currents), and imagine it spinning slowly counterclockwise around the center point, and watch each arrow spin past the horizontal line that goes toward the right edge of the paper, you will see the phase sequence (i.e., Phase A voltage crosses first, then Phase B voltage, then Phase C voltage).
Think of a vector as being an arrow. It has a beginning point, and heads out in some direction. It does not end in a point, but rather in an arrow head. To describe the vector, you need two things: its length and its direction. The exact location of the beginning point is not important. But once you have the beginning point, you have to go in the given direction for the given distance to find the arrow head.
For example, draw an arrow on a sheet of paper, making it exactly one inch long, and having it point exactly towards the right hand edge of the sheet. Now draw another arrow on the same sheet, also making it exactly one inch long, and having it point exactly towards the right hand edge of the sheet. How many vectors do you see? Here?s a hint: the answer is not ?two.? There exists only one vector that meets the description I gave above. What you see on your paper are two representations of that one and only vector. Thus, a vector is really an abstract concept, but then so are the numbers 1, 2, 3, and any others you care to name. You can point to ?one apple,? but you cannot point to ?one? itself. It is the same with vectors.
A phasor is an engineering tool (actually, a mathematical tool, but we engineers have stolen it for our own purposes). All such phasors are vectors; each has a length and a direction. We chose the length to represent a physical quantity (such as the number of volts from line to line). We chose a direction to represent an angle (such as the angle between voltage and current). This tool allows us to perform calculations in a far, far simpler way than would be possible using trigonometry.
One of the benefits of this tool comes from our ability to represent differences between two voltages (like Phase A to Ground versus Phase B to Ground), and the differences between a voltage and a current. If you look at a phasor diagram (basically a collection of arrows representing a bunch of voltages and a bunch of currents), and imagine it spinning slowly counterclockwise around the center point, and watch each arrow spin past the horizontal line that goes toward the right edge of the paper, you will see the phase sequence (i.e., Phase A voltage crosses first, then Phase B voltage, then Phase C voltage).
crossman
Senior Member
- Location
- Southeast Texas
Re: Vectors vs Phasors
I found the most terrific animated gif file that tells the story! And it is right what I was thinking, I just hadn't made the connection in my head.
Is it okay to link an image from another website on this forum? Or should I just post the link itself?
I found the most terrific animated gif file that tells the story! And it is right what I was thinking, I just hadn't made the connection in my head.
Is it okay to link an image from another website on this forum? Or should I just post the link itself?
Re: Vectors vs Phasors
It is my understanding that a phasor is the polar representation of a vector as a function of time, that is:
e^^jwt = sin(wt) + jcos(wt)
Since it is a function of time, it does rotate, but is not used in time domain analysis which has no provision for complex numbers. And, steady state analyses have no provision for time.
It is my understanding that a phasor is the polar representation of a vector as a function of time, that is:
e^^jwt = sin(wt) + jcos(wt)
Since it is a function of time, it does rotate, but is not used in time domain analysis which has no provision for complex numbers. And, steady state analyses have no provision for time.
crossman
Senior Member
- Location
- Southeast Texas
Re: Vectors vs Phasors
The link below is excellent.
Explanation of Phasors
Here is the animated gif from that website:
The blue line is a phasor that rotates in time, like the winding in a generator rotates in a generator stator. The red line is the voltage vector. Notice that it is either pointing to the left, pointing to the right, or zero. The voltage itself as a physical quantity never has an actual angle (or you could say 0 or 180 degrees). It is either pointing left, or pointing right.
The red line could also represent a current. ?As for current, think of the x-axis in the animation as the wire. The current alternates in direction and in magnitude but always on the same line.
Voltage phasors and current phasors can certainly have an angle between them, anywhere from +90 to -90 degrees. The vectors of the current and voltage have only two choices. They can both point the same way, or they can point opposite ways.
Very cool stuff.
Now, if the source voltage phasor is sitting on the 45 degree line, the projected voltage is the RMS or effective voltage. (effective voltage = peak voltage x .707 = peak voltage x sin45)
So, phasors do not represent the actual voltage and current vectors directly. The phasor "projections" onto the x-axis are the vectors. And they are always either pointing left or pointing right.
[ January 31, 2005, 02:06 PM: Message edited by: crossman ]
The link below is excellent.
Explanation of Phasors
Here is the animated gif from that website:
The blue line is a phasor that rotates in time, like the winding in a generator rotates in a generator stator. The red line is the voltage vector. Notice that it is either pointing to the left, pointing to the right, or zero. The voltage itself as a physical quantity never has an actual angle (or you could say 0 or 180 degrees). It is either pointing left, or pointing right.
The red line could also represent a current. ?As for current, think of the x-axis in the animation as the wire. The current alternates in direction and in magnitude but always on the same line.
Voltage phasors and current phasors can certainly have an angle between them, anywhere from +90 to -90 degrees. The vectors of the current and voltage have only two choices. They can both point the same way, or they can point opposite ways.
Very cool stuff.
Now, if the source voltage phasor is sitting on the 45 degree line, the projected voltage is the RMS or effective voltage. (effective voltage = peak voltage x .707 = peak voltage x sin45)
So, phasors do not represent the actual voltage and current vectors directly. The phasor "projections" onto the x-axis are the vectors. And they are always either pointing left or pointing right.
[ January 31, 2005, 02:06 PM: Message edited by: crossman ]
crossman
Senior Member
- Location
- Southeast Texas
Re: Vectors vs Phasors
Here is another link for phasors:
another phasor link
This one does not show the projected voltage and current vectors though. It would be instructional if they did.
Here is another link for phasors:
another phasor link
This one does not show the projected voltage and current vectors though. It would be instructional if they did.
Re: Vectors vs Phasors
Crossman,
Neat little diagram. Let me explain it this way. The length of the blue line represents the magnitude of an AC voltage (or current). The projection onto the x-axis (the real axis) represents the instantaneous voltage (or current)as a function of time, that is v(t) or i(t).
But the blue line is the phasor because it has a magnitude and a direction. The projections onto the x and y axis are components of the phasor. In this example, the imaginary component has no meaning and is omitted.
Now your observation about RMS is interesting, but we should remember that the RMS factor has been developed without phasors.
Crossman,
Neat little diagram. Let me explain it this way. The length of the blue line represents the magnitude of an AC voltage (or current). The projection onto the x-axis (the real axis) represents the instantaneous voltage (or current)as a function of time, that is v(t) or i(t).
But the blue line is the phasor because it has a magnitude and a direction. The projections onto the x and y axis are components of the phasor. In this example, the imaginary component has no meaning and is omitted.
Now your observation about RMS is interesting, but we should remember that the RMS factor has been developed without phasors.
Re: Vectors vs Phasors
Imagine the blue phasor is our voltage:
V*e^jwt
If that voltage is applied to a linear AC circuit with passive elements, the current will also be sinusoidal, and can be represented by the phasor:
I*e^jwt+x
where x is the phase angle of the current with respect to the impedence.
It is easy to imagine the current phasor rotating with the voltage phasor, maybe lagging it by 30 deg. for example. And it is easy to imagine the projection of the real current onto the x axis.
If you imagine the two phasors rotating in sync, it is obvious that the current and voltage are related by a simple function.
If we take the voltage phasor, and divide by the current phasor, we get:
(V*e^jwt )/(I*e^jwt+x) = (V/I)e^(jwt-(jwt+x))
=(V/I)e^(-x)
Notice that this phasor doesn't rotate (the jwt has canceled out). It only has a magnitude and a phase angle.
Some are claiming we can NOT call that phasor impedence
Imagine the blue phasor is our voltage:
V*e^jwt
If that voltage is applied to a linear AC circuit with passive elements, the current will also be sinusoidal, and can be represented by the phasor:
I*e^jwt+x
where x is the phase angle of the current with respect to the impedence.
It is easy to imagine the current phasor rotating with the voltage phasor, maybe lagging it by 30 deg. for example. And it is easy to imagine the projection of the real current onto the x axis.
If you imagine the two phasors rotating in sync, it is obvious that the current and voltage are related by a simple function.
If we take the voltage phasor, and divide by the current phasor, we get:
(V*e^jwt )/(I*e^jwt+x) = (V/I)e^(jwt-(jwt+x))
=(V/I)e^(-x)
Notice that this phasor doesn't rotate (the jwt has canceled out). It only has a magnitude and a phase angle.
Some are claiming we can NOT call that phasor impedence
Re: Vectors vs Phasors
First, V and I are peak values, not RMS although in this case, the magnitude of Z is correct.
Second, your expression for I is wrong. It should be,
I*e^j(wt +x)
Then your result would have been,
(V/I)e^-jx = (V/I)(sin(-x) + j*cos(-x))
Which can be considered the complex form of impedance, but it is not Z @ -x.
Furthermore, you cannot divide v(t) by i(t) in the time domain because the quotient would swing between +/- infinity if there is any phase angle.
My contention is that phasors, impedance, RMS, and complex numbers cannot be used in time domain analysis. This example is not time domain analysis because it introduces complex numbers.
Two of my genius friends have agreed with me on this.
Now if you had done this:
(Vrms @ 0)/(Irms @ x), that would yield Z @ -x, which indeed is an impedance.
Furthermore, the phase angle of the current is relative to the voltage, not the impedance.
Rattus
[ February 03, 2005, 04:08 PM: Message edited by: rattus ]
Steve, there is something wrong here:Originally posted by steve66:
Imagine the blue phasor is our voltage:
V*e^jwt
If that voltage is applied to a linear AC circuit with passive elements, the current will also be sinusoidal, and can be represented by the phasor:
I*e^jwt+x
where x is the phase angle of the current with respect to the impedence.
It is easy to imagine the current phasor rotating with the voltage phasor, maybe lagging it by 30 deg. for example. And it is easy to imagine the projection of the real current onto the x axis.
If you imagine the two phasors rotating in sync, it is obvious that the current and voltage are related by a simple function.
If we take the voltage phasor, and divide by the current phasor, we get:
(V*e^jwt )/(I*e^jwt+x) = (V/I)e^(jwt-(jwt+x))
=(V/I)e^(-x)
Notice that this phasor doesn't rotate (the jwt has canceled out). It only has a magnitude and a phase angle.
Some are claiming we can NOT call that phasor impedence
First, V and I are peak values, not RMS although in this case, the magnitude of Z is correct.
Second, your expression for I is wrong. It should be,
I*e^j(wt +x)
Then your result would have been,
(V/I)e^-jx = (V/I)(sin(-x) + j*cos(-x))
Which can be considered the complex form of impedance, but it is not Z @ -x.
Furthermore, you cannot divide v(t) by i(t) in the time domain because the quotient would swing between +/- infinity if there is any phase angle.
My contention is that phasors, impedance, RMS, and complex numbers cannot be used in time domain analysis. This example is not time domain analysis because it introduces complex numbers.
Two of my genius friends have agreed with me on this.
Now if you had done this:
(Vrms @ 0)/(Irms @ x), that would yield Z @ -x, which indeed is an impedance.
Furthermore, the phase angle of the current is relative to the voltage, not the impedance.
Rattus
[ February 03, 2005, 04:08 PM: Message edited by: rattus ]
crossman
Senior Member
- Location
- Southeast Texas
Re: Vectors vs Phasors
Rattus said: My contention is that phasors, impedance, RMS, and complex numbers cannot be used in time domain analysis.
I agree and I am assuming that Power factor, vars, volt-amps, and reactance as defined for use with AC sine wave voltages are RMS quantities. Also, many of the assumptions we make for RMS quantities cannot be applied in instantaneous calculations.
Rattus said: My contention is that phasors, impedance, RMS, and complex numbers cannot be used in time domain analysis.
I agree and I am assuming that Power factor, vars, volt-amps, and reactance as defined for use with AC sine wave voltages are RMS quantities. Also, many of the assumptions we make for RMS quantities cannot be applied in instantaneous calculations.
Ed MacLaren
Senior Member
Re: Vectors vs Phasors
Ed
IMO the term RMS can only be used to describe a value that varies in magnitude and alternates in polarity, namely, AC voltage or current.
Ed
Ed MacLaren
Senior Member
Re: Vectors vs Phasors
Ed
[ February 03, 2005, 06:55 PM: Message edited by: Ed MacLaren ]
Right, that's the term I should have used.
I've never seen it used for DC. The term "Average Value" is used for the pulsating DC output of a rectifier.
Ed
[ February 03, 2005, 06:55 PM: Message edited by: Ed MacLaren ]
Re: Vectors vs Phasors
Ed,
For example, one could compute the RMS value of a full wave rectified single phase voltage. It would be 0.707 * Vp. It could be applied to a resistive load, but would not work with impedance. Why? Because reactance and impedance are based on pure sinusoids and cannot be used with any other waveforms.
Of course you already knew that!
[ February 03, 2005, 07:42 PM: Message edited by: rattus ]
Ed,
For example, one could compute the RMS value of a full wave rectified single phase voltage. It would be 0.707 * Vp. It could be applied to a resistive load, but would not work with impedance. Why? Because reactance and impedance are based on pure sinusoids and cannot be used with any other waveforms.
Of course you already knew that!
[ February 03, 2005, 07:42 PM: Message edited by: rattus ]
- Status