Phasor Concept
Review
A Inc.
Phasor Concept Review
Phasor for periodic i(t) or v(t) signals
Project the tip of the red arrow
onto the “orange” line and mark
the spot with a red dot.
-1.0
1.0
A Inc.
Phasor Concept Review
Phasor for periodic i(t) or v(t) signals
Project the tip of the red arrow
onto the “orange” line and mark
the spot with a red dot.
Mentally rotate the red line segment
in a counter clockwise manner.
-1.0
1.0
A Inc.
Phasor Concept Review
Phasor for periodic i(t) or v(t) signals
Project the tip of the red arrow
onto the “orange” line and mark
the spot with a red dot.
Mentally rotate the red line segment
in a counter clockwise manner.
As you visualize the phasor rotating counter
clockwise, each location where the projection of the
rotating line contacts the dotted circle is assigned a
cosine value. Each of these cosine values is
represented on the orange horizontal axis.
-1.0
1.0
A Inc.
Phasor Concept Review
Phasor for periodic i(t) or v(t) signals
time
Project the tip of the red arrow
onto the “orange” line and mark
the spot with a red dot.
Mentally rotate the red line segment
in a counter clockwise manner.
As you visualize the phasor rotating counter
clockwise, each location where the projection of the
rotating line contacts the dotted circle is assigned a
cosine value. Each of these cosine values is
represented on the orange horizontal axis.
-1.0
1.0
The values on the “orange” line change with time
to produce a pattern of red dots as a function of
time.
A Inc.
Phasor Concept Review
Phasor for periodic i(t) or v(t) signals
time
Project the tip of the red arrow
onto the “orange” line and mark
the spot with a red dot.
Mentally rotate the red line segment
in a counter clockwise manner.
As you visualize the phasor rotating counter
clockwise, each location where the projection of the
rotating line contacts the dotted circle is assigned a
cosine value. Each of these cosine values is
represented on the orange horizontal axis.
-1.0
1.0
The values on the “orange” line change with time
to produce a pattern of red dots as a function of
time.
A Inc.
Phasor Concept Review
Phasor for periodic i(t) or v(t) signals
time
Project the tip of the red arrow
onto the “orange” line and mark
the spot with a red dot.
Mentally rotate the red line segment
in a counter clockwise manner.
As you visualize the phasor rotating counter
clockwise, each location where the projection of the
rotating line contacts the dotted circle is assigned a
cosine value. Each of these cosine values is
represented on the orange horizontal axis.
-1.0
1.0
The values on the “orange” line change with time
to produce a pattern of red dots as a function of
time.
A Inc.
Phasor Concept Review
Phasor for periodic i(t) or v(t) signals
time
Project the tip of the red arrow
onto the “orange” line and mark
the spot with a red dot.
Mentally rotate the red line segment
in a counter clockwise manner.
As you visualize the phasor rotating counter
clockwise, each location where the projection of the
rotating line contacts the dotted circle is assigned a
cosine value. Each of these cosine values is
represented on the orange horizontal axis.
-1.0
1.0
The values on the “orange” line change with time
to produce a pattern of red dots as a function of
time.
A Inc.
Phasor Concept Review
Phasor for periodic i(t) or v(t) signals
time
Project the tip of the red arrow
onto the “orange” line and mark
the spot with a red dot.
Mentally rotate the red line segment
in a counter clockwise manner.
As you visualize the phasor rotating counter
clockwise, each location where the projection of the
rotating line contacts the dotted circle is assigned a
cosine value. Each of these cosine values is
represented on the orange horizontal axis.
-1.0
1.0
The values on the “orange” line change with time
to produce a pattern of red dots as a function of
time.
A Inc.
Phasor Concept Review
Phasor for periodic i(t) or v(t) signals
time
Project the tip of the red arrow
onto the “orange” line and mark
the spot with a red dot.
Mentally rotate the red line segment
in a counter clockwise manner.
As you visualize the phasor rotating counter
clockwise, each location where the projection of the
rotating line contacts the dotted circle is assigned a
cosine value. Each of these cosine values is
represented on the orange horizontal axis.
-1.0
1.0
The values on the “orange” line change with time
to produce a pattern of red dots as a function of
time.
A Inc.
Phasor Concept Review
Phasor for periodic i(t) or v(t) signals
time
Project the tip of the red arrow
onto the “orange” line and mark
the spot with a red dot.
Mentally rotate the red line segment
in a counter clockwise manner.
As you visualize the phasor rotating counter
clockwise, each location where the projection of the
rotating line contacts the dotted circle is assigned a
cosine value. Each of these cosine values is
represented on the orange horizontal axis.
-1.0
1.0
The values on the “orange” line change with time
to produce a pattern of red dots as a function of
time.
The red dots will “sketch” out a cosine wave as
the phasor rotates around its reference circle.
A Inc.
Phasor Concept Review
Phasor for periodic i(t) or v(t) signals
Project the tip of the red arrow
onto the “orange” line and mark
the spot with a red dot.
As you visualize the phasor rotating counter
clockwise, each location where the projection of the
rotating line contacts the dotted circle is assigned a
cosine value. Each of these cosine values is
represented on the orange horizontal axis.
The values on the “orange” line change with time
to produce a pattern of red dots as a function of
time.
The red dots will “sketch” out a cosine wave as
the phasor rotates around its reference circle.
time
Mentally rotate the red line segment
in a counter clockwise manner.
The period of this
cosine wave.
1.0
-1.0
|d 1 >
The blue curve represents this cosine wave.
Every time the phasor rotates back to its starting
point the wave has traveled 1 wavelength of
distance.
A Inc.
Now you should appreciate that
there are two ways to think about
a sinusoidal wave as a function of
time.
A cosine (or if you
prefer a sine) wave.
Phasor for periodic i(t) or v(t) signals
time
Phasor Concept Review
The period of this
cosine wave.
1.0
-1.0
A phasor
Which one should you use?
|d 1 >
A Inc.
Now you should appreciate that
there are two ways to think about
a sinusoidal wave as a function of
time.
A cosine (or if you
prefer a sine) wave.
Phasor for periodic i(t) or v(t) signals
time
Phasor Concept Review
The period of this
cosine wave.
1.0
-1.0
A phasor
Which one should you use?
|d 1 >
It does not matter!! However since
other engineers use both, maybe you
should be comfortable with both.
A Inc.
Phasor Concept Review
V 0 sin (ω t + ) Sinusoidal notation
The model equation that predicts
the voltage ( current) behavior is;
V0 <
Phasor notation
Phasor Circuit Elements
By themselves
voltage
phasor
With a friend
(phasors not drawn to the same scale)
2 phasors
current
phasor
(These two phasors are
never on top of each
other –out of phase)
ELI the
A Inc.
Phasor Concept Review
V 0 sin (ω t + ) Sinusoidal notation
The model equation that predicts
the voltage ( current) behavior is;
V0 <
Phasor notation
Phasor Circuit Elements
By themselves
voltage
phasor
With a friend
(phasors not drawn to the same scale)
2 phasors
current
phasor
ELI the
ICE man
current
phasor
voltage
phasor
(These two phasors are
never on top of each
2 phasors other –out of phase)
A Inc.
Phasor Concept Review
V 0 sin (ω t + ) Sinusoidal notation
The model equation that predicts
the voltage ( current) behavior is;
V0 <
Phasor notation
Phasor Circuit Elements
By themselves
voltage
phasor
With a friend
(phasors not drawn to the same scale)
2 phasors
current
phasor
voltage
phasor
3 phasors
ELI the
ICE man
current
phasor
“resistance”
phasor
current
phasor
voltage
phasor
These three phasors
are always on top of
each other – in phase)
2 phasors
A Inc.
Phasor Concept Review
V 0 sin (ω t + ) Sinusoidal notation
The model equation that predicts
the voltage ( current) behavior is;
V0 <
Phasor notation
Phasor Circuit Elements
By themselves
voltage
phasor
With a friend
(phasors not drawn to the same scale)
2 voltage
phasors
2 phasors
vL
current
phasor
voltage
phasor
vR
3 phasors
ELI the
ICE man
current
phasor
(In series circuits, the 2 curernt phasors
usually not the focus of attention!)
“resistance”
phasor
current
phasor
voltage
phasor
2 phasors
2 voltage
phasors
These three phasors
are always on top of
each other – in phase)
vC
vR
(In series circuits, the 2 curernt phasors
usually not the focus of attention!)
A Inc.
Phasor Concept Review
V 0 sin (ω t + ) Sinusoidal notation
The model equation that predicts
the voltage ( current) behavior is;
V0 <
Phasor notation
Phasor Circuit Elements
By themselves
voltage
phasor
With a friend
(phasors not drawn to the same scale)
2 phasors
vL
current
phasor
voltage
phasor
current
phasor
voltage
phasor
2 phasors
ZR
(In series circuits, the 2 curernt phasors
usually not the focus of attention!)
“resistance”
phasor
current
phasor
XL
vR
3 phasors
ELI the
ICE man
2 “impedance”
phasors
2 voltage
phasors
2 voltage
phasors
These three phasors
are always on top of
each other – in phase)
2 “impedance”
phasors
ZR
vC
vR
XC
(In series circuits, the 2 curernt phasors
usually not the focus of attention!)
A Inc.
End of
Presentation
But remember this phasor could
be a voltage, current, resistance
or impedance phasor
A Inc.