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ELE 102/102 Dept of E&E MIT Manipal 1
Introduction to Phasors
v(wt) = Vm sin wtv() = Vm sin
t
v Vm
0
Vm
Vm
-Vm
0
N S
a
b Coil
Rotation
A phasor is a graphical representation of the magnitude and angular
position of a time varying quantity such as a voltage or current in
which variation is sinusoidal.
A phasor diagram can be used to show the relative relationship of two
or more sine waves of the same frequency.
ELE 102/102 Dept of E&E MIT Manipal
The operator ‘j’ :
The operator ‘j’ rotates the given vector by 90 degrees in anti-clockwise direction.
jAAj )(
AAjjAj 2)(
1j 1;j Therefore, 2
RefA
jA
Aj2
jAAj3
ELE 102/102 Dept of E&E MIT Manipal
Phasor representation
Rectangular form:
Trigonometric Form:
Exponential Form:
Polar form:
jXRA
SinAjCosAA ||||
jeAA ||
|| AA
ELE 102/102 Dept of E&E MIT Manipal
Conversion from R ↔ P:
R
Xtanθ
;XR|A|
1
22
Rectangular to Polar:
Polar to Rectangular:
sin||
cos||
AX
AR
ELE 102/102 Dept of E&E MIT Manipal
Conversion from R ↔ P using calculator:
Convert the following into polar form using calculator
j6-8 3)
j68 2)
j4 31
)
36.87-10
36.87 10
53.135
4510)3
603)2
305)1
07.7j07.7
59.2j5.1
5.2j33.4
Convert the following into rectangular form using calculator
ELE 102/102 Dept of E&E MIT Manipal
Addition & Subtraction of Phasors
Rectangular form is used
Addition:
(R1+jX1)+(R2+jX2) = (R1+R2)+j(X1+X2)
Subtraction:
(R1+jX1)-(R2+jX2) = (R1-R2)+j(X1-X2)
ELE 102/102 Dept of E&E MIT Manipal
Multiplication & Division of Phasors
Polar form is used
Multiplication:
Division:
)(|]|*|[|||*|| 21212211 AAAA
)(||
||
||
||21
2
1
22
11
A
A
A
A
ELE 102/102 Dept of E&E MIT Manipal
A phasor diagram can be used to show the relative
relationship of two or more sine waves of the same
frequency.
Graphical Representation of Phasors
Real
A
B
C
O
Imaginary
A phasor can be resolved into two components at right angles to each other.
OA is a phasor.
Horizontal component = OB
Vertical component OC = AB
OA = OB + jOC = R + jX
ELE 102/102 Dept of E&E MIT Manipal
Rectangular form:
Polar form:
jXRA
|| AA
ELE 102/102 Dept of E&E MIT Manipal
Graphical Addition of Phasors
Phasors are represented in Polar form.
Mehod 1:
Method 2:
ELE 102/102 Dept of E&E MIT Manipal
Graphical Subtraction of Phasors
Phasors are represented in Polar form.
The Second phasor is reversed and added with the first phasor.
ELE 102/102 Dept of E&E MIT Manipal
Multiplication and Division are
NOT possible
using graphical method