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EE 1270: Introduction to Electric Circuits
Lecture 18:
Phasors
Chapter 9: Sinusoidal SteadyState Analysis
Section 9.3, 9.4
EE 1270 Introduction to Electric Circuits
Suketu Naik
Representation of Complex Numbers
1
Rectangular Form (real and imaginary)
a  jb; j   1
Imaginary
Polar Form (magnitude and phase)
c
Real
Exponential Form
ce
 j
 c cos   j sin 
c  a b
a  c cos  ; b  c sin 
1 b
  tan
a
EE 1270 Introduction to Electric Circuits
2
2
Suketu Naik
2
Phasors
v  Vm cost     Re{Vm e
j (t  )
j
jt
}  Re{Vm e e }
V  Vm e j  Vm 
Phasor Transform or
Phasor Representation
1) A phasor is a complex number that represents the
amplitude and phase of a sinusoid
2) Phasors provide a simple means of analyzing linear
circuits excited by sinusoidal sources
EE 1270 Introduction to Electric Circuits
Suketu Naik
Phasors: Addition, Subtraction, Multiplication, and Division
3
Amplitude and Phase
Complex Conjugate
Addition
Subtraction
Multiplication
Division
EE 1270 Introduction to Electric Circuits
Suketu Naik
Phasors
4
v  Re{Vm e j e jt }
EE 1270 Introduction to Electric Circuits
Suketu Naik
Example 9.5: Hard Way
5
Problem
Solution
EE 1270 Introduction to Electric Circuits
Suketu Naik
Example 9.5: Easy Way
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Problem
Solution
Use Phasors
EE 1270 Introduction to Electric Circuits
Suketu Naik
AP 9.1, AP 9.2
7
1090
V
518
(e)(5545)(0.1  45)mA
(d )
EE 1270 Introduction to Electric Circuits
Suketu Naik
Phasor Notation for Resistor
EE 1270 Introduction to Electric Circuits
8
Suketu Naik
Phasor Notation for Inductor
9
Verify in SPICE
1) Transient
2) AC Sweep
Voltage leads Current by 90° in an Inductor
EE 1270 Introduction to Electric Circuits
Suketu Naik
Phasor Notation for Capacitor
10
i  CVm sin( t  V )
I  CVm e j (V 90)
 CVm e jV e  j 90
 jCVm e jV
 jCV
Verify in SPICE
1) Transient
2) AC Sweep
Current leads Voltage by 90° in a Capacitor
EE 1270 Introduction to Electric Circuits
Suketu Naik
Impedance and Reactance
EE 1270 Introduction to Electric Circuits
11
Suketu Naik
AP 9.3, AP 9.4
EE 1270 Introduction to Electric Circuits
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Suketu Naik