ECE 1270 Introduction to Electric Circuits Suketu Naik
0ECE 1270: Introduction to Electric Circuits
Lecture 18:
Phasors
Chapter 9: Sinusoidal Steady-
State Analysis
Section 9.3, 9.4
ECE 1270 Introduction to Electric Circuits Suketu Naik
1Representation of Complex Numbers
Rectangular Form (real and imaginary)
Polar Form (magnitude and phase)
Exponential Form
1; jjba
sincos jcce j
c
a
b
cbca
bac
1
22
tan
sin;cos
Imaginary
Real
ECE 1270 Introduction to Electric Circuits Suketu Naik
2Phasors
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
}Re{}Re{cos )( tjj
m
tj
mm eeVeVtVv
m
j
m VeVV
Phasor Transform or
Phasor Representation
ECE 1270 Introduction to Electric Circuits Suketu Naik
3Phasors: Addition, Subtraction, Multiplication, and Division
Amplitude and Phase
Complex Conjugate
Addition
Subtraction
Multiplication
Division
ECE 1270 Introduction to Electric Circuits Suketu Naik
4Phasors
}Re{ tjj
m eeVv
Note that Vm is the amplitude and φ is the phase
ECE 1270 Introduction to Electric Circuits Suketu Naik
6Example 9.5: Easy Way
Solution
Problem
Use Phasors
ECE 1270 Introduction to Electric Circuits Suketu Naik
7AP 9.1, AP 9.2
mAe
Vd
)451.0)(4555)((
185
9010)(
ECE 1270 Introduction to Electric Circuits Suketu Naik
9Phasor Notation for Inductor
How to verify in Multisim
1) Transient
2) AC Sweep
+90° phase shift (voltage shifts to the left by 90 °)
or
Voltage leads Current by 90° in an Inductor
ECE 1270 Introduction to Electric Circuits Suketu Naik
10Phasor Notation for Capacitor
-90° phase shift (voltage shifts to the right by 90 °)
or
Voltage lags Current by 90° in a Capacitor
How to verify in Multisim
1) Transient
2) AC Sweep