ECE 1270: Introduction to Electric Circuits 0 Lecture 18 ...faculty.weber.edu/snaik/ECE1270/Lec18_Phasors.pdf · ECE 1270 Introduction to Electric Circuits Suketu Naik ... Lecture

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


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


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


3Phasors: Addition, Subtraction, Multiplication, and Division

Amplitude and Phase

Complex Conjugate

Addition

Subtraction

Multiplication

Division


4Phasors

}Re{ tjj

m eeVv

Note that Vm is the amplitude and φ is the phase


5Example 9.5: Hard Way

Solution

Problem


6Example 9.5: Easy Way

Solution

Problem

Use Phasors


7AP 9.1, AP 9.2

mAe

Vd

)451.0)(4555)((

185

9010)(


8Phasor Notation for Resistor


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


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


11Impedance and Reactance


12AP 9.3, AP 9.4

Documents

ECE 1270: Introduction to Electric Circuits 0 Lecture 18 ...faculty.weber.edu/snaik/ECE1270/Lec18_Phasors.pdf · ECE 1270 Introduction to Electric Circuits Suketu Naik ... Lecture