1. ECE 1270: Introduction to Electric Circuits
Lecture 18:
Phasors
Chapter 9: Sinusoidal Steady-State Analysis
Section 9.3, 9.4

2. Representation of Complex Numbers
Rectangular Form (real and imaginary)
Imaginary
Polar Form (magnitude and phase)
Real
Exponential Form

3. Phasors
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

4. Phasors: Addition, Subtraction, Multiplication, and Division
Amplitude and Phase
Complex Conjugate
Addition
Subtraction
Multiplication
Division

5. Phasors
Note that Vm is the amplitude and φ is the phase

6. Example 9.5: Hard Way
Problem
Solution

7. Example 9.5: Easy Way
Problem
Solution
Use Phasors

8. AP 9.1, AP 9.2

9. Phasor Notation for Resistor

10. Phasor Notation for Inductor
+90° phase shift (voltage shifts to the left by 90 °) or
Voltage leads Current by 90° in an Inductor
How to verify in Multisim
1) Transient
2) AC Sweep

11. Phasor 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

12. Impedance and Reactance

13. AP 9.3, AP 9.4