Figure 1.1 A telephone system.

Figure 1.1 A telephone system.

ECE 1270: Introduction to Electric Circuits 1 Lecture 18: Phasors Chapter 9: Sinusoidal SteadyState Analysis Section 9.3, 9.4 ECE 1270 Introduction to Electric Circuits Suketu Naik Representation of Complex Numbers 2

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 2 c a b 2 a c cos ; b c sin b tan a

ECE 1270 Introduction to Electric Circuits 1 Suketu Naik Phasors v Vm cost Re{Vm e j (t ) 3 j jt

} 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 ECE 1270 Introduction to Electric Circuits

Suketu Naik Phasors: Addition, Subtraction, Multiplication, and Division 4 Amplitude and Phase Complex Conjugate Addition Subtraction Multiplication Division ECE 1270 Introduction to Electric Circuits Suketu Naik

Phasors 5 v Re{Vm e j e jt } Note that Vm is the amplitude and is the phase ECE 1270 Introduction to Electric Circuits Suketu Naik Example 9.5: Hard Way 6

Problem Solution ECE 1270 Introduction to Electric Circuits Suketu Naik Example 9.5: Easy Way 7 Problem Solution Use Phasors

ECE 1270 Introduction to Electric Circuits Suketu Naik AP 9.1, AP 9.2 8 1090 V 518 (e)(5545 )(0.1 45 )mA (d ) ECE 1270 Introduction to Electric Circuits

Suketu Naik Phasor Notation for Resistor 9 ECE 1270 Introduction to Electric Circuits Suketu Naik Phasor Notation for Inductor 10 +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 ECE 1270 Introduction to Electric Circuits Suketu Naik Phasor Notation for Capacitor 11 -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 ECE 1270 Introduction to Electric Circuits Suketu Naik Impedance and Reactance 12 ECE 1270 Introduction to Electric Circuits Suketu Naik AP 9.3, AP 9.4

13 ECE 1270 Introduction to Electric Circuits Suketu Naik

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