ECE 1270: Introduction to Electric Circuits 0 Lecture 17...

ECE 1270 Introduction to Electric Circuits Suketu Naik

0ECE 1270: Introduction to Electric Circuits

Lecture 17:

1) Sinusoidal Source

2) Complex Numbers

Chapter 9: Sinusoidal Steady-

State Analysis

Section 9.1 & Appendix B


1Chapter 9

Sinusoidal Source


2Sinusoidal Voltage

tVv m cos

Frequency, Angular Frequency, Amplitude, Phase (deg

and radians), Period


3Sinusoidal Voltage: Phase Angle ϕ

0;cos tVv m

Example of Phase Change in Matlab

Positive phase change: shift to the left

Negative phase change: shift to the right


4Sinusoidal Voltage: RMS Value

mm

rms

Tt

t

mrmsm

VV

V

dttVT

VtVv

707.02

cos1

cos0

0

22

RMS=Root Mean Squared

Important for Power Calculations and Noisy Waveforms

Vrms


5RMS of Noisy Signal

N

m

mrms VN

V1

1

Vrms


6Wall Outlet Signal in RMS

1) Wall outlet (voltage delievered from power plant) has

120 Vrms at 60 Hz

2) Actual voltage peak =169.7 V


7P9.7: Find the RMS value


8Appendix B

Complex Numbers


9Representation of Complex Numbers

Rectangular Form (real and imaginary)

Polar Form (magnitude and phase)

Exponential Form

1; jjba

jce

c

a

b

cbca

bac

1

22

tan

sin;cos


10What are Complex Numbers?

-Complex numbers are used to represent reactive

components such as inductor and capacitor

-Think in terms of phase change (voltage and current in

reactive components)

-Multisim Examples of Inductor and Capacitor


11Examples


12B.3 (p725): Complex Arithmatic

Tips

1) When adding or subtracting, use rectangular form

2) When multiplying or dividing or finding power, use polar or

exponential form

3) Complex number x Complex Conjugate = amplitude2

Examples

?*

?j43

?B) -B)/(A (A

?B) (A *A

j6 4 B j5, 2A

?135513.5310

?312168

5

BB

jj

ECE 1270: Introduction to Electric Circuits 0 Lecture 17...

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