ece 1270: introduction to electric circuits 0 lecture 17...
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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
ECE 1270 Introduction to Electric Circuits Suketu Naik
2Sinusoidal Voltage
tVv m cos
Frequency, Angular Frequency, Amplitude, Phase (deg
and radians), Period
ECE 1270 Introduction to Electric Circuits Suketu Naik
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
ECE 1270 Introduction to Electric Circuits Suketu Naik
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
ECE 1270 Introduction to Electric Circuits Suketu Naik
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
ECE 1270 Introduction to Electric Circuits Suketu Naik
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
ECE 1270 Introduction to Electric Circuits Suketu Naik
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
ECE 1270 Introduction to Electric Circuits Suketu Naik
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