The document provides an introduction to sinusoidal alternating waveforms in circuit analysis, focusing on their characteristics, phase relationships, and calculations of average and effective values. It covers various topics such as instantaneous values, peak amplitude, frequency, and the general format for sinusoidal voltage or current. The content is accompanied by figures that illustrate key concepts and relationships related to alternating current (AC) and voltage.

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Introductory Circuit Analysis, 12/e
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Chapter 13
Sinusoidal Alternating Waveforms
Imam Ja'afar Al-Sadiq University
Computer Technical Engineering
First Class
Asst. Lec.
Sadiq M.B Fakhruldeen

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OBJECTIVES
• Become familiar with the characteristics of
a sinusoidal waveform and general format.
• Be able to determine the phase
relationship between two sinusoidal
waveforms of the same frequency.
• Understand how to calculate the average
and effective values of any waveform.

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INTRODUCTION
FIG. 13.1 Alternating waveforms.
Alternating waveforms
The term alternating indicates only that
the waveform alternates between two
prescribed levels in a set time sequence.

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SINUSOIDAL ac VOLTAGE
CHARACTERISTICS AND DEFINITIONS
Generation
FIG. 13.2 Various sources of ac power: (a) generating plant; (b) portable ac generator;
(c) wind-power station; (d) solar panel; (e) function generator

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SINUSOIDAL ac VOLTAGE
CHARACTERISTICS AND DEFINITIONS
FIG. 13.3 Important parameters for a sinusoidal voltage.
• Instantaneous value, Peak amplitude
• Peak-to-peak value, Periodic waveform
• Period (T), Cycle, Frequency
(Hz)
1
T
f 

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FREQUENCY SPECTRUM
FIG. 13.8 Areas of
application for specific
frequency bands.

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Defined Polarities and Direction
FIG. 13.11 (a) Sinusoidal ac voltage sources; (b)
sinusoidal current sources.

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THE SINUSOIDAL WAVEFORM
FIG. 13.14 There are 2π radians in one full circle of 360°.

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THE SINUSOIDAL WAVEFORM
FIG. 13.15 Plotting a sine wave versus (a) degrees and (b) radians.

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THE SINUSOIDAL WAVEFORM
FIG. 13.17 Demonstrating the effect of ψ on the
frequency and period.
t

 
T


2

f

 2


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GENERAL FORMAT FOR THE
SINUSOIDAL VOLTAGE OR CURRENT
FIG. 13.18 Basic sinusoidal function.
i = Imsint = Imsin
e = Emsint = Emsin

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PHASE RELATIONS
FIG. 13.28 Defining the phase shift for a
sinusoidal function that crosses the
horizontal axis with a positive slope after
0°.
FIG. 13.29 Phase relationship between a
sine wave and a cosine wave.

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AVERAGE VALUE
FIG. 13.40 Defining average value.

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AVERAGE VALUE
FIG. 13.41 Effect of distance (length)
on average value.
FIG. 13.42 Effect of depressions
(negative excursions) on average value.

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AVERAGE VALUE
FIG. 13.44 Example 13.14.

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EFFECTIVE (rms) VALUES
FIG. 13.59 An experimental setup to establish a relationship between dc and
ac quantities.

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EFFECTIVE (rms) VALUES
• The equivalent dc value of a
sinusoidal current or voltage is
0.707 of its peak value.

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EFFECTIVE (rms) VALUES
FIG. 13.61 Example 13.21.

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EFFECTIVE (rms) VALUES
FIG. 13.62 Example 13.22.
FIG. 13.63 The squared waveform of Fig.
13.62.

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