Download Generating A Sine Wave - McGraw Hill Higher Education

8-1
Electricity
Principles & Applications
Eighth Edition
Richard J. Fowler
Chapter 8
Alternating
Current and Voltage
(student version)
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8-2
INTRODUCTION
• Types of Waveforms
• Induced Voltage
• Generating a Sine Wave
• Ac Terminology
• Three-Phase Ac
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8-3
Dear Student:
This presentation is arranged in segments. Each segment
is preceded by a Concept Preview slide and is followed by a
Concept Review slide. When you reach a Concept Review
slide, you can return to the beginning of that segment by
clicking on the Repeat Segment button. This will allow you
to view that segment again, if you want to.
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8-4
Concept Preview
• Direct voltages never change direction. (page 206)
•Direct voltages never change polarity. (page 206)
•Alternating current periodically
changes direction. (page 206)
•Rapidity of an ac waveform can be
specified by its frequency or its period. (page 207)
•Amplitude can be given in peak, peak-topeak, average, or rms(effective) values. (page 209)
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8-5
Electrical Waveforms (page 206)
Alternating current or voltage
Pulsating direct current or voltage
Fluctuating direct current or voltage
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8-6
Common Alternating Current Waveforms (page 206)
Sinusoidal Wave
Triangular Wave
Square Wave
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8-7
Ac Waveform Terminology
Voltage or Current
1st cycle
+2
+1
0
1
-2 0
2nd cycle
peak
to
peak
0.2 s
(Page 207)
3rd cycle
+ peak
- peak
0.6 s
0.4 s
Time
T = period = time to complete 1 cycle = 0.2 s
f = frequency = 1 / T = 1 / 0.2 s = 5 Hz
Peak amplitude can be either negative or positive.
Peak-to-peak amplitude includes both the
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- and + peaks.
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8-8
Specifying Sine-Wave Amplitude (Page 209)
rms = 0.707 peak
av = 0.637 peak
peak
peak-to-peak
peak = (1 / 0.707) rms = 1.414 rms
peak = (1 / 0.637) av = 1.57 av
peak = peak-to-peak / 2
Examples:
20 Vp-p / 2 = 10 Vp and 10 Vp x 0.707 = 7.07 V
8 Aav x 1.57 = 12.56 Ap
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8-9
Wave-Form Quiz
The ____ dc waveform never reaches or crosses
the zero reference line.
fluctuating
The part of the waveform that includes its complete
negative and positive excursions is called a ____.
cycle
The ____ is the time required to complete one cycle. period
The base unit of frequency is the ____.
hertz
For a sine wave, 30 VP = ____ V.
21.21
For a sine wave, 10 AP-P = ____ A.
3.535
For a sine wave, 25 V = ____ VP.
35.35
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8 - 10
Concept Review
• Direct currents never change direction.
• Direct voltages never change polarity.
• Alternating current periodically
changes direction.
• Rapidity of an ac waveform can be
specified by its frequency or its period.
• Amplitude can be given in peak, peakto-peak, average, or rms(effective) values.
Repeat Segment
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8 - 11
Concept Preview
(Page 211)
• Cutting flux at a 90 angle produces Vpeak.
• Cutting flux at 45 produces 0.707 Vpeak.
• Producing a sine wave requires circular
motion, constant speed, and uniform flux.
• A two-pole generator produces one cycle
for each revolution of the rotating coil.
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8 - 12
Induced Voltage in a Constant-speed Conductor (Page 212)
N
N
N
N
S
S
S
S
If motion is
parallel to the
flux, no flux
is cut; thus
no voltage
is induced.
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When motion
is at an angle,
some flux is
cut; and some
voltage is
induced.
When
motion is
perpendicular
to the flux,
maximum
voltage is
induced.
Reversing the
direction of
motion,
reverses the
polarity of
the induced
voltage.
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8 - 13
Generating A Sine Wave (Page 212)
S
N
Motion is parallel to the flux. No voltage is induced.
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8 - 14
Generating A Sine Wave
S
N
Motion is 45 to flux. Induced voltage is 0.707 of maximum.
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8 - 15
Generating A Sine Wave
S
x
N
Motion is perpendicular to flux. Induced voltage is maximum.
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8 - 16
Generating A Sine Wave
S
N
Motion is 45 to flux. Induced voltage is 0.707 of maximum.
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8 - 17
Generating A Sine Wave
S
N
Motion is parallel to flux. No voltage is induced.
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8 - 18
Generating A Sine Wave
S
N
Notice current in the conductor has reversed.
Motion is 45 to flux. Induced voltage is 0.707 of maximum.
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8 - 19
Generating A Sine Wave
S
N
Motion is perpendicular to flux. Induced voltage is maximum.
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8 - 20
Generating A Sine Wave
S
N
Motion is 45 to flux. Induced voltage is 0.707 of maximum.
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8 - 21
Generating A Sine Wave
S
N
Motion is parallel to flux. No voltage is induced.
Ready to produce another cycle.
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8 - 22
Ac Generation Quiz
Maximum voltage is produced when a
conductor is moving ____ to the flux.
perpendicular
No voltage is produced when a conductor
is moving ____ to the flux.
parallel
When a conductor is moving at 45° to the
flux, the voltage is ____ of maximum value.
0.707
For a two-pole generator, one cycle of ac is
produced during ____ revolution(s).
one
To produce a sine wave the flux field
must be ____.
uniform
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8 - 23
Concept Review
• Cutting flux at a 90 angle produces Vpeak.
• Cutting flux at 45 produces 0.707 Vpeak.
• Producing a sine wave requires circular
motion, constant speed, and uniform flux.
• A two-pole generator produces one cycle
for each revolution of the rotating coil.
Repeat Segment
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8 - 24
Concept Preview
(Page 217)
• Adjacent waveforms in a three-phase
system are separated by 120.
• The algebraic sum of the instantaneous
voltages in a three-phase system is zero.
• Three-phases devices can be connected
in either a wye or a delta configuration.
• A three-phase system can use both wyeand delta-connected devices.
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8 - 25
Three-Phase Waveform
Phase 1
120
240
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Phase 2
Phase 3
120
120
(Page 217)
Phase 2 lags phase 1 by 120.
Phase 3 lags phase 1 by 240.
Phase 2 leads phase 3 by 120.
Phase 1 lags phase 3 by 120.
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8 - 26
Generation Of Three-Phase Ac (Page 218)
Phase 1 Phase 2 Phase 3
The
algebraic
sum of the
instantaneous
voltages of
the three
phases equals
zero.
Phase 1 is ready to go positive.
Phase 2 is going more negative.
Phase 3 is going less positive.
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S
x
x
N
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8 - 27
Delta Connections
(Page 218)
Line 1
Line 2
Phase 3
Line 3
Delta-Connected Source
The sum of the instantaneous
phase voltages equals zero.
Delta-Connected Load
Each load resistor will be
connected to one of the phases.
For the delta-to-delta connection, Vline = Vphase = Vload.
For the delta-to-delta connection, Iline = 1.732 Iphase = 1.732 Iload.
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8 - 28
Wye Connections
(Page 220)
Line 1
Line 2
Line 3
Wye-Connected Source
Wye-Connected Load
For the wye-to-wye connection with a balanced load:
I line = Iphase = Iload.
Vline = 1.732 Vphase = 1.732 Vload.
There is no voltage between the source and load star-points.
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8 - 29
Three-Phase Ac Quiz
In a three-phase system, the phases are separated
by ____ electrical degrees.
120
In a three-phase system, the phase coils are
separated by ____ mechanical degrees.
120
The algebraic sum of the instantaneous phase
voltages equals ____.
zero
The phase coils in a ____ connected source
are connected in series.
delta-
Phase and line currents are equal in a ____
connected system with balanced loads.
wye-
In a delta-connected system, the line current
equals ____ times the phase current.
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1.732
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8 - 30
Concept Review
• Adjacent waveforms in a three-phase
system are separated by 120.
• The algebraic sum of the instantaneous
voltages in a three-phase system is zero.
• Three-phases devices can be connected
in either a wye or a delta configuration.
• A three-phase system can use both wyeand delta-connected devices.
Repeat Segment
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8 - 31
REVIEW
• Types of Waveforms
• Induced Voltage
• Generating a Sine Wave
• Ac Terminology
• Three-Phase Ac
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