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electronics fundamentals
circuits, devices, and applications
THOMAS L. FLOYD
DAVID M. BUCHLA
Chapter 8 – AC Circuits
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AC Circuits
Alternating Voltage is a voltage that:
1. Continuously varies in magnitude
2. Periodically reverses in polarity
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AC Circuits
Symbol for a sinusoidal voltage
source.
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AC Circuits
Sine waves
The sinusoidal waveform (sine wave) is the fundamental
alternating current (ac) and alternating voltage waveform.
Electrical sine waves are
named from the
mathematical function
with the same shape.
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AC Circuits
Generation of a sine wave
Sinusoidal voltage sources
Sinusoidal voltages are produced by ac generators and
electronic oscillators.
When a conductor rotates in a constant magnetic
field, a sinusoidal wave is generated.
C
N
D
B
S
A
B
C
D
A
Motion of conductor
Conduc tor
the conductor
is moving
parallel with to
When When
the loop
is moving
perpendicular
the of
linesflux,
of flux,
voltage is induced.
the lines
thenomaximum
voltage is
induced.
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AC Circuits
Sine waves
Sine waves are characterized by the amplitude and period.
1. The amplitude is the maximum value of a voltage
or current
2. The period is the time interval for one complete
cycle.
20 V
15 V
The amplitude (A)
of this sine wave
is 20 V
The period is 50.0 s
A
10 V
0V
t (s)
25
0
37.5
50.0
-10 V
-15 V
-20 V
T
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AC Circuits
Sine waves
The period (T) of a sine wave can be measured
between any two corresponding points on the
waveform.
TT T T
A
T
T
A
By contrast, the amplitude of a sine wave is only
measured from the center to the maximum point.
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AC Circuits
Frequency
Frequency ( f ) is the number of cycles
that a sine wave completes in one second.
Frequency is measured in hertz (Hz).
If 3 cycles of a wave occur in one second, the frequency
is 3.0 Hz
1.0 s
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AC Circuits
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AC Circuits
Period and frequency
The period and frequency are reciprocals of each other.
1
f
T
and
1
T 
f
If the period is 50 s, the frequency is 0.02 MHz = 20 kHz.
(The 1/x key on your calculator is handy for converting between f and T.)
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AC Circuits
Sine wave voltage and current values
• Instantaneous value (v): Voltage or current at
any point on the curve.
• Peak value (VP for voltage): The amplitude of
a sine wave.
20 V
15 V
10 V
The peak voltage of
this waveform is 20 V.
0V
v
VP
t (s)
0
25
v
37.5
50.0
-10 V
-15 V
-20 V
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AC Circuits
Sine wave voltage and current values
Peak to peak value: Value from positive peak
to negative peak. Equation =
20 V
15 V
V  2V I  2 I
PP
P
PP
10 V
0V
P
t (s)
0
25
37.5
50.0
-10 V
-15 V
RMS (root mean squared) value: Is the
sinusoidal wave with the same heat value
as a DC voltage source (known as the
effective value)
-20 V
V  0.707V
rm s
P
V  1.414V
p
vms
I  0.707 I
rm s
P
I  1.414 I
p
vms
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AC Circuits
Sine wave voltage and current values
VP = 20 volts
20 V
15 V
The peak-to-peak
voltage is 40 V.
10 V
Vrms
0V
0
VPP
t (s)
25
37.5
50.0
-10 V
The rms voltage
is 14.1 V.
-15 V
-20 V
VP  1.414Vrms
VPP  2.828Vrms
This is magnitude Vpp
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AC Circuits
Phase of a Sine Wave
Phase:
Angular measurement that specifies the position on
the sine wave relative to a reference point.
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AC Circuits
Phase shifts
Occurs when a sine wave is shifted right or left in
relation to the base/reference sine wave.
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AC Circuits
Phase shift – Lead/Lag
Occurs when a sine wave is shifted right or left in
relation to the base/reference sine wave.
A - Leads
B – Lags by 450
A - Lags
B – Leads by 300
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AC Circuits
Phase shift
Example of a wave that lags the reference (not on
guided notes)
…and the equation
has a negative phase
shift
Referenc e
40
Peak voltage
30
v = 30 V sin (q - 45o)
Voltage (V)
20
10
0
0
45
90
135 180
225
270
315
360
405
-20
-30
- 40
Notice that a lagging sine
wave is below the axis at 0o
Angle ()
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AC Circuits
Phase shift
Example of a wave that leads the reference (not on guided
notes)
Notice that a leading sine
Referenc e
o
wave
is
above
the
axis
at
0
40
Peak voltage
30
Voltage (V)
20
v = 30 V sin (q + 45o)
10
-45
0 0
-10
-20
-30
-40
45
90 135
180
225
270
315
360
…and the equation
has a positive phase
shift
Angle ()
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AC Circuits
PolyPhase power
An important application of phase-shifted sine waves is in
electrical power systems.
• Electrical utilities generate ac with three phases that are
separated by 120o.
• 3-phase power is delivered to the user with three hot lines
plus neutral. The voltage of each phase, with respect to
neutral is 120 V.
120o
120o
120o
0o
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AC Circuits
Sine wave equation
Instantaneous values of a wave are shown as v or i.
The equation for the instantaneous voltage (v) of a sine
wave is v  V sin q
p
where
Vp = Peak voltage
q (theta) = Angle in rad or degrees
If the peak voltage is 25 V, the instantaneous
voltage at 50 degrees is 19.2 V
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AC Circuits
Sine wave equation
A certain sine wave has a positive-going zero crossing
at 0° and an peak value of 40V. Calculate its
instantaneous voltage for the degrees listed below for
the sine wave below.
30
20
Voltage (V)
v  V p sin q
40
10
0
Vp = Peak voltage
q (theta) = Angle in rad or degrees
-1 0
-2 0
-3 0
- 40
45°, 125°, 180°, 220°,325°
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AC Circuits
Phasors
Phasor (aka Phase Vector):
Representation of a sine wave whose amplitude (A)
and angular frequency (ω - omega) are a constant rate.
90
180
0
0
90
180
360
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AC Circuits
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AC Circuits
Power in resistive AC circuits
A
sinusoidal
voltage
produces a
sinusoidal
current
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AC Circuits
Power in resistive AC circuits
Kirchhoff’s voltage law applies to
AC circuits just like DC circuits
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AC Circuits
Power in resistive AC circuits
Power in AC circuits is calculated using
RMS values for voltage and current.
The power formulas are:
P  Vrms I rms
2
Vrms
P
R
2
P  I rms
R
The dc and the ac sources produce the
same power to the bulb:
120 Vdc
0V
ac or dc
source
170 Vp
= 120 Vrms
0V
Bulb
WHY?
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AC Circuits
Power in resistive AC circuits
Assume a sine wave with a peak value of 40 V is
applied to a 100 W resistive load. What power is
dissipated?
40
30
Voltage (V)
20
10
0
-1 0
-2 0
-3 0
- 40
Vrms = 0.707 x Vp = 0.707 x 40 V = 28.3 V
2
Vrms
28.3 V 2
P

 8W
R
100 W
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AC Circuits
AC generator (alternator)
• Generators convert rotational energy to electrical energy.
• The armature has an induced voltage, which is connected
through slip rings and brushes to a load.
• The armature loops are wound on a magnetic core (not
shown for simplicity).
Small alternators may use a
permanent magnet
Others use field coils to produce
the magnetic flux.
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AC Circuits
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AC Circuits
AC generator (alternator)
• Increasing the number of poles increases the number of
cycles per revolution.
• A four-pole generator will produce two complete cycles
in each revolution.
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AC Circuits
Output Frequency of an AC Generator
Ns
f 
120
f – frequency (Hz)
N – number of poles
s - speed in RPM
1
4
2
3
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AC Circuits
Alternators
• In vehicles, alternators generate ac, which is converted to
dc for operating electrical devices and charging the
battery.
• AC is more efficient to produce and can be easily
regulated, hence it is generated and converted to DC by
diodes.
Housing
The output is taken from the
rotor through the slip rings.
Stator coils
Rotor
Diode plate
Diodes
Slip rings
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AC Circuits
AC Motors
There are two major classifications of ac motors.
1. Induction motor
2. Synchronous motor.
3. Both types use a rotating field in the stator windings.
Induction motors work because current is induced in the rotor by the
changing current in the stator. This current creates a magnetic field that
reacts with the moving field of the stator, which develops a torque and
causes the rotor to turn.
Synchronous motors have a magnet for the rotor. In small motors, this
can be a permanent magnet, which keeps up with the rotating field of the
stator. Large motors use an electromagnet in the rotor, with external dc
supplied to generate the magnetic field.
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AC Circuits
Rotating the stator produces
a net magnetic field
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AC Circuits
Rotating the stator produces a
net magnetic field
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AC Circuits
Induction vs. Stator Motors
Squirrel Cage
Rotor
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AC Circuits
Induction vs. Stator Motors
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AC Circuits
Pulse definitions
Ideal pulses
Leading (rising) edge
Leading (falling) edge
Trailing (falling) edge
Trailing (rising) edge
Baseline
Am plitude
Am plitude
Baseline
Pulse
width
(a) Positive-going pulse
Pulse
width
(b) Negative-going pulse
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AC Circuits
Repetitive pulse waveforms
• Periodic waveforms repeat at fixed intervals.
• Pulse repetition frequency: Rate at which the pulses
repeat.
• Duty Cycle – Ratio of pulse width (tw) to the period (T)
Percent Duty Cycle
=
 tw 
 100
T 
Vavg = baseline = (duty cycle)( amplitude)
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AC Circuits
Nonsinusoidal Wave Forms
• Define terms on page 359
• Rise time:
• Fall time:
• Pulse width:
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AC Circuits
Voltage ramps
Ramp – Linear increase or decrease in voltage or current.
Yaxis  V  I

or
Slope =
Xaxis
t
t
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AC Circuits
Triangular and Sawtooth waves
Triangular and sawtooth waveforms are formed by
voltage or current ramps (linear increase/decrease)
Triangular waveforms
have positive-going and
negative-going ramps of
equal duration (same
T
T
slope either increasing or
decreasing).
T
T
The sawtooth waveform consists
of two ramps, one of much longer
duration than the other. (unequal
slopes in either direction).
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AC Circuits
Oscilloscope
A device that traces the graph of a measured
electrical signal on its screen.
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AC Circuits
Video on Osciloscope
• http://www.cleanvideosearch.com/media/acti
on/yt/watch?v=8VEg6L2QG5o
• The name of video is: AC vs Dc explain how
to use an oscilloscope
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AC Circuits
Reading an Oscilloscope
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AC Circuits
Calculate for each wave: Period, Peak, Peak
to Peak, RMS
T= 3.0 ms
Vp = 1250 mv
Vpp = 2500 mv
RMS = 833.8 mV
T= 20 ms
Vp = 1.5 v
Vpp = 3.0 v
RMS = 1.06 V
500 mv
0.5 ms
T= 6000 µs; 6 ms
Vp = 20.4 v
Vpp = 40.8 v
RMS = 14.4 V
T= 30 µs
Vp = 24 v
Vpp = 48 v
RMS = 16.97 V
6v
300 µs
12 v
15 µs
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AC Circuits
Selected Key Terms
Sine wave A type of waveform that follows a cyclic
sinusoidal pattern defined by the formula
y = A sin q.
Alternating Current that reverses direction in response to a
current change in source voltage polarity.
Period (T) The time interval for one complete cycle of a
periodic waveform.
Frequency (f) A measure of the rate of change of a periodic
function; the number of cycles completed in 1 s.
Hertz The unit of frequency. One hertz equals one
cycle per second.
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AC Circuits
Selected Key Terms
Instantaneous The voltage or current value of a waveform at
value a given instant in time.
Peak value The voltage or current value of a waveform at
its maximum positive or negative points.
Peak-to-peak The voltage or current value of a waveform
value measured from its minimum to its maximum
points.
rms value The value of a sinusoidal voltage that indicates
its heating effect, also known as effective
value. It is equal to 0.707 times the peak value.
rms stands for root mean square.
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AC Circuits
Quiz
1. In North America, the frequency of ac utility voltage is
60 Hz. The period is
a. 8.3 ms
b. 16.7 ms
c. 60 ms
d. 60 s
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AC Circuits
Quiz
2. The amplitude of a sine wave is measured
a. at the maximum point
b. between the minimum and maximum points
c. at the midpoint
d. anywhere on the wave
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AC Circuits
Quiz
5. The time base of an oscilloscope is determined by the
setting of the
a. vertical controls
b. horizontal controls
c. trigger controls
d. none of the above
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AC Circuits
Quiz
6. A sawtooth waveform has
a. equal positive and negative going ramps
b. two ramps - one much longer than the other
c. two equal pulses
d. two unequal pulses
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AC Circuits
Quiz
8. For the waveform shown, the same power would be
delivered to a load with a dc voltage of
a. 21.2 V
b. 37.8 V
c. 42.4 V
d. 60.0 V
60 V
45 V
30 V
0V
t (s)
0
25
37.5
50.0
-30 V
-45 V
-60 V
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AC Circuits
Quiz
10. A control on the oscilloscope that is used to set the
desired number of cycles of a wave on the display is
a. volts per division control
b. time per division control
c. trigger level control
d. horizontal position control
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