1. electronics fundamentals
circuits, devices, and applications
THOMAS L. FLOYD
DAVID M. BUCHLA
Chapter 8 – AC Circuits

2. Alternating Voltage is a voltage that:
Continuously varies in magnitude
Periodically reverses in polarity

3. Symbol for a sinusoidal voltage source.

4. A wave is a disturbance.
Unlike water waves, electrical waves cannot be seen directly but they have similar characteristics.
All periodic waves can be constructed from sine waves, which is why sine waves are fundamental to alternating current.

5. 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.

6. 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. D B C A
When the loop is moving perpendicular to the lines of flux, the maximum voltage is induced.
When the conductor is moving parallel with the lines of flux, no voltage is induced.

7. Sine waves Sine waves are characterized by the amplitude and period.
The amplitude is the maximum value of a voltage or current
The period is the time interval for one complete cycle. A
The amplitude (A) of this sine wave is
20 V T
The period is
50.0 ms

8. Sine waves
The period (T) of a sine wave can be measured between any two corresponding points on the waveform. T T T T A T T A
By contrast, the amplitude of a sine wave is only measured from the center to the maximum point.

10. 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

12. Period and frequency
The period and frequency are reciprocals of each other.
and
If the period is 50 ms, the frequency is
0.02 MHz = 20 kHz.
(The 1/x key on your calculator is handy for converting between f and T.)

13. 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. VP v
The peak voltage of this waveform is
20 V. v

14. Sine wave voltage and current values
The average value (actually the half-wave average) is used when comparing power supplies.
The average value for the sinusoidal voltage is
Vavg
12.7 V.

15. Sine wave voltage and current values
Peak to peak value: Value from positive peak to negative peak. Equation =
RMS (root mean squared) value: Is the sinusoidal wave with the same heat value as a DC voltage source (known as the effective value)

16. Sine wave voltage and current values
VP = 20 volts
The peak-to-peak voltage is
Vrms
40 V.
VPP
The rms voltage is
14.1 V.
This is magnitude Vpp

17. Angular Measurement Degree:
Angular measurement equal to 1/360 of the circumference of a circle.
Radian (rad):
Angle formed when the distance along the circumference of a circle equal the radius of the circle.
PI ( ):
The ratio of the circumference of a circle to its diameter. Has a constant value ≈

18. Angular measurement
Angular measurements can be made in degrees (o) or radians.
There are 360o or 2p radians in one complete revolution.

19. Angular measurements

20. Angular measurement
There are 2p radians in one complete revolution and 360o in one revolution. To find the number of radians, given the number of degrees:
This can be simplified to:
To find the number of degrees, given the number of radians:

21. How many radians are in 45o?
Angular measurement
How many radians are in 45o?
How many degrees are in 1.2 radians?

22. Sine wave angles

23. Phase of a Sine Wave Phase:
Angular measurement that specifies the position on the sine wave relative to a reference point.

24. Phase shift
Phase Shift of a sine wave is an angular measurement that specifies the position of a sine wave relative to a reference wave.
Sine wave shifted right (lags) –
Sine wave shifted left (leads) +
where
f =
Phase shift

25. Phase shifts
Occurs when a sine wave is shifted right or left in relation to the base/reference sine wave.

26. 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

27. Phase shift
Example of a wave that lags the reference (not on guided notes)
…and the equation has a negative phase shift
v = 30 V sin (q - 45o)
Notice that a lagging sine wave is below the axis at 0o

28. Phase shift
Example of a wave that leads the reference (not on guided notes)
Notice that a leading sine wave is above the axis at 0o
v = 30 V sin (q + 45o)
…and the equation has a positive phase shift

29. 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

30. 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
where
Vp =
q (theta) =
Peak voltage
Angle in rad or degrees
If the peak voltage is 25 V, the instantaneous voltage at 50 degrees is
19.2 V

31. 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.
Vp =
q (theta) =
Peak voltage
Angle in rad or degrees
45°, 125°, 180°, 220°,325°

32. Sine wave equation
A plot of the example in the previous slide (peak at 25 V).
The instantaneous voltage at 50o is 19.2 V as previously calculated.
4.34v
24.64v
What is the voltage at 100 and 800?

33. Phasors Phasor (aka Phase Vector):
Representation of a sine wave whose amplitude (A) and angular frequency (ω - omega) are a constant rate.

35. Power in resistive AC circuits
A sinusoidal voltage produces a sinusoidal current

36. Kirchhoff’s voltage law applies to AC circuits just like DC circuits
Power in resistive AC circuits
Kirchhoff’s voltage law applies to AC circuits just like DC circuits

37. Power in resistive AC circuits
Power in AC circuits is calculated using RMS values for voltage and current.
The power formulas are:
The dc and the ac sources produce the same power to the bulb:
120 Vdc
0 V
170 Vp
= 120 Vrms
0 V
WHY?

38. 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?
Vrms = x Vp = x 40 V = V
8 W

39. Superimposed dc and ac voltages
DC and AC voltages can be combined in a waveform.
Algebraically they produce a composite waveform of an AC voltage “riding” on a DC level.
If dc voltage > ac voltage, the sine wave never goes negative.

40. Superimposed dc and ac voltages

41. Schematic for Superimposed DC and AC voltages

42. Superimposed dc and ac voltages

43. Superimposed dc and ac voltages
VMAX = 22V
VMIN = 2V
VMAX = 16V
VMIN = -4V

44. 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.

46. 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.

47. Output Frequency of an AC Generator
f – frequency (Hz)
N – number of poles
s - speed in RPM 1 4 2 3

48. 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.
The output is taken from the rotor through the slip rings.

49. AC Motors There are two major classifications of ac motors.
Induction motor
Synchronous motor.
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.

50. Rotating the stator produces a net magnetic field

51. Rotating the stator produces a net magnetic field

52. Induction vs. Stator Motors
Squirrel Cage Rotor

53. Induction vs. Stator Motors

54. NONSINUSODIAL WAVE FORMS
Pulse:
Transition from one voltage/current level (baseline) to another level ( leading edge) and after an interval of time (t) transitioning back to the baseline (tailing edge)
Going positive – Rising edge
Going negative – Falling edge
Rise Time (tr) – Time required to go from 10% amplitude to 90% amplitude
Fall time (tf)– Time to go from 90% amplitude to 10% amplitude
Pulse width (tw) - Interval of time from when tr is at 50% amplitude and tf is at 50% amplitude

55. Pulse definitions
Ideal pulses

56. Pulse definitions Non-ideal pulses
Notice that rise and fall times are measured between the 10% and 90% levels whereas pulse width is measured at the 50% level.

57. 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 =
Vavg = baseline = (duty cycle)( amplitude)

58. Nonsinusoidal Wave Forms
Define terms on page 359
Rise time:
Fall time:
Pulse width:

59. Voltage ramps
Ramp – Linear increase or decrease in voltage or current.
Slope =

60. 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 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).

61. Harmonics Repetitive non-sinusoidal waveforms are composed of:
fundamental frequency (repetition rate of the waveform) &
harmonic frequencies.
Odd harmonics are frequencies that are odd multiples of the fundamental frequency.
Even harmonics are frequencies that are even multiples of the fundamental frequency.
Composite Waveform – Any deviation from a “normal” sine wave

62. Harmonics
A square wave is composed only of the fundamental frequency and odd harmonics (of the proper amplitude).

63. Oscilloscope
A device that traces the graph of a measured electrical signal on its screen.

64. Oscilloscopes
The oscilloscope is divided into four main sections.

65. Video on Osciloscope
The name of video is: AC vs Dc explain how to use an oscilloscope

66. Reading an Oscilloscope

67. Calculate for each wave: Period, Peak, Peak to Peak, RMS
T= 3.0 ms
Vp = 1250 mv
Vpp = 2500 mv
RMS = 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 = V
6 v
300 µs
12 v
15 µs

68. Selected Key Terms Sine wave
Alternating current
Period (T)
Frequency (f)
Hertz
A type of waveform that follows a cyclic sinusoidal pattern defined by the formula y = A sin q.
Current that reverses direction in response to a change in source voltage polarity.
The time interval for one complete cycle of a periodic waveform.
A measure of the rate of change of a periodic function; the number of cycles completed in 1 s.
The unit of frequency. One hertz equals one cycle per second.

69. Selected Key Terms Instantaneous value
Peak value
Peak-to-peak value
rms value
The voltage or current value of a waveform at a given instant in time.
The voltage or current value of a waveform at its maximum positive or negative points.
The voltage or current value of a waveform measured from its minimum to its maximum points.
The value of a sinusoidal voltage that indicates its heating effect, also known as effective value. It is equal to times the peak value. rms stands for root mean square.

70. Quiz
1. In North America, the frequency of ac utility voltage is 60 Hz. The period is
a. 8.3 ms
b ms
c. 60 ms
d. 60 s

71. 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

72. Quiz
3. An example of an equation for a waveform that lags the reference is
a. v = -40 V sin (q)
b. v = 100 V sin (q + 35o)
c. v = 5.0 V sin (q - 27o)
d. v = 27 V

73. Quiz 4. In the equation v = Vp sin q , the letter v stands for the
a. peak value
b. average value
c. rms value
d. instantaneous value

74. 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

75. 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

76. Quiz
7. The number of radians in 90o are
a. p/2
b. p
c. 2p/3
d. 2p

77. Quiz
8. For the waveform shown, the same power would be delivered to a load with a dc voltage of
a V
b V
c V
d V

78. Quiz 9. A square wave consists of a. the fundamental and odd harmonics
b. the fundamental and even harmonics
c. the fundamental and all harmonics
d. only the fundamental

79. 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

80. Quiz
Answers:
1. b
2. a
3. c
4. d
5. b
6. b
7. a
8. c
9. a
10. b