Lesson 4(1).pdf electronics The sinusoidal waveform 2. Voltage and current values sine waves

Lesson 4 electronics

1. Electronics Fundamentals 8
th
edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
electronics fundamentals
circuits, devices, and applications
THOMAS L. FLOYD
DAVID M. BUCHLA
Lesson 4

2. Electronics Fundamentals 8
th
edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
OUTLINES:
1.The sinusoidal waveform
2.Voltage and current values sine waves
3.Superimposed DC and AC voltages
4.Non-sinusoidal waveforms
5.Angular measurement of a sine wave
6.Power in resistive AC circuits

3. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
The sinusoidal waveform (sine wave) is the fundamental
alternating current (ac) and alternating voltage waveform.
Sine waves
Electrical sine waves are
named from the
mathematical function with
the same shape.
5
Alternating current (AC)
Lesson 4
Positive
alternation
Negative
alternation

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5. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
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.
Sine waves
Example
0 V
10 V
-10 V
15 V
-15 V
-20 V
t (s)
0 25 37.5 50.0
20 V
The amplitude (A)
of this sine wave
is 20 V
The period is 50.0 s
A
T
5Lesson 4

6. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
3.0 Hz
Frequency
Frequency ( f ) is the number of cycles that a sine wave
completes in one second.
Frequency is measured in hertz (Hz).
Example
If 3 cycles of a wave occur in one second, the frequency
is
1.0 s
5Lesson 4

7. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
The period and frequency are reciprocals of each other.
Period and frequency
T
f
1
=
and
f
T
1
=
Example
If the period is 50 s, the frequency is0.02 MHz = 20 kHz.
5Lesson 4

8. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Sine wave voltage and current values
There are several ways to specify the voltage of a
sinusoidal voltage waveform. The amplitude of a sine
wave is also called the peak value, abbreviated as V
P for
a voltage waveform.
Example
0 V
10 V
-10 V
15 V
-15 V
-20 V
t (s)
0 25 37.5 50.0
20 V
The peak voltage of
this waveform is 20 V.
V
P
5Lesson 4

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Lesson 4
u
???L
u
?
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, ?
???L
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10. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
0 V
10 V
-10 V
15 V
-15 V
-20 V
t (s)
0 25 37.5 50.0
20 V
The voltage of a sine wave can also be specified as either the
peak-to-peak or the rms value. The peak-to-peak is twice the
peak value. The rms value is 0.707 times the peak value.
Sine wave voltage and current values
Example
The peak-to-peak
voltage is 40 V.
The rms voltage
is 14.1 V.
V
PP
V
rms
5Lesson 4

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Lesson 4

12. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Frequently DC and AC voltages are together in a waveform.
They can be added algebraically, to produce a composite
waveform of an ac voltage “riding” on a dc level.
Superimposed DC and AC voltages5Lesson 4

13. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Example
5Lesson 4

14. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Pulse Waveforms:
Basically, a pulse can be described as a very rapid transition
(leading edge) from one voltage or current level (baseline) to
another level; and then, after an interval of time, a very rapid
transition (trailing edge) back to the original baseline level.
The transitions in level are called steps. An ideal pulse consists
of two opposite-going steps of equal amplitude. When the
leading or trailing edge is positive-going, it is called a rising
edge. When the leading or trailing edge is negative-going, it is
called a falling edge.

NONSINUSOIDAL WAVEFORMS 5Lesson 4

15. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Actual pulses, however, are never ideal. Pulses cannot change from one
level to another instantaneously. Time is always required for a transition
(step), as illustrated in Figure 46(a).
5Lesson 4

16. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Rise time (t
r) is the time required for the pulse to go from 10% of its
amplitude to 90% of its amplitude.
Fall time (t
f) is the time required for the pulse to go from 90% of its
amplitude to 10% of its amplitude.
tw :Pulse width is the time between the point on the leading edge
where the value is 50% of the amplitude and the point on the trailing
edge where the value is 50% of the amplitude.
5Lesson 4

17. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Repetitive Pulses Any waveform
that repeats itself at fixed
intervals is periodic. Notice that
in each case, the pulses repeat at
regular intervals. The rate at
which the pulses repeat is the
pulse repetition frequency,
which is the fundamental
frequency of the waveform. An
important characteristic of
periodic pulse waveforms is the
duty cycle.
The duty cycle is the ratio of the pulse width (t
W) to the period (T) and
is usually expressed as a percentage.
5Lesson 4

18. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Example
5Lesson 4

19. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Square Waveforms:
A square wave is a pulse waveform with a duty cycle of 50%. Thus, the
pulse width is equal to one-half of the period. A square wave is shown in
Figure 49.
5Lesson 4

20. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
The Average Value of a Pulse Waveform :
The average value of a pulse waveform is equal to its baseline value plus
the product of its duty cycle and its amplitude. The lower level of a
positive-going waveform or the upper level of a negative-going waveform
is taken as the baseline. The formula for average voltage is as follows:
5
=
T
0
dt.V
T
1
V
avg
Average value
Lesson 4

21. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Example
5Lesson 4

22. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Triangular and sawtooth waves
5Lesson 4

23. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Example
5Lesson 4

24. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Triangular Waveforms:
Figure 53 shows that a triangular waveform is composed of positive-
going and negative-going ramps having equal slopes. The period of this
waveform can be measured from one peak to the next corresponding peak,
as illustrated. This particular triangular waveform is alternating and
has an average value of zero.
Figure 54 depicts a triangular waveform with a nonzero average value. The
frequency for triangular waves is determined in the same way as for sine waves,
that is, f = 1/T.
5Lesson 4

25. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Sawtooth Waveforms The sawtooth waveform is actually a special case
of the triangular waveform consisting of two ramps, one of much longer
duration than the other. Sawtooth waveforms are used in many
electronic systems. For example, a sawtooth waveform is used in
automatic test equipment, control systems, and certain types of displays,
including analog oscilloscopes.
Figure 55 is an example of a sawtooth waveform. Notice that it consists
of a positive-going ramp of relatively long duration, followed by a
negative-going ramp of relatively short duration.
5Lesson 4

26. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Harmonics
All repetitive non-sinusoidal waveforms are composed of a fundamental
frequency (repetition rate of the waveform) and harmonic frequencies.
Odd harmonics are frequencies that are odd multiples of the fundamental
frequency.
Odd harmonics are frequencies that are odd multiples of the fundamental
frequency. For example, a 1 kHz square wave consists of a fundamental
of 1 kHz and odd harmonics of 3 kHz, 5 kHz, 7 kHz, and so on. The 3 kHz
frequency in this case is the third harmonic; the 5 kHz frequency is the
fifth harmonic; and so on.
Even harmonics are frequencies that are even multiples of the fundamental
frequency. For example, if a certain wave has a fundamental of 200 Hz, the
second harmonic is 400 Hz, the fourth harmonic is 800 Hz, the sixth
harmonic is 1200 Hz, and so on. These are even harmonics
5Lesson 4

27. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
A square wave is composed only of the fundamental frequency and odd
harmonics (of the proper amplitude).
Composite Waveform A non-sinusoidal wave is a composite of the
fundamental and the harmonics. Some types of waveforms have only odd
harmonics, some have only even harmonics, and some contain both.
Harmonics5Lesson 4

28. T
T
PhasorsLesson 4
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29. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Angular measurements can be made in degrees (
o
) or
radians. The radian (rad) is the angle that is formed when
the arc is equal to the radius of a circle. There are 360
o
or
2 radians in one complete revolution.
Angular measurement
R
R
1.0
-1.0
0.8
-0.8
0.6
-0.6
0.4
-0.4
0.2
-0.2
0
0 2
2

4

4
3 
2
3
4
5 
4
7
5Lesson 4

30. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
There are 2 radians in one complete revolution and 360
o

in one revolution. To find the number of radians, given
the number of degrees:
2 rad
rad degrees
360

=

180
deg rad
rad

=
To find the number of degrees, given the number of
radians:
Angular measurement
This can be simplified to:
rad
rad degrees
180

=

5Lesson 4

31. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Instantaneous values of a wave are shown as v or i. The
equation for the instantaneous voltage (v) of a sine
wave is
Sine wave equation
Example
If the peak voltage is 25 V, the instantaneous
voltage at 50 degrees is
sin
pVv=
19.2 V
V
p =  = Peak voltage Angle in rad or degrees
5Lesson 4

32. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Sine wave equation
v = = 19.2 V V
p
sin
V
p
90
500
= 50
V
p
V
p
= 25 V
A plot of the example in the previous slide (peak at
25 V) is shown. The instantaneous voltage at 50
o
is
19.2 V as previously calculated.
5Lesson 4

33. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
0
0
90
90
180
180
360
The sine wave can be represented as the projection of a
vector rotating at a constant rate. This rotating vector is
called a phasor. Phasors are useful for showing the
phase relationships in ac circuits.
Phasors5Lesson 4

34. دادعإ :أ.د .ينوتيزلا ميركلادبع
Lesson 4

35. PhasorsLesson 4
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36. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Phase shift
where
 = Phase shift
The phase of a sine wave is an angular measurement
that specifies the position of a sine wave relative to a
reference. To show that a sine wave is shifted to the
left or right of this reference, a term is added to the
equation given previously.
()=sin
PVv
5Lesson 4

37. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Phase shift
V
o
lt
a
g
e

(
V
)
270 3600 90 180
40
45 135 225 315
0
Ang le ()
30
20
10
-20
-30
-40
405
Pe a k v o l t a g e
Re f e re n c e
Notice that a lagging sine
wave is below the axis at 0
o
Example of a wave that lags the
reference
v = 30 V sin ( − 45
o
)
…and the equation
has a negative phase
shift
5Lesson 4

38. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Phase shift
V
o
lt
a
g
e

(
V
)
270 3600 90 180
40
45 135 225 3150
Ang le ()
30
20
10
-20
-30
-40
Pe a k voltage
Re f e re n c e
-45
-10
Notice that a leading sine
wave is above the axis at 0
o
Example of a wave that leads the
reference
v = 30 V sin ( + 45
o
)
…and the equation
has a positive phase
shift
5Lesson 4

39. Phasors
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Lesson 4

40. Phasors
Lesson 4
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41. Phasors: Exercise
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Lesson 4

42. Phasors
Exercise
دادعإ :أ.د .ينوتيزلا ميركلادبع
Lesson 4

44. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
The power formulas are:
Power in resistive AC circuits
rms rms
2
2
rms
rms
PVI
V
P
R
PIR
=
=
=
ac or dc
source
Bulb
The power relationships developed for dc circuits apply
to ac circuits except you must use rms values in ac
circuits when calculating power.
0 V
0 V
For example, the dc and the ac sources
produce the same power to the bulb:
120 V
dc
170 V
p
= 120 V
rms
5Lesson 4

45. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Assume a sine wave with a peak value of 40 V is
applied to a 100  resistive load. What power is
dissipated?
Power in resistive AC circuits
2 2
28.3 V
100
rms
V
P
R
== =

Example
V
o
lt
a
g
e

(V
)
40
0
30
20
10
-1 0
-2 0
-3 0
-40
SolutionV
rms = 0.707 x V
p = 0.707 x 40 V = 28.3 V
8 W
5Lesson 4

46. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Sine wave
Alternating
current
Period (T)
Frequency (f)
Hertz
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 type of waveform that follows a cyclic
sinusoidal pattern defined by the formula
y = A sin 
Selected Key Terms
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.
5Lesson 4

47. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Instantaneous
value
Peak value
Peak-to-peak
value
rms value
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 voltage or current value of a waveform at
a given instant in time.
Selected Key Terms
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.
5Lesson 4

48. Electronics Fundamentals 8
th
edition
Floyd/Buchla
Chapter 8
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Radian
Phase
Amplitude
Pulse
Harmonics
The maximum value of a voltage or current.
A type of waveform that consists of two equal and
opposite steps in voltage or current separated by a
time interval.
A unit of angular measurement. There are 2
radians in one complete 360
o
revolution.
Selected Key Terms
The frequencies contained in a composite
waveform, which are integer multiples of the pulse
repetition frequency.
The relative angular displacement of a time-varying
waveform in terms of its occurrence with respect to
a reference.
5Lesson 3