bekg

1. BEKG 1123
PRINCIPLES OF ELECTRIC &
ELECTRONICS

2. 2
CHAPTER 4:
AC Sources

3. Learning Outcome
• In this chapter, we will cover on:
4.1 AC generator
4.2 Signal generator
4.3 Waveform type
4.4 AC characteristic
3

4. 4
INTRODUCTION
• AC is an electrical current whose magnitude and
direction vary sinusoidally with time.
• Such as current reverses at regular time intervals
and has alternately positive and negative values.

5. 5
INTRODUCTION..cont
• The circuits analysis is considering the time-varying
voltage source or current source.
• Circuits driven by sinusoidal current or voltage
sources are called ac circuits.
• A sinusoid can be express in either sine or
cosine form.

6. Difference between DC and AC
DC AC
6
V
5V
1kHz
R
I
V/I
t
V
5V
I
R
V/I
t

7. What is AC Generator?
• Is a device that converts the mechanical
energy into electrical energy.
• Generators, dynamos and alternators are
machines that convert mechanical power
into electrical power. Basically it has a coil
rotating in a magnetic field that will
produce the electrical energy/power.
7

8. GENERATING AC VOLTAGE
8
• Sinusoidal voltages are produced by ac
generators and electronic oscillators.
• One way to generate an ac voltage is to rotate a
coil of wire at constant angular velocity in a
uniform magnetic field.
• The magnitude of the resulting voltage is
proportional to the rate at which flux lines are
cut.(Faraday's Law)

9. 9
Generating AC Voltage…cont

10. Generating AC Voltage..cont
BEKP 2323 10

11. Function Generator
DENE1113 11
Function generators
Function selection
Frequency
Output level (amplitude)
DC offset
CMOS output
Range
Adjust
Duty cycle
Typical controls:
Outputs
Readout
Sine Square Triangle

12. AC Characteristics
12
• AC signals are generated by:
– AC generator
– Electronic function generator
• Types of AC waveforms:
– Sine wave
– Square wave
– Triangle wave
– Saw-tooth wave

13. Characteristics of sine wave
• The sinusoidal waveform (sine wave) is the fundamental of
13
AC current and AC voltage waveform.

14. Characteristics of sine wave
14
• Sine waves are characterized by the amplitude and period
of waveform.
• Amplitude:
– Is the maximum value of voltage or current.
• Period:
– Is time interval for 1 complete cycle.
15 V
10 V
0 V
-10 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

15. Characteristics of sine wave
15
• The period of a sine wave can be measured between any two
corresponding points on the waveform.
T T T T
T T
A
By contrast, the amplitude of a sine wave is only measured from the
center to the maximum point.

16. Characteristics of sine wave
16
• 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
3.0 Hz
1.0 s

17. Characteristics of sine wave
17
• Relationship between period and frequency
– The period and frequency are reciprocals of each other.
and
T
1
T
f

– Frequency = 1/ time for 1 complete cycle
• Examples:
1
f

– If the period is 50 s, what is the frequency?
– If frequency is 60Hz, what is the period?

18. 18
Waveform Terms &
Definitions
Definitions:
Period – the time taken to complete a cycle, T (s)
Peak value – the maximum instantaneous value measured from its zero value, Vp @
Vm (V)
Peak-to-peak value – the maximum variation between the maximum positive
instantaneous value and the maximum negative value, Vp-p (V)
Instantaneous voltage / current - has a value that corresponds to a specific time t.
Every waveform has an infinity number of instantaneous values. Such a waveform
is described as the parameter as a function of time. In the case of a voltage it will
be written as v(t).
Cycle – the portion of a waveform contained in one period of time. For a sine wave,
it is the complete event starting with a rise from zero energy to a maximum
amplitude, its return to zero, the rise to a maximum in the opposite direction, and
then its return to zero.

19. 19
WAVEFORM TERMS & DEFINITIONS contd.

20. 20
Sinusoids
• Consider the expression of a sinusoidal voltage
where
( )  sin m v t V t


= the amplitude of the sinusoid
= the angular frequency in radians/s
= the argument of the sinusoid
m V
t

21. SINUSOIDS contd.
• The sinusoid repeats itself every T seconds, thus
21
T is called the period of the sinusoid or the time
taken to complete one cycle. (s)

22. 22
SINUSOIDS contd.
• The number of cycles per second is called
frequency, f. (Hz)
1
f
T

• Angular frequency, ω. (rad/s)
  2 f
• An important value of the sinusoidal function is
its RMS (root-mean-square) value.
m
 
RMS dc
2
V
V V

23. 23
SINUSOIDS contd.
• Note: Radian measure
– ω is usually expressed in radian/s
– 2 radians = 360
– to convert from degrees to radians, multiply by /180.
– to convert from radians to degrees, multiply by 180/.
• From the general expression of the sinusoidal
voltage, we can find the value of voltage at any
given instant of time.

24. 24
SINUSOIDS contd.
• If the waveform does not pass through zero at
t=0, it has a phase shift.
• For a waveform shifted left,
• For waveform shifted right,
where
( )  sin   m v t V t
( )  sin   m v t V t
 = phase angle of the sinusoid function

25. 25
SINUSOIDS contd.

26. 26
SINUSOIDS contd.
Example:
1. Find the amplitude, phase, period and
frequency of the sinusoid
Solution:
v(t) 12sin50t 10
Amplitude, V= 12V
m Phase, 
= 10˚
Angular frequency, ω = 50rad/s
thus the period, T =
The frequency, f =
2 2
 

50
0.1257s
 
7.958
1
z
T
 H

27. 27
SINUSOIDS contd.
2. A sinusoidal voltage is given by the expression
V = 300 cos (120t + 30).
a) What is the frequency in Hz?
b) What is the period of the voltage in miliseconds?
c) What is the magnitude of V at t = 2.778ms?
d) What is the RMS value of V?
Solution:
a) Given ω = 120 = 2f, thus f = 60Hz
b) T = 1/f = 16.67ms
c) V = V = 300 cos (120x2.778m + 30)
= 300 cos (60 + 30) = 0V
d) Vrms = 300/√2 = 212.13V

28. 28
SINUSOIDS contd.
• Consider the following:
v1(t ) Vm sint   2( ) sin m v t V t 

29. 29
SINUSOIDS contd.
• The v2 is occurred first in time.

• Thus it can be said that v2 leads v1 by or v1

lags v2 by .

• If ≠ 0 we can say v1 and v2 are out of phase.

• If = 0 we can say v1 and v2 are in phase.
• v1 and v2 can be compared in this manner
because they operate at the same frequency (do
not need to have the same amplitude).

30. 30
SINUSOIDS contd.
• Transformation between cosine and sine form
and Converting from negative to positive
magnitude
o
t t
  
sin sin( 180 )
o
 
t t
  
cos cos( 180 )
o
 
t t
  
cos sin( 90 )
o
 
t t
sin   cos( 

90 )


31. at t = 0.5s
v = 6 cos (50 rad +60˚)
31
SINUSOIDS contd.
Example:
1. For the following sinusoidal voltage, find the
value v at t = 0s and t = 0.5s.
v = 6 cos (100t + 60˚)
Solution:
= 4.26V
at t = 0s
v = 6 cos (0+60˚)
= 3V

Note: both ωt and must be in same unit before adding them up.

32. 32
SINUSOIDS contd.
2. Calculate the phase angle between
v1 = -10 cos (ωt + 50)
v2 = 12 sin (ωt - 10)
State which sinusoid is leading.
Solution:
In order to compare v1 and v2, we must express them in
the same form (either in cosine or sine function) with
positive magnitude. Note: the value of 
must be
between 0 to 180
v1 = -10 cos (ωt + 50) = 10 cos (ωt + 50 - 180)
= 10 cos (ωt - 130)

33. 33
and
SINUSOIDS contd.
v2 = 12 sin (ωt - 10) = 12 cos (ωt - 10 - 90)
= 12 cos (ωt - 100)
the equation v2 can be written in the following form
v2 = 12 cos (ωt - 130 + 30)
‘+30’ in the above expression means v2 leads v1 by 30