SVES Students – you have a date in October 2016 on the Stuart Highway be looking for you...
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SVES Students – you have a date in October 2016 on the Stuart Highway be looking for you “mate” prof.alan for more info contact Bindu Lakshmi, SVECW, [email protected]
SVES Students you have a date in October 2016 on the Stuart
Highway be looking for you mate prof.alan for more info contact
Bindu Lakshmi, SVECW, [email protected]
Slide 2
Sinusoidal Alternating Waveforms A.C.
Slide 3
Introduction Alternating waveforms The term alternating
indicates only that the waveform alternates between two prescribed
levels in a set time sequence.
Slide 4
Sinusoidal ac Voltage Characteristics and Definitions
Generation An ac generator (or alternator) powered by water power,
gas, or nuclear fusion is the primary component in the
energy-conversion process. The energy source turns a rotor
(constructed of alternating magnetic poles) inside a set of
windings housed in the stator (the stationary part of the dynamo)
and will induce voltage across the windings of the stator.
Slide 5
Various sources of ac power: (a) generating plant; (b) portable
ac generator; (c) wind-power station; (d) solar panel; (e) function
generator.
Slide 6
Sinusoidal ac Voltage Characteristics and Definitions
Generation: Wind power and solar power energy are receiving
increased interest from various districts of the world. The turning
propellers of the wind-power station are connected directly to the
shaft of an ac generator. Light energy in the form of photons can
be absorbed by solar cells. Solar cells produce dc, which can be
electronically converted to ac with an inverter. A function
generator, as used in the lab, can generate and control alternating
waveforms.
Slide 7
Symbol for a sinusoidal voltage source
Slide 8
The electromechanical ac generator, cutaway view (courtesy of
General Electric).
Slide 9
AC Generator The ac generator has slip rings that pick up the
induced voltage through a complete rotation cycle The induced
voltage is related to the number of lines of flux being cut. When
the loop is moving parallel with the lines of flux, no voltage is
induced. When the loop is moving perpendicular to the lines of
flux, the maximum voltage is induced
Slide 10
Basic ac generator operation.
Slide 11
One revolution of the wire loop generates one cycle of the
sinusoidal voltage.
Slide 12
Frequency is directly proportional to the rate of rotation of
the wire loop in an ac generator.
Slide 13
Multi-pole ac Generator By increasing the number of poles, the
number of cycles per revolution can be increased
Slide 14
Four poles achieve a higher frequency than two poles for the
same r p s.
Slide 15
Electronic Signal Generators In the lab, we usually use a
signal generator to produce a variety of waveforms at a wide range
of frequencies An oscillator in the signal generator produces the
repetitive wave We are able to set the frequency and amplitude of
the signal from the signal generator
Slide 16
Typical signal generators. (Copyright Tektronix, Inc.
Reproduced by permission.)
Slide 17
Function generator.
Slide 18
Sinusoidal ac Voltage Characteristics and Definitions Waveform:
The path traced by a quantity, such as voltage, plotted as a
function of some variable such as time, position, degree, radius,
temperature and so on. Instantaneous value: The magnitude of a
waveform at any instant of time; denoted by the lowercase letters
(e 1, e 2 ). Peak amplitude: The maximum value of the waveform as
measured from its average (or mean) value, denoted by the uppercase
letters E m (source of voltage) and V m (voltage drop across a
load).
Slide 19
Sinusoidal ac Voltage Characteristics and Definitions
Definitions Peak value: The maximum instantaneous value of a
function as measured from zero-volt level. Peak-to-peak value:
Denoted by E p-p or V p-p, the full voltage between positive and
negative peaks of the waveform, that is, the sum of the magnitude
of the positive and negative peaks. Periodic waveform: A waveform
that continually repeats itself after the same time interval.
Slide 20
Important parameters for a sinusoidal voltage.
Slide 21
Sine Wave The sine wave is a common type of alternating current
(ac) and alternating voltage
Slide 22
Alternating current & voltage.
Slide 23
Sinusoidal ac Voltage Characteristics and Definitions
Definitions Period (T): The time interval between successive
repetitions of a periodic waveform (the period T 1 = T 2 = T 3 ),
as long as successive similar points of the periodic waveform are
used in determining T Cycle: The portion of a waveform contained in
one period of time Frequency: (Hertz) the number of cycles that
occur in 1 s
Slide 24
Period of a Sine Wave The time required for a sine wave to
complete one full cycle is called the period (T) A cycle consists
of one complete positive, and one complete negative alternation The
period of a sine wave can be measured between any two corresponding
points on the waveform
Slide 25
Graph of one cycle of a sine wave.
Slide 26
Defining the cycle and period of a sinusoidal waveform.
Slide 27
Measurement of the period of a sine wave. Thomas L. Floyd
Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e
Copyright 2004 by Pearson Education, Inc. Upper Saddle River, New
Jersey 07458 All rights reserved.
Slide 28
Frequency of a Sine Wave Frequency ( f ) is the number of
cycles that a sine wave completes in one second The more cycles
completed in one second, the higher the frequency Frequency is
measured in hertz (Hz) Relationship between frequency ( f ) and
period (T) is: f = 1/T
Slide 29
Illustration of frequency.
Slide 30
Demonstrating the effect of a changing frequency on the period
of a sinusoidal waveform.
Slide 31
The period of a given sine wave is the same for each
cycle.
Slide 32
Cycles in one second of time
Slide 33
Slide 34
Areas of application for specific frequency bands.
Slide 35
Seismogram from station BNY (Binghamton University) in New York
due to magnitude 6.7 earthquake in Central Alaska that occurred at
63.62N, 148.04W, with a depth of 10 km, on Wednesday, October 23,
2002.
Slide 36
Peak Values of Sine Waves The peak value of a sine wave is the
value of voltage or current at the positive or negative maximum
with respect to zero Peak values are represented as: V p and I
p
Slide 37
Peak values.
Slide 38
Peak-to-Peak Values The peak-to-peak value of a sine wave is
the voltage or current from the positive peak to the negative peak
The peak-to-peak values are represented as: V pp and I pp where: V
pp = 2V p and I pp = 2I p
Slide 39
Peak-to-peak value.
Slide 40
Instantaneous Values of Sine Waves The instantaneous values of
a sine wave voltage (or current) are different at different points
along the curve, having negative and positive values Instantaneous
values are represented as: v and i
Slide 41
General Format for the Sinusoidal Voltage or Current The basic
mathematical format for the sinusoidal waveform is: where: A m is
the peak value of the waveform is the unit of measure for the
horizontal axis
Slide 42
Sine Wave Formula The general expression for a sine wave is: y
= A sin Where:y = an instantaneous value (v or i) A = amplitude
(maximum value) = angle along the horizontal axis
Slide 43
Example of instantaneous values of a sinusoidal voltage.
Slide 44
Sine wave angles.
Slide 45
One cycle of a generic sine wave showing amplitude and
phase.
Slide 46
Illustration of the instantaneous value of a voltage sine wave
at = 60.
Slide 47
Right triangle derivation of sine wave formula, v = V p sin
.
Slide 48
Sine wave represented by a rotating phasor.
Slide 49
Average Value The algebraic sum of the areas must be
determined, since some area contributions will be from below the
horizontal axis. Area above the axis is assigned a positive sign
and area below the axis is assigned a negative sign. The average
value of any current or voltage is the value indicated on a dc
meter over a complete cycle the average value is the equivalent dc
value.
Slide 50
Average Value Understanding the average value using a sand
analogy: The average height of the sand is that height obtained if
the distance form one end to the other is maintained while the sand
is leveled off.
Slide 51
Average Value of a Sine Wave The average value is the total
area under the half-cycle curve divided by the distance in radians
of the curve along the horizontal axis V avg = 0.637V p I avg =
0.637I p
Slide 52
Half-cycle average value.
Slide 53
Effective (rms) Values How is it possible for a sinusoidal ac
quantity to deliver a net power if, over a full cycle the net
current in any one direction is zero (average value = 0).
Irrespective of direction, current of any magnitude through a
resistor will deliver power to that resistor during the positive
and negative portions of a sinusoidal ac current, power is being
delivered at each instant of time to the resistor. The net power
flow will equal twice that delivered by either the positive or the
negative regions of sinusoidal quantity.
Slide 54
RMS Value of a Sine Wave The rms (root mean square) value, or
effective value, of a sinusoidal voltage is equal to the dc voltage
that produces the same amount of heat in a resistance as does the
sinusoidal voltage V rms = 0.707V p I rms = 0.707I p
Slide 55
An experimental setup to establish a relationship between dc
and ac quantities.
Slide 56
When the same amount of heat is being produced by the resistor
in both setups, the sinusoidal voltage has an rms value equal to
the dc voltage.
Slide 57
Effective (rms) Values The formula for power delivered by the
ac supply at any time is: The average power delivered by the ac
source is just the first term, since the average value of a cosine
wave is zero even though the wave may have twice the frequency of
the original input current waveform.
Slide 58
Effective (rms) Values The equivalent dc value is called the
effective value of the sinusoidal quantity or and or Where: I m and
E m are max (peak) values
Slide 59
Effective (rms) Values Instrumentation A true rms meter will
read the effective value of any waveform and is not limited to only
sinusoidal waveforms. You should make sure that your meter is a
true rms meter, by checking the manual, if waveforms other than
purely sinusoidal are to be encountered.
Slide 60
Angular Measurement of a Sine Wave A degree is an angular
measurement corresponding to 1/360 of a circle or a complete
revolution A radian (rad) is the angular measure along the
circumference of a circle that is equal to the radius of the circle
There are 2 radians or 360 in one complete cycle of a sine
wave
Slide 61
Phase Relations If a sinusoidal expression should appear as e =
- E m sin t the negative sign is associated with the sine portion
of the expression, not the peak value E m. Phase Measurements When
determining the phase measurement we first note that each
sinusoidal function has the same frequency, permitting the use of
either waveform to determine the period. Since the full period
represents a cycle of 360, the following ratio can be formed:
Slide 62
The Sine Wave If we define x as the number of intervals of r
(the radius) around the circumference of a circle, then C = 2 r = x
r and we find x = 2 Therefore, there are 2 rad around a 360 circle,
as shown in the figure.
Slide 63
Angular measurement showing relationship of the radian to
degrees.
Slide 64
Angular measurements starting at 0 and going
counterclockwise.
Slide 65
Phase reference.
Slide 66
The Sine Wave The quantity is the ratio of the circumference of
a circle to its diameter. For 180 and 360, the two units of
measurement are related as follows:
Slide 67
The Sine Wave The sinusoidal wave form can be derived from the
length of the vertical projection of a radius vector rotating in a
uniform circular motion about a fixed point. The velocity with
which the radius vector rotates about the center, called the
angular velocity, can be determined from the following
equation:
Slide 68
horizontal axis in degrees
Slide 69
horizontal axis in radians
Slide 70
horizontal axis in milliseconds
Slide 71
The Sine Wave The angular velocity ( ) is: Since ( ) is
typically provided in radians per second, the angle obtained using
= t is usually in radians. The time required to complete one
revolution is equal to the period (T) of the sinusoidal waveform.
The radians subtended in this time interval are 2 . or
Slide 72
General Format for the Sinusoidal Voltage or Current The
equation = t states that the angle through which the rotating
vector will pass is determined by the angular velocity of the
rotating vector and the length of time the vector rotates. For a
particular angular velocity (fixed ), the longer the radius vector
is permitted to rotate (that is, the greater the value of t ), the
greater will be the number of degrees or radians through which the
vector will pass. The general format of a sine wave can also be
as:
Slide 73
Demonstrating the effect of on the frequency and period.
Slide 74
Phase of a Sine Wave The phase of a sine wave is an angular
measurement that specifies the position of a sine wave relative to
a reference When a sine wave is shifted left or right with respect
to this reference, there is a phase shift
Slide 75
Expressions for Shifted Sine Waves When a sine wave is shifted
to the right of the reference by an angle , it is termed lagging
When a sine wave is shifted to the left of the reference by an
angle , it is termed leading
Slide 76
Ohmss Law and Kirchhoffs Laws in AC Circuits When time-varying
ac voltages such as a sinusoidal voltage are applied to a circuit,
the circuit laws that were studied earlier still apply Ohms law and
Kirchhoffs laws apply to ac circuits in the same way that they
apply to dc circuits
Slide 77
sinusoidal voltage produces a sinusoidal current
Slide 78
Illustration of Kirchhoffs voltage law in an ac circuit
Slide 79
Superimposed dc and ac Voltages DC and ac voltages will add
algebraically, to produce an ac voltage riding on a dc level
Slide 80
Superimposed dc and ac voltages.
Slide 81
Sine waves with dc levels.
Slide 82
Pulse Waveforms A pulse has a rapid transition (leading or
rising edge) from a baseline to an amplitude level, then, after a
period of time, a rapid transition (trailing or falling edge) back
to the baseline level Pulses can be positive-going, or
negative-going, depending upon where the baseline is The distance
between rising and falling edge is termed the pulse width
Slide 83
Non-ideal Pulse A non-ideal pulse has a rising and falling time
interval, measured between 10% and 90% of its Amplitude Pulse width
is taken at the half-way point
Slide 84
Pulse Waveforms
Slide 85
Repetitive Pulses Any waveform that repeats itself at fixed
intervals is periodic The time from one pulse to the corresponding
point on the next pulse is the period, T ( f =1/T ) The duty cycle
is the ratio of the pulse width (t w ) to the period (T), and is
usually expressed as % Duty cycle = (t w /T)100% Square waves have
a 50% duty cycle
Slide 86
Repetitive Pulses
Slide 87
Square wave
Slide 88
Triangular and Sawtooth Waveforms 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 slope The sawtooth waveform is a
special case of the triangular wave consisting of two ramps, one of
much longer duration than the other. A sawtooth voltage is
sometimes called a sweep voltage
Slide 89
Alternating triangular waveform.
Slide 90
Alternating sawtooth waveform.
Slide 91
Harmonics A repetitive non-sinusoidal waveform is 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 Even harmonics are
frequencies that are even multiples of the fundamental frequency
Composite waveforms vary from a pure sine wave, they may contain
only even harmonics, only odd harmonics or both
Slide 92
Odd Harmonics Produce a Square Wave
Slide 93
Summary Conversions of sine wave values are:
Slide 94
Four-channel digital phosphor oscilloscope. Tektronix TDS3000B
series oscilloscope.
Slide 95
AC-GND-DC switch for the vertical channel of an
oscilloscope.
Slide 96
A typical dual-channel digital oscilloscope..
Slide 97
Connection for voltage probe compensation.
Slide 98
Compensation waveforms.
Slide 99
Proper Display
Slide 100
Slide 101
A typical dual-channel analog oscilloscope.
Slide 102
Proper triggering stabilizes a repeating waveform.
