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Computer as a Technologist Tool.
AC SIGNALS AND OSCILLOSCOPES
1
ALTERNATING CURRENT: THE BASICS
• A waveform is a graph relationship between magnitude and time.
• So far we have been dealing only with direct current (DC) waveforms.
• Current moving in one direction all the time.
• Alternating Current is any current that periodically changes direction
• Term typically used to describe sinusoidal waveforms.
2
ALTERNATING CURRENT: THE BASICS
• Basic AC
Operation
3
ALTERNATIONS AND CYCLES

Alternations – the
positive and negative
transitions

Cycle – the complete
transition through one
positive alternation
and one negative
alternation

Half-Cycle – one
alternation
4
PERIOD (CYCLE TIME)
– Period – the time required to complete one cycle of a
signal
ms
T  4 div  X 5
 20 ms
div
5
FREQUENCY
– Frequency – the rate at which the cycles repeat
themselves
– Unit of Measure – hertz (Hz) = 1 cycle/second
6
PERIOD AND FREQUENCY
– Frequency and period are inversely related
1
f 
T
and
1
T 
f
where
T = the period of the waveform in seconds
= the frequency in Hz
7
PERIOD AND FREQUENCY
ms
T  4 div  X 5
 20 ms
div
1
1
f 
 50 Hz
T 20 ms
8
9
MEASURING AC SIGNALS
Multi-meters are typically used to measure DC
voltages and currents.
 Multi-meters can also measure AC voltages and
currents but are not very accurate



Often the AC signals are assumed to have a 60Hz
frequency.
A better approach that provides a detailed
analysis of an AC signal is to use an
Oscilloscope.
10
OSCILLOSCOPES
The oscilloscope is basically a device that
draws a graph of an electrical signal.
 Two types exist:

 Analogue
Oscilloscopes
 These
are used less and less nowadays but are still
around
 Digital
Storage Oscilloscopes (DSO)
 More
common e.g. Tektronix 2214
11
KEY DSO SPECIFICATIONS

Bandwidth



Record Length


The number of waveform points used to create a record of a signal.
Sample Rate


The frequency range of the instrument.
Sample Rate / 10
How frequently a digital oscilloscope takes a sample of the signal, specified in
samples per second (S/s).
If the sample rate of a scope is 250 Mega-Samples/per second what is the
scope’s bandwidth?
Bandwidth = (250 MS/s ) / 10 = 25 MHz
12
OSCILLOSCOPES

In most applications, the graph shows how
signals change over time:

the vertical (Y) axis represents voltage and the
horizontal (X) axis represents time.
13
OSCILLOSCOPE TIME AND FREQUENCY
MEASUREMENTS

Time Base Control – determines the amount of time
represented by the major divisions along the x-axis
14
DSO FRONT PANEL
15
DSO FRONT PANEL - VERTICAL SYSTEM AND
CONTROLS

Position and Volts-per-division (volts/div)


-
The vertical position control allows you to move the waveform up and
down on the display.
The volts-per-division (volts/div) setting varies the size of the waveform
on the screen. The volts/div setting is a scale factor. E.G If the volts/div
setting is 5 volts, then each vertical division represents 5 volts and the
entire screen of 8 divisions can display 40 volts from top to bottom
Input Coupling
-
Setting determines which part of the signal presented to input is
displayed on the screen:
-
DC coupling shows all of an input signal.
AC coupling blocks the DC component of a signal so that you see the
waveform centered around zero volts.
Ground coupling disconnects the input signal from the vertical system,
which lets you see where zero volts is located on the screen.
16
DSO FRONT PANEL - HORIZONTAL SYSTEM AND
CONTROLS

Position and Seconds-per-division (sec/div)
The horizontal position control allows you to move
the waveform left and right on the display.
 The seconds-per-division (sec/div) setting varies the
rate at which the waveform is drawn across the
screen (also known as the time base setting or
sweep speed).
 The sec/div setting is a scale factor. If the setting is
1 ms, then each horizontal division represents 1 ms
and the entire screen of 10 divisions represents 10
ms.

17
DSO FRONT PANEL -TRIGGER SYSTEM AND
CONTROLS
An oscilloscope’s trigger function synchronizes
the horizontal sweep at the correct point of the
signal, essential for clear signal
characterization.
 Trigger controls allow you to stabilize repetitive
waveforms and capture single-shot waveforms.

18
OSCILLOSCOPE PROBES




Can use BNC to alligator clip cables to connect oscilloscope to
circuit / signal source.
Oscilloscope probes however exhibit higher noise immunity,
especially at high frequencies.
Probes have two settings X1 and X10.
X10 setting provides better noise immunity but “attenuates” the
signal 10 times. If using a X10 probe make sure oscilloscope X10
setting is used.
19
SIGNAL GENERATOR

Device capable of producing many types of
waveforms with varying frequencies and
amplitudes.
20
REVIEW







What is a waveform?
What is the relationship between alternations and cycles?
What is the period of a waveform?
What is the frequency of a waveform? And what are the units
of frequency?
What is an oscilloscope?
What do the trigger controls enable you to do?
Assume you are viewing 4 cycles of a waveform on an
oscilloscope. Then, you double the frequency of the
waveform being displayed. What adjustment (if any) needs to
be made to the time/Div control to display 4 cycles of the
higher frequency waveform on the screen?
21
UNDERSTANDING VOLTAGE MEASUREMENTS
• Peak and Peak-to-Peak Values
– Peak Value – the maximum value reached by
either alternation of the waveform
– Peak-to-Peak Value – the difference between
its positive and negative peak values
VPP  2V pk
and
I PP  2 I pk
22
UNDERSTANDING VOLTAGE MEASUREMENTS
• Instantaneous Value – the
magnitude of a voltage or
current waveform at a
specified point in time
• Lowercase t =
instantaneous time
• Lowercase v =
instantaneous voltage
• Lowercase i =
instantaneous current
v(t) = Vpk*sin(wt)
23
UNDERSTANDING VOLTAGE MEASUREMENTS
• Full-Cycle Average – the average of all the
instantaneous values of voltage (or current)
throughout one complete cycle (always 0 for pure
ac)
• What if the AC signal is riding on a DC offset ?
24
UNDERSTANDING VOLTAGE MEASUREMENTS
• Half-Cycle Average –
the average of all a
waveform’s
instantaneous values
of voltage (or current)
through either of its
alternations
Vave 
2V pk

Where Vpk = the peak value of the waveform
25
EXAMPLE

A sine wave has a peak values of +/- 15V.
Calculate the half cycle average voltage(Vave).
Vave 
2 V pk


2  15v 

 9.55v

26
AVERAGE POWER AND RMS VALUES
– The average value of power generated during each cycle of
the waveform is calculated using rms values
– Root-Mean-Square (rms) – value that, when used in the
appropriate power equation, gives you the average power of
the waveform
– Take the square of a single period of a waveform, then take
its mean, then square root the result.
– The rms values of a waveform are also called effective
values
– Multimeters always read rms values for ac voltage and
current
V pk
Vrms 
 0.707V pk
V pk
2
P  Pave when V 
2
I pk
I rms 
 0.707 I pk
2
27
ROOT MEAN SQUARE
Waveform
Equation
RMS
Sine wave
Square wave
Modified square
wave
Sawtooth wave
Notes:
t is time
f is frequency
a is amplitude (peak value)
c % d is the remainder after floored division
28
EXAMPLE
A circuit consists of a sinusoidal voltage source
whose Vpk = 15 V and a series load resistor
RL= 100Ω
 Find the rms voltage and current

Vrms  0.707 V pk  0.707   15v   10.6v
I rms
 15v 
 0.707 V pk  0.707   
  150mA
 100 
29
EXAMPLE
A circuit consists of a sinusoidal voltage source
whose Vpk = 12 V and a series load resistor
RL= 330Ω
 Calculate the average load power

Vrms  0.707 V pk  0.707  12v   8.48v
2

Vrms
8.48v 
PL 

 218mW
RL
330
2
30
SINE WAVE GENERATION
• Magnetic Induction of Current – current
through a coil can be used to generate a
magnetic field
31
SINE WAVE GENERATION
• Or current can be created by moving a wire
through a magnetic field
32
GENERATING A SINE WAVE
• a sine wave can be generated by rotating a
“loop conductor” through a stationary
magnetic field
33
GENERATING A SINE WAVE
34
PHASE
• the phase of a given point is its position relative to
the start of the waveform, expressed in degrees
35
PHASE
• Phase and time measurements are related
as shown by the equation,
θ
t

360 T
where

= the phase of the point (vx)
t
= the time from the start of the cycle to vx
T = the time required for one complete cycle
36
PHASE
• When the period of a waveform is known, the time from the start of a
waveform to a given phase angle can be found as:
θ
t T 
360
• Given the time instant t, the instantaneous phase angle can also be
determined as :
t
θ  360 
T
37
PHASE AND TIME MEASUREMENTS
• Phase and Time Measurements
38
PHASE ANGLES
• Phase Angles
Red is lagging the blue by 90o .
Blue is leading the red by 90o .
39
EXAMPLE


Find the phase shift between these two waveforms.
Which one is leading and which one is lagging?
t  0.0625 sec
360o
360o
 t
 0.0625 
 45o
T
0.5
t
40
INSTANTANEOUS VALUES
• Instantaneous Values
v  Vpk sin θ
v  10  sin 320o   6.43v
• What is v if Vpeak = 10V ?
41
RADIANS
• Phase Measurements: The Radian Method
– Radian – the angle formed at the center of a circle by two
small radii separated by an arc of equal length
Degrees  Radians 
Radians  Degrees 
180


180
42
THE RADIAN METHOD
• Phase Measurements: The Radian Method
(Continued)
– 2 (rad) = 360º
– 1 rad = 360º/2  57.296º
– Angular Frequency (Velocity) – the rate at which the
phase and instantaneous values of a sine wave change
  2πf
where
 = angular velocity, in radians per second
2 = the number of radians in one cycle
f = the number of cycles per second (frequency)
43
THE RADIAN METHOD
– Instantaneous Values
• If phase angle is known:
vθ   Vpk sin θ
• If frequency is known:
vt   Vpk sin ωt
where
 = 2f (the angular velocity, in radians per second)
t = the designated time interval from the start of the cycle
44
45
STATIC AND DYNAMIC VALUES
– Static Values – do not change during the normal
operation of a circuit. A resistor’s resistance is a static
value.
– Dynamic Values – do change during the normal operation
of a circuit. The instantaneous value of a sine wave is a
dynamic value.
46
STATIC AND DYNAMIC VALUES (CONTINUED)
 Dynamic
Values
vx = 4 V  150º
where: 4 V is the magnitude and
150º is the phase angle
 Always
 Both
has one or more specified conditions
magnitude and phase are necessary to define
the value
DC OFFSET

- A sine wave with a dc offset has:
 Unequal
positive and negative peak values
 An average value that is equal to the dc offset
(rather than 0)
Insert Figure 9.36
ELECTROMAGNETIC WAVE


a waveform that consists of perpendicular electric and magnetic
fields
Eg. Light, Radio-waves, UV rays, infrared, x-rays, gamma rays.
WAVELENGTH

– the physical length of one cycle in space as opposed
to in time
WAVELENGTH (CONTINUED)
 Depends
on
 Speed
(velocity)
 Period of the waveform (cycle time)
 In
a vacuum, electromagnetic waves travel at the
speed of light
 1.86
X 105 m/s (miles per second)
 3 X 108 m/s (meters per second) 299792458 m/s
 300 m/s (meters per microsecond)
 984 ft/s (feet per microsecond)
WAVELENGTH (CONTINUED)
c
  cT 
f
where
c = the speed of light
T = the period of the waveform
f
= the frequency of the waveform being transmitted
HARMONICS

A whole number multiple of a given frequency

Example: a 2 kHz sine wave has harmonics of:
2 kHz X 2 = 4 KHz
2 kHz X 3 = 6 KHz
2 kHz X 4 = 8 KHz
2 kHz X 5 = 10 KHz

Harmonic Series – a group of related frequencies

Fundamental Frequency – the reference frequency,
in this case 2 kHz
HARMONICS
 Octave
– frequency change by a factor of two
f  2 fo
n
 Decade
– frequency change by a factor of ten
f  10 f o
n
f is the frequency
fo is the fundamental frequency
n is the number of decades or octaves
EXAMPLES

What is the frequency that is 5 octaves above
100Hz ?
f  2 f o  2 100  3200 Hz
n

5
What is the frequency that is 5 decades above
100Hz ?
f  10 f o  10 100  10 MHz
n
5
55
NONSINUSOIDAL WAVEFORMS:
• Rectangular Waves
• Time Measurements
56
NONSINUSOIDAL WAVEFORMS
• Rectangular Waves (Continued)
– Duty Cycle – ratio of pulse width to cycle time
PW
duty cycle (%) 
X 100
T
where
PW = the pulse width of the circuit input
T = the period of the circuit input
57
NONSINUSOIDAL WAVEFORMS
• Square Waves (Symmetrical rectangular waves)
– A special-case rectangular waveform that has equal
pulse width and space width values
– Duty Cycle = 50%
58
NONSINUSOIDAL WAVEFORMS
• Sawtooth and Triangular Waves
– Sawtooth Waveform – a waveform that
changes constantly at a linear rate
(sometimes referred to as a ramp)
– Triangular Waveform – a symmetrical
sawtooth waveform
59
NONSINUSOIDAL WAVEFORMS
60