ELEC 103 Unit 5 The Oscilloscope
PURPOSE
To determine whether a circuit is operating properly, or malfunctioning, it is often necessary to
observe the electronic signals in the circuit. A VOM or DMM will give the magnitude of an ac current
or voltage, but is unable to display the signal or provide information to allow the user to determine if
there is distortion on the signal, or if there is an improper phase shift in the circuit. The oscilloscope
allows the technician to view these signals and determine the circuit operating characteristics. The
purpose of this exercise, is to use the ac meter and the oscilloscope to make voltage and current
measurements in an ac circuit. The student will be able to describe the procedure to measure voltage,
period, frequency, and phase relationships for ac waveforms with the oscilloscope.
EQUIPMENT AND MATERIALS REQUIRED
Oscilloscope with 2 probes
2 each DMM’S and VOM’s
Powered Protoboard
Audio Signal Generator
Frequency Counter
Resistor, ½W, 5%, 1.5kΩ
Capacitor, 35V, 10%, 0.1µF
INTRODUCTION
There is a wide variety of test equipment available to the technician, which provides information on
circuit operation. All test equipment, used to measure voltage in a circuit, must have a high input
impedance to prevent the test equipment from loading the circuit under test and thereby provide
inaccurate measurements. The VOM usually has a moderately high input impedance while the DMM
and oscilloscope have a high input impedance of 1MΩ or higher. This high input impedance assures
the measurements will be accurate since loading does not occur.
The VOM and DMM are used to measure ac currents and voltages in the same way they were used in
the ELEC 111 course experiments. Since the polarity of the waveform is constantly changing, there is
no polarity to consider when making ac voltage and current measurements.
The oscilloscope provides a visual representation of the voltage at any point in the circuit on a CRT.
As a result, the technician may view the display and determine the shape of the waveform, the
amplitude of the waveform, the frequency of the waveform, the phase relationships between voltage
waveforms at various points in the circuit, or the duration of some event lasting one or more cycles.
An ac voltage is one that is continuously changing in magnitude and direction, with respect to time.
These ac signals have a frequency of repetition measured in Hertz (cycles per second), which is the
number of complete waveforms created in one second. The symbol for frequency is f, and the unit of
measurement is the Hertz (Hz). Reference may also be made to the amount of time required for two
alternations, which make up one cycle, of the signal, which is called the period of the waveform. The
period of the waveform uses the symbol T, and has the second as the unit of measurement. There is an
inverse relationship between the frequency and period of the waveform. This may be expressed as:
1
f= T
<5 − 1>
The analog waveform used to carry information in an ac circuit is the sinewave. These sinusoidal
signals may be symmetrical above and below a zero volt reference, or they may be riding on a dc level.
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ELEC 103 Unit 5 The Oscilloscope
The amplitude of a signal is the height of the signal above or below the reference. In most cases, the
reference used is zero volts or ground.
The polarity of a signal refers to the waveform’s value, with respect to the common level in the
system, which is usually ground or zero volts. All parts of the signal that rise above the zero volt level
have a positive voltage polarity, and all parts of the signal that fall below the zero volt level have a
negative voltage polarity.
The sinewave in Figure 5 − 1 has equal excursions above
and below the zero volt reference. The maximum positive
level from the zero volt reference is called the positive
peak voltage, VPP, and the maximum negative level from
the zero volt reference is called the negative peak voltage,
−VP. Since the variation above and below the reference is
the same, the magnitude of VP is equal to −VP. While this
is the case for Figure 5 − 1, it is not required. An ac
information signal may also ride on a dc level. When the
dc level is such that there is no excursion about the zero
volt reference, but is always either above or below zero
volts, this signal is no longer an ac waveform but a
pulsating dc voltage. The amplitude is defined as the
voltage level between the positive and negative peaks,
FIGURE 5 − 1
and is called the peak−to−peak voltage, or VPP. When the
magnitude of VP is equal to the magnitude of −VP, we may determine VPP from the equation:
VPP = 2VP
The amplitude of the ac signal may be measured and defined in different formats. The instantaneous
voltage is the value of the voltage at a particular time. The symbol v is used to denote an instantaneous
voltage, and the unit of measurement is the Volt. The time at which we wish to determine the
instantaneous voltage may be θ (theta) and is measured in either degrees or radians, or time ( t )
measured in seconds. Both θ and t must be measured with respect to some defined reference of the
signal. This is normally when the signal is at zero volts and rising, or zero degrees. When the
instantaneous voltage is determined using t, the time must first be multiplied by 2 π f, which is the
angular velocity (also known as ω) of the voltage. The units of measurement for ω is rad/s (radians per
second). Since the voltage is sinusoidal, the instantaneous voltage may be determined from the
equations:
v = VP Sin θ
v = VP Sin (2 π f t)
Another measurement to define an ac voltage or current is the effective or Root−Mean−Square (rms)
voltage. This measurement is important, since the rms voltage or current has the same heating value as
the corresponding dc voltage or current. The symbol used to denote an rms voltage measurement is
Vrms, and is measured in Volts. Current measurements use the symbol Irms, and have the Ampere as the
unit of measurement. The VOM and DMM provide rms voltage and current measurements. The rms
voltage may be calculated from the peak voltage using the equation:
Vrms =
VP
2
which equals Vrms = 0.707 Vrms
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ELEC 103 Unit 5 The Oscilloscope
The final measurement, used to refer to an ac voltage or current, is the average value. The average
value for an ac voltage is the average of all the voltage levels for one−half of a cycle of an ac voltage.
This measurement is important since it corresponds to the deflection of the pointer for an analog ac
meter, even though the ac meter scale is calibrated to provide rms readings. The relationship between
the peak and average voltage of a sinusoidal ac voltage or current is:
2VP
VPP
=
= 0.6366 VP
π
π
Remember that VPP, VP, Vrms, and Vav values are equivalent methods to define the same voltage. The
type of measurement made is determined by the equipment used to make the measurement. A VOM
would indicate 120Vrms supplied to the home, while an oscilloscope would indicate the same voltage as
169.71VP, and 339.41VPP. To find the relationship between the rms and average voltages recall:
Vav =
VP =
2 Vrms
and
⎛ π⎞
VP = Vav ⎜ ⎟
⎝ 2⎠
Therefore, if we equate these two readings we obtain:
⎛ π ⎞
⎛π⎞
2 Vrms = Vav ⎜ ⎟ and Vrms = Vav ⎜
⎟
2
⎝ ⎠
⎝ 2 2 ⎠
Since π, 2, and 2 2 are constants, we may solve for the constants in the previous equation and obtain:
Vrms = 1.1107Vav and Vav = 0.9 Vrms
The oscilloscope is used to measure the amplitude of a voltage, displayed on the vertical axis, against
time, which is displayed on the horizontal axis. The vertical and horizontal axis have marked
graduated scales, in each direction, calibrated into major and minor divisions. A range switch, in
conjunction with the vertical amplifier, controls the vertical deflection of the electron beam in the
oscilloscope, while the time base and associated circuitry control the horizontal sweep speed.
The vertical gain of the scope is calibrated in volts per division. The signal is applied to the vertical
deflection circuitry of the scope that deflects an electron beam vertically on the face of the oscilloscope
according to the polarity and magnitude of the applied voltage. To determine the amplitude of the
voltage, count the number of divisions over which the beam is deflected, and multiply this value by the
gain setting. If the measurement is made between the zero volt reference, and the peak value, a peak
voltage is being measured, while a measurement between the positive and negative peaks is a
peak−to−peak voltage measurement. For Figure 5 − 1, if the beam is deflected 7.2 divisions between
the positive and negative peaks, and 3.6 major divisions between the zero volt reference and the
positive peak, with the vertical gain set to 5 V/div, the voltage represented by this deflection is:
VPP = 7.2 div x 5 V/div = 36VPP and VP = 3.6 div x 5 V/div = 18VP
The horizontal deflection on the oscilloscope is controlled by a sweep generator. The sweep generator
is used to move the beam from the left side of the CRT to the right side of the CRT. When the beam
reaches the right side of the CRT, it is swept back very rapidly and the process is repeated. The control
for the sweep speed is calibrated in seconds/division, and the horizontal axis is used to measure time.
Therefore, on the horizontal axis of the scope, you will be able to determine the period of the
waveform.
To determine the frequency of a waveform, with an oscilloscope, the period of one cycle is usually
determined. The sweep speed is adjusted until more than one complete cycle occupies the horizontal
axis of the oscilloscope. Then the number of divisions for one cycle is counted and multiplied by the
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ELEC 103 Unit 5 The Oscilloscope
sweep speed. For Figure 5 − 1, if the sweep speed is set to 0.5 ms/div and one cycle occupies 6.6
major divisions, the period for one cycle is:
T = 0.5 ms/div x 6.6 div = 3.30 ms
Since the frequency of a waveform is the inverse of the period, the frequency of the signal in Figure 5
− 1 is:
1
1
f = T = 3.3ms = 303 Hz.
When two or more waveforms of the same frequency are present at the same time in a circuit, it is
possible to define the time relationship between corresponding values of the waveform. This
relationship is called the phase or phase angle. The phase angle uses θ as the symbol of measurement,
and has either degrees or radians as the units of measurement. Two waveforms are in phase when both
waveforms begin at zero volts and rise or fall together. If both waveforms are zero volts at the same
time, but one waveform rises as the other falls, the waveforms are antiphase (θ is 180o or π rads out of
phase). Waveforms may also be 90o out of phase, which is referred to as phase quadrature.
The phase angle of one waveform in a circuit may
lead or lag the other. Assume waveform A in Figure
5 − 2 is the reference voltage for the circuit, usually
the supply voltage. Since waveform B is at zero
volts and rising, after waveform A is at zero volts
and rising, waveform B lags waveform A by some
phase angle θ. Using the same analogy, we may also
say that waveform A leads waveform B by the
phase angle θ. A leading phase angle is considered
positive, while a lagging phase angle is negative.
The phase angle may be any value between 0o and
180o (0 and π rads).
Figure 5 − 2 contains two signals of the same
frequency applied to the inputs of an oscilloscope.
FIGURE 5 − 2
The amplitude of each channel may be determined,
and each channel may have the vertical gain set to different levels. To determine the phase relationship
between the two waveforms. First, select the channel that contains the reference waveform. Assume
waveform A is the reference signal for Figure 5 − 2. The vertical gain is adjusted to provide maximum
deflection about the zero volt reference, and both signals must have the same zero volt reference on the
CRT. The sweep speed is adjusted to provide a minimum of 180o for each signal. This oscilloscope
has ten major divisions across the CRT. That breaks down to 18o per division. Notice, in Figure 5 − 2,
the horizontal divisions are usually calibrated in milliseconds per division or microseconds per
division and this scope display is no different. However, we will convert the horizontal directly into
degrees, using a ratio.
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ELEC 103 Unit 5 The Oscilloscope
Usually, the number of divisions across the horizontal are divided into
180o
180o, the number of degrees in the one alternation being displayed.
= α = 18o/ div
10div
That provides the number of degrees per division. If you measure the
number of divisions along the zero volt reference that waveform A and
⎛ 2div ⎞
waveform B are displaced from one another, you can calculate the
θ = 180o ⎜10div⎟
⎝
⎠
phase angle. The phase angle between waveform A and waveform B
may be calculated using a proportion, as shown to the left. Since one
θ = 36o
alternation is 180o and there are 10 divisions, a displacement of two
divisions between the waveforms equals a phase shift of 36o.
The oscilloscope may be used to measure the phase angle between two waveforms of the same
frequency by displaying a pattern known as the Lissajous Figure. Under this method, the time base or
sweep speed is disconnected from the horizontal deflection circuitry.
The reference signal is connected to the horizontal (X) deflection circuitry, an unknown signal is
connected to the vertical (Y) deflection circuitry, and the sweep speed selector is set to the X−Y mode.
With no signals applied, a dot will appear on the CRT.
Do not leave the CRT in this mode for too long at a high intensity or damage to the
phosphor coating on the CRT will occur.
The dot is adjusted so the dot appears at
the intersection of the horizontal and
vertical scales. The input signals are
applied, and a waveform similar to that of
Figure 5 − 3 will appear on the CRT.
Make certain the pattern is centered on
the zero axis and the amount of deflection
for A and B is measured. The phase
angle, θ, may be determined from the
equation:
A
θ = sin−1 B
FIGURE 5 − 3
NOTE
When connecting line−powered equipment to a circuit, make sure the ground terminals from
all devices are connected to the circuit ground as indicated on the schematic diagram.
PROCEDURE
1.
Measure the values for R and C and record the values in Table 5 − 1.
2.
Calculate and record the values for Table 5 − 2 and Table 5 − 3 using information in the tables.
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ELEC 103 Unit 5 The Oscilloscope
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Build the circuit of Figure 5 − 4. Make certain
the ground leads of the frequency counter (FC)
and the audio generator (VS) are connected to the
same point in the circuit. Connect one DMM
across the output terminals of the audio
generator, and insert the second DMM to
measure the current. Adjust the settings of the
DMM’s to their proper positions.
Connect a probe to the oscilloscope Channel 1
Figure 5 − 4
terminal. The other probe will be connected to
Channel 2 later in the experiment. Connect the ground lead, of the oscilloscope probe
connected to CH 1, to the same point in the circuit as the ground lead of the audio generator.
Connect the other lead of the oscilloscope probe to measure the voltage across the resistor.
Set the oscilloscope to trigger internally on Channel 1. Make sure all controls are set to their
calibrated position. Check all circuit connections.
Apply power to all the equipment. Adjust the frequency of the audio generator until the
frequency counter reads 500 Hz. Adjust the voltage output of the audio generator until the
DMM reads 3V.
Adjust the sweep speed to obtain a display similar to Figure 5 − 1. It would probably be better
to view two or three cycles instead of the single cycle displayed in Figure 5 − 1.
Slide the selector under the CH 1 vertical gain control, marked AC−GND−DC, to the GND
position. Adjust the CH 1 position control to place the trace in the center of the CRT. Move the
CH 1 selector to AC, and adjust the vertical gain until the amplitude of the signal looks similar
to Figure 5 − 1. Use the CH 1 selector to make sure the vertical position of the trace is centered
on the CRT.
Measure the period of the waveform with the oscilloscope and record the data in Table 5 − 1.
Using the data from step 9, calculate the frequency of the waveform and record the results as a
measured value in Table 5 − 1.
Measure the applied voltage (Vrms) with the DMM and record the results in Table 5 − 2 on the
appropriate line.
Measure the total circuit current (Irms) with the current DMM and record the results in Table 5
− 3 on the appropriate line.
Measure VP and VPP with the oscilloscope, and record the data in Table 5 − 2.
From the data in step 13, calculate IP by dividing VP by R and record the result as the measured
value in Table 5 − 3. Repeat for IPP.
Adjust the voltage output of the audio generator until VP on the oscilloscope reads 7V. Then,
repeat steps 11 to 14.
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ELEC 103 Unit 5 The Oscilloscope
16.
17.
18.
19.
20.
21.
22.
23.
Adjust the voltage output of the audio generator until
VPP on the oscilloscope reads 20V. Then, repeat steps
11 to 14.
Remove power. Build the circuit in Figure 5 − 5.
Connect CH 1 of the oscilloscope across the audio
generator. Connect the second probe to the CH 2 input
of the oscilloscope and then connect CH 2 across the
resistor as shown in Figure 5 − 5.
FIGURE 5 − 5
Apply power to all equipment. Adjust the frequency of
the audio generator to 1000Hz, and the voltage output to 5Vrms. Place the CH 1 and CH 2
AC−GND−DC selectors to GND and center the traces on the CRT. Return the CH 1 and CH 2
selectors to the AC position.
Adjust the oscilloscope, as necessary, to obtain a display similar to Figure 5 − 2. Measure and
record the readings for the Number of Divisions for 180o and the number of divisions the two
waveforms are displaced from one another along the zero axis, where they cross the zero axis
going positive, and enter the data in Table 5 − 4.
Calculate the Phase Angle, and record the result in Table 5 − 4.
Set the sweep speed to the X−Y position. Place the CH 1 and CH 2 AC−GND−DC selectors to
GND and center the dot on the CRT. Return the CH 1 and CH 2 selectors to the AC position.
Adjust the oscilloscope as necessary to obtain a display similar to Figure 5 − 3.This is best
accomplished by adjusting the amplitude of both channels for the same deflection, one channel
at a time. Disconnect channel one by moving the AC−GND−DC selector to GND and adjust
channel two for a specific amplitude. Then disconnect channel two and adjust channel one to
the same amplitude. After both channels are adjusted for the same number of divisions
deflection, activate both channels and record the readings for the Number of Divisions for
distance A and for distance B in Table 5 − 5.
Calculate the Sine θ and the Phase Angle. Record the results in Table 5 − 5.
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ELEC 103 Unit 5 The Oscilloscope
DATA TABLES
Value
R
C
f
T
Rated
1.5kΩ
0.1µF
500 Hz
2 ms
Measured
TABLE 5 − 1
Voltage
Vrms
Calculated
3V
VP
VPP
Measured
Calculated
5V
Measured
Calculated
15V
Measured
TABLE 5 − 2
Current
Calculated
Irms
IP
IPP
2mA
Measured
Calculated
4.67mA
Measured
Calculated
13.33mA
Measured
TABLE 5 − 3
Number of Divisions from
0o to 180o
Waveform A to B
Phase Angle
TABLE 5 − 4
Number of Divisions from
A
B
Sine θ
TABLE 5 − 5
Page 8
Phase Angle