The George Washington University
School of Engineering and Applied Science
Department of Electrical and Computer Engineering
ECE 11 – LAB
Experiment # 6
Introduction to AC Circuits using the Oscilloscope and Function Generator
Equipment:
Lab Equipment
Equipment Description
Digital Multimeter (DMM)
Keithley Model 178
Function Generator
Tektronix AFG3021B
Analog Oscilloscope
Instek GOS-620FG
Digital Oscilloscope
Tektronix TDS460A
BNC T Connector
NONE
(2) BNC Cables
NONE
Banana-to-mini-grabber test leads
NONE
(2) BNC-to-mini-grabber test leads
NONE
Prototype Breadboard
NONE
Table A – Equipment List
Components:
Kit Part #
Part Description
Symbol name
(used in schematics
throughout this lab manual)
R
1kΩ Resistor
R2
R
2kΩ Resistor
R3
C
0.1μF Capacitor
C1
AND130CR
Red LED
D1
Table B – Components list
Objectives:
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Use the Tektronix function generator to generate an AC voltage waveform
Use the Instek analog oscilloscope to measure an AC voltage waveform
Use the Tektronix digital oscilloscope to measure an AC voltage waveform
Compare and explain the results obtained from the DMM and the analog oscilloscope for
measurements of different periodic waveforms
Use the Instek analog oscilloscope to measure the voltage drop across components in an AC
circuit
Use the Instek analog oscilloscope to measure the phase shift between the AC voltage
waveforms
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Introduction:
The circuits encountered in the first half of ECE 11 have had DC signals only. We use the DC power
supply to produce the DC signals and then use the DMM to measure the signals.
In the second half of ECE 11, circuits will have AC signals. We will use a two new pieces of equipment to
produce and measure these signals in our circuits. The first piece of equipment, the function generator,
will be used to produce AC signals. The second piece of equipment, the oscilloscope, will be used to
measure the AC signals in the circuit.
This lab will introduce AC signals and circuits. It will familiarize you with how to generate AC signals
using a function generator, and how to measure them using an oscilloscope.
Introduction to the Oscilloscope
DISPLAY
CONTROL PANEL
Fig. 1.1 – Oscilloscope – Display & Control Panel
The Basics:
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An oscilloscope measures and displays voltage as it changes with time.
It consists of a display screen with an x & y-axis and control panel (see Figure 1.1).
The y-axis of the display represents voltage.
The x-axis represents time.
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Setting the Scales for the X & Y-Axes:
4V
2V
0
2V
0
5ms
5ms 10ms …
Fig. 1.2a – Display
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Fig. 1.2b – x-axis
Fig. 1.2c – y-axis
On the control panel, the value of the x-axis scale is set using the “TIME/DIV” knob (see Fig
1.2b).
o Note: The “TIME/DIV” knob in Fig. 1.2b, indicates each horizontal division represents
2ms.
The value of the y-axis scale is set using the “VOLTS/DIV” knob (see Fig 1.2c).
o Note: The “VOLTS/DIV” knob in Fig. 1.2c, indicates each vertical division represents 2V.
Fig 1.2a shows a sine wave with a 20ms period and amplitude of 4V.
Channels:
Fig 1.3 – Display Showing Two Channels
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The oscilloscope in Fig. 1.1 allows two different signals to be displayed simultaneously (one on
each of the two channels) (see Fig. 1.3).
The vertical position dials allow each signal to be shifted up and down, independently of one
another. This is done to separate overlapping signals and to position the signals to make it easier
to estimate their amplitudes.
Waveform Math:
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The outer conductor of the coaxial BNC cables used by oscilloscopes is always grounded.
Therefore, oscilloscopes cannot directly measure the voltage across a component, unless one
end of the component is grounded. Instead, oscilloscope measurements are limited to nodevoltage measurements (node voltages are measured with respect to ground by definition).
For an oscilloscope to measure the voltage across a component, the node voltages waveforms
on each side of the component must be acquired and then subtracted (technically, one node
voltage must be inverted and the added to the other node voltage).
Most oscilloscopes have a mode for adding signals acquired on the channels for this purpose.
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Triggering:
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The oscilloscope’s trigger function synchronizes the horizontal sweep to produce a stable
waveform.
Oscilloscopes display a moving wave. When the wave runs out of space on the display screen, it
continues, starting at the far left of the display screen. When that section of the wave starting at
the left of the display screen is not aligned with the section of the wave already on the display
screen, it is untriggered and appears to be moving (see Fig. 1.4a).
Adjusting the trigger level dial defines where on wave to trigger (either on the way up or the way
down), as illustrated in Fig. 1.4b, until the wave becomes stable (see Fig. 1.4c).
Fig. 1.4a – Untriggered Display
Fig. 1.4b – Trigger Setup
Fig. 1.4c – Triggered Display
AC Signal Characteristics:
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The voltage of a time-varying signal can be described in various ways.
o Peak-to-Peak Voltage (VPP): maximum voltage – minimum voltage
o Peak Voltage (VP):
(also called amplitude)
o Root-Mean-Squared Voltage (VRMS): (sine), (triangle),
(square)
The frequency (f) a waveform is equal to the number of repetitions per unit time (units of Hz).
o NOTE: When frequency is given in units of radians/second, the variable ω is usually used
(ω = 2πf).
The period (T) of a signal is the duration of one cycle of a repeating event (units of seconds).
The phase shift of one signal with respect to another is the ratio of the offset between them to
their period (assumes each signal has the same period) (units of degrees or radians).
o
NOTE:
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Introduction to the Function Generator
Fig. 2.1 – Function Generator – Display & Control Panel
The Basics:
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A function generator produces time-varying voltage signals that can be used in AC circuits.
The time varying signal can be configured using the following parameters (see Figure 2.1):
o Function type: The basic types of waveforms are sine, square, and sawtooth (triangle or
ramp).
o Frequency: number of repetitions per unit time (units of Hz)
o Amplitude: voltage magnitude of the signal (may be define by the peak voltage or peakto-peak voltage).
o Phase Shift: offset of the signal (in time) with respect to an unshifted signal
o DC-Offset: offset of the signal (in voltage) with respect to ground
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Prelab Problems:
Question #1:
1) Go to the ECE 11 website, Labs page, Lab Equipment section and review the specifications for
the Instek analog oscilloscope and the Tektronix digital oscilloscope.
2) Find the values for maximum input voltage, input impedance, and maximum frequency for both
oscilloscopes.
Question #2:
The above graph shows two overlapping sine waves. The oscilloscope is set as follows:
 TIME/DIV knob is set to: 50 μs
 VOLTS/DIV knob on channel 1 is set to: 10V
 VOLTS/DIV knob on channel 2 is set to: 5mV
If the blue waveform is on channel 1 and the red waveform is on channel 2, what are the following values
for each?
Blue Waveform
Red Waveform
VPP
VP
VRMS
Period
Frequency
What is the phase difference between the red and blue waveform?
Question #3:
Given the knobs minimum and maximum values in Figures 1.2b and 1.2c, answer the following questions:
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What is the lowest frequency AC signal you can measure with the analog oscilloscope?
What is the highest frequency AC signal you can measure with the analog oscilloscope?
What is the highest voltage you can measure in terms of VPP, VP, VRMS with the oscilloscope?
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Prelab Quiz Preparation
In the event of a prelab quiz, you should be familiar with the following from the introduction of today’s lab:
 Understand the quantities that are represented by the x and y-axes of an oscilloscope display.
 Understand the basic settings on an oscilloscope control panel.
 Understand the basic waveform settings on a function generator control panel.
 Be able to define peak-to-peak voltage, peak voltage, RMS voltage, period of a signal, and the
frequency of a signal.
 Be able to describe how to determine the voltage across a circuit element when that element is
not grounded.
Lab:
Part 1 – Generate Sine, Square, and Sawtooth Waveforms
Set up the Function Generator
 POWER: On
 FUNCTION: Sine
 MODE: Continuous
 AMPLITUDE/HIGH: Use dial to set VPP = 5V
 OFFSET/LOW: Use dial to set Offset = 0V
 FREQUENCY/PERIOD: Use dial to set Freq = 4kHz
 Set load impedance to 50 Ω
o Using the menu buttons, select Output Menu … Load Impedance … 50 Ω
o Press the Top Menu button to return to the main menu
1) Connect the BNC T-connector to the 50Ω output of the function generator.
2) Connect a BNC cable from the T-connector to the CH1 input of the analog oscilloscope.
3) On the function generator press the Channel On button to enable the signal.
Set up the Analog Oscilloscope
 POWER: On
 CH1 VOLTS/DIV: display the positive and negative portions of the signal on the screen
entirely
 Vertical Position: adjust such that the signal is centered on the screen
 Vertical Mode: CH1
 Connection Mode: DC
 TIME/DIV: display at least one complete cycle of the signal on the screen
 Horizontal Position: make adjustments in order to more easily estimate the period of the
signal
 Trigger Source: CH1
 Trigger Mode: AUTO
 Trigger Level: adjust if the signals is not stable
 Calibrate CH1 using the fine-tuning knob at the center of the VOLTS/DIV knob
o Using the position of the VOLTS/DIV knob, compute how many divisions should
separate the peaks of the sine wave from the function generator (VPP = 5V).
o Turn the fine-tuning knob until the correct numbers of divisions separate the peaks.
Once CH1 is calibrated, do not move the fine-tuning knob for the remainder of
the experiment.
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Set up the DMM
 Configure the DMM to measure AC Voltage
 Set the DMM for Auto scale
4) Sketch the oscilloscope display, including the scale of the voltages and time axes. Make note of
the VP, VPP, and VRMS voltages, as well as the frequency and period.
5) Connect a BNC-to-mini-grabber test lead to the T-connector. Connect a banana-to-mini-grabber
test lead to the DMM. Connect the mini-grabbers and measure the AC voltage of the function
generator. How does it compare to the voltages measured with the oscilloscope?
6) Change the signal from a Sine function to Square function and repeat steps 4-5.
7) Change the signal from a Square function to a Sawtooth (triangle) function and repeat steps 4-5.
Set up the Digital Oscilloscope
 POWER: On
 Select CH 1
 Select Vertical Menu
o CH 1 Coupling Impedance: DC
o Input Impedance: 50Ω
o Press Menu button to exit
 Select Trigger Menu
o Edge Source: CH 1
o Press Menu button to exit
 Vertical Scale: display the positive and negative portions of the signal on the screen entirely
(The Volts/Division will appear at the bottom of the display.)
 Vertical Position: adjust such that the signal is centered on the screen
 Horizontal Scale: display at least one complete cycle of the signal on the screen (The
Seconds/Division will appear at the bottom of the display.)
 Horizontal Position: make adjustments in order to more easily estimate the period of the
signal
8) Disconnect the analog oscilloscope and connect the digital oscilloscope (CH1) in its place.
9) Repeat steps 4-7 using the digital oscilloscope.
Part 2 – Waveform Math
NOTE: Use the analog oscilloscope for the remainder of the lab.
1)
2)
3)
4)
Assemble the circuit illustrated in Fig. 3.1.
Complete the analog oscilloscope setup, as described above, for CH2
Switch the Vertical Mode to DUAL.
Use one set of the BNC-to-mini-grabber test leads to measure the voltage of Node A with respect
to Node C (GND) on CH 1. Use another BNC-to-mini-grabber test lead to measure the voltage of
Node B with respect to Node C (GND) on CH 2. NOTE: The voltage across R2 cannot be
measured directly, because the outer conductor of the oscilloscope input channel is always
shorted to ground.
5) Use the VOLTS/DIV knobs and the Vertical Position knobs to position CH 1 above CH 2, so that
the channels do not overlap.
6) Sketch CH 1 (label as V2) and CH 2 (label as VR3). Label the voltage and time axes appropriately.
7) Press the CH2 INV button and switch the Vertical Mode to ADD. Sketch the resulting waveform
(label as VR2). Label the voltage and time axes appropriately.
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Fig. 3.1 – AC Circuit 1
Part 3 – Phase Shift
1) Assemble the circuit illustrated in Fig. 4.1.
2) Switch the Vertical Mode to DUAL.
3) Use one set of the BNC-to-mini-grabber test leads to measure the voltage of Node A with respect
to Node C (GND) on CH 1. Use another BNC-to-mini-grabber test lead to measure the voltage of
Node B with respect to Node C (GND) on CH 2.
4) Use the VOLTS/DIV knobs and the Vertical Position knobs to position CH 1 above CH 2, so that
the channels do not overlap.
5) Sketch CH 1 (label as V2) and CH 2 (label as VC1). Label the voltage and time axes appropriately.
6) Use the VOLTS/DIV knobs and the Vertical Position knobs to position CH 1 above CH 2, so that
the channels do overlap.
7) Sketch CH 1 (label as V2) and CH 2 (label as VC1) on the same axes. Label the voltage and time
axes appropriately.
8) Estimate the phase shift of VC1 with respect to V2. Use the Horizontal Position Knob to shift the
signals to make it easier to estimate the phase shift.
Fig. 4.1 – AC Circuit 2
Part 4 – AC Circuit Analysis using PSPICE
1) The GTA will describe how to simulate an AC circuit in PSPICE and obtain time-varying voltage
differences across circuit elements.
2) Provide the simulations and analysis for AC Circuits 1 and 2 in the lab report.
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Part 5 – Blinking LED Circuit (Extra Credit)
1) Refer to Figure 5.1 to design a circuit for illuminating the LED. Set the source voltage, VS, equal
to 5V. Assume that the voltage drop across D1 is equal to 1.9V. The resistor R1 is used to control
the current flowing through the LED. If the voltage across R1 is equal to VS – 1.9V = 3.1V, what
must the resistance of R1 be set to in order to limit the current through the circuit to be less than
30mA? Select a standard resistor value.
Fig. 5.1 – LED Circuit
2) Replace VS with a time-varying voltage source V1 (VPP = 5.0V, DC-Offset = 2.5V, Frequency =
1Hz, Function = Square), as shown in Figure 2. (You can think of V1 as a DC source that is at 5V
for 0.5 seconds and then 0V for 0.5 seconds.)
Fig. 5.2 – Blinking LED Circuit
3) Once the circuit is assembled, turn on the function generator. The LED should blink on then off
once per second. Adjust the frequency generator’s settings to find the frequency at which the
LED appears to stop blinking (appears to be at a constant illumination).
Part 6 – Post-lab Analysis
1) Is it possible to measure the AC voltage across a resistor directly using an oscilloscope? If not,
why?
2) What steps are necessary to determine the AC voltage across resistor using an oscilloscope?
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References:
“XYZs of Oscilloscopes”, Tektronix, accessed 1 October 2010,
http://www2.tek.com/cmswpt/tidetails.lotr?ct=TI&cs=Primer&ci=2280&lc=EN.
“XYZs of Signal Generators”, Tektronix, accessed 1 October 2010,
http://www2.tek.com/cmswpt/tidetails.lotr?ct=TI&cs=pri&ci=12608&lc=EN.
“Agilent DSO5014A Oscilloscope Tutorial”, Agilent Technologies, accessed 1 October 2010,
http://www.home.agilent.com/upload/cmc_upload/All/AgilentDSO5014A_Oscilloscope_Tutorial.pdf.
“Agilent 33220A Function Generator Tutorial”. Agilent Technologies, accessed 1 October 2010,
http://www.home.agilent.com/upload/cmc_upload/All/Agilent33220A_FuncGenerator_Tutorial.pdf.
Ahmadi, Shahrokh, “Introduction to the Oscilloscope”, George Washington University.
Appendix I: Matlab Code for Plotting a Time-varying Signal
t1 = <start time>;
%seconds
t2 = <end time>;
%seconds
f = <frequency>;
%Hz
ps = <phase shift>;
%degrees
V0 = <voltage amplitude>;
%Volts
offset = <DC offset>;
%Volts
t = t1:(t2-t1)/1000:t2;
w = 2*pi*f;
y = V0*sin(w*t-ps*pi/180)+offset;
plot(t,y)
ylabel('Voltage (V)')
xlabel('Time (s)')
axis([t1 t2 min(y) max(y)])
set(gca,'YTick',min(y):(max(y)-min(y))/8:max(y))
set(gca,'XTick',t1:(t2-t1)/10:t2)
grid on
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