ECE 2A Lab #3
Lab 3
Waveforms and
The Oscilloscope
Overview
Thus far we have focused on constant-voltage or constant-current measurements (DC). For
time-varying signals the oscilloscope is an extremely valuable measurement and visualization
tool. This lab will investigate the use of the Bench Function Generator to generate various
types of time-varying signals, and will explore many features of the Bench Oscilloscope for
observing time-varying signals in circuits. While modern digital scopes have simplified
waveform measurements in some respects, it remains important for every self-respecting
electrical engineer to understand the oscilloscope inside and out in order to use it
intelligently. We will also introduce the diode and LED in this lab.
Table of Contents
Background Information
Periodic Waveforms
Coaxial Cables and Connectors
Grounding Issues
Pre-lab Preparation
Before Coming to the Lab
Required Equipment
Parts List
In-Lab Procedure
3.1
Basic Oscilloscope Operations
Earth Grounding on the Scope Connectors?
Waveform Display and Measurement
Triggering for Periodic Signals
DC Offsets, DC/AC Coupling
Display Cursors
3.2
Probing Waveforms in Circuits
The Diode
Displaying Multiple Traces; Rectifier Circuit
An LED Blinker Circuit
1
2
2
3
4
6
6
6
6
6
6
6
7
7
8
9
9
9
9
10
© Bob York
2
Waveforms and The Oscilloscope
Background Information
Voltage (or Current)
Periodic Waveforms
Electrical signals in real systems (telecommunications, computer data links, radar, etc) are
often complicated, but superposition allows us express such signals as sums of
mathematically simpler waveforms. Sinusoidal waveforms in particular play an especially
important role in electrical engineering for this reason. Fourier series or Fourier transform
methods provide the mathematical foundation for expressing arbitrary time-varying signals in
terms of sinusoids. Furthermore, sinusoidal waveforms are naturally produced by the rotating
electromagnetic machinery used in power generation (e.g. turbines in coal-fired plants,
hydroelectric facilities, windmills, etc.), so sinusoidal waveforms also play an important role
in AC power engineering and power transmission. But sinusoids are not the only simple
waveforms that will be important in our studies. Square waves, pulse trains, exponential
waveforms, and linear ramp waveforms also arise naturally in various circuits or situations.
In general we distinguish between two types of waveforms: 1) periodic signals, those that
repeat continuously over a very long time, and 2) transient signals, those that exist for a
short time and eventually die off. Sinusoidal signals are clearly examples of periodic signals.
The sudden burst of current in a light bulb when it is switched “on” is an example of a
transient signal. This lab will focus on periodic signals. The function generator on your
bench is designed to generate various types of periodic waveforms, and the oscilloscope is
used for observing them.
vmax
v p p
vave
vmin
T
Time
Figure 3-1 – An example of a periodic waveform and associated parameters.
Figure 3-1 is intended as an example of a generic periodic waveform, annotated with
certain important descriptive elements that are widely used to characterize such waveforms:
the time period T ; the maximum and minimum values, vmax and vmin ; the “peak-to-peak”
value, v p  p  vmax  vmin ; and the average value, vave . It is important to note that these
properties apply any periodic quantities, not just voltages, so the “v” in these variables could
represent anything.
The average value of the waveform is found by integrating the function over one period
and then dividing by the period.
vave 
1
T

t T
v(t ) dt
(1.1)
t
The starting point for integration doesn’t matter. The average value of the waveform is often
referred to as a DC offset, since the waveform is shifted vertically by a constant (DC) value.
© Bob York
3
Background Information
The frequency of the signal is related to the time period. Experimentally the frequency
f is usually expressed in hertz [Hz], or cycles per second, so f  1 / T . For sinusoidal
signals it is also common to use a “cyclical frequency”  which describes the total phase
change per second. By definition a sinusoid goes through a 2 phase change in one period,
which gives the following relationships (memorize these if you haven’t already!)
1
2

 2 f [rad/s]
(1.2)
[Hz]
T
T
We often talk about frequency in hertz but use  in our analyses, so a common source of
error is to forget the extra factor of 2 in the conversion. Try to remember that the units of
 are always radians per second, not hertz!
Electrical power or energy is computed from the square of voltage and current. For this
reason it is common to define another quantity called the RMS (root-mean-square) value,
given by
f 
vrms 
1
T

t T
v 2 (t ) dt
(1.3)
t
The average power can then be expressed easily in terms of the RMS value. For the special
but important case of a zero-average sinusoidal signal with a peak amplitude of vmax ,
substituting v(t )  vmax sin t into (1.3) gives
v
vrms  max
for v(t )  vmax sin t
(1.4)
2
In AC power systems the voltages and currents are almost always specified in terms of their
RMS values. For example, the nominal voltage on the wall outlets in the U.S. is around
120V rms, so the actual peak voltage is 120 2  170 V .
.
Insulating jacket
(PVC)
Outer conductor/shield
(foil/braided wire)
Insulator
(PE or PTFE)
Center
conductor
BNC connectors
Figure 3-2 – Coaxial cable construction and BNC connectors commonly used in instruments.
Coaxial Cables and Connectors
By now you should appreciate that at least two conductors are always needed for
interconnecting circuits or measurement equipment. Multi-conductor interconnects are often
called “transmission-lines”. For low-level and/or time-varying signals we often use a
shielded conductor system which helps isolate the electrical signals from external interference
and also prevents the signal from radiating away (an important consideration for highfrequency interconnects). Coaxial cables are a common and ubiquitous choice for two-
4
Waveforms and The Oscilloscope
conductor interconnects, ad consist of a central conductor (usually solid copper wire)
surrounded by a cylindrical outer conductor, with some insulating material in between (often
PTFE, or Teflon). Such cables can be used for signals into the GHz range (“gigahertz”, where
1 GHz=109 Hz).
Coaxial cables are designed for a specific characteristic impedance (in Ohms). For
example, the cable TV connections in your home typically use 75Ω cables; for other
instruments or higher frequencies 50Ω cables are more common. Your later coursework in
electromagnetics or high-frequency communications will teach you more about transmissiontheory and how the characteristic impedance influences the electrical behavior of a system,
but in ECE 2, the frequencies will generally be low enough that this parameter doesn’t play
much of a role. It turns out that characteristic impedances in the range of 50-75Ω have very
good power-handling and low-loss features, which is why those cable impedances are
commonly used.
Figure 3-3 – Comparison of coaxial connectors (source: www.fujikura.co.uk).
Getting signals in and out of the cables efficiently proves somewhat challenging at highfrequencies so special connectors have been developed for certain applications. Figure 3-3
illustrates just some of the most commonly-encountered types for frequencies below 18GHz.
You are probably familiar with the type-F connector found on most cable-TV boxes and
connections. BNC connectors are very attractive for lab instruments because of their quickconnect “twist-and-lock” feature (no screw threads). The choice of connector ultimately
limits the upper frequency range of a given cable. BNC connectors work well up to a few
hundred MHz, and have become the de facto standard in most electronic labs and equipment.
Grounding Issues
In instrument connections the outer conductor on the coax/BNC connection is universally the
reference node, and this is also usually connected to the instruments chassis (metal housing),
and to earth ground through the instrument’s power cable. The inner conductor is then the
signal of interest: e.g. the output signal of the function generator, or the signal to be measured
© Bob York
5
Background Information
by the oscilloscope. Our lab cables have red and black alligator clips added to the coax
section – red to the inner and black to the outer conductor.
Wall Outlet
Function
Oscilloscope
Generator
Ch1
Ch2
BNC
BNC
A
Red
Red
R1
Coax
Black
Coax
B
Black
R2
C
Figure 3-4 – Example of an incorrect test setup. R2 is effectively shorted out in this
measurement because both ends are connected to earth ground (the outer conductor of the BNC
connectors are grounded via the power cords of the two instruments).
An oscilloscope measures time-varying voltages. The measurements are therefore similar
to an ordinary voltmeter measurement. However, unlike the DMM the oscilloscope reference
is already internally connected to earth ground, and this has important and sometimes
unintended consequences in measurements. Figure 3-4 shows an example. Here a simple
voltage divider is attached across the output terminals of the function generator, and the
oscilloscope is attached in a naive attempt to measure the voltage across R1 directly.
However, this connection actually shorts out R2, because the outer conductors of both the
function generator and oscilloscope are connected to earth ground via the power cords
(shown as the dotted lines inside the instruments). To avoid this in the future we will always
make the outer conductors of the instruments a common reference by connecting all the black
leads on the coaxial cables to the same node in the circuit. If we need a DC power supply, we
will attach the COM terminal to earth ground (using a jumper wire on the power supply). In
this way all the oscilloscope measurements can be safely made with respect to the common
(ground) node by simple moving the clip for the inner (red) conductor to various parts of the
circuit.
So, back to Figure 3-4, if we wanted to observe the voltage across R1 the correct way to do
this would be to first make node C the common (ground) reference. We would then use a
feature built into most oscilloscope that allows us to add or subtract the signals coming into
channels 1 & 2. Thus if channel 1 is connected to node A and channel 2 to node B,
subtracting the two signals would yield the voltage across R1.
Of course these comments strictly apply only if the instruments are in fact connected to
earth ground. This will always be true in our ECE 2 lab, but it is possible to make “floating”
measurements, either by defeating the grounding of the power cord (not recommended!), or
by using battery-powered instruments.
6
Waveforms and The Oscilloscope
Pre-lab Preparation
Before Coming to the Lab
□
Read through the details of the lab experiment to familiarize yourself with the
components and testing sequence.
□
One person from each lab group should obtain a parts kit from the ECE Shop.
Required Equipment
■ Provided in lab: Bench power supply, Function Generator, and Oscilloscope
■ Student equipment: Solderless breadboard, and jumper wire kit
Parts List
Qty
2
1
1
1
1
Description
1 k-Ohm 1/4 Watt resistor
100 k-Ohm 1/4 Watt resistor
1N4148 Diode
Red LED, 725mcd @ 20mA
Yellow LED, 725mcd @ 20mA
If the 1k resistors are not in your kit, you should have some leftovers from lab #1.
Alternatively you can substitute the 510Ohm resistors from Lab #2.
In-Lab Procedure
Read the instructions carefully. If you skim through the text too quickly you may miss
something important.
□
Each critical step begins with a check box like the one at the left. When you complete a
step, check the associated box.
Be sure to document all steps and results in your notebook for inclusion in your lab report.
3.1 Basic Oscilloscope Operations
The overriding goal here is to make you aware of the many features on the scope which will
be crucial for success in ECE 2 and beyond. This lab is the ONLY time we will discuss the
operation of the scope in this much detail, so it is critical that you pay close attention. The
key impediment for students nowadays is undoubtedly the “AutoSet” button. Beware of this
button! It may often be a reasonably thing to press at the start, but the more you rely on it
the less chance you will have of ever understanding waveform measurements and making
intelligent use of the oscilloscope in the future.
Earth Grounding on the Scope Connectors?
□
With the oscilloscope and function generator off, check for continuity between the
reference terminals of the oscilloscope and function generator. These are the metallic
© Bob York
Basic Oscilloscope Operations
7
outer barrels of the Ch 1 and Ch 2 BNC terminals of the scope and the “Main Out” BNC
terminal of the function generator. Recall that a continuity check is just a resistance
measurement where any low number of ohms constitutes a connection. Now check
continuity between any of these terminals and the Ground terminal of the power supply
(temporarily disconnect the jumper wire between COM and Ground). Are they all
connected? (The correct answer is “yes”!) Temporarily unplug the function generator to
verify that the earth ground connection is through the power cords.
Waveform Display and Measurement
Connect the Function Generator’s Main Output to Channel 1 of the oscilloscope – red to red
and black to black. For later convenience, attach the alligator clips to wires on your
breadboard, rather than directly to each other.
□
Set the function generator to output a 1 kHz, 4 V peak-to-peak amplitude, sine wave.
Make sure the DC Offset knob is pushed in, and that the Main 0.2 Vp-p button is out.
Press the Ch1 menu button on the scope and select the follow: DC coupling, BW Limit
off, Probe 1x, and Invert off. Adjust the scope’s time scale, SEC/DIV knob, to get 2-3
cycles of the waveform displayed (you can estimate this from the signal frequency).
□
Press the Measure button to bring up the scope’s measurement screen. Set the
measurement boxes to use Ch1 as the source, and select Freq, Cyc RMS, Pk-Pk, and
Mean as the measurement types. Record the values shown.
□
Configure the DMM as a voltmeter and connect it to the function generator output along
with the scope – COM to ground and V/Ω to signal out. Record and compare the
voltmeter readings for AC and DC volts. Change the function generator to triangle, and
then to square wave, comparing the DMM to the scope. Do the two instruments compute
the same RMS value? Which is closest to the theoretical value for the amplitude?
□
Does frequency measured by the oscilloscope match the frequency in the function
generator display? Measure the period of the sinewave by counting divisions, and
compute frequency as 1/T. Do you agree with the scope? Change the measurement type
of one of the measurement boxes to Period. Are the scope’s period and frequency
measurements self consistent?
□
Use the Horizontal position knob to move the waveform left and right, and then leave it
centered. Notice the black arrow at the top of the screen, and the M Pos readout that tells
you how far off center you are. Likewise use the Vertical position knob to move the trace
up and down, and then leave it centered vertically. Do any of the measurement values
change when you adjust the horizontal or vertical position?
Triggering for Periodic Signals
Oscilloscope triggering is probably the most important yet misunderstood aspect of
oscilloscope operation. The scope can only display a finite time interval on the screen, set via
the “SEC/DIV” knob. After it finishes recording and displaying the waveform for some time
interval it has to start over again for the next time interval. Consequently, to create a still
image on the screen the scope has to start recording/plotting the waveform at the same point
within the signal period each time. This is the trigger point, and is set as a certain threshold
voltage (Trigger Level) and Slope (Rising/Falling):
□
Press the Trigger button to access the scope’s trigger menu. Select Edge, not Video,
Slope Rising, Source Ch1, Mode Auto, and Coupling DC. Be sure you still have 2-3
8
Waveforms and The Oscilloscope
cycles of the waveform visible on the screen. Notice the black trigger arrow on right of
screen. Adjust trigger level using the Trigger Level knob. What relation is there between
the level of the trigger arrow and the value of the waveform at time zero, v(t  0) ?
□
Change Slope to “Falling”. What changes? Now change the trigger level; is the
relationship between trigger level and v(t  0) the same as before? What happens if
trigger-level raised beyond amplitude of the trace? Notice the “T Trig’d” at the top
changes to “R Auto”.
□
Press Run/Stop. What happens? Notice the Stop sign. Press Run/Stop again. With the
trigger level still greater than the signal amplitude, change the trigger Mode to Normal.
The trigger status is now “R Ready”. Adjust the trigger level back down to 500mV.
□
Press AutoSet.. What all changed? Lesson: Don’t press AutoSet unless you’re prepared
to have all your settings changed!
□
Adjust the function generator to make the output peak-to-peak 1.0V. Make sure you have
a triggered, stable display, then disconnect the scope ground (black clip) from the
function generator ground. Is it still stable.
□
Reconnect the ground. Press the 0.2Vp-p button on the function generator. Verify that
you now have a peak-to-peak amplitude of 100mV. 20mV/Div would be a good vertical
sensitivity for viewing this waveform. Try to get a triggered, stable display, then
disconnect the scope ground again. Does anything happen? Press Run/Stop to get a look
at the signal. Spread it out in time with the Sec/Div knob if you like.
Differences in the ground references inside the function generator and inside the oscilloscope
lead to unpredictable results in the last step. Some people have trouble seeing waveforms and
others won’t. Even though we verified with the ohmmeter that these nodes are connected to
each other, and to earth ground, it isn’t always a reliable low-resistance connection and is
susceptible to interference from a variety of sources. So we make the connection reliable and
stable by connecting them externally—black alligator clip to black alligator clip.
Measurements of small signals in really high-speed circuits, like radio receivers, need even
better ground connections.
□
Reconnect the ground and change the trigger coupling to HF Reject. Is it easier to trigger
with HF Reject selected? Try the other coupling options.
DC Offsets, DC/AC Coupling
This is also an important section. If we ask you to create a waveform with a certain DC
offset as part of a lab next quarter in ECE 2B, “I don’t remember how” will not be an
acceptable response! Similarly if we ask you to observe a small-amplitude AC signal riding
on a large-amplitude DC offset, “I can’t see the signal on the scope” will not be acceptable!
□
Reset the function generator to the original signal – 1 kHz, sine wave, 4V pk-to-pk. Get a
stable display showing 2-3 cycles of the waveform, triggering at the zero level, rising,
using Auto mode. Press the Measure button to get the measurement screen. Select AC
volts on the DMM. Compare the scope’s Cyc RMS measurement to the DMM’s AC
voltage. Pull out the DC Offset knob on function generator. Adjust until Ch1’s Mean
=1.0V. Did the DMM AC volts change? How about the Cyc RMS value?
□
Press the CH 1 menu button. Change coupling to AC. Press measure. Now what is Cyc
RMS? Mean? What can you conclude about how the scope and DMM measure RMS of
a sinewave with a DC offset?
© Bob York
Probing Waveforms in Circuits
□
9
Put the DMM in DC volts mode and dial in various DC offsets. Does the scope’s display
change when the offset changes? Switch Ch1 back to DC coupling. Push in the DC
offset knob on the function generator. What happens to the offset?
Display Cursors
□
Set the function generator to produce a 1kHz, 0 to 5V square wave. This means the lowvoltage level is 0, or ground level, and the high voltage level is +5V. Trigger on the
rising edge of the square wave. Expand the display using the Sec/Div knob to get a good
view of the rising edge.
□
Press the Cursor button on the scope to bring up the cursor menu. Select Time as the
cursor type and measure the rise time of the square wave. This is the time required for
the voltage to change from 10% of the final value to 90% of the final value. Note that
the vertical position knobs are used to adjust the cursor levels.
□
Change the cursor Type to Voltage and measure the overshoot. That is the amount the
signal rises about the final value (5V) before settling.
□
Press the Measure button and change one of the measurement boxes to Rise Time. Does
the scope get the same answer you did?
□
Change the measurement to Fall Time? Is there a reading? Change the Trigger slope to
trigger on the falling edge. Now is there a Fall Time?
3.2 Probing Waveforms in Circuits
The Diode
In this step we introduce the diode, a
Diode
nonlinear component that will be used to
Anode
Cathode
create a simple wave-shaping circuit and
make the oscilloscope measurements a little
Band marks cathode
on diode package
more meaningful and interesting. The diode
symbol and a representative package are
shown in Figure 3-5.
A diode is the
electronic equivalent of a one-way street,
Figure 3-5 – Diode symbol and typical package.
allowing significant current flow in only one
direction indicated by the arrow in the symbol. If the anode has a higher voltage than the
cathode, current can flow. If the voltage polarity is reversed, very little current can flow.
There is usually a band indicating the cathode side of the device on the package.
Displaying Multiple Traces; Rectifier Circuit
Diodes will be discussed in detail in ECE 2B, you do not need to know much about them for
2A labs. When a diode is used in circuits with time-varying bipolar voltages some interesting
effects can be observed because the diode will respond differently to the positive and
negative parts of the waveforms. In such cases it is helpful to use the oscilloscope to observe
both the input and output waveforms simultaneously. By overlaying the input and output
waveforms we can get an immediate visual impression of how the circuit is functioning.
10
□
□
Waveforms and The Oscilloscope
First set the function generator to produce a
5V amplitude, 1 kHz sine wave, with zero
DC offset, and connect it to a series
diode/resistor circuit as shown in Figure
3-6. Connect channels 1 and 2 of the
oscilloscope as indicated. Using the Ch 2
menu button, verify that Channel 2 is set
for DC coupling.
CH2
1N4148
CH1
Function
Generator
100 kΩ
GND
Press AutoSet to get an initial acquisition of
the two waveforms. If both Ch1 and Ch 2
are not displayed, press the menu button of Figure 3-6 – Simple diode “rectifier” circuit
the one which isn’t. You can alternately
press the Ch 1 and Ch 2 menu buttons to see how to remove or recall a trace from the
display.
□
Using the Volts/Div knobs set both channels to the same vertical scale. Using the vertical
position knobs center both traces; that is, put the zero reference level exactly at the
center. Notice the two black arrows on the left of the screen, indicating where these are.
Sketch the resulting waveform. Can you explain the waveforms based on the simple
statement above describing the operation of the diode?
□
What RMS values do the scope and DMM make for the waveform of channel 1? This is
called a half-wave rectified signal.
□
Pull out the DC offset knob and adjust the DC offset of the function generator. Can you
get an entire sine wave to appear on the resistor (channel 1)? What DC offset is
required? Zero the DC offset (push in the knob).
□
You may notice that the full input signal does not appear on the resistor – there is some
voltage drop on the diode. To see this in
greater detail, lower the amplitude of the
Anode
function generator output to 1V. Change
the vertical sensitivity of both channels to
LED
500mV/div, making sure the zero reference
Cathode
for each is still the same. Sketch what you
see.
□
Now press AutoSet.
What happens?
Again, the important lesson here is: Don’t
press AutoSet unless you’re prepared to
have your settings changed!
An LED Blinker Circuit
A light-emitting diode (LED) is just that: it is
functionally equivalent to any other kind of
diode, but emits light when current flows
through it. The LED symbol and package
information is shown in Figure 3-7.
© Bob York
Flat on
cathode
side
Anode
(long)
Cathode
(short lead)
Figure 3-7 – Light-Emitting Diode (LED) and
symbol
11
Probing Waveforms in Circuits
□
□
Return the function generator amplitude to 5V and build the circuit shown in Figure 3-8.
Leave the frequency at 1kHz for now. Set channel 1 and 2 once again to have the same
V/div and the same zero reference
position. Both LEDs should be on,
Red
Yellow
although probably not with equal
Func.
brightness.
CH1
CH2
Gen.
Adjust the DC offset until the LEDs
appear equally bright. What offset is
required? From this, which LED would
you say is more efficient?
□
1 kΩ
1 kΩ
GND
Now reduce the function generator
Figure 3-8 – LED circuit.
frequency to 1 Hz. Explain what you
see visually and reconcile this with your oscilloscope waveforms. Do you understand
why both diodes appeared to be simultaneously “on” when the generator was at 1kHz?
Congratulations!
You have now completed Lab 3
As noted in the previous lab: keep all your leftover electrical components!
Specific Discussion Items for Lab Report
Much of this experiment was tutorial in nature, guiding you through the various steps
required to use the oscilloscope and function generator effectively. You do not need to report
on every single step! Some specific ideas for the report might be as follows:
■
■
■
■
■
Re: grounding issues, be sure you understand what is going on in Figure 3-4 and the
ramifications of the internal earth grounding of the oscilloscope inputs.
Re: Oscilloscope triggering: what happens when the triggering threshold is larger than
the waveform amplitude? Can you explain why?
Re: Section on DC Offsets: Calculate the average and RMS values of the 4V peak-topeak sinewave with and without the 1V DC offset. Compare with the measurements
taken with the scope and DMM.
Re: Display Cursors: Report the rise and fall times measured on the square wave.
Calculate an average and RMS value for the square wave used in this section.
Re: Diode Circuits: You measured what was referred to as a “half wave rectified”
sinewave. Explain the waveform observed based on the simple statement above
describing the operation of the diode. Sketch or print out the waveform. Report the peak
value that you measured, compare with the amplitude of the function generator output,
and calculate the average and RMS values of this signal. Based on your measurements,
what is the voltage drop across the diode when it is conducting? Explain why a complete
sinewave could be observed on Ch. 1 when the DC offset was applied.