Download Exercise 11

Exercise 11
The Oscilloscope & AC Signals
I. Purpose
The purpose of this exercise is to teach you how to use a digital oscilloscope to measure
signals that change with time.
II. Equipment
digital oscilloscope
function generator
BNC cables
III. References
Read Appendix B at the back of this lab manual to review how to use the digital oscilloscope
and function generator.
IV. Introduction
In the first two labs of the second section of the course you used multimeters to measure
voltages and currents in some simple electrical circuits. In those circuits when the switch was
closed the voltages and currents were constant. We call this kind of circuit a "dc circuit" where
dc stands for "direct current" to indicate that the current flow is of constant strength and direction
at each point in the circuit.
In this lab, you will use a digital oscilloscope to measure signals that change with time.
We call this kind of circuit an "ac circuit" where ac stands for "alternating current" to indicate
that the current flow varies in direction and strength with time, changing from forward to
backward flow periodically. In fact, most of the electrical devices you are familiar with run on
ac power, so that these circuits are very important technologically.
In an ac circuit, a voltage source supplies a time varying voltage that can drive ac current
through a circuit. These ac sources go by a variety of names, including: ac power supply, signal
generator, function generator, wave generator, oscillator, audio oscillator, or rf generator. You
will be using a function generator that allows you to apply a sinusoidal voltage of the form:
V = V1 sin(2ft + ) + V0
[1]
where you can change the amplitude V1 the frequency f, and the dc voltage offset V0 by
turning knobs. The constant  is called the phase and determines the value of sin(2ft + ) when
t is zero; it will vary depending on your choice of the trigger settings. Set up you spreadsheet as
shown below.
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PART A: Measure an AC Signal
We will now measure the period (TC) and peak-to-peak voltage for a sine wave.
(1) Initialize the scope by using the AUTOSET function.
(2) Using a BNC cable, plug the output from the signal generator into channel 1 of the
oscilloscope.
(3) Turn on the function generator and set it so that it is generating a sine wave at a frequency of
2 kHz.
(4) Activate the TRIGGER Menu and set the functions in the windows appropriately.
(5) Adjust the oscilloscope SEC/DIV knob to about 100 µs/div and the VOLTS/DIV knob to
about 0.5 V/div until you get a nice stable trace.
(6) Turn the amplitude control knob of the function generator and set it so that it is generating a
sine wave with 3 V peak-to-peak voltage difference.
(7) After you have wired up your circuit and set up the oscilloscope and function generator,
have one of your instructors check that you have done it correctly and initial your
checksheet.
(8) Fill in the boxes on the sample spreadsheet in the section labeled “Part B”. See box on the
next page for instructions on how to do this.
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QUESTION 1: Briefly explain how precisely can you measure TC, the period of the sine wave
(see hint below). Recall that the period is the time between consecutive peaks. Also record this
uncertainty for TC in your data table. Use data in spreadsheet in section labeled “Part B” after
reading the box on the next page.
Hint for students - Uncertainties when using CURSOR
Providing a good answer to the above question requires some thought.
To start with, the oscilloscope you are using traces a wave on the screen by
collecting 2500 individual voltage measurements at specific times. It chooses the times so
that there are there are 250 samples per "big" time division on the screen. That means that
the time between one measurement and the next, the sampling interval, is [SEC/DIV]/250
seconds. From this, you might guess that the uncertainty in the time is about
[SEC/DIV]/500 seconds. This is a pretty good answer, but as we will discuss below, it is
not always true.
Similarly, the scope makes voltage measurement with a limited precision. In fact,
the smallest change in voltage that the scope can report is just given by [VOLTS/DIV]/32
volts. Thus if you are on the 1 volt/div scale, the measured voltage can only change in
increments of about 0.033 volts. From this one might conclude that the precision limit from
the voltage step size implies an uncertainty in voltage of about [VOLTS/DIV]/64 volts.
Again, as we will discuss below, this is not necessarily the case.
As we mentioned above, when using the CURSOR, the uncertainties listed above
may not be the appropriate uncertainties. For example, in the exercise above you had to
locate the cursors at successive peaks of the displayed sine wave. To do this, you had to
adjust the cursor so that it is located at a time when the sine wave is at a peak. You probably
found that it is hard to locate the exact top of the peak, especially because the wave is "flat"
at the top and there is some "noise" in the displayed trace.
To estimate the uncertainty in the time at the peak, you can first set the cursor as
best you can at the peak and note the time, tpeak. Then try moving the cursor until you are
sure it is no longer at the peak, and note this time, toffpeak. Using the rule that the
uncertainty will define a range where there is a probability of about 2/3 for the result to lie
in this range, the uncertainty will be given roughly by:
t = (2/3)[|tpeak - toffpeak|] .
A similar situation arises when you use the CURSOR to make voltage
measurements. For example, you used the cursors to find the voltage at the bottom and top
of the sine wave. To estimate the uncertainty in these measurements, set the cursor as best
you can at the peak, note the voltage Vpeak, and then move the cursor until you are sure it is
no longer at the peak, and note this voltage Voffpeak. Using the rule that the uncertainty
will define a range where there is a probability of about 2/3 for the result to lie in this range,
the uncertainty will be given by:
V = (2/3)[|Vpeak - Voffpeak|].
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(9) The time TC is called the period and is related to the frequency of the sine wave by fC=1/TC.
Calculate the frequency of the wave and its uncertainty and record them in your data table. Show
your instructor. Use error propagation to get the uncertainty.
(10) Now use the voltage cursors to measure the difference in voltage between the top of the sine
wave and the bottom of the sine wave. This is called the peak-to-peak voltage, VC. Record the
individual cursor measurements as well as their difference Delta in your data table.
(11) How precisely can you measure the peak -to-peak voltage? Use the rule from the box on the
previous page. Record an uncertainty forV in your data table and show your instructor.
(12) Your digital oscilloscope has some handy features for quickly measuring AC waveforms.
Press the MEASURE button and use the menu keys to set up windows which report the
frequency, fM, period, TM, and peak-to-peak voltage, VM. Record these values.
(13) How precisely does MEASURE give the frequency, period and the peak -to-peak voltage?
Record uncertainty for fM, TM, and VM in your data table and show your instructor.
Uncertainties when using MEASURE
The MEASURE function is very handy, but you will probably see that the values
reported by MEASURE fluctuate with time. This happens because the function generator
does not have a completely stable output signal and there is some noise in the scope and
generator The lack of stability causes the scope's estimate for the peak-to-peak voltage, the
frequency, and the period to change. When you read the values reported by MEASURE,
you should watch the displayed values fluctuate and then estimate an average value and the
uncertainty in that average value based on how much variation you see.
QUESTION 2: You just found values for the frequency using the CURSOR and using the
MEASURE button. (a) How well do the two frequency measurements agree? (b) How well
do your two measurements of the peak-to-peak voltage agree? Comment briefly and don't
forget that you need to give both the values and their uncertainty in order to answer this
question.
PART B: Measuring Voltage at a series of Times
(1) Set the function generator so that it is generating a sine wave with 5 V peak-to-peak voltage
difference at a frequency of 20 kHz. Display 1-2 wavelengths.
(2) Have one of your instructors check that you have done it correctly and initial your
check sheet.
(3) Use the CURSOR to measure the voltage and time at about 10 different points along the
curve, covering slightly more than one cycle. Record the times and voltages in your data
table. Pick the 10 times corresponding to the vertical lines on the scope. Assume these times
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have no uncertainty. The voltages do have an uncertainty.
(4) How accurately and precisely can you measure the voltages? Record an uncertainty for VC in
your data table.
(5) Press the MEASURE button and find the frequency, fM, and peak-to-peak voltage, VM in
the appropriate windows. Record these values in your data table, plot the data, and show
your instructor.
- Email a copy of your work to yourself and save to the hard disk, send a copy to your instructor
using WebCT.
- Turn in your checksheet.
V. Homework Problems
Complete the Questions in the lab and the homework problems below. Then E-Mail in your
completed data table and answers to all the problems.
1. Is It Really a Sine Wave?
Take your data for the sine wave in Part C and:
(a) Plot your data as V versus t,
(b) Put error bars on your plot
(c) Create a theory column for V at time t by using equation 1.
(d) Set up a 2 calculation and vary the amplitude V1, the frequency f, the phase and the
offset V0 until you get a best fit (this is a good place to use the Solver).
(e) Plot the best fit theory on the same plot as your data.
(f) How well do your best fit values agree with the scopes "measured" values you found in C?
(g) Does the sine wave generator produce a good sine wave? Explain briefly using your 2
result and P(2,v).
2. Amplitude and Peak-to-Peak Voltage
In a few complete sentences explain what the voltage amplitude and the peak-to-peak voltage
are, and how they are related.
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