EXPERIMENT 6A:
ACCELEROMETERS, FUNCTION
GENERATOR, AND FREQUENCY
SPECTRA
Why do we care about frequency?
Read about how a radio works:
http://electronics.howstuffworks.com/radio4.htm
Cell phones:
http://electronics.howstuffworks.com/cellphone.htm
Televisions
http://entertainment.howstuffworks.com/tv1.htm
Learning about how to sample correctly is an important
part of information transfer!
 For a good read, and some extra background info,
check out Phill’s notes:
http://www.mines.edu/~pbradfor/melnotes.html
 LabVIEW:
Use Waveform.vi – like Lab #3
 Function generator:
http://www.tequipment.net/GlobalSpecialties2001A.html
E
D
C
B
A
F
G
B*A = frequency
Use these dials to control your frequency.
C.) Sets sine, triangle, or square wave output
D. ) controls the amplitude of your output wave
Vpp = peak to peak voltage…
E.) Fine tune of wave amplitude
F.) DC offset:
Offset = 0
Negative offset:
Positive offset
0
0
0.5
1
1.5
2
0
0.5
1
1.5
2
G.) Hook up your BNC clip to this to get your output signal
With Function Generator create:
1. Square wave, 100 Hz, 2 V peak to peak, 0 offset
2. Square wave, 100 Hz, 100 mV peak to peak, 0 offset
3. Sine wave, 200 Hz, 3 V pp, +1 V offset
 Oscilloscope:
0.5
http://www2.tek.com/CSBU/ITG/manuals/download.fwx
http://www.tek.com/site/ps/0,,40-15314-INTRO_EN,00.html
this is not exactly your model… but close enough!
power
Autoset:
J
J
J
J
H
A
B
C
E
F
G
D
If you have changed thin
around and cannot see y
signal hit autoset to go
back to default settings.
I
H, E, A = controls for CH1
Whatever wires you have coming into CH1,
this will display it
A moves CH1 line on your screen up and down
E sets your y axis
H attach your bnc clip here
I, F, B = controls for CH2
Whatever wires you have coming into CH1,
this will display it
Again…
B moves this line on your screen up and down
F sets your y axis
I attach your bnc clip here for CH2
C, G = x axis stuff
G = seconds per division (how large the grids
are)
C = move you rline from side to side
J’s – look on the screen to the left of the button. Push
the button to disply:
Frequency
Vpp – peak to peak voltage
Period
Etc…
Note: This frequency might be wrong – it may be
reading noise instead of your signal so look at the
graph and make sure the f readings make sense…
D = controls what voltage you trigger at. On the left
hand side of the graph there is an arrow – D
moves this arrow up and down. It will trigger
where the arrow is. Move the arrow until your
signal looks good!
Don’t be afraid to push buttons / turn knobs to find
out what they do. If you get stuck, you can always hit
autoset to get back to where you were.
Experiment 6A Pre-lab:
1. Remember nyquist sampling rate from lab 3???
http://www.mines.edu/fs_home/jmoss/32.doc
 Example of bad sampling rate
Sampling rate is too small
Measured frequency not equal to actual frequency
Actual signal
Measured
signal
 Better example = minimum sampling rate
Nyquist sampling rate: fsample > 2factual
Actual signal
Measured
signal
 Best example:
Sampling rate much larger than signal frequency
Actual signal
Measured signal
2.)
3) FFT = Fast Fourier Transform = transforms
between time and frequency domains
do some research, find some equations that do
this!
Also, see Phill’s page:
http://www.mines.edu/~pbradfor/melnotes.html
5) If you want, copy the pictures of the scope/generator
and use these in you diagrams…
Experiment 6A Report
1.) Sketch your signal on something similar to the
below graph.
Label axes with units and numbers:
20
15
10
5
0
0
-5
-10
-15
-20
0.5
1
1.5
2
2a. What is used for most electrical appliances?
3.) You will need to know how to use the function
generator and oscilloscope for the final exam, so take
this as an opportunity to learn how to use these!
4.) Fill in the following table:
(fnyquist = 2*fsignal)
largest peak 2nd largest peak
3rd largest peak 4
0.5*Fnyquist
0.75*Fnyquist
1.0*Fnyquist
1.25*Fnyquist
10*Fnyquist
Change the line style on your plots so that you can see
the data points…
Below Nyquist you should see aliased signals
Actual signal
Measured
signal
Above Nyquist you should see the actual signal
Actual signal
Measured signal
So… anything below Nyquist should change with
sampling rate, anything above Nyquist should remain
constant.
5.) Be sure to set your axis so that everything is clearly
displayed.
7.) TTL logic:
high level = on
low level = off
#8) Use something other than a sine wave for this one…
#11) comments on square waves:
Square waves are made from a combination of sine
waves:
Sine wave:
2v
Vout 
Sin  t

 
Vout 
2v
Vout 
2v


Sin  t  
2v
Sin 3 t .
3
Sin  t  
2v
2v
Sin 3 t  
Sin 5 t 
3
5
Vout 
2v

Sin  t  
2v
2v
2v
Sin 3 t  
Sin 5 t  
Sin 7 t 
3
5
7
Almost a square wave…!
so on your f domain graph you should have peaks at:
 …
and the amplitudes should be
1, 1/3, 1/5, 1/7… respectfully
Experiment 6A – Big Picture, Corrections, Guidance & PreLab Help
Big Picture: For experiment 6A you’ll be familiarizing yourself with a “Function
Generator” and Oscilloscope and the Acquire Waveforms & Graph.VI we’ve used once
before (vibrating beam, Expt. 3).
You’ll get an opportunity to experience, 1st hand in lab, the affect of the “Nyquist
Frequency Theorem” and “Fourier Transforms”... Sound scary? Don’t worry; it’ll be fun
& painless.
No external circuits to hook up... Yea!! A break from those protoboards, bridge circuits
and those pesky trimpots.
We’ll learn how to connect the pieces of equipment together & generate waveforms on
both the oscilloscope & Labview!
Next week, Lab 6B, we’ll utilize this knowledge, add an accelerometer to the mix and
take vibration & shock data! Woo Hoo!
Experiment 6A – Corrections to Lab Manual
You need to add a “12 volt Power Brick” to your list of equipment & supplies needed.
The power brick is simply an AC to DC transformer that supplies 3 different pairs of DC
voltage & amperage. It will be used for the CSM signal generator.
Only a couple of small typos on the 6A report:
Q4) Describe the function generator and oscilloscope settings that were used in 3.
Q10) Explain why the peaks shift on the power spectrum graph per the table in question
8.
Experiment 6A – Some Info you’ll Find Useful
“Signal Generator” is synonymous with “Function Generator” (old lab equipment vs.
new).
I definitely recommend reading the pages in the manual on:
pp 140-141 Function Generator
pp 162
Sampling Rate (Nyquist Theorem)
I also highly recommend Reading &/or Printing the “Operating Basics” Chapter
from the Oscilloscope Manual online – pages 35-37 of pdf file (23-35 of manual).
We have some booklets in lab, but we’ll be using the oscilloscopes quite a bit over the
rest of the semester, so you may want your own copy to make notes on.
Go to Next Page for…
Instructions on how to find & download the Oscilloscope Manual.
Instructions on how to find & download the Oscilloscope Manual:
The Tektronix Digital Storage Oscilloscope TDS201 manual from the Tektronix web
site:
Go to http://www2.tek.com/CSBU/ITG/manuals/download.fwx
In the Product box scroll down & find: “TDS200 Series”
In the serial number box type in “071-0398-01” or “CO32699”
Then select the “TDS 200 Series Digital Real Time Oscilloscope Users Manual – In
English”.
(2nd one in list, 71039803.pdf)
You’ll have to register to get the link to come up then you can download the file.
The manual is 132 pages long and you don’t want all of it.
I would only print the 13 page Chapter on “Operating Basics”-- pages 35-47 of the
132 page .pdf file (page # 23-35 of Manual). It has lots of pictures with helpful
descriptions.
Maybe one person from each team can print out one copy for the group to share.
A Brief Fourier Glossary:
Fourier Series – mathematically describes the various frequencies () and amplitudes
(A0, A1, …, B0, B1,… etc.) of a multiple frequency wave using a series of sines &
cosines1. It can be expressed as a sum of each component of the wave, or more formally
as an integral.
Fourier Transform – mathematically transforms the Fourier series from (in our case)
the time domain into the frequency domain, where 1/ = . Spatial descriptions can
also be transformed into frequency, like the regular or irregular pattern of a brick wall in
one direction (horizontal or vertical).
Fast Fourier Transform (FFT) – Fourier transformation is an analytical process, which
uses integral calculus in order to perform the transformation (see above). In
experimental engineering and physics, however, the integrand is typically not
continuous but a set of discrete data points and the integrand becomes a sum, a Discrete
Fourier unveiled these “innovative” mathematical functions (trigonometrical series”) in
an important memoir On the Propagation of Heat in Solid Bodies (1804 - 1807). A
committee consisting of Lagrange, Laplace, Monge and Lacroix did not approve of his
“Fourier Series”. Today, this memoir is very highly regarded but at the time it caused
controversy.
1
Fourier Transform. The Fast Fourier Transform is a mathematical algorithm developed
by J.W. Cooley and J.W. Tukey in 1965, which allows a computer to perform the
Discrete Fourier Transform efficiently.
On John Baptiste Joseph Fourier (from Phil’s site):
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Fourier.html
See next page for links to Online Tutorials re. Fourier Series & Transforms…
Regarding Fourier Series, Fourier Transforms check out:
FG, Oscill, 6A Lab Report Info, Fourier Series, Nyquist  Jamie Turner’s Home
Page
http://www.mines.edu/fs_home/jmoss/6A.doc
The Frequency Domain, FFT  Phil Bradford’s Page (under “Expts 6A & 6B”)
http://www.mines.edu/~pbradfor/melnotes.html
Fourier Series  NST site
http://www.nst.ing.tubs.de/schaukasten/fourier/en_idx.html
European site which has an applet (play tool) that allows you to CREATE your Own
Wave!
FFT  NI Free Tutorials 
http://www.ni.com/events/tutorials/campus.htm
Scroll to the bottom of the page, click on the FFT icon. You’ll have to register in order to
access it, but it’s well worth it. Plug in your headphones so you can hear the audio
portion or just follow along with the text on the bottom. I was not able to get any of the
demos to work, but you may.
pp 138-139
Frequency Domain (Fourier Transform)
Experiment 6A – Help on PreLab Questions
Q1)
Read about the Nyquist theorem on the Sampling Rate page (pg. 158), and know
that they are asking about household (residential) electrical supply, i.e. 110-120 v,
60 Hz AC.
Q2)
Read the “Frequency Domain” page. I suggest using a sketch + some verbiage.
A picture is worth a thousand words.
Q3)
You may want to access a computer w/ LabVIEW on it in order to see the Sub
VI they’re talking about here. The main things we’re looking for here are:
 Define acronym “FFT”
 Explain what happens when you use a Fourier Transform, with regards to
time and frequency (for our case).
 Talk briefly about output of Fourier Transform. In particular we are
interested in the coefficients which give us the amplitudes of the various
frequencies, which in turn give us the Power = |Amplitude|2. The Power
Spectrum on the Front Panel of this VI is Log Power vs. Freq.
 Open Labview and “Search” for “spectrum” in the Labview Help Menu.
Find the “FFT Power Spectrum”. It should tell you more about what the
Power Spectrum in the Acquire Waveforms & Graph.VI is doing (bottom
plot). I’ll show you in class Thursday how to go into our Block Diagram, find
the Power Spectrum icon, click on it & type <Ctrl-H> for context help.
Q4)
Main purpose of this lab is to acquaint you with the Function Generator,
Oscilloscope & Acquire waveforms & Graph.vi so you’ll be ready to add the
accelerometer sensor next week.
Oscilloscope Section (Q1-Q4): You’ll be experimenting with Function
Generator Output using the Tektronix Oscilloscope only.
Signals Section (Q5-Q10): You’ll add the Acquire Waveform & Graph.VI to the
connection, viewing output on both the Oscilloscope & our LabVIEW.VI Front
Panel.