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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/cell- phone.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 A B C D E 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 Positive offset Negative offset: 0 0.5 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: 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: If you have changed thin around and cannot see y signal hit autoset to go back to default settings. A B C D J J J J E F G H 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 0.5 1 1.5 2 -5 -10 -15 -20 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: Vout 2v Sin t Sin t Sin3 t . 2v 2v Vout 3 Sin t Sin3 t Sin5 t 2v 2v 2v Vout 3 5 Sin t Sin3 t Sin5 t Sin7 t 2v 2v 2v 2v Vout 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 1 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. 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.tu- bs.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.
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