EXPERIMENT 6A: ACCELEROMETERS, FUNCTION GENERATOR, AND FREQUENCY SPECTRA

Why do we care about frequency?

Read about how a radio works:

Cell phones:

Televisions

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:
  • LabVIEW:

Use Waveform.vi – like Lab #3

  • Function generator:

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 = 0Positive offset Negative offset:

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:

this is not exactly your model… but close enough!

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???
  • Example of bad sampling rate

Sampling rate is too small

Measured frequency not equal to actual frequency

  • Better example = minimum sampling rate

Nyquist sampling rate: fsample > 2factual

  • Best example:

Sampling rate much larger than signal frequency

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:

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:

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 / 4th largest peak
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

Above Nyquist you should see the actual 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:

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 140-141Function Generator

pp 162Sampling Rate (Nyquist Theorem)

I also highly recommend Reading &/or Printing the “Operating Basics” Chapter from the Oscilloscope Manualonline – 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

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 & cosines[1]. It can be expressed as a sum of each component of the wave, or more formally as an integral.

Fourier Transform – mathematically transformsthe 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 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):

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

The Frequency Domain, FFT Phil Bradford’s Page (under “Expts 6A & 6B”)

Fourier Series NST site

European site which has an applet (play tool) that allows you to CREATE your Own Wave!

FFT NI Free Tutorials 

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 138-139Frequency 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, OscilloscopeAcquire 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.

[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.