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Work of fracture with analog electronics

Work of fracture with analog electronics

For this experiment, we will be measuring the work of fracture for a polyacrylamide hydrogel. A relevant reference can be found here. To carry out this measurement, your task will be to develop a Wheatstone bridge amplifier that is compatible with the force transducer provided. Work of fracture is defined as the work per unit volume to cause a material to ultimately fail. This can be readily calculated from a loading curve when loading a sample to failure.

We will also introduce analog electronics to help you develop your amplifier circuit. A Wheatstone bridge amplifier is a common application for circuit design in mechanical engineering, and is versatile. There are some key considerations concerning how the bridge is `driven,' or powered, and what the mean voltage of the bridge will be. These can all be addressed in different ways. To get to an amplifier, we will start at square one, with passive circuits. These form the bedrock of all analog circuits, and will likely prove useful in their own right along the way.

If you feel intimidated by the use of gels, please don't - we will be making the samples for you. It can be helpful if you read a bit to familiarize yourselves with this material.

Readings

Week 1

A simple website introduction to the oscilloscope: How to Use an Oscilloscope - learn.sparkfun.com

I also encourage you to read the appendix of the Art of Electronics (AoE) on the oscilloscope. This is available in both the 2nd and 3rd (most recent) editions of the book.

Week 2
Read about transistors (AoE 2nd Ch. 2, through 2.05) and op-amps (AoE 2nd Ch. 4, through 4.22 - stop at comparators)

Week 3

Recorded lecture now available: Zoom link

A nice overview of the operating principles of the Wheatstone bridge can be found in this video. It's only 10 minutes, and covers the essential structure and purpose of the Wheatstone bridge.

I emphatically recommend this article by Jim Williams* for information on amplification of Wheatstone bridge circuits. The first few pages introduce the measurement challenge in detail.

Read this short handout on instrumentation amplifiers. It should be clear after reading this why one would use an instrumentation amplifier - particularly in a Wheatstone Bridge circuit.

For more details, but not required, you can read chapters 4, 7 and 8 in the HBM handout on Wheatstone Bridge circuits (wikipedia Wheatstone bridge if you've never seen it before)

If you can find the 2nd edition of AoE, read 15.03 on measuring strain and displacement - it covers almost any type of tranducer that you'd ever be interested to use in measurement applications (!)

Week 4

Read the reference on gel structure-property relations. Take note of how cross-linking concentration alters material properties.

For a general discussion of error analysis and general error propagation, this website has a great, concise summary - from Werner Boeglin. You should understand how error in measured quantities used to derive another quantity can be used to determine the error bounds on the derived quantity.

From the Keithley low level measurements handbook, 7. ed (link below in resources): section 1.2, 1.4, all of section 3.

Exercises

Week 1

Familiarize yourself with the oscilloscope and other bench-top instrumentation at your desk. A suggested starting point is to feed a sine wave from the function generator into the oscilloscope input, and monitor the wave on the scope. Set up a proper trigger for the experiment. Measure the frequency - does it exactly correspond to the frequency of the function generator?

Propose and conduct an experiment to verify that a resistor satisfies Ohm's law
Make a voltage divider, and explain why the output voltage takes on the value that you measure
Drive a resistive load with your voltage divider, and continue to monitor the output voltage. Does this value change when you attach the load? Why or why not? Try this for a few values of R, varying from less than to greater than the resistor value you used in the original divider.
Make a low-pass filter using a resistor and a capacitor
Make a high-pass filter using another resistor and capacitor pair (they can have the same values as the components you used in the low-pass filter)
Propose and conduct an experiment to measure the 3 dB frequency for each of these filters (hint: the function generator has a sweep feature). Does the value agree with your expectation based on the capacitance and resistance values you used?
Bonus: make a bandpass filter

Week 2

Use an npn transistor to make an emitter-follower using ~ 1kOhm on the emitter leg to ground, and between 10 and 15 V on the collector; use 100 Ohm on the base leg. What happens when you drive the base at 5 V peak-to-peak?
Now connect the 1kOhm on the emitter leg to -15V, leaving everything else as it was. What changes about the output signal?
Plug in & power (with the correct polarity) the op-amp (LF411 in lab). Monitor the output of the amplifier with an oscilloscope probe. If you short the inverting and non-inverting inputs, what do you observe on the oscilloscope? Do you see oscillations, or a steady signal? Is the signal anywhere near the power-supply voltage?
Construct an op-amp follower. How does this circuit behave when compared to the emitter follower you made in exercise 1 when driven with a 5Vpp sinusoidal input?
Build a non-inverting amplifier with a 10k in the feedback loop, and a 1k to ground. Drive the input with a sinusoid, and observe the magnitude of the output swing by varying the input magnitude. What sets the limit of the output swing at 1kHz? Now, increase the driving frequency by a lot (hint ~ 1 MHz) - do you observe a change in the amplifier's response? How did the response change? Is there a value from the data sheet can account for the observed change?
Build an inverting amplifier using the same resistor values as the previous exercise, and measure it's input impedance by inserting a 1k between the function generator and the 1k leg of the amplifier. What is the input impedance? What sets the input impedance value of the inverting amplifier?

Week 3

Add your groups to the wiki
Your primary task today is to build an amplifier circuit for a load cell. You are to supply a voltage at +10, and measure the output of the bridge. What is the common-mode voltage you expect for your bridge circuit? Do you require high common-mode rejection for this application?
Design a circuit that addresses the primary needs of this application - include a voltage supply for the Wheatstone bridge (e.g. Ref 102). Why is it better to use the Ref 102 than e.g. the power supply on your desk? Refer to the datasheet to answer this question.
The bridge resistor values of the load cell are around 300 Ohm. What current do you expect when the load cell is not loaded? How does this compare to the current output specification of the Ref 102? If needed, can you find a circuit in the REF 102 datasheet that can use the Ref 102 and a pnp transistor to supply more current with the same voltage output?
Select an amplifier for this application. Will you use an INA or OPA? Find the datasheet for your amplifier. How will you connect the wires for the 20N HBM load cell? Note that the load cell generates 2 mV / V excitation at full scale.
If you need to measure 0.1 N very accurately (e.g. 0.1 N at 5 V output from your amplifier), what gain will you need for your amplifier?
Once you are happy with the circuit, and it is constructed on your group's small breadboard, contact the teaching assistants to obtain the loading apparatus. Use this apparatus to calibrate your load cell with a known test mass. Use a two-point calibration.

Week 4

Use your amplifier circuit with the testing apparatus to measure the work of fracture for your gel sample.
How does your measured work of fracture compare with your expectations based on the reading for today? If they disagree, can you formulate a hypothesis for why? If they agree, write to P. Kolinski, and measure another sample after it has dehydrated, and try to explain whether the work of fracture should change for the dehydrated sample.