Real area of contact & analog electronics

Contact Mechanics VIA Analog Electronics

Aim of this measurement

In this class, we will attempt to reproduce the `real area of contact' measurement of Bowden and Tabor using contact resistivity. The principle of the measurement is to use two conductive bodies of a known geometry and force them into contact while simultaneously monitoring the applied load and measuring (somehow) the junction resistance. As you might know, resistivity is a bulk property, and scales inversely with the size of the resistive junction. The junction resistance is inversely related to the area of contact under certain limits, and thus can be used to measure the real (as opposed to projected) area of contact.

In the spirit of this course, this module will rely extensively on analog electronic devices that we make in the lab. This will of course require us all to be on the same page with respect to analog electronics, which will be the focus of the first two meetings of this module. 

Analog Electronics

We will first learn a some of the basics about how analog electronics work. For us to work with this type of equipment in the lab, we will make extensive use of the DLL equipment on the bench. This includes a function generator, an oscilloscope, multimeters and a power supply, as well as the breadboard (and ultimately some of the functionality) of the National Instruments Elvis II + education board, which can replicate the functionality of most of the benchtop instrumentation to some extent.

In the spirit of the class, the lab exercises will be quite open ended - you'll find that the exercise doesn't necessarily have a unique solution, and leaves it up to you to come up with an approach that sufficiently addresses the exercise.

Meeting locations for on- and off-campus students:

off campus: Please note that we have moved to a Piazza forum: link here.

Zoom link for 9a.m. discussion meeting: here

On campus: Class will be held off campus until further notice.

Remote access to the experimental computer is available via NoMachine. Instructions on how to connect in general can be found here. Note that a successful connection requires the use of the EPFL VPN.

The host IP address is:

The user name is: EMSI_LAB.

The password is: emsilab


Lab exercises #1:

Lab exercises #2:

Lab exercises, week 3

Lab exercises week 6: 

1. Build a comparator circuit using the LF411; 

2. Separately, build a comparator circuit using the LM311. 

3. Compare the comparators by driving them with a sinusoidal input through a 1k resistor on the input. What happens: for small amplitudes, e.g. 100 mV? For 1V amplitudes at high frequencies?

4. Convert your LM311 circuit to a Schmitt trigger circuit, using 300k and 1k to make the positive feedback gain loop and introduce hysteresis. Measure the hysteresis. Observe the voltage at the non-inverting input - can you explain this behavior?

5. Use the LM311 comparator to build a relaxation oscillator - Use a 100k and a 10k to make the positive feedback loop; use a 100k and a 0.01 microF capacitor to make the negative feedback loop. What frequency do you measure? Is the oscillation stable? 

6. Wien bridge oscillator circuit - build the Wien bridge oscillator using the LF411 as described in the notes, and compare it's output with the output from the lab function generator using the FFT of the lab's scope.

Lab exercises week 7

1.Devise an experiment using LTSpice that demonstrates the enhanced performance of the instrumentation amp (LT1167) compared with the standard op-amp (AD711) for a differential signal at high common-mode voltage, with comparable gain. For a guide, consider the standard output levels of a strain-gauge signal driven with 10V supply, varying up to 20 mV at full scale.

2.Using the points for discussion on the instruments required to perform the Tabor measurement, in particular the challenges mentioned in the Keithley low-level measurement handbook, develop a schematic that includes the non-trivial elements of the measurement – e.g. thermoelectric effect, etc. Implement these circuit elements in LTSpice.

3.What are the strategies advocated by the Keithley handbook for making low-R measurements? Will these require any special circuitry to achieve? If so, what performance will you require for your current source?

4.On the basis of the requirements identified in exercise 3, design and test a current source that can complete your measurement, that will drive the current to ground through the load, capable of sourcing up to 10 mA. Using a resistive load, measure the voltage drop over the junction when the current passes through it.

Lab exercises week 8:

You are now working on your LTSpice simulations for the crossed silver wire measurements. We will provide exercises from now on that make progress toward this measurement. In parallel, we will provide instructions for the remote experiment closer to the end of the class.

1.What non-idealities of op-amp behavior will play a role in our measurement of the junction resistance? Is there anything we can do to address these shortcomings of the LF411, for instance? Are there better op-amps to use for our application? Why are these better op-amps for our measurement?

2.Return to the 3rd exercise from last week. In light of non-ideal behavior of op-amps, what processes or steps can we take to ensure our voltage amplifier will work for our measurement?

3.Return to the 4th exercise from last week. Use your current source to drive current through a 1mOhm resistor. Measure the voltage over this resistor using an op-amp of your choice, and see whether the signal is amplified appropriately according the prescribed feedback gain.

4.Now, set up a noise simulation for this measurement. I recommend this source for guidance on LTSpice simulation of noise:link here

Lab exercises, week 9

1.Identify a method for eliminating line noise (the 50 or 60 Hz noise from power-supply pickup) that is recommended by Keithley. Can you propose a circuit to carry out this technique? Hint: it might have multiple components, such as an integrator and a zero-crossing detector.

2.Explain in detail why the lock-in technique will not work as well as the delta measurement method for our measurement. This should be included in your report in the methods section.

3.Conceive a way to implement either the delta mode measurement or the offset compensation method for your current source.

4.Using simulated thermoelectric potentials, verify that with the current source implemented you’ve implemented can be used to recover a 1 mOhm resistance via Ohm’s law.

5.Determine a means of introducing line noise into your LTSpice model. Can you also include white noise in the line noise to make it more realistic? Post your LTSpice models for the line noise on Piazza.

Bonus: can you design a lock-in or phase-sensitive detection scheme for your load cell? There is a design proposed on the Analog website that could prove useful. This part is not available in LTSpice; perhaps you can find a zero-drift alternative, which implements a chopper-stabilization method similar to phase-sensitive detection?

Exercises: week 10

1. Recover the key Hertz contact scaling results using the geometry and elastic properties of Silver, for bars that are 6.35 mm in diameter.

2. Estimate the estimated junction resistance for these bars at an applied load of 10g, 100g, 300 g and 3 kg. Use the value of silver bulk conductivity provided in the Tabor manuscript, or the value we measure in the second video.

3. Install NoMachine software on your computer, and initiate a connection with the lab's experimental computer as a trial run. Message me on Piazza to notify me when you're ready to try the connection.

4. Prepare a detailed experimental protocol to carry out the measurement using the equipment presented in today's lecture. The sooner you submit this to me via email, the better. This is an individual assignment, as each student must carry out a measurement.

Videos, course notes & readings


Day 1: Please refer to our Switch channel, located here. I request that you please review the introductory remarks video, the Wien bridge oscillator demo, the Hertz theory video, and finally the introduction to resistors and simple circuit laws video, from 8 a.m. until 10 a.m. tomorrow morning.

Day 2: Lecture on switchtube is here

Day 3: lecture on switchtube is here

Day 4: lecture, part 1 here; part 2 here

Day 5: lecture on switchtube is here.

Day 6: lecture is in two parts: part 1 is here, part 2 is here will be posted shortly to our Switchtube channel

Day 7: lecture on switchtube here 

Day 8: lecture on switchtube here shortly.

Day 9: lecture posted to switchtube here.

Day 10: lecture - no audio :( - posted to switchtube here. Second recording available here. Demonstration video here.

Day 11: No lecture video; just introduction to remote experiment here.

Day 13: Lecture video on grading for final reports: here

Day 14: Videos for today: an overview of experimental methods, Instability in Dynamic Fracture, Mechanical measurements in life sciences, Large-scale experiments in engineering mechanics with industrial applications

Videos prepared by your classmates: Lerville-Rouyer, Pierson and SchouweyA presentation of results from Hugo, Antoine and David (, Arnaud and Mengbo present their work.

pdf notes 2020:

Day 1: Hertz theory and introduction to analog electronics. Notes 2019, Notes 2018, Reading (linked) The reading is from The Art of Electronics (AoE), chapter 1. These readings remain relevant for the entire module.

Day 2: Notes

Day 3: Notes 

Day 4: Notes

Day 5: Notes

Day 6: Notes

Day 7: Notes

Day 8: Notes

Day 9: Notes; readings: one, two, three

Day 10: Notes; readings below in manuals, etc.

Day 12: LTSpice experimental introductory video 

Day 13: Slides on the grading rubrick.

Manuals, datasheets and references

Oscilloscope manual

Function generator manual

Multimeter manual

Power supply manual

NI Elvis II + manual

Bowden and Tabor reference

Transistor datasheets: BP547 and 2N2905ACA3096, CA3046 (used in lab week 4)

Instrumentation amplifiers

Current sources

REF 102 datasheet (Described in Week 7)

Harold S. Black's article on negative feedback amplification

LF 411 datasheet

LF 412 datasheet

LM 311 datasheet

INA 122 datasheet

Keithley low-level measurements handbook (see ch. 3 for low-voltage measurements)

Keithley nanovoltmeter manual

Keithley current source manual

AL6B load cell datasheet

LTSpice tutorial, spice files: bandpass filter, emitter amplifier

Kethley instrument manuals: nanovoltmeter, programmable current source

Keysight 34470A DMM manual (the device measuring the load cell amplifier's output)