Notes for Section I, Multidisciplinary Engineering Laboratory (MEL-1)

A collection of notes and resources from MEL-1 Instructors, edited by Phillips V. Bradford, Sc.D.

Jamie Turner's Notes. MEL-1 Former Instructor, Jamie Turner, has prepared a set of helpful notes for the MEL-1 experiments, available on this link, which have been preserved by Les Hammer, adjunct instructor.

Matt Young's Notes on Uncertainty Analysis. Matt has an excellent presentation on uncertainty analysis at this link.

Notes on specific experiments:

Experiments 1-A & 1-B; Voltage Dividers and Thermistors:
- A Voltage Divider Calculator
- A voltage divider applet.
- Note on common temperatures: The most reliable, common and available temperature source for these experiments is that of a ice and water mixture in equilibrium, which is 32 degrees F. Room temperature is available on the room thermostat. Human body temperatures in the peripheral appendages, such as measured within one's closed palm are significantly lower than the "under the tongue" standard of 98.6 degrees F. I recommend using the temperature in the closed inside elbow joint, which is 92.5 degrees F, after three minutes. The crock-pot temperature is well below the boiling point of water, since the pot will not boil water. The boiling point of water in Golden, CO is about 201 degrees F, depressed from 212 degrees due to its elevation at about 6000 feet above sea level. The crock-pot temperature is about 180 (+/-) 10 degrees F. To better calibrate the thermistors, we should have an independent measurement of the crock pot temperature. Recently lab 1-B has been rewritten to require only three temperatures, the freezing point of water, room temperature, and body temperature as measured in the crook of your elbow.
- Manufacturer's Data: Thermometrics, and thermistor Spec. Sheets: D10.3, and D9.5. These are the thermistors used in the MEL-1 experiments.
- Another supplier of themistors, U.S.Sensor. This site also provides some good tutorial material.
- Comment: The quartic equation showing ln(R) in terms of powers of (1/T), as in the manufacturer's spec sheets, is an empirical "curve fitting" equation with break-points for different temperature ranges. The value of the first coefficient, a, is simply the reciprocal of 25 degrees celsius temperature as expressed in kelvins. In the newly rewritten lab (rewritten in 2004), since the coefficient, a, is a known constant, the remaining three can be solved with three independent equations as long as the three temperatures used are within the same temperature range specified by the manufacture's spec sheet.
- Note: Don't forget to take into account the internal resistance load of the Digital Multi-meter, which is about ten million Ohms. How much does this error source affect the accuracy of the measurement of the voltage divider output voltage ? Does this error depend on the temperature?
Experiments 2-A & 2-B; The Wheatstone Bridge and Strain Gages:
- See the Table of Resistivity and Temperature Coefficient at 20 C originally from Giancoli, for various materials at 20 degrees C. What is Manganin? Click on it. Why would Manganin be a good material for strain gages? Resistance of a length of wire with a uniform cross section = (Resistivity of the material of which the wire is made)(L )/(A), where L is the length of the wire, and A is the cross sectional area of the wire. If Resistivity is in units of Ohm-meters, then L should be in meters and A in square meters. If under increasing strain, a wire's length, L, increases and its cross-sectional area decreases, such that its volume, V = (A)(L) remains constant, then since the Resistivity and the Volume of a wire are constant, then the Resistance should increase as the square of the Length, L, and the change in Length should be proportional to the strain on the wire. Does your data show that the Resistance of the strain gage increases as the square of the strain? If not, why not? Is your data good enough to determine Poisson's Ratio?
- You have been provided with a steel scale to measure the beam dimensions. How much would your measurement precision improve if you used a vernier caliper?
- Using Thevenin Equivalents on Wheatstone Bridge, by Harold Hallikainen. For the advanced student, this site provides an analysis for the general case of an unbalanced bridge.
- Historical photos of antique commercial L. M. Ericsson Wheatstone bridges.
- The Strain Gage, a tutorial provided by Omega.
Experiment 3: Beam Vibrations.
- Young's Modulus, E, in the frequency formula must be in the correct units. Note that the units for E are Force/Area (the same as Pressure). Note that since the frequency formula is derived from Hooke's Law: F = kx, and Newton's Law: F = ma, the forces should be expressed in Inertial Force Units, not gravitational force units (i.e. "weight"). Thus, in the SI "metric" case (preferred), Young's Modulus is expressed in Newton's per square meter. In free space, one Newton (abbreviated "N") will provide a mass of one Kilogram to accelerate at one meter per second squared (Even though Sir Isaac Newton never knew what a Newton was, because the SI unit system was not established until long after his time. It is a little ironic that the SI unit of force should be named after the famous English mathematician and scientist. In English (Imperial) units, the inertial unit of force is the poundal, abbreviated "pdl" which is the force that provides one pound of mass with an acceleration of one foot per second squared. In the frequency formula of Experiment 3, if the SI "metric" system is used, Young's modulus, E, should be expressed in Newtons per square centimeter, which is 10,000 times smaller than in Newtons per square meter, and the beam dimensions should be expressed in centimeters. Likewise, if English units are used, Young's modulus, E, should be expressed in "twelfth poundals" per square inch, and the beam dimensions should be expressed in inches. The conversion rate is: One poundal = 0.138255 Newtons, and one "twelfth poundal" = one twelfth of that. A "twelfth poundal" will accelerate a mass of one pound to a rate of one inch per second squared. Have you considered what would happen if the beam were mounted sideways and caused to vibrate horizontally instead of vertically? Would the frequency be different? If so, how much different?
- The vibration frequency formula includes a term, b, representing the width of the beam. Intuitively, however, the vibration frequency should be independent of, b, the beam width. Imagine two identical beams mounted side-by-side and vibrating together just touching each other. Would attaching them together with glue, and thereby doubling the width if treated as a single beam, change the frequency of vibration? How does the beam width, b, get cancelled out in the formula?
Experiment 4: Thermal expansion.
- See the Vishay table on the Thermal Expansion Coefficients of Engineering Materials .
Experiment 5: Pressure Transducers.
- Manufacturers Notes Omega.
- Manufacturers Notes Micron Instruments.
- Comment: The Bourdon tube gauge (or gage) is the most commonly used means of measuring pressure. This type of gage has many mechanical variations., covers wide ranges of pressures and vacuum applications, and can be made economically. They can be made to provide measurements accurate to 0.1 % of their full scale meter reading.
- Comment: Pressure measurements can also be made by bellows devices, barometers, manometers, and Pitot tubes. Using electrical transducers, such a strain gages, one can measure pressure at remote locations or in unfriendly environments. What factors are involved in the widespread adoption of electronic methods to replace mechanical ones in pressure measurements? In what industries has this already happened?
- What alloys are used to make Bourdon tubes and what alloys should be used for strain gage applications in pressure measurements? See Brush Wellman.
- The future?:
  - Wireless Strain gages MicroStrain.
  - Wireless Sensor Networks - Agile-Link.
Experiments 6A & 6B: Accelerometers, ..., Frequency Spectra.
- Why are we doing these experiments? Please read carefully the text beginning on the bottom of page 57 through the end of page 60; entitled Why Learn About Sampling Rate and the Frequency Domain. While this text is focused on an application in vibration analysis for packaging, these two experiments also provide the MEL-1 students, their first exposure to SIGNAL ANALYSIS. Experiment 6-A is primarily a lesson in how to use a waveform generator, an oscilloscope, and certain appropriate virtual instruments (vi 's) in LabView software. Prior to these experiments, the MEL-1 students were exposed only to "direct current" (d.c.) measurements. In Experiments 6A & 6B, we will look at "alternating current" (a.c.) and waveforms to measure and analyze.
- Historically, oscilloscopes were made to provide a continuous analog representation of an electrical signal. As technology progressed, digital representations of signals became needed in order to allow digital computers to process them. Also, signals needing analysis quickly reached frequencies that were beyond the time response specifications of cathode ray tubes (CRTs) of oscilloscopes to handle. The result was that analog signals and high frequency waveforms were "sampled" at discrete times, and engineers developed new methods, based on mathematical techniques (most of which were developed earlier), to "reconstruct" waveforms. One of the pioneers in the sampling and reconstruction of signal waveforms was Harry Nyquist (1889-1976). The Nyquist theorem: "... the sampling rate must be at least twice the highest frequency present in the sample in order to reconstruct the original signal." was discovered by Harry Nyquist in the 1920s (see bio below), and published in his paper: Certain Topics in Telegraph Transmission Theory, Trans. A.I.E.E., pp 617-644, April 1928. If one were to use a sampling rate less than twice the highest frequency present, there is a possibility that reconstructed signals will include aliases, typically at lower frequencies, which are false representations of the signal being analyzed.
- Everyday (nearly) Examples of Aliasing Phenomena:
  - Moire patterns. See the The Magic Moving Picture Book by Bliss, Sands & Co. Why does seeing a scene of one fence behind another produce "waves"? See: Moire Patterns.
  - Why do TV news anchors, talk show hosts, and other "talking heads" avoid vertically striped suits and ties? Does the television camera "sample" its view with each frame?
  - Why do motion pictures often show cars with wheels going backwards? Does a motion picture "sample" the real scene of a moving car?
- The frequency domain. The representation of an electrical signal, such as a voltage v(t), varying with time, t, is often adequate for analysis. However, since many useful electrical signals are in the form of regular and repeated waveforms, such as sine waves, square waves, saw-tooth patterns, etc., engineers have made use of several important alternative representations in order to simplify the analysis and synthesis of electrical circuits and systems for analyzing and processing electrical signals.
  Many physical phenomena, and sensor technologies are responsive to frequencies. Our own human ears separate sounds by their tones, and our eyesight discrimates colors and patterns. Signals carried by radio, television, radar, transmission lines, fiber optics, and even atomic vibrations are characterized by their frequencies and wavelengths rather than by their time dependent functions. Who can recognize the sounds of a trumpet and compare it to a clarinet playing different notes at the same time by looking at the minute air pressure fluctuations in their sound waves as a function of time? Nature knows that it's better for us humans to separate the sounds into a frequency spectrum using our Cochlea
  In experiment 6A we will set up the equipment complement to process a complicated signal from an accelerometer that is to be bounced around, then in Experiment 6B we will actually process such a signal. The beginning student may wonder why we would go to so much trouble as to take a Fourier Transform of an accelerometer signal, but the point to be made here is that there are techniques to be learned for processing and measuring a wide variety of electrical signals in order to extract meaningful data from such signals and convey INFORMATION.
  Some students may be surprised to learn that alternative representations of mathematical functions in frequency rather than time preceeded their practical application by 100 to 200 years. Pierre Laplace (1749-1827) and Joseph Fourier (1768-1830), (links to their biographies below), were not burdoned with the thought that the transforms and series named for them would be the everyday tools of engineers 200 years later.
  And, some modern students (and professors as well!) might be surprised to learn that the mathematical work associated with transform functions is still not complete. For example, the precise necessary and sufficient conditions pertaining to a periodic function for it to be represented by a Fourier Series are yet UNKNOWN. [Source: Konrad Knopp; Theory and Application of Infinite Series, page 379. See also: Gibbs' Phenomenon].
  Despite these pesky details, the use of Fourier Series and Transforms is a valuable tool which has been implemented in hardware and software for engineers and it is in common use, and all students should learn how to use the frequency spectrum in engineering work. For our purposes, the LabView virtual instrument software will do the necessary transforms, but it is important to know what it is doing, and its limitations.
  The Fast Fourier Transform (FFT), is an algorithm which is a faster method of calculating a Fourier Transform to yield the frequency spectrum of a time based signal. There are commercially available single semiconductor chips that serve as FFTs and there are software programs. See also Intro. to Fourier Theory.
  In Experiment 6B, we will analyse the output of an accelerometer attached to a [Approx. 500 g.] wooden block. The wooden block will be hung from the lab bench with rubber bands, and allowed to oscillate up and down. Its exact mass may be determined by weighing it on the lab scale. The specifications sheets provided by the vendors of the accelerometers are:
  - Analog Devices ADXL 105.
  - Crossbow CXL50LP1.
  Hooke's Law can be used to relate the force imparted by the rubber bands on the wooden block, as a function of the vertical displacement of the wooden block, F = kx. Can we determine k, by placing small additional weights on the block, and measuring the resulting displacement?
  Newton's Law, F = ma, can be used to determine the acceleration of the wooden block subject to the forces imposed on it. How does one write the equations of motion to take the effects of gravity into account?
  Using the Crossbow accelerometer, we will introduce shock to the wooden block by dropping it on packaging material, and determining the results by analysing the output of the accelerometer.
Experiments 7A , 7B, & 7C: Microphones, Filters, Oscilloscopes, and Amplifiers.
- Experiment 7A. For these experiments we will be needing to learn about Decibels and Bode plots
- Experiment 7B.
  - See the following link regarding Operational Amplifiers. Please note that on this web site, a high-pass filter Op-Amp circuit is also called a "differentiator" and a low-pass filter Op-Amp circuit is called an "integrator". What is the rationale for this?
  - For the complex number methods of Op-Amp circuits, this link may be helpful.
  - For an historical and technical summary of Op-Amp technology, see this link. It also shows the circuit inside the Op-Amp.

Historical and Humanist adenda, through Biographies

About 10 minutes of each lab session is devoted to a brief introduction to the lives of historical persons who have been instrumental in the development of multidisciplinary electrical measurements. The purpose of this is to provide the students with a context for creative thinking by showing the problems that were solved and the barriers that were faced by these historical figures. The World Wide Web (WWW) provides an opportunity to easily present these biographies. At present, the material presented is not required for subsequent examination, but it is hoped that some students will find it interesting, entertaining, or inspiring.

Georg Simon Ohm. Why did Ohm face so much difficulty in gaining acceptance for the fundamental law named in his honor ? Is it a physical law, or just a mathematical realtionship of a tautological nature ? How would you define electrical resistance ?
- Gabriel Daniel Fahrenheit What was the basis of the Fahrenheit temperature scale? Was there, and is there, any connection between "degrees" of temperature and "degrees" in the measurement of angles?
- Anders Celsius Why did Celsius want to have the freezing point of water to be 100 degrees and boiling to be 0 degrees, and why was it turned around after he died ? Did Celsius think in terms of degrees of "solidity" or some such idea?
- William Thompson, a.k.a. Lord Kelvin How did Lord Kelvin relate temperature to energy, when his predecessors related it to the expansion of a column of mercury ? Do equal amounts of water at boiling and at freezing temperatures become 50 degrees C, when mixed ? Can we be sure that mercury expands linearly with added equal increments of thermal energy ? Lord Kelvin studied such things, among many others as the "Lord of measurements". Today students may enjoy his famous (and often ridiculous) quotes, but could he have done a disservice to the British Empire's advancement of science when a man of his influence and stature in Victorian England pronounced that "X-rays would prove to be a fraud", that "radio has no future" and that "man would never make a heavier-than-air flying machine" ?
Charles Wheatstone Wheatstone commercialized the bridge for electrical measurements, orginally invented by Samuel Hunter Christie, the son of the founder of Christie's Auction House in London. Could there be a connection between the ability of taut wires to carry vibrations for musical instruments and the electrical properties of those wires?
Thomas Young A Physicist and a Physician (Medical Doctor) with great literacy, Young was primarily interested in optical matters. What connections might he have made between the optical qualities of metals and their electrical properties? Does the strength of a metal (its Young's Modulus) affect the way it reflects light or conducts electricity?
Sophie Germaine: Using the genderless pseudonym "M. LeBlanc", Sophie connected the acoustical properties of metals to their elastic properties and won a major scientific award in Paris. She (perceived as He) was a correspondent with, and was admired by: Carl Frederick Gauss and Jean Baptiste Joseph Fourier. How did she develop an interest in acoustics and elasticity, and contribute to knowledge in these areas without access to a laboratory? For what was she best known?
Pierre Laplace (1749-1827) discovered the Laplace transform.
Joseph Fourier (1768-1830), discovered the Fourier Series and the Fourier Transform.
Dr. Karl Ferdinand Braun (1850-1918), the inventor of the oscilloscope.
Harry Nyquist (1889-1976), communications pioneer, who anticipated the digital age.
Hendrik Wade Bode, for whom the "Bode plot" was named.
George A. Philbrick, the designer of the first commercially successful Op-Amp (Operational Amplifier) - but he was not the inventor, as we learn by visiting this web page!