Supplemental sheets, draft 3

This post updates and replaces the Supplemental sheets, draft 2. It reflects the redesign of the course based on running a prototype version of the course in as a group tutorial in Winter 2013.

Lecture Course

Undergraduate Supplemental Sheet
Information to accompany Request for Course Approval
Sponsoring Agency: Biomolecular Engineering
Course #: 101
Catalog Title: Applied Circuits for Bioengineers

Please answer all of the following questions using a separate sheet for your response.
1. Are you proposing a revision to an existing course? If so give the name, number, and GE designations (if applicable) currently held.

This is not a revision to any existing course.A prototype version of the course was run as BME 194 Group Tutorial in Winter 2013. Notes on the design and daily running of that prototype can be found at https://gasstationwithoutpumps.wordpress.com/circuits-course-table-of-contents

2. In concrete, substantive terms explain how the course will proceed. List the major topics to be covered, preferably by week.

The Applied Circuits course is centered around the labs in the accompanying lab course.  Concepts are taught as needed for the labs, with design and analysis exercises in the lecture course cementing the understanding. The recurring theme throughout the course is voltage dividers: for change of voltage, for current-to-voltage conversion, for high-pass and low-pass RC filters, in Wheatstone bridges, and as feedback circuits in op amp circuits.  The intent of this course is to provide substantial design experience for bioengineering students early in their studies, and to serve both as as bridge course to entice students into the bioelectronics concentration and as a terminal electronics course for those students focussing on other areas.

1. Basic DC circuit concept review: voltage current, resistance, Kirchhoff’s Laws, Ohm’s Law, voltage divider, notion of a transducer.
   The first week should cover all the concepts needed to do the thermistor lab successfully.
2. Models of thermistor resistance as a function of temperature. Voltage and current sources, AC vs DC, DC blocking by capacitors, RC time constant, complex numbers, sine waves, RMS voltage, phasors. The second week should cover all the concepts needed to do the electret microphone lab successfully.
3. Low-pass and high-pass RC filters as voltage dividers, Bode plots. Concepts necessary for properly understanding digitized signals: quantized time, quantized voltage, sampling frequency, Nyquist frequency, aliasing.
4. Amplifier basics: op amps, AC coupling, gain computation, DC bias for single-power-supply offsets, bias source with unity-gain amplifier.  In the lab, students will design, build, and test a low-gain amplifier (around 5–10 V/V) for audio signals from an electret microphone. We’ll also include a simple current-amplifier model of a bipolar transistor, so that they can increase the current capability of their amplfier.
5. Op amps with feedback that has complex impedance (frequency-dependent feedback), RC time constants, parallel capacitors, hysteresis, square-wave oscillator using Schmitt triggers, capacitance-output sensors, capacitance-to-frequency conversion.   Topics are selected to support students designing a capacitive touch sensor in the accompanying lab.
6. Phototransistors and FETs for the tinkering lab and for the class-D amplifier lab. In preparation for the lab in which students model a pair of electrodes as R+(C||R), we will need a variety of both electronics and electrochemistry concepts: variation of parameters with frequency, impedance of capacitors, magnitude of impedance, series and parallel circuits, limitations of R+(C||R) model, and at least a vague understanding of half-cell potentials for the electrode reactions: Ag → Ag⁺ + e^-, Ag⁺ + Cl^- → AgCl, Fe + 2 Cl^-→ FeCl₂ + 2 e^-.
7. Differential signals, twisted-pair wiring to reduce noise, strain gauge bridges, instrumentation amplifier, DC coupling, multi-stage amplifiers.
   Topics are selected to support the design of a 2-stage amplifier for a piezoresistive pressure sensor in the lab.
8. System design, comparators, more on FETs. Students will design a class-D power amplifier to implement in the lab.
9. A little electrophysiology: action potentials, electromyograms, electrocardiograms. Topics are chosen so that students can design a simple 3-wire electrocardiogram (EKG) in the lab.There will also be a bit more development of simple (single-pole) filters.
10. The last week will be review and special topics requested by the students.

3. Systemwide Senate Regulation 760 specifies that 1 academic credit corresponds to 3 hours of work per week for the student in a 10-week quarter. Please briefly explain how the course will lead to sufficient work with reference to e.g., lectures, sections, amount of homework, field trips, etc. [Please note that if significant changes are proposed to the format of the course after its initial approval, you will need to submit new course approval paperwork to answer this question in light of the new course format.]

The combination of BME101 and BME101L is 7 units (21 hours per week).  The time will be spent approximately as follows:

• 3.5 hours lecture/discussion
• 3.5 hours reading background and circuits text
• 3 hours read lab handouts and doing pre-lab design activities
• 6 hours lab
• 5 hours writing design reports for lab

4. Include a complete reading list or its equivalent in other media.

No existing book covers all the material.  For the prototype run of the course, we relied heavily on Wikipedia articles, which turned out to be too dense for many of the students.  Other alternatives (such as Op amps for everyone by Ron Mancini http://www.e-booksdirectory.com/details.php?ebook=1469 Chapters 1–6 and Op Amp Applications Handbook by Analog Devices http://www.analog.com/library/analogDialogue/archives/39-05/op_amp_applications_handbook.html Sections 1-1 and 1-4) were also much too advanced.

In future we will most likely use the free on-line text All about Circuits as the primary text, with material not covered there (such as the various sensors) coming mainly from Wikipedia and the datasheets for the components.

5. State the basis on which evaluation of individual students’ achievements in this course will be made by the instructor (e.g., class participation, examinations, papers, projects).

Students will be evaluated primarily on design reports with some in-class or take-home quizzes to ensure that they do the needed reading on theoretical concepts.

6. List other UCSC courses covering similar material, if known.

EE 101 covers some of the same circuit material, but without the focus on sensors and without instrumentation amps.  It covers linear circuit theory in much more depth and focuses on mathematical analysis of complicated linear circuits, rather than on design with simple circuits.  The expectation for bioengineering students is that those in the bioelectronics track would take BME 101 before taking EE101, and that those in other tracks would take BME 101 as a terminal electronics course providing substantial engineering design.  The extra material in BME 101 would prepare the bioengineering students better for EE 101.

Physics 160 offers a similar level of practical electronics, but focuses on physics applications, rather than on bioengineering applications, and is only offered in alternate years.

7. List expected resource requirements including course support and specialized facilities or equipment for divisional review. (This information must also be reported to the scheduling office each quarter the course is offered.)

The lecture part of the course needs no special equipment—a standard media-equipped classroom with a whiteboard, screen, and data projector should suffice. Having a portable laptop-connected oscilloscope would make demos much easier to do, but is not essential.

The lecture course is not really separable from the associated lab course,whose equipment needs are described on the supplemental sheet for that course.

The course requires a faculty member (simultaneously teaching the co-requisite Applied Circuits lab course) and a teaching assistant or undergraduate group tutor for discussion sections and assistance in grading.  The same TA/group tutor should be used for both the lecture and the lab courses.

8. If applicable, justify any pre-requisites or enrollment restrictions proposed for this course. For pre-requisites sponsored by other departments/programs, please provide evidence of consultation.

Students will be required to have single-variable calculus and a physics electricity and magnetism course. Both are standard prerequisites for any circuits course. Although DC circuits can be analyzed without calculus, differentiation and integration are fundamental to AC analysis. Students should have already been introduced to the ideas of capacitors and inductors and to serial and parallel circuits.

The prerequisite courses are already required courses for biology majors and bioengineering majors, so no additional impact on the courses is expected.

9. Proposals for new or revised Disciplinary Communication courses will be considered within the context of the approved DC plan for the relevant major(s). If applicable, please complete and submit the new proposal form (http://reg.ucsc.edu/forms/DC_statement_form.doc or http://reg.ucsc.edu/forms/DC_statement_form.pdf) or the revisions to approved plans form (http://reg.ucsc.edu/forms/DC_approval_revision.doc or http://reg.ucsc.edu/forms/DC_approval_revision.pdf).

This course is not expected to contribute to any major’s disciplinary communication requirement, though students will get extensive writing practice in the design reports (writing between 50 and 100 pages during the quarter).

10. If you are requesting a GE designation for the proposed course, please justify your request making reference to the attached guidelines.

No General Education code is proposed for this course, as all relevant codes will have already been satisfied by the prerequisites.

11. If this is a new course and you requesting a new GE, do you think an old GE designation(s) is also appropriate? (CEP would like to maintain as many old GE offerings as is possible for the time being.)

No General Education code is proposed for this course, as all relevant codes (old or new) will have already been satisfied by the prerequisites.

Lab course

Undergraduate Supplemental Sheet
Information to accompany Request for Course Approval
Sponsoring Agency Biomolecular Engineering
Course # 101L
Catalog Title Applied Circuits Lab

Please answer all of the following questions using a separate sheet for your response.
1. Are you proposing a revision to an existing course? If so give the name, number, and GE designations (if applicable) currently held.

This is not a revision to any existing course. A prototype version of the course was run as BME 194F Group Tutorial in Winter 2013. Notes on the design and daily running of that prototype can be found at https://gasstationwithoutpumps.wordpress.com/circuits-course-table-of-contents

2. In concrete, substantive terms explain how the course will proceed. List the major topics to be covered, preferably by week.

The course is a lab course paired with BME 101, Applied Circuits for Bioengineers.  The labs have been designed to be relevant to bioengineers and to have as much design as is feasible in a first circuits course.  The labs are the core of the course, with lecture/discussion classes to support them. There will be six hours of lab a week, split into 2 3-hour sessions. Lab assignments will generally take two lab sessions, with data collection in the first lab session, and data analysis and design between lab sessions.   Some of the more straightforward labs will need only a single session.  Except for the first intro lab, these labs have been used in the prototype run of the class as 3-hour labs.  Most did not fit in one 3-hour lab session and would benefit from being split into two separate lab sessions with data analysis and design between the sessions.

1. Intro to parts, tools, and lab equipment (single session)
2. Thermistor
3. Microphone
4. Sampling and aliasing (single session)
5. Audio amp
6. Hysteresis oscillator and soldering lab
7. FET and phototransistor
8. Electrode modeling
9. Pressure sensor and instrumentation amp (soldered)
10. Class-D power amplifier
11. EKG (instrumentation amp with filters, soldered)

1. Intro to parts, tools, and lab equipment
   Students will learn about the test equipment by having them use the multimeters to measure other multimeters. What is the resistance of a multimeter that is measuring voltage? of one that is measuring current? what current or voltage is used for the resistance measurement? Students will be  issued their parts and tool kits, learn to use the wire strippers and make twisted-wire cables for the power supplies to use all quarter.  They will learn to set the current limits on the power supplies and  measure voltages and currents for resistor loads around 500Ω.  This lab will not require a written lab report.
   Lab skills developed: wire strippers, multimeter for measuring voltage and current, setting bench power supply
   Equipment needed: multimeter, power supply
2. Thermistor lab
   The thermistor lab will have two lab sessions involving the use of a Vishay BC Components NTCLE413E2103F520L thermistor or equivalent.
For the first lab session, the students will use a bench multimeter to measure the resistance of the thermistor, dunking it in various water baths (with thermometers in them to measure the temperature). They should fit a simple curve to this data based on standard thermistor models. A class period will be spent on learning both the model and how to do model fitting with gnuplot, and there will be a between-lab exercise where they derive the formula for maximizing | dV/dT | in a voltage divider that converts the resistance to a voltage.
   For the scond lab session, they will add a series resistor to make a voltage divider. They have to choose a value to get as large and linear a voltage response as possible at some specified “most-interesting” temperature (perhaps body temperature, perhaps room temperature, perhaps DNA melting temperature).  They will then measure and plot the voltage output for another set of water baths. If they do it right, they should get a much more linear response than for their resistance measurements. 
Finally, they will hook up the voltage divider to an Arduino analog input and record a time series of a water bath cooling off (perhaps adding an ice cube to warm water to get a fast temperature change), and plot temperature as a function of time.
   Lab skills developed: use of multimeter for measuring resistance and voltage, use of Arduino with data-acquisition program to record a time series, fitting a model to data points, simple breadboarding.Equipment needed: multimeter, power supply, thermistor, selection of various resistors, breadboard, clip leads, thermoses for water baths, secondary containment tubs to avoid water spills in the electronics lab. Arduino boards will be part of the student-purchased lab kit. All uses of the Arduino board assume connection via USB cable to a desktop or laptop computer that has the data logger software that we will provide.
3. Electret microphone
   First, we will have the students measure and plot the DC current vs. voltage for the microphone. The microphone is normally operated with a 3V drop across it, but can stand up to 10V, so they should be able to set the Agilent E3631A  bench power supply to various values from 0V to 10V and get the voltage and current readings directly from the bench supply, which has 4-place accuracy for both voltage and current. Ideally, they should see that the current is nearly constant as voltage is varied—nothing like a resistor.  They will follow up the hand measurements with automated measurements using the Arduino to measure the voltage across the mic and current through it for voltages up to about 4v.  The FET in the microphone shows a typical exponential I vs. V characteristic below threshold, and a gradually increasing current as voltage increases in the saturation region.  We’ll do plotting and model fitting in the data analysis class between the two labs.
   Second, we will have them do current-to-voltage conversion with a 5v power supply and a resistor to get a 1.5v DC output from the microphone and hook up the output of the microphone to the input of the oscilloscope. Input can be whistling, talking, iPod earpiece, … . They should learn the difference between AC-coupled and DC-coupled inputs to the scope, and how to set the horizontal and vertical scales of the scope. They will also design and wire their own DC blocking RC filter (going down to about 1Hz), and confirm that it has a similar effect to the AC coupling on the scope. Fourth, they will play sine waves from the function generator through a loudspeaker next to the mic, observe the voltage output with the scope, and measure the AC voltage with a multimeter, perhaps plotting output voltage as a function of frequency. Note: the specs for the electret mic show a fairly flat response from 50Hz to 3kHz, so most of what the students will see here is the poor response of a cheap speaker at low frequencies.
   EE concepts: current sources, AC vs DC, DC blocking by capacitors, RC time constant, sine waves, RMS voltage, properties varying with frequency.Lab skills: power supply, oscilloscope, function generator, RMS AC voltage measurement.Equipment needed: multimeter, oscilloscope, function generator, power supply, electret microphone, small loudspeaker, selection of various resistors, breadboard, clip leads.
4. Sampling and Aliasing
   Students will use the data logger software on the Arduino to sample sine waves from a function generator at different sampling rates.  They will need to design a high-pass RC filter to shift the DC voltage from centered at 0 to centered at 2.5v in the middle of the Arduino A-to-D converter range.  They will also design a low-pass filter (with corner frequency below the Nyquist frequency) to see the effect of filtering on the aliasing.
   EE concepts: quantized time, quantized voltage, sampling frequency, Nyquist frequency, aliasing, RC filters.
   Equipment needed:  function generator, Arduino board, computer.
5. Audio amplifier
   Students will use an op amp to build a simple non-inverting audio amplifier for an electret microphone, setting the gain to around 6 or 7. The amplifier will need a a high-pass filter to provide DC level shifting at the input to the amplifier. Note that we are using single-power-supply op amps, so they will have to design a bias voltage supply as well. The output of the amplifier will be recorded on the Arduino (providing another example of signal aliasing).
   The second half of the lab will add a single bipolar transistor to increase the current and make a class A output stage for the amplifier, as the op amp does not provide enough current to drive the 8Ω loudspeaker loudly.
   EE concepts: op amp, DC bias, bias source with unity-gain amplifier, AC coupling, gain computation.
   Lab skills: complicated breadboarding (enough wires to have problems with messy wiring). If we add the Arduino recording, we could get into interesting problems with buffer overrun if their sampling rate is higher than the Arduino’s USB link can handle.
   Equipment needed: breadboard, op amp chip, assorted resistors and capacitors, electret microphone, Arduino board, optional loudspeaker.
6. Hysteresis and capacitive touch sensor
   For the first half of the lab, students will characterize a Schmitt trigger chip, determining V_IL, V_IH, V_OL, and V_OH. Using these properties, they will design an RC oscillator circuit with a specified period or pulse width (say 10μs), and measure the frequency and pulse width of the oscillator.
   For the second half of the lab, the students will build a relaxation oscillator whose frequency is dependent on the parasitic capacitance of a touch plate, which the students can make from Al foil and plastic food wrap. In addition to breadboarding, students will wire this circuit by soldering wires and components on a PC board designed for the oscillator circuit. Students will have to measure the frequency of the oscillator with and without the plate being touched. We will provide a simple Arduino program that is sensitive to changes in the pulse width of the oscillator and that turns an LED on or off, to turn the frequency change into an on/off switch.  Students will treat the oscillator board as a 4-terminal component, and examine the effect of adding resistors or capacitors between different terminals.
   EE concepts: frequency-dependent feedback, oscillator, RC time constants, parallel capacitors.
   Lab skills: soldering, frequency measurement with digital scope.
   Equipment needed: Power supply, multimeter, Arduino, clip leads, amplifier prototyping board, oscilloscope.
7. Phototransistor and FET
   First half: characterize phototransistor in ambient light and shaded.  Characterize nFET and pFET.
   Second half: students will “tinker” with the components they have to produce a light-sensitive, noise-making toy.
   EE concepts: phototransistors, FETs.
   Equipment needed: breadboard, phototransistor, power FETs, loudspeaker, hysteresis oscillator from previous lab, oscilloscope.
8. Electrode measurements
   First, we will have the students attempt to measure the resistance of a saline solution using a pair of stainless steel electrodes and a multimeter. This should fail, as the multimeter gradually charges the capacitance of the electrode/electrolyte interface.Second, the students will use a function generator driving a voltage divider with a load resistor in the range 10–100Ω. The students will measure the RMS voltage across the resistor and across the electrodes for different frequencies from 3Hz to 300kHz (the range of the AC measurements for the Agilent 34401A Multimeter). They will plot the magnitude of the impedance of the electrodes as a function of frequency and fit an R2+(R1||C1) model to the data, most likely using gnuplot. There will be a prelab exercise to set up plotting of the model and do a little hand tweaking of parameters to help them understand what each parameter changes about the curve.Third, the students will repeat the measurements and fits for different concentrations of NaCl, from 0.01M to 1M. Seeing what parameters change a lot and what parameters change only slightly should help them understand the physical basis for the electrical model.Fourth, students will make Ag/AgCl electrodes from fine silver wire. The two standard methods for this involve either soaking in chlorine bleach or electroplating. To reduce chemical hazards, we will use the electroplating method. As a prelab exercise, students will calculate the area of their electrodes and the recommended electroplating current.  In the lab, they will adjust the voltage on the bench supplies until they get the desired plating current.Fifth, the students will measure and plot the resistance of a pair of Ag/AgCl electrodes as a function of frequency (as with the stainless steel electrodes).Sixth, if there is time, students will measure the potential between a stainless steel electrode and an Ag/AgCl electrode.EE concepts: magnitude of impedance, series and parallel circuits, variation of parameters with frequency, limitations of R+(C||R) model.Electrochemistry concepts: At least a vague understanding of half-cell potentials, current density, Ag → Ag⁺ + e^-, Ag⁺ + Cl^- → AgCl, Fe + 2 Cl^-→ FeCl₂ + 2 e^-.Lab skills: bench power supply, function generator, multimeter, fitting functions of complex numbers, handling liquids in proximity of electronic equipment.Equipment needed: multimeter, function generator, power supply, stainless steel electrode pairs, silver wires, frame for mounting silver wire, resistors, breadboard, clip leads, NaCl solutions in different concentrations, beakers for salt water, secondary containment tubs to avoid salt water spills in the electronics lab.
9. Pressure sensor and instrumentation amplifier
   Students will design an instrumentation amplifier with a gain of 300 or 500 to amplify the differential strain-gauge signal from a medical-grade pressure sensor (the Freescale MPX2300DT1), to make a signal large enough to be read with the Arduino A/D converter. The circuit will be soldered on the instrumentation amp/op amp protoboard. The sensor calibration will be checked with water depth in a small reservoir. Note: the pressure sensor comes in a package that exposes the wire bonds and is too delicate for student assembly by novice solderers. We will make a sensor module that protects the sensor and mounts the sensor side to a 3/4″ PVC male-threaded plug, so that it can be easily incorporated into a reservoir, and mounts the electronic side on a PC board with screw terminals for connecting to student circuits.  This sensor is currently being prototyped, and if it turns out to be too fragile, we will use a Freescale MPX2050GP, which has a sturdier package, but is slightly less sensitive and more expensive. (It also isn’t made of medical-grade plastics, but that is not important for this lab.) Note that we are deliberately notusing pressure sensors with integrated amplifiers, as the pedagogical point of this lab is to learn about instrumentation amplifiers.EE concepts: differential signals, twisted-pair wiring, strain gauge bridges, instrumentation amplifier, DC coupling, gain.Equipment needed: Power supply, amplifier prototyping board, oscilloscope, pressure sensor mounted in PVC plug with breakout board for easy connection, water reservoir made of PVC pipe, secondary containment tub to avoid water spills in electronics lab.
10. Class-D power amplifier
11. Electrocardiogram (EKG)
    Students will design and solder an instrumentation amplifier with a gain of 2000 and bandpass of about 0.1Hz to 100Hz. The amplifier will be used with 3 disposable EKG electrodes to display EKG signals on the oscilloscope and record them on the Arduino.Equipment needed: Instrumentation amplifier protoboard, EKG electrodes, alligator clips, Arduino, oscilloscope.

3. Systemwide Senate Regulation 760 specifies that 1 academic credit corresponds to 3 hours of work per week for the student in a 10-week quarter. Please briefly explain how the course will lead to sufficient work with reference to e.g., lectures, sections, amount of homework, field trips, etc. [Please note that if significant changes are proposed to the format of the course after its initial approval, you will need to submit new course approval paperwork to answer this question in light of the new course format.]

The combination of BME101 and BME101L is 7 units (21 hours per week).  The time will be spent approximately as follows:

• 3.5 hours lecture/discussion
• 3.5 hours reading background and circuits text
• 3 hours read lab handouts and doing pre-lab design activities
• 6 hours lab
• 5 hours writing design reports for lab

4. Include a complete reading list or its equivalent in other media.

Lab handouts: there is a 5- to 10-page handout for each week’s labs, giving background material and design goals for the lab, usually with a pre-lab design exercise.  The handouts from the prototype run of the course can be found at http://users.soe.ucsc.edu/~karplus/bme194/w13/#labs
Data sheets: Students will be required to find and read data sheets for each of the components that they use in the lab.  All components are current commodity components, and so have data sheets easily found on the web.  Other readings are associated with the lecture course.

5. State the basis on which evaluation of individual students’ achievements in this course will be made by the instructor (e.g., class participation, examinations, papers, projects).

Students will be evaluated on in-lab demonstrations of skills (including functional designs) and on the weekly lab write-ups.

6. List other UCSC courses covering similar material, if known.

CMPE 167/L (sensors and sensing technologies) covers some of the same sensors and design methods, but at a more advanced level.  BME 101L would be excellent preparation for the CMPE 167/L course.

Physics 160 offers a similar level of practical electronics, but focuses on physics applications, rather than on bioengineering applications, and is only offered in alternate years.

7. List expected resource requirements including course support and specialized facilities or equipment for divisional review. (This information must also be reported to the scheduling office each quarter the course is offered.)

The course will need the equipment of a standard analog electronics teaching lab: power supply, multimeter, function generator,  oscilloscope,  computer, and soldering irons. The equipment in Baskin Engineering 150 (commonly used for EE 101L) is ideally suited for this lab. There are 12 stations in the lab, providing a capacity of 24 students since they work in pairs rather than as individuals.  The only things missing from the lab stations are soldering irons and circuit board holders (such as the Panavise Jr.), a cost of about $45 per station.  Given that a cohort of bioengineering students is currently about 35–40 students, two lab sections would have to be offered each year.

In addition, a few special-purpose setups will be needed for some of the labs, but all this equipment has already been constructed for the prototype run of the course.

There are a number of consumable parts used for the labs (integrated circuits, resistors, capacitors, PC boards, wire, and so forth), but these are easily covered by standard School of Engineering lab fees.  The currently approved lab fee is about $131, but may need some adjustment to change exactly what tools and parts are included, particularly if the students are required to buy their own soldering irons (a $20 increase).

The course requires a faculty member (simultaneously teaching the co-requisite Applied Circuits course) and a teaching assistant (for providing help in the labs and for evaluating student lab demonstrations). Because the lab is such a core part of the combined course, it requires faculty presence in the lab, not just coverage by TAs or group tutors.

8. If applicable, justify any pre-requisites or enrollment restrictions proposed for this course. For pre-requisites sponsored by other departments/programs, please provide evidence of consultation.

Students will be required to have single-variable calculus and a physics electricity and magnetism course. Both are standard prerequisites for any circuits course. Most of the labs can be done without calculus, but it is essential for the accompanying lecture course.

9. Proposals for new or revised Disciplinary Communication courses will be considered within the context of the approved DC plan for the relevant major(s). If applicable, please complete and submit the new proposal form (http://reg.ucsc.edu/forms/DC_statement_form.doc or http://reg.ucsc.edu/forms/DC_statement_form.pdf) or the revisions to approved plans form (http://reg.ucsc.edu/forms/DC_approval_revision.doc or http://reg.ucsc.edu/forms/DC_approval_revision.pdf).

This course is not expected to contribute to any major’s disciplinary communication requirement, though students will get extensive writing practice in the design reports (writing between 50 and 100 pages during the quarter).

10. If you are requesting a GE designation for the proposed course, please justify your request making reference to the attached guidelines.

No General Education code is proposed for this course, as all relevant codes will have already been satisfied by the prerequisites.

11. If this is a new course and you requesting a new GE, do you think an old GE designation(s) is also appropriate? (CEP would like to maintain as many old GE offerings as is possible for the time being.)

No General Education code is proposed for this course, as all relevant codes (old or new) will have already been satisfied by the prerequisites.

Teaching students to build and use models

In a comment on her post Student Thinking About Abstracting, Mylène says

What frustrates me and disorients my students is that those justifications are never discussed, and even the fact that this is a model is omitted. To further “simplify” (obscure) the situation, most discussions of the matter don’t distinguish between two ideas: “the model has a change in behavior at 0.7V,” vs. “they physical system has a change in behavior at 0.7V.” Finally, the chapter starts with the most abstracted model (1st diode approximation) and ends with the less abstracted (3rd diode approximation).

On getting students to understand models:  I agree that this is a huge problem.  I’ve been trying various techniques and can’t claim to have found a silver bullet.

One thing I tried in class yesterday (disguised as a gnuplot tutorial) was to build up a model a little at a time to match measured data.  I was trying to build an equivalent-circuit model for a loudspeaker, so I started by gathering data (rms voltage measurements across the loudspeaker and across a series resistor at different frequencies) and plotting magnitude of impedance vs. frequency from the data, then building the model a component at a time.  Before doing the modeling, we had spent some time looking at the behavior of building-block circuits (R+C, R||C, R+L, R||L, C||L, C||L||R) using gnuplot, so I could ask them things like “how can we model the impedance increasing with frequency above about 1kHz?”  We could then immediately modify the model and plot the results.  Once things were close, we could use gnuplot’s “fit” command to tweak the parameters.

We didn’t start with “loudspeakers are …”, though we did start with one of the specs—that this was an 8Ω loudspeaker—for our first model. I didn’t even point out to the students that the frequency of main resonance peak is given as a spec on the data sheet. The data sheet gives it at 191Hz, while our measured data show 148Hz (more than 22% off, while factory tolerances for the resonant frequency are usually ±15%). They also give the voice coil inductance as 0.44mH, while our model gets 35µH, a factor of 12.6 difference! And they give the Q_es of the resonance peak as 3.52, while our model of the R||L||C for the peak has .

Maybe the inductance difference can be explained by the standard measurement for the voice-coil inductance being made at 1kHz for the Theile-Small parameters, while I fitted for a wider frequency range and added an extra 112µH inductor in parallel with a 32Ω resistor to bump up the impedance around 10kHz. Or maybe my fitting is a really bogus way to get the inductance, since I’m only looking at the amplitude and not the phase of the signal, and non-linear resistance could throw things off. Or maybe the Parts-Express people mis-measured or had a typo—I have no idea what measurements they made to get the parameters they report, or maybe these loudspeakers were so cheap because they didn’t meet the specs, though they are certainly good enough for our lab.

I think that one could do the same sort of model-building with diodes (the part whose models Mylène’s students were confusing with reality): start by measuring the I-vs-V characteristics. The setup I used to get a lot of data points with the Arduino for characterizing the FET in an electret mic might be a good one for them to use, though the unipolar ADC in the Arduino might be more challenging for characterizing diodes.  Then try fitting different curve families to the data.  Forget about physics for explaining how the diodes work, but concentrate on finding simple models that fit the data. For example, the FET models we used for the mic are not quite the standard ones, since there is a clear slope in the saturation region, and it doesn’t match the channel-length modulation model—but it can be fit with some simple curves.

Of course, I gave up on some modeling before even having the students collect data themselves—the power FETs they are using are incredibly messy, having threshold voltages that shift a lot as the transistors warm up and having an undocumented negative dynamic resistance region when diode-connected.

So it is important that their attempts to build models be of phenomena that are relatively easy to model, but they should build and fit the models (with some guidance) rather than just be handed them. I made the mistake of handing them models to fit for the electret mic lab and for the electrode lab.  They not only didn’t understand the models, but they didn’t understand how to do the fitting.

I’m planning next year to do the model-building/gnuplot tutorial much earlier in the quarter, before they do the electrode labs, so that they can build the electrode models with some understanding. I’ll need to rearrange some other material, to do inductors much sooner, if I plan to use the loudspeaker data again.  I may want to rearrange the labs a lot next year, since all of my first three labs involved model fitting, and the students weren’t ready for it.  It may be better to move the sampling lab (which is currently lab 6) into the beginning, so that students can learn to use the Arduino in a simpler lab.  As currently written, though, that lab calls for designing a high-pass filter for DC level shifting and a low-pass filter for removing aliasing, neither of which are suitable for a first-week lab in circuits.

Scheduling the labs and the classes is difficult. Fitting in all the topics they need before each lab is a tricky jigsaw problem, particularly when I discover them having problems with topics that I assumed they knew or could pick up quickly. Sigh, some stuff in the first week or two of lab is probably going to have to be “magic” as they’ve learned so little in physics classes that I can’t count on them having any useful lab or modeling skills when they come into the class.  I just have to decide which things I’m willing to give them, rather than having them do for themselves.

Currently, I’m leaning toward having every lab have a design component, and to have them build models for important concepts, but I’m willing to give them a model for thermistor behavior that they just have to fit the parameters for.  The design in the first two labs this year is very light (selecting a resistor value), but the measuring and model fitting is pretty heavy.  The electrode lab has no design currently, but a lot of measuring and model fitting.   I think I underestimated the relative difficulty of model fitting and design for these students, and may need to move the model fitting later in the quarter.  I don’t think I can start with RC filters in the first week though, as they need voltage dividers, complex numbers, sinusoids, and complex impedance—probably at least 4 classes worth of material.  Maybe by week three, though.

Thirteenth day of circuit class and first op-amp lab

If you’re wondering what happened to the 12th day of circuits class, that was discussed in Quiz too long and too hard. On Wednesday, I did some do-now problems to check on some basics and to provide a hook for the day’s topics.  I asked for the voltage gain (Vout/Vin) for the following circuits:

First question: a voltage divider they are familiar with, and which almost everyone got right.

A different voltage divider circuit, stressing the fact that voltage is between two points. Only about half the class got this, because I had not given enough examples of voltages other than to ground. Students who had the correct answer had two different ways of getting there: starting from Ohm’s Law, or simple proportional reasoning. I pointed out that a third way would be to compute the voltages of the two voltmeter leads using the voltage divider formula.

A reminder of the one op-amp circuit they’d seen (last Friday). Only about half the class remembered this one, so I did another derivation of it using a finite-gain amplifier instead of an ∞-gain op amp, showing what happens as gain goes to infinity. I think that I should do more of that, since many of the students are uncomfortable with infinity.

A hook for the main material of the day: non-inverting amplifiers. Only one student correctly guessed the gain of this circuit (one of the top students in the class—I think he “cheats” by reading the assignments when they are assigned to be read—I wish more students would do that).

After reviewing the unity-gain buffer, but before getting into the non-inverting amplifiers, I made a digression into what would happen if we swapped the two inputs to the unity-gain buffer.  Doing the algebra for the gain computation with a finite-gain amplifier and taking the limit, we again get a solution where the output voltage is equal to the input voltage.  I then stepped them through what would happen if there was a small perturbation in the input, which does not result in the amplifier settling down to the new value, but keeps getting bigger until the output slams into one of the power rails.  I used this to discuss positive feedback and the difference between a stable and an unstable design, but did not give them any tools for analyzing stability other than hand-simulating what happens if you add a small perturbation to the input.

Finally I got to the non-inverting amplifier, and stepped them through the reasoning behind the gain computation.  I think most of them followed it, though some are still disturbed that the voltage divider in the circuit has “Vout” and “Vin” labels reversed from how they are used to thinking of voltage dividers.  I have to wean the students away from the notion that formulas contain sacred variable names, and into thinking about them as having slots that get filled according to context.  That is, I have to have them attach semantics to the formulas, rather than relying on name-based pattern matching.

I was originally going to do inverting amplifiers as well, but I think I’ll leave those until next week.  I also decided not to have the students try to do a single-supply design for their first op-amp lab, but to use a dual-supply design, which is a little simpler conceptually.  I’ll have to rewrite the lab handout for next year, as I had originally planned to do a single-power-supply design.  I realize now that is too ambitious for the first op-amp assignment.  There was a mention in the lab handout of a DC-blocking capacitor on the output, but that is not needed in the dual-supply design, so just confused a couple of the students.

After the non-inverting op amp, I introduced them to the notion of block diagrams, and together we developed the following block diagram:

Block diagram for audio amp

We didn’t do it all at once, of course, and it took some prompting to get the various parts all there. We started easily enough with the microphone and the loudspeaker, then added the amplifier. I had to prompt them a bit to remember that the microphone was best thought of as having a current output, but that the amplifiers we knew how to design were voltage amplifiers. Since their second lab converted the microphone current to a voltage, they got the I-to-V converter pretty quickly. We tried to guesstimate the gain needed by saying we wanted the loudspeaker to swing rail to rail (±3V) on a loud input, and I asked the students what they had measured on lab 2 as the AC voltage swing. A couple of students had something in their lab notebooks. I pointed out (again) the value of keeping good lab notebooks, since you never know what detail you might need later on. We used one of the estimates to pick a gain of about 50 for the amplifier.

I then pointed out a problem: the I-to-V converter they used in Lab 2 had a 1V DC offset, and if they put that into the amplifier, they would pin the output at the upper power rail, since it couldn’t go to 50V. After a bit of reminder that DC was a frequency of 0Hz, they came up with the need for a high-pass filter, and could even remember the voltage divider circuit to get it. But figuring out the corner frequency stumped them, because none of them remembered the frequencies of human hearing. Eventually someone came up with 20Hz to 20kHz, which goes a bit higher than humans hear, but is a typical stereo specification. We only cared about the low-frequency end anyway. I pointed out that knowing what sort of signal one was dealing with was an essential part of the design process, and one of the first questions they should ask when doing a design. They eventually settled on 10Hz as a reasonable corner frequency, though anything between 1Hz and 30Hz would probably do, given that their speakers have very poor bass response anyway (they are very fine 10W speakers for about $1 each, but they are still small speakers).

I think that I’ll continue to have the development of the block diagram as an in-class discussion (not try to put it into the lab handouts), so that the students can develop it themselves with guidance from me, rather than being handed it.  This decomposition of a design problem into smaller easily solved problems is one of the essential parts of engineering, and most of the bioengineering students have not had much experience with it.

I ordered them to pair up right away and come to lab with designs already done and ready to implement and debug. I think that too many of them have been under-prepared for labs, having just looked over the lab handouts the night before. From now on, I’m going to make sure they do some serious work on each lab before they touch wire to breadboard on it. (This will be particularly important on the last two labs, where they’ll be soldering the instrumentation amplifiers—unsoldering components is no fun at all.)

Today’s lab went great! Everyone got a working audio amplifier (generally with a gain of 40× or 50×), and could see the gain on a dual-trace oscilloscope (superimposing the signals at the mic and the output with different volts/division setting, which was particularly satisfying for showing the gain of 50).  They also observed clipping of the output with loud input signals, and the inability of the op amp to drive the 8Ω load of the loudspeaker all the way (it has only a ±23mA output capability).  I reassured them that we would design an amplifier later in the quarter capable of delivering loud sounds.

A few students came in with non-functional designs, but they were all quite close, and a few minutes of discussion at the whiteboard about how the resistors for the non-inverting amplifiers needed to be designed got them back on the right track when the circuits they built failed. I refused to look at designs until they had wired them up—I’m making “Try it and see!” the mantra for the class.  Perhaps we should put it on the t-shirts.

Some students also had a little trouble converting their schematics to wires on the board, but a little debugging and tracing wires was enough for me to point out discrepancies between what they showed me in the schematic and what I saw on the breadboard.  This was enough to get them back on track without my having to touch their boards.

I thought that this lab would be one of the toughest ones so far, but it turned out be the smoothest sailing.  Everyone finished on time with working circuits demoed!  Perhaps the op amps are not as hard as I expected for them, perhaps the design assignment the day before left them more prepared, perhaps they’re beginning to get the hang of things now after a somewhat rocky start.  Whatever the reason, I was really proud of what they managed to do today.  This is only lab 5 for them, and they are already doing more in the lab than the EE 101 students achieve by the end of the quarter!

Next week they’ll do a “tinkering” lab without a clearly specified objective, but with some strong constraints. In the course of the lab, they’ll learn about phototransistors (though not all the characteristics of them) and FETs as switches.  The lab is very thrifty, making use of the hysteresis oscillator board that they soldered up for the capacitance-touch sensor as a component without modifying what is on the board. They’ll also learn about a different style of engineering: tinkering, where one plays around with stuff to see what can be done.  I don’t think that most of them have had much opportunity to tinker in the past, and it is an excellent way to develop the mental models that allow one to reason about circuits without tedious calculations.  (Some calculations may still be needed, of course.)  Some of them may get frustrated with the  somewhat undirected nature of the play, I’ll undoubtedly get a headache from loud squealing of loudspeakers at high frequencies, and someone may burn a finger on an overheating FET, but I think that next week’s lab may be the most fun one of the quarter, and it should prepare them well for the class-D power amplifier later in the quarter.

Tomorrow I’ll start on group-work quiz corrections (the last student is taking the quiz in the morning), and have them try to finish the quiz corrections over the weekend. If the quiz corrections are problematic still, we’ll use Monday for more group work on them and possibly some Socratic lectures (they’ve had all the material they need—they just need some guidance on how to apply it).

More likely, on Monday we’ll do some work on gnuplot, so that students who need to redo one of the labs that involve model fitting will have a better handle on what they are doing.  If we do that, I’ll ask students to bring in their laptops, so that they can do some interactive work on gnuplot scripting.  I thought that the first script I gave them would be sufficient example, but I didn’t realize at the time the difficulty they would have in generalizing the example, so I’ll step them through a worked example, with them gradually building a script that does what they need. I hope to be able to address the scope-of-variables problem that I think is tripping some of them up, as well as detecting other conceptual stumbling blocks.

Although I started this week very depressed about the quiz results and having sleepless nights worrying about how to modify my teaching to get the concepts across, I’m now feeling very positive about the class.  The op amp lab went great, and I see ways that I think have a very good chance of getting the students comfortable with the material.  In about two weeks, I’ll give them another quiz (similar to the one that was so painful for everyone on Monday, with perhaps a couple of op amp questions), with the reasonable expectation that they’ll be able to nail it.

Second lab was smoother than the first

As predicted last week, today’s microphone lab  was shorter than last week’s thermistor lab—almost everyone finished within the 3-hour window.

I do have to make some changes in the lab handout for next year:

• The handout should discuss how to set the current limits for the power supplies.  My co-instructor insisted on our going around to each bench and helping students figure out how to do that.  He’s seen too many blown fuses on ammeters in student labs.  In fact, one of the benches had an ammeter with a blown fuse, because the EE TAs are not trained to make everyone set current limits the first time they use the power supplies, and someone inevitably wires up an ammeter like a voltmeter.  Since the bench supplies default to a 6A current limit, and the ammeters are fused at 3A, a use is blown.  It is not unusual for both ammeters on a bench to have blown fuses, as students switch ammeters rather than fixing their circuits.  I’m pleased to say that we did not blow any ammeter fuses today.
  I should also include some information about how to hook up wires to the binding posts on the power supplies.  We don’t have banana plugs, so students need to strip an inch from the end of the wires and thread the wires through the vertical holes in the binding posts, then screw the cap in place to hold the wires.  One group had just wrapped the wire, and not stripped it far enough, so the binding post was just squeezing the insulation and not making contact with the wire.
• We did not do the DC-blocking capacitor at the end of the lab, because we have not gotten to the theory of capacitors yet.  I think we’ll probably cover sinusoids and complex impedance on Monday.  I’ll cut that from the lab, but add it to some later lab (probably the op amp lab, where it becomes important).
• There is no point to trying to measure the amplitude at the microphone when playing signals from the signal generator through speakers.  With 5 or 6 loud loudspeakers all going at once, the noise levels in the room are too high for any sort of careful measurement.  It was more a time for students to play with the oscilloscopes and the function generators.  I need to come up with a more playful task for this part of the lab—perhaps sweeping the frequency up and noticing at what frequencies the microphone amplitude is largest.  There is a pretty obvious peak at the speaker resonant frequency (around 200 Hz), and the amplitude goes up at the high frequencies.
• I need to explain how much of the wire to strip for the breadboards—some of the students had stripped over an inch of wire, which could easily result in shorting adjacent wires together, but 5mm is a more reasonable amount to strip.

As I planned last week, I gave each group of students the option of turning in the lab report either on Monday or on Wednesday, with no difference in credit.  Everyone chose to have the extra time for the report, rather than early feedback.  Maybe next week some will choose the Monday option instead.

I’m very pleased with the 78¢ speakers (well, $1.28 with tax and shipping) , which can handle 10W RMS (20W max).  With 8Ω speakers, 10W is about 9V RMS or 12.6V peak-to-peak, so no one was likely to fry their loud speaker hooking it up to the function generator.  I understand that the usual tiny speakers that are provided in the EE courses are only 0.25W speakers and are routinely destroyed in the circuits course—and they’re not significantly cheaper.

I think that all the students now know the basics of using a breadboard, though most of them are using wires that are too long, which will become a problem for them when we move to more complex circuits.  This lab called for a trimpot, a resistor, a microphone and the Arduino for getting the current vs. voltage plot for the  microphone.  I think that everyone got that circuit wired up and working and gathered good data with it (hundreds of points worth of good data, with currents from 1µA to 200µA). I think that the students got a good appreciation for the value of the Arduinos for collecting data points, as most ended up with several hundred data points for a minute or two of collecting data, rather than just the 10 points they got with hand-collected data. Some of the students were quite excited to be able to wire up the circuit, collect data, design an appropriate pull-up resistor, and see sound on the oscilloscope.  I was pretty excited myself at how much they were learning and getting done, even though I’ve done the lab myself several times trying to tweak it into something they could do with really minimal prior knowledge.

I worked individually with a few students to help them get their gnuplot scripts working—the lectures I’d given in class had not been very successful in getting them to learn gnuplot, but about 10 minutes of one-on-one (or one-on-two) tutoring got them to the point where they understood what all the commands they were using did.  I suspect that they could have learned on their own, but lacked the confidence to do so.  I’ll be doing more individual tutoring with gnuplot after class on Monday, but I think that several of the students now have enough understanding to help out others in the class. Some of them even got the point of providing reasonable initial values for the parameter fitting, as a working script broke when they rescaled from amps to microamps.  Adding a reasonable initial value (which was 6 orders of magnitude different from the previous fit) made the fitting converge again.

I hope that the students remember to include all the data on their plots, including the hand-collected data at higher voltages.  I also hope that they can figure out how to get the parameters they fit to appear in the key for the plot (the gnuplot script for the first lab showed them how to do it, but some are having trouble abstracting from that example to create a new example).

The maintenance of the multimeter leads and scope probes in the lab left a lot to be desired.  We had at least 2 bad sets of multimeter leads (broken wires at the strain relief of the clip) and at least 3 bad scope probes (broken ground leads that looked intact). Most of the function generators didn’t have any leads at all, though the BNC-to-clip-lead cables are under $6 each.

On Monday, I’ll do continuity checks on all the scope probes for the analog scopes and try to get the lab support people to repair or replace the broken ones.  Since a pair of oscilloscope probes (of better quality than the ones that the lab supplied) costs only $13, it may be worth adding to the parts kit, so that students don’t have the aggravation of having to deal with probes that someone else broke.  That will only work as long as the lab has scopes with BNC-connector inputs, though.  If they surplus the old analog scopes and use just the digital Tektronix scopes, much more expensive proprietary leads would be needed.  I doubt that as many of those are broken, since it takes forever to learn to use the baroque menu interface on the Tektronix scopes, so almost everyone prefers the end-of-lifespan analog Kikusui scopes.  Certainly the circuits lab, which is the first lab in which students encounter oscilloscopes, would be much better off with a dozen working analog scopes, with the digital scopes moved to senior design labs and other labs where their greater capability would justify the much greater amount of time it takes to learn to use them.

I think I’ve come up with a nice “do now” question for tomorrow—one that they can solve with their current methods, but which becomes somewhat easier after they’ve had Thévenin equivalents, which is the main topic of tomorrow’s lecture by my co-instructor.

In Monday’s lecture, I’m going to cover sinusoids and complex impedance, so that we can do DC-blocking capacitors, RC filters, and the models that we’ll need for the electrode lab.

Fifth day of circuits class

I feel pretty good about today’s lecture, though things got a little rushed at the end.

Three-resistor voltage divider for the first question.

I started with a “do now” question, similar to the one from Monday. Actually, I started with 2 questions. The first just asked what the output voltage would be for a 3-resistor voltage divider. The second repeated the question from Monday, but with the additional constraint that the power supply was 5 volts:

You have sensor whose resistance varies from 1kΩ to 4kΩ with the property it measures and a 5v power supply.  Design a circuit whose output voltage varies from 1v (at 1kΩ) to 2v (at 4kΩ).

Several students realized that the first question was a hint for the second one and that the variable resistor had to be RB or RC, and could set up the equations and solve for RA and RC.  This is a better performance than on Monday’s “do now”, but only about 1/3 of the class got it completely, and several of them were not confident of their results, so we again took time to go over the whole solution. I think that everyone (or almost everyone) understood the design process and how to set up and solve the equations by the end of the presentation, which I drew out of the students as much as possible.  I also mentioned that we could have solved the problem with a different circuit (putting RC in parallel with RB instead of in series), but did not further elaborate on that point.

The do-now plus going over the solution took about 33 minutes, which is a little more time than I’d like to be spending on these questions.  It would be good to get the time down to 15 minutes, but I don’t see how to do that without losing half the class.  If the problems are easy enough that everyone gets them, then there is no point to taking up any class time with them, and if they are hard enough that 1/3 to 2/3 of the class don’t get them, then they need to be gone over in class.

After the do-now, we spent a little time discussing the “fit” command of gnuplot, since the students have to fit models to the data they collect tomorrow, and I’m not providing them a script this time (though they can modify the script that was provided in the first lab).

Finally, we got to the theoretical meat of the class—we discussed what sound was (ending up with variations in pressure for a fluid, though we discussed briefly transverse and shear waves in solids).  Then I introduced microphones as transducers, trying to get the students to remember their elementary mechanics, so that we could do pressure→force→displacement→1/capacitance→voltage for electret mics.  The hardest part was getting students to remember that a spring-mounted object had force proportional to displacement (a lot remembered the energy was somehow related to displacement squared and got stuck on that formula).  I suspect that the local physics department would not be seeing a high score on the Force Concept Inventory for students coming out of their physics classes, as a lot of them seem to have concentrated on cramming formulas rather than learning fundamental concepts.  Someone did remember Q=CV and someone else could reason from wanting voltage proportional to displacement to needing constant charge which let me introduce both conventional capacitance microphone (with a large resistor to voltage source) and electrets.  I also explained that the electret had an enormous resistance, so we couldn’t get any measurable current out of it, and we needed an FET transistor to convert the voltage to a current.

Because both the do-now and extracting vague memories of physics from the students took longer than I had planned, we were a bit rushed for the last part of the lesson, which was a simple model of I_ds vs V_ds for the FET output stage of the electret mic. I asked for advice on drawing the plots for resistors and for current sources, and got the appropriate straight lines.  I then drew a smooth transition between them and claimed that the simple FET models usually consisted of a linear region at low voltage (which my co-instructor refers to as the “triode” region, a usage I’ve seen in some other presentations) and a saturation region at high voltage, and that we usually try to stay out of the sublinear region in between.

I also said that the saturation region is not really constant, but has a slight upward slope, since they will be measuring the I-vs-V characteristic of the electret microphones tomorrow, and they will certainly be observing that.  The lab handout gives them 4 models to fit: linear, constant current, an empirical blend of the two, and a model that allows current increase in the saturation region.  Neither the 3rd nor the 4th model match the ones usually used in circuit simulators, but I had trouble fitting parameters to those models, even with voltage-modulated channel lengths, so I gave up and produced simple models with few parameters that can be fit pretty easily. We’ll be revisiting FETs again before the power-amp lab (where they’ll use pMOS and nMOS power FETs to make a class-D amplifier). Somewhere around then, I’ll have to give them some usable models for how saturation current varies with gate voltage, which I deliberately did not cover in this lecture.

I’m a bit worried about how big tomorrow’s lab is.  There are again 2 parts:

• the DC characterization of the mic using the Arduino to gather data (plus a few hand-collected points for higher voltages than we can subject the Arduino to)
• designing a pull-up resistor to bias the mic into its normal operating range (in the saturation region) and observing the microphone output on the oscilloscope.  I also asked students to hook up their loudspeakers to the signal generators, to provide known inputs to the mic, and some other little stuff, but I’ll probably be happy if everyone gets the first part done and manages to observe waveforms on the scope.

On Friday, most of the lecture will be standard EE stuff by my co-instructor (probably current sources, Thévenin equivalents, and Norton equivalents).  I may have a do-now question at the beginning of the class, if I can come up with one that I think is pedagogically useful.