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2015 April 26

Comments for class after grading

Friday’s lecture went fairly well.

There were a few questions at the beginning of class, one of which lent itself well to my talking about choosing different models for the same phenomenon and using the simplest model that worked for the design being done.  In this case it was about the relaxation oscillator using a 74HC14N Schmitt trigger and where the constraints on the feedback resistor came from.  I told them about some more detailed models we could do of the Schmitt trigger, including input capacitance (max value on the data sheet), input leakage current (not specified, but probably fairly small, under 1µA), and output resistance (which would get added to the feedback resistance).  I’ll have to incorporate some of those ideas into the book, when I rewrite those chapters this summer—the hysteresis lab needs the most rework of anything so far this quarter.

After the questions I mainly talked about polarizable and non-polarizable electrodes developing the R +  (R||C) + half-cell model of an electrode that they will be fitting (without the half cell) in labs this week.

This weekend’s grading was a bit painful, and I’m probably going to have to spend all of Monday’s lecture filling in gaps in their prior education that I had not anticipated.  Some holes also became apparent from e-mail questions I got from students over the weekend.

I’ll try to gather the common problems here, so that I can use the list as lecture notes tomorrow.

  • There were a lot of REDO grades for errors on schematics.  I hate giving REDO (since it doubles my grading load), but I told students at the beginning of the quarter that any error on the schematics was an automatic REDO.  I plan to stick to that, despite the pain for both me and the students, because they have to develop the habit of double and triple checking their non-redundant documents (schematics, PCR primers, …).  Sloppy documentation is a serious problem in engineering and too many faculty and graders have been perpetuating the myth that the almost right idea is good enough.  I’m particularly harsh on students who change kHz into Hz or pF into nF.  Off-by-a-factor-of-1000 is not good enough!  The most extreme case so far is someone who specified a capacitor as being in the gigafarads (they’d typed 109 instead of 10-9). A factor of 1,000,000,000,000,000,000 off is not the sort of thing one can ignore.  I also get annoyed by students who randomly pick a unit (H when they need Ω, or Ω when they need Hz), as if all units were just decorations to please a teacher, with no real meaning to them
  • Frequency is 1/period.  For the relaxation oscillator, they do two charge/discharge calculations to get the period as a multiple of RC (though many blindly copied one of the formulas for just the charge time without understanding it, and assumed it was the period). But even after computing the charging time students blindly used  2πf = 1/(RC) as a magic incantation.  That formula was relevant for the corner frequency of RC filters, but has nothing to do with the oscillation frequency of the relaxation oscillator.
  • The capacitance calculation being done in the prelab was for the capacitance of a finger touch to the touch plate, but a lot of students claimed that it was the calculation to determine the size of the ceramic capacitor.  Only a couple of groups bothered to explain the connection between the two capacitances. I think I need to rewrite the prompts in the book to force the values to be more different, so that students have to think which capacitance they are talking about.
  • I find that students often talk about “the voltage” or “the capacitance” as if there was only one in their circuit, and when asked which one they are talking about are completely mystified—to them invoking the magic word is all that can be expected of them—actually knowing what it refers to is unreasonable.
  • Students in general were doing too much ritual magic. They would put down a formula they thought was relevant (often copying it incorrectly), then claim that from that formula they got some number for their design.  Often the formula was not relevant, or additional assumptions needed to be made (like choosing arbitrary values for some variables).  At the very least, there was some substantial algebra to be done to convert the formula into a usable form.  Some students claimed that Wolfram alpha gave them the solution (when there was not enough information to solve for the variable they wanted a value for).  Basically, I’m a bit angry at the students for trying to bullshit their way through the assignment. One pair of students said quite honestly that they did not know how to do a computation and got the value they used from the students at the next bench.  I gave them bonus points, and I’ll help them figure out how to do the computation they were having trouble with—I have no problems with students not knowing how to do something new and somewhat tricky, but I do have trouble with students deliberately looking dishonest and stupid by writing bullshit.
  • The computation that the honest students had trouble with is one that many students had trouble with, so I’ll go over it in class.  I gave the students a derivation of a formula for the charging time of the capacitor in the relaxation oscillator, but I didn’t have time to step them through the derivation.  It seems like most of the class can’t read math, since many just copied the final formula without reading the text that said it was the time to charge the capacitor.  There was an exercise immediately afterwards asking students to compute the time to discharge the capacitor, but this exercise was added to the book after the students had done their prelab exercises, so they didn’t bother to look at the exercise. What they needed to do for the lab was to add the charge and discharge times (which are not quite the same) to get the period.
  • I need to remind the students that they are turning in design reports, not lab reports.  I’m not looking for fill-in-the-blank worksheets, but descriptions of how they designed and tested their circuits.  Omitting the design steps is omitting the most important part of the report!
  • I gave the students three models to fit to the data, and showed them how to do the fits for two of the models in Wednesday’s lecture.  There wasn’t time to get to the third model, so I just told them to use the same technique as the second model, but with the different formula.  Most of the class never bothered to fit the third model (the only one that really fits the data well)—if I didn’t do all the work for them in lecture, then they weren’t going to generalize even a tiny bit to do it themselves.
  • A lot of students did not do a good job of fitting the models, because they fit the data with linear scaling, rather than with log scaling as I had shown them.  This is a fairly subtle point (errors on a linear y axis are differences, but on a log y axis are ratios), so I’ll review it in class.
  • I  think that some students don’t have any idea when one would use a log-log plot, a log-linear plot, a linear-log plot, or a linear-linear plot.  I thought that was covered in precalculus, but I guess not. So tomorrow I’ll present the idea that the only curve most people understand visually is a straight line, so one wants to choose axis scaling so that the expected relationship is a straight line.  Linear plots are for linear (or affine) models, log-log plots are for power laws, log-linear are for exponentials, and linear-log are for logarithmic relationships.  I’ll put a general straight line on each and derive the form of the function that matches that straight line.
  • The purpose of the Tuesday lab was to collect data and model the loudspeaker with a few parameters.  But many students neglected to report those parameters in their design reports!  They produced a plot and fitted models to it, but nowhere on the plot, in the figure caption, or in the main body (in decreasing order of usefulness) did they report what the parameter values were that the fit produced.  For students who are so focussed on answer getting that they neglect to explain how they came up with their answers, this seems like a strange omission.
  • For the Thursday lab, no one did back calculations from their observed frequencies to estimate the capacitance of the 74HC14N input, of the untouched touch plate, or even of the touch itself, to see whether their observations were consistent with their design predictions. One group of students claimed to have done sanity checks, but I don’t believe them, as they also reported oscillations around 20Hz, instead of 20kHz.
  • For the prelab, it seems that a lot of students computed R + \omega L instead of | R + j \omega L|, though most got it right in the gnuplot scripts for the lab itself.  I have to remind students that |A+B| \neq |A|+|B|.
  • On the typesetting front, I’m making some progress on getting students to put their plots in as figures with captions, though way too many are still referring to “the plot below” rather than to “Figure 3”.  I’m also having some difficulty getting them to be sure to refer to all the figures in the main body text.  A lot of times they’ll toss in a handful of plots with no reference to them at all.
  • On the opposite side of the coin, I have to teach them that equations are properly part of a sentence, generally as a noun phrase, and are not standalone sentences.  When there is an explanation of variables after a formula (“where A is this, and B is that”), the where-clauses are still part of the same sentence.
  • Some other little things to tell them:
    • The word “significant” should be reserved for its technical meaning of “statistical significance”—very unlikely to have occurred by chance according to the specified null model. It should not be used in the normal English way to mean “big”, “important”, or “something I like”.
    • To get gnuplot to produce smooth curves when there are sharp changes in function, it is necessary to do set samples 3000 to compute the function at more points than the small default number.
    • Students have been misusing the word “shunt” for any resistor. Properly, it is a low resistance used to divert current from some other part of the circuit—in our designs, it is the resistor being used to sense current and change it into voltage. I wonder if I should switch terms and talk about a “sense” resistor, though “shunt” is the standard term for ammeters.
    • A minor pet peeve of mine: I hate the word “utilize”. I have yet to see a context in which “use” does not do the same job better.

2015 April 23

Very long couple of days

Yesterday and today have been draining.

Yesterday, I had three classes each 70 minutes long: banana slug genomics, applied electronics for bioengineers, and a guest lecture for another class on protein structure.  I also had my usual 2 hours of office hours, delayed by half an hour because of the guest lecture.

The banana-slug-genomics class is going well.  My co-instructor (Ed Green) has done most of the organizing and has either arranged guest lectures or taught classes himself. This week and part of next we are getting preliminary reports from the 5 student groups on how the assemblies are coming.  No one has done an assembly yet, but there has been a fair amount of data cleanup and prep work (adapter removal, error correction, and estimates of what kmer sizes will work best in the de Bruijn graphs for assembly).  The data is quite clean, and we have about 23-fold coverage currently, which is just a little low for making good contigs.   (See for more info about the data.) Most of the data is from a couple of lanes of HiSeq sequencing (2×100 bp) from 2 libraries (insert sizes around 370 and 600) , but some is from an early MySeq run (2×300bp), used to confirm that the libraries were good before the HiSeq run.  In class, we decided to seek a NextSeq run (2×250bp), either with the same libraries or with a new one, so that we could get more data quickly (we can get the data by next week, rather than waiting 2 or 3 weeks for a HiSeq run to piggyback on).  With the new data, we’ll have more than enough shotgun data for making the contigs.  The mate-pair libraries for scaffolding are still not ready (they’ve been failing quality checks and need to be redone), or we would run one of them on the NextSeq run.  We’ll probably also do a transcriptome library (in part to check quality of scaffolding, and in part to annotate the genome), and possibly a small-RNA library (a UCSC special interest).

The applied electronics lecture had a lot to cover, because the material on hysteresis that was not covered on Monday needed to be done before today’s lab, plus I had to show students how to interpret the 74HC15N datasheet for the Schmitt trigger, as we run them at 3.3V, but specs are only given for 2V, 4.5V, and 6V.  I also had to explain how the relaxation oscillator works (see last year’s blog post for the circuit they are using for the capacitance touch sensor).

Before getting to all the stuff on hysteresis, I had to finish up the data analysis for Tuesday’s lab, showing them how to fit models to the measured magnitude of impedance of the loudspeakers using gnuplot.  The fitting is fairly tricky, as the resistor has to be fit in one part of the curve, the inductor in another, and the RLC parameters for the resonance peak in yet another.  Furthermore, the radius of convergence is pretty small for the RLC parameters, so we had to do a lot of guessing reasonable values and seeing if we got convergence.  (See my post of 2 years ago for models that worked for measurements I made then.)

After the overstuffed electronics lecture, I had to move to the next classroom over and give a guest lecture on protein structure.  For this lecture I did some stuff on the chalk board, but mostly worked with 3D Darling models. When I did the guest lecture last year, I prepared a bunch of PDB files of protein structures to show the class, but I didn’t have the time or energy for that this year, so decided to do it all with the physical models.  I told students that the Darling models (which are the best kits I’ve seen for studying protein structure) are available for check out at the library, and that I had instructions for building protein chains with the Darling models plus homework in Spring 2011 with suggestions of things to build.  The protein structure lecture went fairly well, but I’m not sure how much students learned from it (as opposed to just being entertained).  The real learning comes from building the models oneself, but I did not have the luxury of making assignments for the course—nor would I have had time to grade them.

Speaking of grading, right after my 2 hours of office hours (full, as usual, with students wanting waivers for requirements that they had somehow neglected to fulfill), I had a stack of prelab assignments to grade for the hysteresis lab.  The results were not very encouraging, so I rewrote a section of my book to try to clarify the points that gave the students the most difficulty, adding in some scaffolding that I had thought would be unnecessary.  I’ve got too many students who can’t read something (like the derivation of the oscillation frequency for a relaxation oscillator on Wikipedia) and apply the same reasoning to their slightly different relaxation oscillator.  All they could do was copy the equations (which did not quite apply).  I put the updated book on the web site at about 11:30 p.m., emailed the students about it, ordered some more inductors for the power-amp lab, made my lunch for today, and crashed.

This morning, I got up around 6:30 a.m. (as I’ve been doing all quarter, though I am emphatically not a morning person), to make a thermos of tea, and process my half-day’s backlog of email (I get 50–100 messages a day, many of them needing immediate attention). I cycled up to work in time to open the lab at 10 a.m., then was there supervising students until after 7:30 pm. I had sort of expected that this time, as I knew that this lab was a long one (see Hysteresis lab too long from last year, and that was when the hysteresis lab was a two-day lab, not just one day).  Still, it made for a very long day.

I probably should be grading redone assignments today (I have a pile that were turned in Monday), but I don’t have the mental energy needed for grading tonight.  Tomorrow will be busy again, as I have banana-slug genomics, a visiting collaborator from UW, the electronics lecture (which needs to be about electrodes, and I’m not an expert on electrochemistry), and the grad research symposium all afternoon. I’ll also be getting another stack of design reports (14 of them, about 5 pages each) for this week’s lab, to fill up my weekend with grading. Plus I need to update a couple more chapters of the book before students get to them.

2015 April 8

Optimization and model fitting went well today

Filed under: Circuits course — gasstationwithoutpumps @ 21:47
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Today’s lecture in BME 101 (the Applied Electronics for Bioengineers class) went very smoothly. I started with a little light entertainment: a video about blowing up capacitors, sent to me by Jameco: This video reinforced the message that I had given them in lab last week about electrolytic capacitors.

I had two topics to cover: the optimization problem from last weekend’s homework, which only one student had managed to do, and model fitting to extract parameters for the thermistor model from the data collected in lab yesterday.

I gave the students the choice of order for the topics, and they wanted the optimization first.  The problem is fairly straightforward from an engineering standpoint: we want to maximize the sensitivity of the circuit that converts temperature to voltage at a specific operating temperature Topt. I first sketched very rough plots of what the voltage would look like as a function of temperature: monotone increasing but not particularly linear. I reminded them that sensitivity is the change in output that you get for a given change in input: dV/dT.  I coaxed out of the class the idea that to maximize the function dV/dT, we need to take its derivative and set it to 0: \frac{d^2 V }{d T^2} = 0.  We only have one free variable in our circuit to change (the load resistor R), so we need to take that equation and solve it for R, to get the value of R that maximizes sensitivity.

I reminded them of the simple model for the resistance of a thermistor that we’d had on Monday: R_{T} = R_{\infty} e^{B/T}, and they had no trouble coming up with the equation for the output voltage V = V_{in} \frac{R}{R+R_{\infty} e^{B/T}}.  I then suggested using Wolfram Alpha to solve the equation, and switched from the chalkboard to the screen to type

solve d^2 (R/(R+S e^(B/T)))/ dT^2 = 0 for R

(changing R to S, to avoid confusing Wolfram Alpha with subscripts).
Wolfram Alpha conveniently replied with two solutions: R=0 (which would result in a constant 0 output voltage, clearly a minimum sensitivity) and R= S e^{B/T} \frac{B-2 T}{B+ 2T}. I pointed out that the first part was just the resistance of the thermistor at the temperature we were optimizing for, and the second term scales that down a little.

We then moved on to fitting the model. I showed three data sets that students had sent me—one which was a little messy, but still quite usable, one that was a little better, and one that was really beautiful.  I continued with the really good data set.  I explained that gnuplot tries to minimize the error on the y-axis for a function of things on the x-axis, and the students decided that minimizing the temperature error for a given resistance was probably best here. (I suspect it doesn’t make much difference with this data, but it is good to get them to think about that as a decision that needs to be made for each modeling problem.)

On the board, I turned around the equation for the model, to get temperature in terms of R: T = \frac{B}{\ln R - \ln R_{\infty}}.

I then developed the gnuplot script for the problem live, debugging as I went.  Some of the errors to debug were ones I introduced deliberately, others were inadvertent, but all were good for teaching both the process of debugging and the notion of doing sanity checks.  My first mistake was an inadvertent one: I capitalized a variable differently in the parameter list and in the function body, and gnuplot is case-sensitive.  This was very easy to find and fix, and gave me an opportunity to tell students that gnuplot was sensitive to case, since that had not come up previously. My second mistake was a deliberate one: I typed in the model exactly as we had derived it on the board, knowing full well that the model was for °K, but the data was for °C.  I’d even reminded students of that earlier, when we were doing the optimization problem.

I then ran the fit in gnuplot and asked students if we were done, or if there was a sanity check we could do.  A couple of them asked if we could plot the model and the data on the same plot, so I did that. The fit was very obviously completely wrong. So I asked the students what was wrong and how we could fix it. I did dice-assisted cold calling to put 3 or 4 students on the spot, getting not very useful answers, then took answers from a couple of students who raised their hands. The second student pointed out the °C vs °K problem.

So I fixed the formula and ran the fit again, expecting everything to work fine.  It didn’t! So we went into debugging mode, trying to see if starting with better estimates of B and R would help. Nope. Then I realized that I had made a second inadvertent error: I’d put in 273.15 with the wrong sign! I fixed that, ran the fit again, and again things failed (producing negative values for R).  This time, though when I put in better initial estimates, everything converged to a very good fit, which gave me a teachable moment about the need to have decent estimates before fitting, so that the optimization algorithm that did the fitting could converge.

The final script was

temp(R,B,Rinf) = B / ( log(R) - log(Rinf)) - 273.15
B=3000; Rinf=1e-4
fit temp(x,B,Rinf) 'student-thermistor-data-3.txt' using 2:1 via Rinf,B
plot 'student-thermistor-data-3.txt' using 2:1, \
      temp(x,3435,10*exp(-3435/(25+273.15))), \

The second curve of the plot is using the data sheet values for the B value and for R25°C=10kΩ.
Here is the plot produced:

Notice that I did not have axis labels, title, nor echoing of the parameters in the key.  We covered that last week and I'm hoping that students can carry skills over from one week to the next.

Notice that I did not have axis labels, title, nor echoing of the parameters in the key. We covered that last week and I’m hoping that students can carry skills over from one week to the next.

The model fit is slightly better than the data sheet values, but the data sheet values were closer than I had expected based on previous years’ fits. I think that it may be that the students had a properly calibrated thermometer (I’d removed any digital thermometers that reported ice water as warmer than 0.5°C—about 1/3 of them were that far out of calibration), and that this particular pair of students had been very careful with their measurements.

2013 February 26

Better model for loudspeaker

Filed under: Circuits course — gasstationwithoutpumps @ 11:34
Tags: , , , , , ,

In Seventeenth day of circuits class: inductors and gnuplot tutorial, I introduced two linear circuit models for the JAMO 30466/30462 loudspeakers that we’re using in the class:

    The model we developed in class for the 10W loudspeakers that the students bought in their parts kits.

The model we developed in class for the 10W loudspeakers that the students bought in their parts kits.

The improved model that matches the measured magnitude of the impedance better at high frequencies.

The improved model that matches the measured magnitude of the impedance better at high frequencies.

The second model fits better and is one of the standard ways of modeling loudspeakers, though I did not realize that at the time I developed the model.  I looked into some other ways people have modeled the slower-than-f^1 rise of impedance for loudspeakers.  There seem to be three popular approaches:

  • Adding more (R||L) sections in series.  This approach is handy when dealing with circuit simulators, since it remains a fully linear circuit.  It has a lot of parameters, though, and tends to produce fits that waver around the observed data.  The phase tends to be affected quite a bit by the extra sections.
  • Adding a “semi-inductor” that has impedance Z=\sqrt{j\omega}K (or a semi-inductor in parallel with an inductor).
  • Using a frequency-dependent inductor with Lhi being proportional to a power of frequency, rather than constant.

I tried both semi-inductors and frequency-dependent inductors, and I was not very impressed with the semi-inductor approach.  It took more parameters to get a worse fit.  The frequency-dependent inductor fit is excellent, though, and really has about as few parameters as a model of this data can:

Three simple models of a loudspeaker: R+L+(R||L||C), R+L+(R||L||C) + (R||L), and R+L(f)+(R||L||C), where the frequency dependency in the final model is simply a power law.

Three simple models of a loudspeaker: R+L+(R||L||C), R+L+(R||L||C) + (R||L),
and R+L(f)+(R||L||C), where the frequency dependency in the final model is simply a power law. 
The numbers may be slightly different from previous fits, because I redid the fitting, and small changes in the initial estimates or the order  in which fits are done can affect the result slightly.

To really distinguish between the different models of the loudspeaker, I should have recorded data that would allow me to try to figure out the phase as well as the magnitude of the impedance.  I don’t have the tools to measure phase directly (though I’ve been thinking about making a circuit to do that), but I could have measured  three RMS voltages instead of just two in the 47Ω + loudspeaker test circuit.  I measured the voltage across the resistor and across the loudspeaker, but not across the two in series.  The extra measurement would have allowed me to estimate the phase difference between current and voltage (though not the sign of the phase difference).  Maybe I’ll do that when I have a couple hours to spare to redo all the measurements.

In the lab handout for next week’s lab, I’ll explain Zobel networks for compensating the loudspeaker to get resistive behavior at high frequencies (but we won’t use a Zobel network, because it wastes a lot of power)  and designing LC filters to suppress the high frequencies.  The designs will be done with the frequency-dependent inductor model:

Model for the loudspeaker with one frequency-dependent component (the inductor).

Model for the loudspeaker with one frequency-dependent component (the inductor).

I’ll have to provide a lot of scaffolding for the LC design, as the students don’t have the programming ability (even for simple scripting in gnuplot) to do the optimization.  I’ll probably give them a script that produces graphs like the following, so that they can choose their components without having to do messy calculations, though they’ll have to modify the script a little bit:

Power to the loudspeaker for various LC low-pass filter designs.

Power to the loudspeaker for various LC low-pass filter designs.  Note that they probably won’t be using a ±3.3V power supply, and they’ll probably have a series resistor on the loudspeaker, for observing current waveforms on the oscilloscope.

Incidentally, this post is the 1000th post on this blog.  I was going to write something celebratory for the 1000th, but my son convinced me I should save the celebration for the real round number in post 1024 (which is where I run out of fingers for counting the posts).

2013 February 16

Teaching students to build and use models

Filed under: Uncategorized — gasstationwithoutpumps @ 11:45
Tags: , , , , , ,

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 Qes of the resonance peak as 3.52, while our model of the R||L||C for the peak has Q_{es}=R\sqrt{C/L} = 5.71.

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.

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