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2019 May 22

Interaction between bias resistor and active high-pass filter

Filed under: Circuits course — gasstationwithoutpumps @ 00:02
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In grading the preamplifier lab, I made a mistake when correcting a number of student papers.  Students who had used a bias resistor rather than a transimpedance amplifier to convert the microphone’s current output to voltage had not taken into consideration the interaction between the bias resistor and the input impedance of the next stage, which was usually an active high-pass filter.  In grading, I overcorrected the student work, changing both the i-to-v gain and the first-stage gain, when the correct action would have been to change either one, leaving the other alone.

Schematic of bias resistor and active high-pass filter. The input is the current I_in.

The passband gain for the circuit is R_b\frac{R_f}{R_b + R_i} = (R_b || R_i) \frac{R_f}{R_i}. The first version corrects the gain of the filter, while the second version corrects the gain of the current-to-voltage conversion. In my grading, I mistakenly applied the correction twice getting (R_b || R_i) \frac{R_f}{R_b + R_i}.

There are two ways to get to the correct answer: using Thévenin equivalence and from first principles.

If we replace the current input and R_b with a Thévenin equivalent, whose AC voltage is the AC component of I R_b and whose resistance is R_b, then we get a simple active high-pass filter with passband gain \frac{R_f}{R_i + R_b} for a total passband gain of R_b\frac{R_f}{R_b + R_i} and a corner frequency of \frac{1}{2 \pi (R_i+R_b) C_1}.

For those who don’t quite trust themselves to do Thévenin equivalence, we can use first principles to reason about the various currents in the schematic. The negative-feedback loop holds the op amp’s negative input to V_{ref}, and the input node has a voltage, so we get
V_{input} = V_{dd} - I_b R_b = V_{ref}-I_f \frac{j\omega R_i C_1 + 1}{j \omega C_1}
which we can rearrange to get
I_b = \frac{V_{dd} - V_{ref}}{R_b} + I_f \frac{j \omega R_i C_1 + 1}{j\omega R_b C_1}.
Because I = I_b + I_f, we get
I= \frac{V_{dd} - V_{ref}}{R_b} + I_f \frac{j \omega R_i C_1 + 1}{j\omega R_b C_1} + I_f
and can solve for I_f to get
I_f = (I- \frac{V_{dd} - V_{ref}}{R_b}) \frac{j\omega R_b C_1}{1+j\omega(R_b+R_i)C_1}.

Finally, because V_{out}-V_{ref} = I_f R_f, we get
V_{out}-V_{ref} = R_f (I- \frac{V_{dd} - V_{ref}}{R_b}) \frac{j\omega R_b C_1}{1+j\omega(R_b+R_i)C_1}.

Our transimpedance gain (including the DC offsets for input current and output voltage) is
\frac{V_{out}-V_{ref}}{I- \frac{V_{dd} - V_{ref}}{R_b}} = R_f \frac{j\omega R_b C_1}{1+j\omega(R_b+R_i)C_1}.
At DC, this has the appropriate gain of 0, and for high frequencies (in the passband), the gain is approximately \frac{R_f R_b}{R_b + R_i}, as claimed earlier. The corner frequency, where the real and imaginary parts of the denominator match is at \omega = \frac{1}{(R_b+R_i)C_1}.

2014 June 1

Blood pressure monitor

I thought of a new variant on the pressure sensor lab for the circuits course: a blood pressure monitor.  I happen to have a home blood pressure monitor with a cuff and squeeze bulb that can be detached from the monitor and hooked up to the MPS2053 pressure sensor instead.  With this setup and an instrumentation amp, I can easily record the pressure in the cuff and observe the oscillations in the cuff pressure that are used for oscillometric blood pressure measurement.

Cuff pressure measurements using an MPX2053DP sensor, and instrumentation amp, and a KL25Z microcontroller board running PteroDAQ software.

Cuff pressure measurements using an MPX2053DP sensor, and instrumentation amp, and a KL25Z microcontroller board running PteroDAQ software.

The fluctuations can be observed by removing a baseline (fitting an exponential decay to the dropping pressure, for example, and the subtracting it out) or by using some sort of digital filter. I tried using a 0.3Hz–6Hz bandpass filter (4th order Bessel filter, applied using scipy.signal.filtfilt):

Oscillations corresponding to the pulse are very visible when the slow pressure decay is filtered out.  I've zoomed in on just the time of the dropping pressure, marked with lines on the previous plot.

Oscillations corresponding to the pulse are very visible when the slow pressure decay is filtered out. I’ve zoomed in on just the time of the dropping pressure, marked with lines on the previous plot.

The pulse is very easy to see (about 40.4bpm in this sample—low even for me), but figuring out the systolic and diastolic pressure from the fluctuations is a bit messy:

The oscillometric method of measuring blood pressure with an automated cuff yields valid estimates of mean pressure but questionable estimates of systolic and diastolic pressures. Existing algorithms are sensitive to differences in pulse pressure and artery stiffness. Some are closely guarded trade secrets. Accurate extraction of systolic and diastolic pressures from the envelope of cuff pressure oscillations remains an open problem in biomedical engineering.  
[Charles F Babbs, Oscillometric measurement of systolic and diastolic blood pressures validated in a physiologic mathematical model, BioMedical Engineering OnLine 2012, 11:56 doi:10.1186/1475-925X-11-56 http://www.biomedical-engineering-online.com/content/11/1/56]

One shortcut is to find the maximum amplitude of the envelope of the oscillations, and look at the pressures at fractions of the amplitude:

However, it has been shown that the pressure, Pm, at which the oscillations have the maximum amplitude, Am, is the mean arterial pressure (MAP). Empirical and theoretical work has shown that the systolic and diastolic pressures, Ps and Pd respectively, occur when the amplitudes of oscillation, As and Ad respectively, are a certain fraction of Am:

  • Ps is the pressure above Pm at which As/Am = 0.55
  • Pd is the pressure below Pm at which Ad/Am = 0.85

[Dr. Neil Townsend, Medical Electronics, Michaelmas Term, 2001, http://makezine.com/go/obpm]

I’m too lazy right now to try to come up with a good envelope follower and find the times for 55% and 85% of peak. The peak seems to be around 48.3s in this plot with magnitude of 0.336kPa and a predicted MAP of 16.28kPa (122mm Hg).  I based the MAP on low-pass filtering the signal to remove the fluctuations and make a good smooth curve for finding the systolic and diastolic pressure, once times on the envelope are picked.  Again, a 4th order Bessel filter applied with filtfilt looks good:

Low-pass filtering removes the fluctuations, so that picking two time points can give clean pressure readings for the systolic and diastolic pressure.

Low-pass filtering removes the fluctuations, so that picking two time points can give clean pressure readings for the systolic and diastolic pressure.

From the standpoint of the course, the filtering to get a good signal is probably too difficult, but students could record the cuff pressure and observe the fluctuations. They might even be able to do some crude RC filtering, though this is really an application that calls out for digital filtering.

2013 February 21

Sampling lab went ok

Filed under: Circuits course,Data acquisition — gasstationwithoutpumps @ 21:14
Tags: , , , , ,

Today’s sampling and aliasing lab was one I expected to go fairly quickly, but it took longer than I thought.  The students had two design tasks and then a bunch of observations. The design tasks were supposed to have been easy ones that they did as a prelab, but everyone took a bit longer than I thought, and some really struggled with them.

The first design task was to design a high-pass filter to do level shifting of a signal from a signal generator (the signal generator is capable of being set to center at a voltage other than 0v, but I needed students to practice level shifting before they do the class-D audio amplifier and the EKG labs).  I gave them a very low corner frequency (0.03Hz).  Students didn’t have trouble with the RC time constant (mostly), but they did have trouble with the notion of using a voltage divider as a Thévenin equivalent of a resistor to the desired center voltage, though we had just done that yesterday in class in analyzing the do-now problems.  I think that they all got it in the end, but I’ll definitely have to consider including some sort of level-shifting question on the quiz.

They looked at the signal output from the high-pass filter using the scope (to make sure that the voltage range was appropriate), then hooked it up to the Arduino and ran the DataLogger code.  I had them run the signal into two pins, with one sampling at 40Hz or 50Hz and the other at 1/5 that (8Hz or 10Hz), and then look at various frequencies.  I may have to specify some specific frequencies for them to look at next year, since they tended to pick simple multiples of 1Hz, which does not reveal some of the interesting beat patterns that you get at 4.9Hz and 5.1Hz.  The DataLogger code worked quite well for this application, though one student managed to tickle an error message by leaving the down-sampling field blank (it should probably default to 1 in that case, rather than reporting an error).  One could do all the visualization with a purely software simulation lab, but the students learned a fair amount by designing and wiring the RC filters, as well as getting more experience with the oscilloscopes and function generator.

The second design task was to design a low-pass filter with a corner frequency of 4Hz.  For this one, most of them chose to do a 2.5v virtual ground with an op-amp circuit, though there was no need, since the capacitor blocks any DC and so could have been connected directly to ground. Using a virtual ground actually makes it harder to use the electrolytic capacitors without reverse biasing them.  This may get to be important in the LC filter for the class-D amplifier, so I’ll probably have to talk about proper biasing of electrolytic capacitors in class.

I did do the strobe demo at the beginning of lab time, but it was not as good a demo as I had hoped to do.  I’ll have to think of ways to improve it for next year.  Problems included that the strobe light was not bright enough (you can’t turn off all the lights in the lab) and that the spinning paper propeller did not have an adjustable speed, so I couldn’t match the propeller to the strobe (just the strobe to the propeller).  Perhaps I need to choose a better moving object next year, where the strobe light will have a more obvious relationship to the sampling of sine waves in the rest of the lab.

Tomorrow I’ll need to start teaching about instrumentation amps, and get the students to choose lab partners to work with over the weekend, so that they can come in with questions on Monday, since the first instrumentation amp lab is likely to cause them problems.

 

 

2013 February 7

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.

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

do-now-2-2013-feb-6

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.

do-now-3-2013-feb-6

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.

do-now-4-2103-feb-6

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

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.

2013 January 28

Ninth day of circuit class

After the last class I wrote

So we have the basics now of Bode plots (just for gain, as I’m not sure we want to do much with phase in this class, at least not for a while).  I did not get to any electrochemistry or why stainless steel is a good mechanically and chemically, but not electrically, for implants.

I think that Monday will see more gnuplot plotting, looking at the impedance of more complicated circuits, so that they can better understand the behavior of polarizable electrodes like the stainless steel electrodes they were characterizing.  If I can show them how the Bode plots help think about and sketch the behavior quickly, I hope that they’ll have a better appreciation of this shortcut.  Given that plotting with gnuplot is easy, I’ll have to convince them of the usefulness of the Bode plots for thinking about circuits, rather than the classical approach of using them to do quick sketches of behavior.

It may be Wednesday before we get to hysteresis and the hysteresis oscillator that they will build on Thursday.

One other thing I wanted to do today but spaced: I wore my banana slug genomics t-shirt so that we could discuss the possibility of designing a t-shirt for this course, but then I forgot to discuss it.  I think I want to use the same basic “slug-dreaming” design, but put something different in the thought balloon.  I don’t have any good ideas yet for the thought balloon.  Given how much we’ll be doing with voltage dividers, doing something like an RC low-pass filter with the appropriate gain equation is not too bad an idea. [This did get discussed today, and students liked the idea of a T-shirt.]

Well, it will definitely be Wednesday before we get to hysteresis.  We did not get to talking much about stainless steel, though we did do some plotting of the electrode circuit.  The problem is that I started with a quick “do now” question to check that they had absorbed Friday’s material:

For each of the following circuits, give the gain at 1Hz, 1kHz, and 1MHz:

The four circuits I put on the board.  Of course, I used 0.01µF, not 10nF, and 0.56µF, not 560nF, since no one uses the milli- and nano- prefixes for capacitance, but CircuitLab is incapable of that distinction.

The four circuits I put on the board. Of course, I used 0.01µF, not 10nF, and 0.56µF, not 560nF, since no one uses the milli- and nano- prefixes for capacitance, but CircuitLab doesn’t seem to realize that.

I expected that most of the class would be able to do the resistance voltage divider, and half the class would get the low- and high-frequency gain values for the RC circuits. I expected that students would have trouble with the capacitance voltage divider, since I had suggested they look at it at the end of last Friday’s class, but with little expectation that any of them would have the curiosity to actually do it without being required to.

I was a little disappointed that no one in the class got any of the questions, even with far more time than I had planned to spend on them. I guess I’ve been guilty of pseudoteaching—something that looks like good teaching, but the students don’t actually learn. So we went over the 4 problems in class, with me extracting the answers from the students and pointing out where sanity checks are needed (like whether the corner frequency is 1000 or 0.001, based on keeping track of units). So what was intended as a 5–10-minute check on what students had retained turned into a 45-minute repeat of the previous class.

I’ve also told the students that there will be a quiz next Tuesday, covering everything we’ve done with impedance and voltage dividers. I’ll be making the quiz closed notes, since far too many students wasted time looking for magic formulas in their notes, rather than thinking about what they knew and using it. I will expect students to bring a calculator to class from now on also.

Now I have to come up with a quiz—and if it turns out that most of the class can’t learn this stuff without pages of mindless drill, then I’ll have to start assigning pages of problem sets, an approach to education that I’ve always hated.

That repeat teaching left me with less time than I had planned, so the only new material I covered was plotting impedance versus frequency for the model we had for the electrode pair:

The model the students are supposed to fit to the data from last week's lab—a standard model for a pair of polarizable electrodes.

The model the students are supposed to fit to the data from last week’s lab—a standard model for a pair of polarizable electrodes.

Before showing them how to set up gnuplot to plot the model, I first had them think about what happens at DC and at ∞ frequency.  After a bit of fishing, I finally got them to elucidate the behavior of a capacitor (open circuit at DC and short circuit at very high frequency), and figure out what that meant for the overall impedance.

I showed them the following gnuplot script (and walked them through it line-by-line, since I’m not confident that they understand function definition yet):

set xlabel "frequency (Hz)"
set ylabel "|Z| (ohms)"

set logscale xy
unset key

# voltage divider
divider(z1,z2) = z2/(z1+z2)

# two impedances (resistances) in parallel
parallel(z1,z2) = z1*z2==0? 0: z1*z2/(z1+z2)

# impedance of a capacitor at a given frequency
j = sqrt(-1)
Z_C(c,f) = 1/(j*2*pi*f*c)

# corner frequency for an RC time constant
freq(RC) = 1./(2.*pi*RC)

 R1=150.
 C1=3e-5
 R2 = 5.

 min(a,b) = a<b? a:b
 max(a,b) = a<b? b:a

set xrange [1:1e6]	# 1Hz to 1MHz
# set yrange [0.9*R2:1.1*(R1+R2)]
set yrange [*:*]

unset label
unset arrow

set label "f(R1*C1)" at freq(R1*C1),R1+R2
set arrow from freq(R1*C1),1e-12 to freq(R1*C1),1e12  nohead lw 0.5
set label "f(R2*C1)" at freq(R2*C1),R2
set arrow from freq(R2*C1),1e-12 to freq(R2*C1),1e12  nohead lw 0.5

set title sprintf("(%.3gF || %.3gohm) + %.3gohm", C1, R1,R2)
plot abs(parallel(Z_C(C1,x), R1)+ R2), \
 		R1+R2, R2

For those who don’t have gnuplot handy in another window, here’s what the script produces:

Plot of impedance of a model of polarizable electrodes, showing the asymptotes and the critical points.

Plot of impedance of a model of polarizable electrodes, showing the asymptotes and the critical points.

I had a little time to show them the plot of data that I had taken on the stainless steel electrodes and the somewhat poor fit I got. I also explained (a little) what the resistances and capacitance corresponded to physically: R2 is the saline solution, C1 is the insulation of the chromium oxide layer on the steel (and maybe other insulating effects), and R1 is leakage through the insulating layer.

After class, I went to the lab for office hours, and spent another 2 hours explaining the model, how to represent it in gnuplot, how to get impedance from the voltages they measured, and what plots I expected. I also talked a bit about the meaning of models—how there are no “correct” models, just ones that are more or less useful. One of the students had tried to fit a simple capacitance model to the electrode data, and the resulting plot was instructive in seeing where that simple model failed (the resistance is not infinite at DC, nor does it go to zero at very high frequency).

The students seemed to be understanding what I was talking about (I ask a lot of questions and draw most of the stuff out of the students, rather than just talking at them), but the same was true in class last Friday, but nothing was retained for today’s “do now” question. One of the students commented that he/she could do the problems with a few hints, but was lost without them. That’s actually an encouraging sign—the student has almost learned the material, and if they can just learn to give themselves the hints, they’ll be all set. One habit I want to wean them of is memorizing huge numbers of formulas. There are very few formulas in circuits worth the trouble to memorize—a few basic principles and an ability to apply them is far more versatile and less prone to stupid mistakes.

Maybe I should recommend some generic problem-solving books, like Polya’s How to Solve It, since it seems that the class has not been taught many problem-solving skills. I keep feeling that I’m teaching stuff that they should have had much earlier, but clearly haven’t, as if every teacher they’ve ever had has pushed off teaching the important stuff in order to cram in more factoids. There are times when I’m tempted to kick the can down the road myself, but these are all seniors, and it seems almost criminal to let them graduate as engineers without ever having been taught to think like engineers. I’m going to end up working them pretty hard, trying to get them up to speed in circuits, writing design reports, and how-to-think-like-an-engineer in just 7 more weeks.

After the office hours, I chatted a bit with a student in the EE circuits course who was in the lab trying to make up their first lab (which is a somewhat simpler voltage divider lab than our thermistor lab). The total set of parts for the EE circuits class is a lot smaller than for our applied circuits class and undoubtedly much cheaper (no sensors, no instrumentation amp, no PC boards, no solder sucker, only a handful of resistors in selected sizes, a 0.2W speaker instead of a 10W speaker, no transistors, …). The student was a bioengineering student who was taking the EE course because he wanted to do bioelectronics and EE won’t accept my course as a prereq for any of theirs (turf battles). He was envious of the more interesting labs that we were doing, even if they did take a lot longer. He also said that the EE course has not gotten to capacitors or impedance yet—they’ve spent all three weeks on equivalent circuits with resistors, voltage sources, and current sources.

I suspect that at the end of the quarter my students would not be able to pass the final exam for the regular circuits class (they have only a vague understanding of equivalent circuits), but could do all the labs and design exercises. I suspect that the EE circuits students would not be able to pass the final exam nor do the labs for my class.  Although both courses are intro circuits courses, we’ve chosen to emphasize very different aspects of the subject.

On Wednesday, I need to cover the following topics:

  • RMS voltage. I keep putting off a discussion of the 3 different systems for reporting AC voltage (amplitude, peak-to-peak, and RMS), so I’d better start with it.
  • hysteresis.  I have a pretty decent writeup (I think) in the lab handout, but I’m going to have to step the students through it, because I’m not sure that all of them learn well from reading.
  • hysteresis oscillator. Yet another time to talk about RC time constants.  The problem here is going to be that there is a somewhat arbitrary scaling of the RC time constant based on what the threshold voltages are, and I’m not sure I can convey that clearly, since I’m sure that developing the differential equation for charging and discharging capacitors through a resistance will just make their eyes glaze over.  They had all that in physics, and doing it again isn’t going to make it stick any better than last time.  I’ll have to think about this some for tomorrow, and see what I can come up with to make it more intuitive for them.

I also need to give them generic feedback on the second lab report—they got the lab reports back with specific feedback for individual reports, but no general comments that applied to several groups.  I think I’ll do that on the class website, though, rather than taking up class time.

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