# Gas station without pumps

## 2013 January 30

### Tenth day of circuit class

In today’s class I had originally planned 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.

After last night’s late-night blog post, I decided to add a few minutes at the beginning of the class talking about the “comfort zone” and the “zone of proximal growth”, and how it was ok (even good) to be uncomfortable, but that I was trying to hit the sweet spot of maximizing learning for them without good feedback on when I had hit it.  There were likely to be times when I went too fast or too far, and took them into the range of “impossible”, where they either shut down or ran around in mental circles without getting there.  I pointed out that I was out of my comfort zone in teaching this class, and learning a lot about how to teach the subject, since the class was not quite like any of my previous courses, which had either involved students who had already started “thinking like engineers” or for which that was not a major goal.

As it turned out, there was a natural segue to this topic, as several students complained about how much time they were spending struggling with gnuplot.  They were reporting times in excess of 12 hours on gnuplot, when I had expected the plots for last week’s lab to take them only an hour.  They reported having more trouble using gnuplot than with the circuits concepts and electrochemistry that the lab was supposed to be helping them learn. I believe that learning to use a plotting and model-fitting tool will be very useful for them no matter what branch of bioengineering they end up working in.

I don’t think that the problems they were having are unique to gnuplot and changing tools is not likely to help—in fact, gnuplot has one of the simplest interfaces of tools that can fit multiple parameters for complicated functions. I’m not sure, however, where the conceptual difficulty is for them, and so I asked if one or two of the ones who were having the most difficulty could sit down with me and show me where they were getting stuck (after lab tomorrow, on Friday, or after class on Monday).  Perhaps by watching them work, I can get a better idea where the difficulty is and devise a lesson, handout, or other intervention to get them unstuck.  I also offered one-on-one tutoring to them (again after lab or in Monday’s office hours), but until I know what the sticking point is, my tutoring is likely to be pseudoteaching again, where I guide them through the process and we’re all convinced they’ve got it, but when they try a real problem on their own, they still get stuck.

Not everyone who was introduced to gnuplot is having this difficulty (a few students have reported to me that they are now applying gnuplot for their senior theses), but enough were having trouble that I certainly can’t dismiss the problem as irrelevant nor can I expect the students to tutor each other (an intervention that works well when most of the class understands the concepts, since explaining to the few who need help can help people clarify their own understanding).

The circuits topics that I wanted to teach went well.

I introduced RMS voltage as the DC voltage that provides the same average power as the AC signal of a given amplitude, and we did the definite integral for computing the average power.  (I gave them trig formula $\cos(2\theta) = 2\cos^2(\theta)-1$, and reassured them that I did not expect them to remember trigonometry—this may be the only place this quarter where we use a trig identity.)  I also had them derive the RMS voltage for a square wave, so they could see that the $\sqrt{2}/2$ ratio was a special case for sine waves and not a general phenomenon.

I then covered digital amplifiers and hysteresis, using the figures from the lab handout.  I think I got across the idea of hysteresis using the figures and  the example of a thermostat and furnace that you don’t want to cycle on and off a lot. It’s hard to tell whether they’ve really gotten the idea or not, though, and I don’t know how to check other than by seeing what they write in their lab reports.

The relaxation oscillator was not as thoroughly covered.  We stepped through the charging and discharging of the capacitor, but did not derive formulas for how long it takes to charge and discharge, as a function of R, C, the two threshold voltages, and the two output voltages.  We did wave our hands at the idea that all the times are proportional to the RC time constant, but did not attempt to determine what the proportionality constant is.  I suggested that they determine it empirically in the lab, rather than deriving the formula, since I’m not confident that they could derive the constants, given that the input voltage is decaying exponentially towards the output voltage.  The math seems simple to me, but explaining it to them would take more time than we had in class today, and I’m not sure how much they would retain of it.  I’m hoping that some of the more diligent students will attempt the derivation on their own, as it provides another concrete use for the $\omega=\frac{1}{RC}$ formula.  I suspect that most of them can handle the algebra for the exponential decay towards 0V, but that they will have trouble with expressing the exponential decay towards 4V (the output high voltage).

I did demo the relaxation oscillator, using the same PC board that they’ll be soldering and displaying the output waveform with the BitScope USB oscilloscope I bought.  I had to power the Arduino board and the oscillator with a separate power supply, since my trials ahead of time showed me that the BitsSope could not display the signal if I powered the Arduino from the laptop.  I think that the problem has to do with the difference between the BitScope ground and the USB ground that is shared with the Arduino—I’ve not yet tried to track it down.  But with a separate power supply everything worked ok.  The projection of the BitScope oscilloscope display worked ok (despite their projection-unfriendly insistence on a black background), and I hope to be able to use it again in a later class.  It is a bit of a pain to set up before class, though, so I’ll want to use it only when the live demo is worth the time and the risk of equipment failure.