Today’s class started with two more do-now problems: What are the voltage gains of the following circuits?
I walked the students though the analysis of the inverting amplifier from the first principles of op amps and the currents through the resistors. One student properly brought up the question of stability, so we checked what would happen with a small perturbation. This is indeed a stable negative-feedback loop. I did promise the students that we wouldn’t always have that—sometimes we might want to design oscillators or other unstable circuits. In fact, I had originally had a third circuit that wasn’t a simple inverting or non-inverting amplifier, but decided to cut it in the interests of time.
Before the discussion of the do-now problems, though, I handed back the Lab 4 reports (the hysteresis lab), and told the students that they all needed to redo the reports. It wasn’t that the reports were particularly bad this time, but even the best students had gotten into the habit of being sloppy about their calculations (off by 10 orders of magnitude in one case) and their schematics (power-ground shorts and missing wires), and that just isn’t going to work for them for the last three labs (nor in the real world). This lab was a good one to have them do another draft on, because it had fairly simple schematics and calculations, as well as a fairly easily explained design goal. Just about everyone should be able to improve this report to high quality without having to go back to the lab to redo anything. I also urged them to read each other’s reports looking for good things that they could incorporate into their own writing and providing feedback. I’m hoping that everyone will read at least 4 of the reports, and that I’ll get much more polished work (the sort of work I’d like to see the first time they turn things in) by the end of the week. My co-instructor reminded them that they can’t think about the messy wiring on the breadboards, but need a neat schematic model to think about their circuits. He also pointed out to them that most of the debugging that has happened in the labs has been finding differences between the wires in the real world and the schematics—that doesn’t help if the schematics are wrong.
After the lab report return and the introduction to inverting amplifiers, I had the students think about the effect on the circuit you were measuring of hooking up the ×2 or ×–2 amplifiers to a signal (say one that came from a voltage divider with a 40kΩ pullup and a 10kΩ pulldown. They had no trouble with seeing that the non-inverting amplifier had little effect on the circuit, because of its near-infinite input impedance, but were lost when thinking about the inverting amplifier. I went over the concept of input impedance, and they eventually managed to figure out that the input impedance of the amplifier was just the 1kΩ resistor (because the feedback look held the negative input to the op amp to 0v). Figuring out what that would do to a voltage divider was again challenging for them—they really need this week’s prelab and lab, which get them thinking about parallel resistors and capacitors in a circuit context. I’m hoping to get them to the point where they can start doing sanity checks on their calculations.
After the amplifier discussion, I took an unplanned detour into what a “bypass” capacitor means, since they had one on the hysteresis oscillator board, but none of them knew what it was for and many drew it in the wrong place in their schematics (as a DC-blocking capacitor on the output, for example). I did not try to teach them how to size bypass capacitors (an arcane art not much practiced by working engineers, who just sprinkle whatever standard value their design shop uses next to each chip), but I hope I got across why we need them.
We ended up with doing the quiz corrections together. Basically, I went around the room asking each student in turn for an answer, and having people interrupt whenever they had a different answer. For a couple of the questions, students were still confused, and I tried to do another explanation of how to work the problem. We ran out of time and will continue with the quiz corrections on Wednesday. I did remember to ask them all to bring laptops on Wed, so that we can do a hands-on tutorial on curve fitting with gnuplot.
I’ve got a nice set of data for them to fit: the magnitude of impedance for their loudspeakers as a function of frequency—I spent a couple of hours after class today in the lab gathering the data. The experimental setup will be easy to explain to them—it is the same as for their electrode labs, but with a loudspeaker in place of the electrodes. There are some gotchas in the data (l deliberately went to higher frequencies than the voltmeters are designed for, for example, and the mechanical resonance of the loudspeaker will come as a surprise to them—at least it did for me the first time I found out about it). I plan to show students how to look for anomalies and what to do about them.
Unfortunately, I did not get to inductors today, which I really wanted to do before the gnuplot tutorial, since we’ll need inductors for some of the modeling. We’ll also need RLC circuits, which will be more than I can do in one day on Wednesday, so we’ll probably have to stretch out the gnuplot tutorial for 2 days, using it for both exploring circuits and for modeling the loudspeaker. I’m thinking that it might be a good idea to delay the inductor information until we need it in modeling—to start with the data and see why resistors and capacitors are not enough (well, they are at low frequencies if you include amplifiers, but for passive-only circuits, we sometimes need inductors).
Having them learn to use plotting as an exploratory tool will probably be good for them—I don’t get the impression that their previous classes have given them much occasion to do exploratory work. I’ll be doing this as a worked example, where they will be building a gnuplot script and a model for the loudspeaker on their computers a step at a time, guided by observations made by the class as a whole.