Today’s class started with one do-now problem: what does the following circuit do?

No one really felt that they had the whole thing, but several people tentatively thought that they had made some progress, so I got them to tell me what they had done. One student made the very important observation that if you split the circuit between the left op amp and the resistors, and treat that node as “ground”, then the right-hand part is a high-pass filter (he got the corner frequency right) and a non-inverting amplifier with a gain of 5. Another student recognized the unity-gain buffer, but it took longer than I expected to get them to come up with the voltage divider making the left op-amp a 2.5V voltage source. I then explained that this circuit is one way they could have done their audio amp last week, if they had been restricted to single-rail power supplies. I think that they may need a circuit like this for the first stage of their class-D amplifiers in two weeks, since we’ll want the dual-rail power supply to be at a higher voltage than the op amps can run.

The main point of today’s do-now problem was to get them to see complicated circuits as a piecing together of simpler building blocks. They’ll need to do that piecing together in their own designs, and they need to be able to take apart the designs they see in the reading into simpler pieces. That systems-level view—seeing complex things as composed of simpler things—is one of the essential components of “thinking like an engineer”.

We then finished doing the quiz corrections together. Again, I went around the room asking each student in turn for an answer, and having people interrupt whenever they had a different answer. Almost everyone was getting the correct answers this time, so it went fairly quickly. I did answer a couple of questions and pointed out that the Wheatstone bridge circuit (one of the circuits they had encountered for the first time on the quiz) was the standard circuit for strain gauges, including the pressure-sensor strain gauges that they’ll be using in their 9th lab.

We then got out laptops to do a hands-on tutorial on gnuplot. I walked them through plotting the raw data I had collected on Monday for RMS voltages across a loudspeaker and across a 47.7Ω resistor (the two in series driven by function generator.). I pointed out some possible anomalies, and showed them how I had collected more data to check on the anomalies. We then went to the data sheet for the Agilent 34401A multimeter (which I had remembered to name in the metadata for the data I’d collected) and looked at the specs for the true RMS voltmeter. The error jumps above 100kHz (to 4% from <1%) and is only specified to 300kHz—the raw data plots looked good to about 1.3MHz, so I commented out all the data above that frequency. I then showed them how to plot impedance vs. frequency for the data. We drew a line on the plot corresponding to 8Ω (our simplest model of loudspeaker), and I pointed out that neither resistors nor capacitors gave us an impedance that went up at high frequency. At that point we ran out of time, and I promised them more gnuplot hands-on work on Friday.

As expected, I did not get to inductors today, so I’ll have to develop them on Friday, along with the gnuplot work. We’ll also need RLC parallel circuits, which may be easiest to do by building a gnuplot formula and plotting the result for differing values. It will be a good tutorial on using gnuplot to explore models, rather than just to analyze data.

[...] had expected the first circuit to be easy for them as it was quite similar to one we did last Wednesday, but students still struggled with it—only one student recognized it as a gain 5 non-inverting [...]

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