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.