# Gas station without pumps

## 2014 April 9

### First mic lab slightly too long

Filed under: Circuits course — gasstationwithoutpumps @ 09:32
Tags: , , , , ,

The first half of the microphone lab took a little longer than anticipated.  I had expected it to take about 2.5 hours, with some groups taking the full 3 hours, but it took more like 3–4 hours.

I have two conjectures about reasons for the extra time:

•  I had the students label all their bags of capacitors. this had originally been planned for a week ago, but the capacitors had not been ordered in time, and Thursday’s lab had been way too packed already, so this was the first opportunity we had.  I probably should have waited until this Thursday, when the lab time is less packed.
• The group that fell the furthest behind had really terrible luck, having sat at a bench where both multimeters had blown fuses and two sets of multimeter leads had open circuits. I helped them debug their setup, but we did not initially suspect the test equipment, and the delay in finding the problem cost them at least half an hour. It also cut into their confidence in debugging their own circuitry later in the lab. Problems with the equipment is one of the difficulties with using a shared lab—a lot of the courses are taught by EE TAs who do not bother to teach students proper use of the lab equipment (if they even know it themselves), so there is often damage of this sort to deal with.

A number of the students in the class are suffering from “imposter syndrome”—not confident of their abilities to master this new material. I’ll have to reassure them that they are doing fine—this class is intended to be pushing them into unfamiliar territory.  I may take a moment in today’s class to mention both “imposter syndrome” and “zone of proximal development”, so that they are aware both that it is ok to be uncomfortable and that I’m trying to maximize what they are learning.

Students had a lot of trouble wiring up their breadboards accurately. Most of the lab time was taken up with students asking for my help and my taking a quick look at the breadboard and telling them that it didn’t match the schematic they had copied. I eventually had the students write on each wire of the schematic what row (or rows) of the breadboard it was on, so that debugging the connections was easier.  I’ll have to try to remember to put that in the instructions for next year, as a way to get the students to learn to debug their breadboard wiring more independently.  I should also add a picture of the trimpot and an explanation of what a potentiometer does—students had a little trouble figuring out what the 3 pins on the package were for.

Many of the groups managed to look at their data in the lab using gnuplot, and collecting more data as a result of what they saw. The students got 1000s of data points that fall nicely along a curve, and they were able to superimpose different data sets that had different scaling for the current measurements. We’ll have excellent data to use in class today for fitting models to. I’m not going to give them real FET models for the FET in the electret mics, though.  Instead we’ll use some simple empirical models:

• current source.  This is the same as a saturation current model.
• resistance. This is essentially the same as the linear-region model for FETs.
• blended model with $R_{FET} = \sqrt{R^2 + (V_{DS}/I_{SAT})^2}$  This is a simpler blend than is usually used in FET models, I think, but it fits the data fairly well.  This blend is mathematically very similar to the ones that compute the gain in RC filters (where we take the magnitude of a complex number and either the real or the imaginary component provides most of the contribution).  Using the same function for rounding the corner when we join two straight lines in different contexts reduces the math burden on the students.
• blended model with $R_{FET} = \sqrt{R^2 + (V_{DS}/I_{SAT})^{2\rho}}$ The extra parameter here is to handle the increase in saturation current with increasing drain-to-source voltage. Normally, that is modeled with a fairly complicated “channel-length” model, and is not even mentioned in intro circuits classes.  But the phenomenon is very obvious in the data, and can be adequately modeled in the electret mic for our purposes with this 3-parameter empirical model.

I will have to give them one more concept about FETs: that the derivative of the saturation current with respect to the gate voltage is proportional to the saturation current. I’m not going to derive that for them from some more general model, because we have no way (in the mic) of actually measuring the gate voltage. Later in the quarter, when we look at FETs again before doing the class-D amplifier, I may give them a slightly more detailed model of an FET.

In addition to gnuplot tutorial today, I want to give them an intro to complex impedance, but I doubt that we’ll get far enough for them to choose the right size for a DC-blocking capacitor for the AC mic lab tomorrow. I may have to suggest that they try one of the biggest sizes of ceramic capacitor that they have (either the 4.7µF or the 0.1µF). We’ll need to get to RC time constants and corner frequencies before next week’s lab though.