Like on Tuesday, on Thursday I spent a long time in the lab, from about 9 a.m. to after 6 p.m., because it takes a fair amount of time to set up and clean up when we are dealing with liquids (in this case, salt water) in the electronics lab. The lab itself went fairly smoothly and the students all seemed to be collecting good data.
As I feared, we ran out of one of the 4 stock solutions: 3l per concentration for 28 students was not enough, unless students shared by transferring solutions from one group to another. Next year I’ll have to get 200ml/student made up, or change the way the lab is run so that students have 6 sets of cups already pre-poured, and just grab a cup that they haven’t already used. I worry a bit about careless students not cleaning and drying their electrodes between uses, though and contaminating a low-salt solution with salty electrodes.
I had one surprise this year. We changed which brand of EKG electrodes we ordered (from Vermed to some foam-backed electrode with no brand name—not a substitution I remember approving, but I probably would have if asked). It turns out that the new electrodes do not seem to be silver/silver-chloride. Instead of resistance around 10Ω as the Vermed electrodes have, the new ones are in the 10MΩ range. They must be using some polarizable electrodes instead of non-polarizable Ag/AgCl. I hope that they work ok for the EKG lab at the end of the quarter (10MΩ should be ok, as the instrumentation amps and op amps have input impedances of 1GΩ and 10TΩ respectively, so a mere 10MΩ resistance should be negligible).
I am going to have to rework a big chunk of the book this summer, though, as the measurements ran into trouble with the input impedance of the voltmeters not being too large to matter, as we usually assume. The AC voltmeters claim to have 1MΩ || 100pF, which is great at low frequency but at 1MHz, that’s only 1.6kΩ. The 1MΩ is tightly specified, but I believe that the 100pF is only an upper bound: there may be considerable variation in the capacitance from meter to meter.
The students who were attempting to measure the impedance of the new foam-backed EKG electrodes were probably actually measuring the impedance of the voltmeter. Several of the measurements of the stainless-steel electrodes were also marred by the input impedance of the voltmeters. On Tuesday afternoon, if I have any spare time in the lab, I’ll try measuring the input impedance of the voltmeters myself, to see what it looks like. The test setup will be a simple one: two voltmeters in series, driven by a function generator. I’ll shunt one of the voltmeters with a smallish resistor (say around 500Ω) and plot the ratio of the two voltages as a function of frequency (I’ll need a moderately high voltage from the function generator to make sure that the voltmeter on the shunt has enough voltage). The voltage ratio should follow a simple pattern: . I can model the meters as a 1MΩ resistor in parallel with an unknown capacitor and fit the parameters (trying both meters having the same capacitance, and having different capacitances). I can even do another set of measurements swapping which meter I shunt.
I think that a lot of the weird data we saw in Tuesday’s lab came from using large shunt resistors, so that the voltmeter impedance became more important (smaller) than the shunt resistor.
I’m considering also putting in the book a derivation of how to compensate for the meter impedance (if it is known). I think that I’ll move the electrode lab later next year, closer to the EKG lab, so that we can go more directly from the microphone lab and the loudspeaker lab into the audio amplifier lab, and so that the electrode characterization is more immediately motivated.
In Friday’s lecture, I talked briefly about the possibility that the problems we were seeing with model fitting were that we had neglected the voltmeter input impedance, but I did not work out the details, because I had to introduce them to op amps and negative-feedback amplifier configurations.
I like to use a generic negative-feedback configuration, which includes inverting and non-inverting amplifiers as special cases, as well as the single-power-supply variants:
On Friday we got through the derivation of the various gain formulas, based on letting the open-loop gain go to infinity, but I’ll have to refresh that on Monday and introduce the unity-gain buffer: especially the unity-gain buffer as a voltage source for a reference voltage between the power supply rails.