In Ag/AgCl electrode lab went ok I wrote
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.
In today’s lab, students did not need much help (they were just playing with their op amp circuits to see what they could measure or change), so I decided to measure the input impedance of the Agilent 34401A voltmeters on bench 1. I made the simplifying assumption that the meters were basically a resistor (about 1MΩ) in parallel with a capacitor (about 100pF), because that is what the Agilent 34401A data sheet claims, and created the following circuit:
I measured the two voltages at frequencies from 3.3Hz to 2.2MHz (using the E6 scale for roughly equal spacing) . I figured that the voltmeters would have different input impedances, so I swapped the shunt resistor to the other meter and made the measurements with that setup also.
I then tried fitting the meter resistances and capacitances to the ratio of the voltages. At low frequencies I expect to see 454 times the shunt voltage on the unshunted meter, but at high frequencies the voltages should be similar. I fitted models of what the ratios should be and got the following results for the two meters on bench 1:
The meters don’t seem to be in spec for the capacitance input—there is an extra 25pF—285pF input capacitance. One possibility is that extra capacitance comes from the wires to the probes. The two meters do have quite different probe sets, and switching the probes from one meter to the other causes the voltages to switch along with the probes—that is, the difference appears to be in the probes, not the meters.
I’ll probably have come up with a wiring scheme that doesn’t include the long wires that seem to be contributing capacitance if I really want to measure the meter input impedance—but even the lesson that wiring capacitance can be throwing their measurements way off could be important to the students.