In today’s class, I planned a discussion of amplifiers. Because several students were late getting to class, I started with an informal request for suggestions for the phototransistor and FET lab. I mentioned some of the labs I had rejected (like the MIT lab on DNA melting or the pulse sensor), and mentioned some of the rather boring ones I had come up with. Students expressed an interest in a sound-based lab, so I promised to look into that. I have a couple of ideas to try out this weekend, and I’ll blog about them in a separate post once I’ve tried them out. I have to work quickly though, as I need to get out the lab handout by Wednesday, to give the students a week to read it. I also have a pile of lab reports to grade and a quiz to write, so this weekend will be pretty busy.
I started today’s amplifier talk by comparing digital and linear amplifiers. We had already discussed digital amplifiers for the hysteresis lab, so I only had to remind them of that and compare the different notions of gain (both being the slope of a line on the Vout vs. Vin graph). I mentioned that there are other amplifiers besides voltage amplifiers, but that we would concentrate of voltage in-voltage out amplifiers.
We then covered inverting vs. non-inverting amplifiers, and I got someone to guess correctly that an inverting linear amplifier had negative gain and a downward slope on the Vout vs. Vin graph.
I then moved to differential amplifiers, getting them to derive the Vout=gain(Vp-Vm) formula from what they would want a differential amplifier to me. We then discussed power supplies, input impedance, and output impedance. It was clear that the students are still struggling with what it means in terms of current to have a very high or very low impedance, but eventually the group managed to converge on the idea that a large input impedance and a small output impedance were desirable. I then declared by fiat (since the idea makes no sense until you use it for a while), that the building block we wanted was a very high gain amplifier (gain over 1000).
Somewhere in there (I don’t remember the order exactly 10 hours later), we had a digression to discuss what the 1x/10x switch on the oscilloscope probes meant. I was pleased that I could remember the oscilloscope input specs (10MΩ in parallel with 25pF), which are conveniently printed on the scopes (doing me no good when the scopes are in a different building from the classroom). Now that I get home and can look at my scope, I see that it is really 1MΩ and 25pF for the Kikusui COS5060 on my bench. Checking on-line, the COS5041 scopes in the lab have the same input impedance. The Tektronix digital scopes are 1MΩ in parallel with 13pF. So I’ll have to tell students to correct their notes: the scopes are 1MΩ input resistance, not 10MΩ, and the 10x switch puts in a 9MΩ resistor, not a 90MΩ resistor.
We did not talk about the other characteristics of real amplifiers, but started looking at ideal op amps, with infinite input impedance, zero output impedance, and infinite gain. I did (repeatedly) say that real circuits can’t achieve these ideals, and that we need to check after doing a design, whether the real op amp chips are close enough that the simplifying assumptions are reasonable. I also reassured them that for the low-frequency designs they’ll be doing in the class, the simplifying assumptions are almost always good.
I did not say that the chips we are using have a gain-bandwidth product of 1MHz, because they would have had no idea what I was talking about, but for the pressure sensor and the EKG lab, where the top frequency is around 100Hz, we have much more gain available than we need. I did mention that we should have a gain around 1000 at 1kHz, and that was plenty. I will have to discuss slew rates later this quarter, since the class-D amplifier does not work efficiently with the low slew rates of the op amps and needs a high-speed comparator chip.
I had the students derive the first rule of linear design with op amps: that the inputs have the same voltage. This is a consequence of having infinite gain but only a finite voltage output.
After giving them the idea of an op amp, we had only a few minutes left, so I gave them the simplest of op-amp circuits, which needs no extra components:
I managed to talk them into believing that the output is the same voltage as the input, not just from the first rule of op amps, but by talking them through what would happen if the input went up, and how the output would have to go up until the difference was zero again. I then tried to get them to think about why one might want an amplifier that wouldn’t change the voltage at all. I tried getting them to compare the effect of a voltage source with a large series resistor driving a resistive load (the voltage divider that is the main theme of the course), with the same source driving the unity-gain buffer which drives the source. I reminded them of oscilloscope probe discussion, where we had talked about the advantages of having the extra series resistance in the probe, despite the smaller signal.
I think that one or two students understood the point of the unity-gain buffer, but I’m not sure that most of them got it. We were out of time, though, so I couldn’t go back and do another approach.
On Monday, we’ll have the quiz. If there is time, I’ll continue the discussion of op amps, but I suspect that too many of the students will have put off reading anything about op amps until after the quiz, so there might not be much point until Wednesday. I also suspect that I’ll make the quiz too long, and we’ll end up using up the whole period on it. I am going to try to scaffold the quiz, with easy questions leading up to harder ones, so that the students are primed with the right ideas for the harder questions. I just hope that is enough to get them past their panicked search for formulas to memorize that cause so many of them to freeze whenever they encounter a slightly unfamiliar problem.
I really want the students to do some of the reading on op amp circuits before Wednesday, so that I can be clarifying and reinforcing ideas for them, rather than having to be their first encounter with the ideas. I think that today’s difficulty in getting any response from the students (even when I was asking for guesses) was in part due to them not having read any of the amplifier material yet. They’ve certainly been much livelier in earlier classes.
On Wednesday, I’ll want to have a brainstorming session on the design they need to wire up and debug in Thursday’s lab, so we’ll have to cover non-inverting feedback amplifiers and how to compute their gain (voltage dividers!) fairly quickly. I’ll want them to bring copies of the lab handout to class, so that they can double-check the design constraints and goals as we do the brainstorming. They’ll need to add DC-blocking capacitors (high-pass filters) between the mic and the amplifier, so this might be a very good time to introduce them to block diagrams. It might also be a good time for small group discussions (groups of 3 or 4 students), designing together what each of the blocks needs to contain.