Suggested references: CA3080 and LM13700 datasheets (available from Aaron's datasheet collection)
a) Assuming that the OTA is operating in a nicely linear region, give an expression relating the output voltage to the input voltage in terms of the current at the control input pin of the OTA. Treat the OTAs and op amps as ideal. (You'll see a substantial amount of circuitry devoted to creating about that current. Don't worry about that now; we'll look at that sort of stuff in another week or so.)
0) VCA from www.synthdiy.com, attributed to Mikko Helin
1) Polyfusion 2010 VCA (see also here) - There's several places to trim offsets that we'll ignore; basically, set the + terminals on the 3080 and the TL081 to ground. Set the gain trim pot wherever you feel like it. Let's see what else... Oh, notice the clever current mode filter (probably designed to dump out noise) between the 3080 and the TL081 - really high frequencies get dumped to ground. You may ignore that in your analysis.
2) Serge Lin/Log VCA - Ignore the audio DC input; just ground the - terminal on the 3080. The cap at the audio AC input is just blocking DC, just short it in your analysis. Ignore the audio trimming circuitry. The 33K running from the + terminal on the TL071 to ground is just compensating for nonideal input currents, you may ignore it. You may also neglect the capacitor in the feedback loop of the TL071; open it, it's just there to cut out noise.
3) Aaron Cram's Apache VCA - Let's just ground the inverting input, and look the "input" to "signal out" relation.
4) Bergfotron CA3080 VCA 1 - Don't worry about the offset trim; just ground the + terminal of the 3080. (Am I imagining things, or does does this VCA invert the signal?)
5) Bergfotron CA3080 VCA 2 Don't worry about the offset triml just ground the + terminal of the 3080. (Am I imagining things, or does does this VCA invert the signal?)
6) Ray Wilson's Dual Voltage Controlled Amplifier - you can analyze either VCA-1 or VCA-2; the basic OTA/Op-Amp follower core of each VCA is the same. You may ignore (open) the cap in the feedback loop.
7) Dirk Lindhof's Exponential VCA - ignore the caps at the inputs; they just block DC. This module has two inputs; it looks like IN2 gives you the option of bypassing the DC blocking cap on that channel. Anyway, just do the analysis for one input. Ignore the trimming circuitry, i.e. just ground the + input on the 3080.
8) ASM-1 VCA - This one has inverting and non-inverting inputs; let's focus on the "+ Input," so ground the + terminal on the 3080. You may ignore (open) the feedback cap on the TL082 in your analysis.
9) PAiA 9710 VCA - Take a look at the bottom part of the diagram; you'll find the LM13600. You may ignore the op amp's feedback cap; you may also ignore the trimming ladder on the + terminal of the LM13600 and just ground that + terminal.
b) What is the input impedance of this VCA?
c) What is the output impedance of this VCA? (It might be "0" - remember we're assuming ideal op amps.)
d) What input voltage to the VCA corresponds to 10 mV at the main signal input pin of the OTA? (In class, we used 10 mV as a rough figure for where the OTA starts to become nonlinear; but you shouldn't consider this number etched in stone. For instance, the LM13700 has special diodes that can be used to give you a wider linear range. We're just using 10 mV in this subpart to keep things simple).
You may readily find such an example in the VCA-based OTA circuit you analyzed above; if not, look around at some of the other examples in that list until you find one.
a) Let's look at the AC input of the Serge VCA linked to above. The input capacitor and the two resistors form a single-pole highpass filter. Find its cutoff frequency. (Note the resistor in series with the cap gives this configuration a non-unity gain.)
b) Check out this link. What kinds of capacitors does the author recommend for use as DC blocking (i.e. "audio coupling") capcitors?
