Normally, if you want to control the gain of an amplifier, you’ll use a variable resistor. You know, like a volume control. But what if you want to control the amplifier’s gain with a voltage? [Engineering Prof] explains a circuit that can do this using a pair of op amps and a pair of matched JFETs.
The analysis is simple because you assume the op amps are not in saturation, so you can assume that the op amp will do what it needs to do to make the input terminals equal. The left-hand op amp has one input grounded, so the output will drive the first FET to ensure the negative terminal is also 0V. It is easy to see that the current through R1 must then be the current through the FET, which is going to be the control voltage (which is negative) divided by R1.
