Notes on Feedback Formula for Negative Gain Summation Op Amp Circuit

Recall the negative gain summation amplifier:

clearly a feedback circuit, but how do we put it in a form like the standard negative feedback model?

¶We can describe the negative gain op amp with the feedback diagram shown below, where g is conductance, and Rin is the 10^12 ohm DC input resistance between + and - pins. The conductances convert voltage to current, and the resistance converts current to output voltage. Notice however the overall gain term Vout/Vin is still dimensionless:

If we take the approximation that RIN >> RF then gF*Rin >> 1 and the original op amp gain of -RF / RS ensues.

If the feedforward gain has a negative sign (as -Rin above does), then the feedback can be positive at the summation point but the overall circuit is still a version of negative feedback. A slightly different expression for output results from the standard form:

which is the same form as the op amp version above.

¶ Note: If we compute IF, we'll see IF = Vout/RF = -(RF/RS) * VS * (1/RF) = -VS/RS = -IS,
implying that its true direction is opposite of the arrow drawn above and that IIN = IS + IF must really be tiny.