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.