# non-ideal op amp closed-loop gain derivation

How do I derive an expression for v_o / v_s?

This answer fills some gaps but it doesn't tell me how they came up with the expression for V^- (corresponding to -v_d in my notation).

ETA: here's what I've worked out. This seems correct but also seems to imply that the expected answer $$\frac{v_o}{V_{s}}=-\dfrac{R_2}{R_1+\dfrac{R_1+R_2}{A} }$$ isn't exactly correct since it doesn't account for the input resistance. I understand that it's negligible, etc. but I'd still like to find an exact expression.

• By defining the Vcm range Aug 12 at 4:07
• Rob, for a standardized approach it's just nodal analysis. Do you know how to apply it?
– jonk
Aug 12 at 4:09