Hello
How do I calculate the ROUT

 

the super fast answer is you either divide or multiply the output/input resistance by the loop gain T + 1 depending on if your input/output is series or shunt. So in this case, to find Rin since the summing junction is in series, you multiply whatever Rin is by T+1. For the output resistance you would divide it by T+1 since its shunt. T is set by your open loop gain μ and your feedback network β. T is also what sets your error percentage among a lot of other things... In general, the higher T is, the more ideal your circuit will behave!

T is equal to a(μ for sedra smith)Xβ

β is simply the resistive divider of how much of Vout is fed back to the summing junction.

for a), R1 = 100Ω , R2 = 10kΩ, Rl=1kΩ and r=100Ω. To find β, just imagine we apply a voltage at the output of the op amp (with it disconnected) and find the fraction we get at the negative pin of the op amp and that is what β is. For this case, the easiest way is to see r//(R2+R1) as a voltage divider with Rl, then you will have the voltage above r which you can apply another voltage divider to find the voltage at R1.
Then just multiply βx100,000 and divide Rout with it

for b) now we have R1 is an open circuit, and since R2 will have near zero current we can assume the voltage at the negative pin is the same as above r, which is just a voltage divider of Vout
(r/r+Rl)xVout
... if you are still stuck post back.

 

the super fast answer is you either divide or multiply the output/input resistance by the loop gain T + 1 depending on if your input/output is series or shunt.

Fine - a very comprehensive answer.
Just to avoid misunderstandings:
* "output/input resistance" are properties from the opamp alone;
* T is the loop gain neglecting the negative sign (because the loop gain for negative feedback always is negative) and (T+1) is the factor for multiplikation/division.