# How to solve this non ideal inverter opamp?

it is asked to make a non ideal inverter opamp that has an input of 2mV or and get an output of -100mV, so I think the next circuit should suffice.

simulate this circuit – Schematic created using CircuitLab

But later there is extra questions: the error in the output voltage must be less than 0.1%, ¿What is the gain in open loop of this op-amp?¿What is the error if the gain is 10000?

I understand there should be a Beta parameter

$$\A_{v}^{ideal}=\frac{1}{\beta}=\frac{-5000}{100}=-50\$$

$$\\beta=-0.02\$$

and the closed-loop gain is

$$\A_{v}=-\frac{R_{2}}{R_{1}}(\frac{A\beta}{1+AB})\$$
but then how can be calculated he error or make it is between the limits required?

$$\A_v^{ideal}\$$ is a special case of $$\A_V\$$ when $$\A\$$ is infinitely large.

In that case, $$\\frac{A\beta}{1+A\beta}\$$ equal one (because 1 is negligible compared to infinite $$\A\cdot \beta\$$, so they just cancel out).

If you plug a finite number for $$\A\$$, the fraction will be less than 1. If you want an error smaller than 0.1%, you need that fraction to equal at least 99.9%

• But then whats the meaning of the gain of 1000 that it has been told. I guess is refering to T=10000/50=200, then what? – avelardo Apr 15 at 20:19
• As I understand the question, you should: 1) calculate open-loop gain needed for error less than 0.1% 2) calculate how big would the error be if open-loop gain was 10000 – Jiří Maier Apr 15 at 20:49
• But if it is used the definition of open loop, it does have a meaning, i,e,:Aol=Vout/V+-V-=-100/0--2=-50, so there is no rom for the FGE to be calculated – avelardo Apr 15 at 21:50
• I don't really understand what you meant by this comment. Open-loop gain is Vout/((V+)-(V-)) but (V+)-(V-) is not 2mV, 2mV is on the left side of R1. If it was an ideal op-amp, V+ would always equal V-. In case of real op-amp, difference between V+ and V- is Vout/Aol, which does not equal the 2mV input. – Jiří Maier Apr 15 at 23:25
• Then how it is suggested to calculate(or proposed) the diference (V+)-(V-)? – riccs_0x Apr 16 at 4:49

Solve for A with error on Av reduction, then visa versa.

I’d like to point out each R tolerance must be 0.05% with infinite gain or assume tolerance is 0% or some other combination.