# Open (closed) loop gain

For the circuit,

(a) Derive an expression for $Vout/Vin$ if $Ri = ?$, $R0 = 0$ and $A$ is finite.

(b) What value of open loop gain A is required for the closed loop gain to be within 1 percent of its ideal value ?

The + input is at zero potential. $V+=0$. The circuit amplifies until $V- =0$ (the – input is virtual ground).The – input does not draw current (ideal amplifier). It means both the resistances 1 K and 100 K have the same current.

$I*100 K= Vout$

$I*1 K = Vin$

$A(closed) =Vout/Vin = 100/1 =100 (1)$

The relation between open and closed gain is

A(closed) = A(open) / (1+ A(open)*Feedback)]

$Feedback =1/100$

$99%*A(closed) =A/(1+A*F)$

$99 =A/(1+0.01*A)$

$99+0.99*A =A$

$0.01*A =99$

$A(open) =9900$