= Finite-input-resistance inverting amplifier
{title2=$G=-\dfrac{R_2/R_1}{1+(1+R_2/R_1+R_2/R_{\rm in})/A}$}
With the noninverting input grounded, a differential <input impedance> $R_{\rm in}$ draws current from the summing node. For zero <output impedance>, $V_o=-Av$ and <Kirchhoff's current law> gives $(v-V_i)/R_1+(v-V_o)/R_2+v/R_{\rm in}=0$. Eliminating $v$ yields the displayed <voltage gain>. The resistor-ratio result requires $|A|\gg1+R_2/R_1+R_2/R_{\rm in}$ as well as stable, unsaturated operation. The same expression applies to small-signal <phasors> with complex $A(f)$.
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