Ideal operational amplifier

An ideal operational amplifier has infinite open-loop gain and input impedance, zero output impedance, unlimited response speed and zero input offset voltage and input bias current. Its input currents vanish. In a stable linear circuit with negative feedback and a finite output, its differential input voltage tends to zero as the open-loop gain tends to infinity. Thus $i_{+}=i_{-}=0$ and $v_{+}=v_{-}$ are the familiar conditional circuit rules. The equality of the input voltages cannot be imposed on an open-loop, unstable or saturated circuit.

Connect a resistor $R_{\mathrm{in}}$ from the input source to the inverting input, a feedback resistor $R_f$ from output to that same input, and ground the non-inverting input. For ideal linear operation the inverting node is a virtual ground. Kirchhoff's current law gives $V_i/R_{\mathrm{in}}+V_o/R_f=0$, yielding the displayed voltage gain. The source sees input impedance $R_{\mathrm{in}}$, even though the amplifier input itself has infinite input impedance.