An operational amplifier, or op-amp, is a high-gain differential amplifier with two inputs and one output.

An idealized open-loop relation is

$$v_o=A(v_+-v_-),$$

where the gain $A$ is treated as extremely large.

The ideal op-amp also has infinite input resistance, so

$$i_+=i_-=0,$$

and zero output resistance.

When negative feedback keeps the amplifier operating away from saturation, the very large gain forces the differential input voltage to be very small. In the ideal limit,

$$v_+\approx v_-.$$

This equality is not an independent device law and does not hold for arbitrary open-loop operation. It is a consequence of high gain together with a feedback configuration that can settle to a linear operating point.

The ideal model makes many useful amplifier circuits analyzable using only Kirchhoff's laws and these two input conditions.