This feedback-forces-equal-inputs lesson treats negative feedback as an ideal op-amp contract: while the output stays inside the rails, the two input pins are driven to the same voltage. The arithmetic is exact only for the stated 0 V input-node row and ideal high-gain feedback model. Real op-amps have finite gain, input offset, bandwidth limits, slew rate, rail headroom, tolerances, finite precision, and measurement uncertainty.

An ideal op-amp in negative feedback is modeled as an exact equal-input contract. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Negative feedback checks equal input voltages

In the linear ideal model, feedback drives the two input pins to 0 volts together.

V+=V−=0 VV_+ = V_- = 0\ \text{V}
Equal input contractThe op-amp feedback contract is checked at both pins.+-op amprails -12 V to 12 VVout 0 VV+ 0 VV- 0 VI+ 0 AI- 0 AV+ = V-contract

The output is still inside the rails

The output is 0 volts, between the dual rails.

−12 V≤0 V≤12 V-12\ \text{V} \le 0\ \text{V} \le 12\ \text{V}
Linear regionThe equal-input claim is only made away from the rails.+-op amprails -12 V to 12 VVout 0 VV+ 0 VV- 0 VI+ 0 AI- 0 AV+ = V-contract