What is the ideal op-amp model and the meaning of a virtual short in negative feedback?

• A. The ideal op-amp has infinite gain and zero input impedance; with negative feedback, V+ ≈ V− (virtual short).
• B. The ideal op-amp has infinite gain and infinite input impedance; with negative feedback, V+ ≈ V−.
• C. The ideal op-amp has finite gain and infinite input impedance; with negative feedback, V+ ≈ V−.
• D. The ideal op-amp has infinite gain and infinite input impedance; with negative feedback, V+ ≈ V− (virtual short).

Answer: (D)

The essential idea is that with negative feedback, an ideal op-amp behaves so that the voltages at its two input terminals become essentially equal. In the ideal model, the gain is infinite and the input impedance is infinite, so the amplifier reacts to even the tiniest difference between V+ and V− by driving the output to make that difference vanish. The result is V+ ≈ V−, even though the inputs are not physically connected; this is the virtual short. The reason it’s called “virtual” is that it looks like a short circuit in voltage between the inputs, but no current actually flows between them because the input impedance is infinite. In real op-amps the difference is not exactly zero, but with very large gain the virtual-short idea remains a good approximation.