Negative feedback and the virtual-short condition

The open-loop equation

A voltage-feedback op amp can be approximated at DC by $V_o=A(V_+-V_-)$ while the output remains in its allowed range. Large open-loop gain means a small differential input can command a large output. It does not mean the inputs are automatically equal. Input bias current and common-mode restrictions also exist in real devices.

Negative feedback returns an output change to the inverting input so that it reduces the differential error. For a stable linear feedback loop with adequate gain and output headroom, V− becomes close to V+. This is the “virtual short” approximation. No wire shorts the two inputs, and the condition fails when the output saturates, the inputs exceed their common-mode range, or the loop is unstable.

Finite-gain example

In a voltage follower, connect output directly to V− and apply Vin to V+. Then $V_o=A(V_{in}-V_o)$, so gain is A/(1+A). With A = 100000 and Vin = 1 V, output is 0.999990 V and differential input is approximately 10 μV. The result is close to 1 V because the loop can correct the error, not because the open-loop input equation disappeared.

If the allowed output range is assumed to be 0.2–3.1 V on a 3.3 V supply, requesting a 3.2 V follower output violates the assumption. The small-error prediction is invalid. These limits are educational values; a selected real part requires its datasheet conditions, output load, and temperature.

Check feedback direction

Imagine a slight output increase. In the follower, V− increases, the input difference decreases, and the commanded output moves downward. That is negative feedback. Connecting output to V+ instead can reinforce the increase and drive a comparator-like state; the virtual-short rule cannot repair that topology.

Before calculating a resistor gain, draw the feedback path and identify input and output limits. See TI's gain and bandwidth discussion for distinctions between amplifier architectures and compensation requirements.