Negative Feedback and Gain Desensitization
The larger the raw gain, the more the gain locks onto 1/β
Slide the raw gain, the open-loop gain A, and the dot on the curve moves to the closed-loop gain at that setting. With negative feedback the closed-loop gain is G = A/(1+Aβ), where β is the fraction of the output fed back to the input. When A is small G is small too, but once the loop gain Aβ is much greater than 1, G approaches 1/β and stops there, regardless of A. With β = 0.1 the ideal gain is 10, the height of the green dashed line. Raise A until the closed-loop gain reaches the ideal value of 10.
Feedback trims the gain
An amplifier's raw gain A is enormous, but it varies from part to part and swings with temperature and frequency, so it cannot be trusted as is. Negative feedback takes a fraction β of the output and subtracts it at the input. The input the amplifier actually sees then shrinks, and the closed-loop gain G = A/(1+Aβ) becomes smaller than the raw gain. The Aβ in the denominator is called the loop gain: the total factor a signal is multiplied by on one trip around the amplifier and feedback network.
With large loop gain, the amplifier drops out
When the loop gain Aβ is much greater than 1, the denominator becomes 1+Aβ ≈ Aβ and the gain simplifies to G = A/(Aβ) = 1/β. A has cancelled out of the closed-loop gain and vanished. So the gain is set not by the amplifier's fickle A but by the reciprocal of the feedback fraction β, fixed precisely by a few resistors. In the non-inverting amplifier, the gain 1/β = 1 + Rf/Rg was exactly this result, and the virtual short tells the same story in the language of circuits.
Desensitization buys precision
Even if A doubles, the closed-loop gain barely moves. Precisely, the relative change in G is the relative change in A shrunk by 1/(1+Aβ), so the larger the loop gain, the less sensitive it is. That is how a cheap, enormous but imprecise raw gain is traded, through negative feedback, for a small but precise and stable gain. It is also why the ideal op-amp's virtual short holds so well: A is practically infinite, the loop gain is overwhelming, and the closed-loop gain is locked completely at 1/β. Negative feedback is a trade that turns surplus gain into precision and stability.
Back to the first screen
As you slid the raw gain A, the closed-loop gain G grew along with it at first, but once the loop gain Aβ passed 1, G stopped growing and settled near the ideal value 1/β = 10 on the green dashed line (β = 0.1). Even as you raised A all the way to the end of the axis, G did not budge from around 10. A had cancelled out of the closed-loop gain, leaving only the precise β. An enormous but untrustworthy raw gain became, through negative feedback, a small but trustworthy gain, and this desensitization is exactly why op-amp circuits solved so cleanly with the virtual short.