Gain-Bandwidth Product: Gain and Speed Are a Trade
Lower the closed-loop gain and watch the band widen
The faint falling line is the open-loop gain dropping with frequency. The bold line is the closed-loop gain set by feedback: flat until it meets that falling line, where it bends and falls along with it. That bend is the bandwidth. Lower the closed-loop gain.
Infinite gain is a fiction: gain falls off
We learned an ideal op-amp has infinite gain, but a real device differs. At low frequency the open-loop gain is very large (often around a hundred thousand), but above some low dominant frequency the gain falls by -20 dB, that is, by a factor of ten, for every tenfold rise in frequency. On a Bode plot with a logarithmic frequency axis, the open-loop gain is flat and then a straight line sloping down at a constant rate. The frequency where this line meets a gain of 1, that is 0 dB, is the unity-gain frequency.
Lower the closed-loop gain, widen the band
With feedback, the closed-loop gain stays flat at the low value we chose. But as frequency rises and that flat line meets the open-loop line sloping down, there is no longer any way to hold that gain, and from there it falls along with it. The frequency of that meeting point is exactly the bandwidth of the closed-loop amplifier. So lowering the closed-loop gain places the flat line lower, meeting the open-loop line further right, at a higher frequency, and the bandwidth widens by that factor.
Gain × band = constant = GBW
Because the slope of the open-loop line is constant, the product of the closed-loop gain and its bandwidth is always the same value, wherever you cut. That value is exactly the unity-gain frequency where the open-loop gain falls to 1, and it is called the gain-bandwidth product, GBW. GBW is a fixed spec the device is born with. So if you want large gain you accept a narrow band, and if you want a wide band you accept a small gain. One amplifier cannot raise both; if you need more, you split the gain across stages or use a device with a larger GBW.
Back to the first screen
With the closed-loop gain set high, the flat line met the open-loop line early and bent at a narrow band. As you lowered the gain, that bend slid right and the band widened. All the while the product of gain and bandwidth did not change one bit, because the open-loop gain falls at a constant slope. That fixed product is GBW, the unity-gain frequency where the gain drops to 1. The ideal of infinite gain holds only at low frequency; in reality you must trade gain for speed. This is the first real-world limit of the op-amp.
What comes next
GBW set the limit of how fast a frequency a small signal can follow. But when the signal is large, another wall appears. The next unit looks at the slew rate, the maximum speed at which the output can change per unit time, and the voltage limit, where the output cannot exceed the supply rails. The small-signal limit and the large-signal limit are different faces.