The gain-bandwidth product is the figure of merit
where is the midband gain and the bandwidth (see Amplifier frequency response). For a given device this product is roughly constant: whatever you do to the design, gain times bandwidth stays about the same. The constancy follows from a single dominant-pole roll-off. With one pole the gain falls at a fixed dB/decade, so the gain–frequency product is fixed; with several comparable poles GB is only an approximation.
Gain and bandwidth are a zero-sum trade
If GB is fixed, then and are inversely linked. Want more gain? You lose bandwidth in proportion. Want more bandwidth? You give up gain. You can’t have both for free: the device only has so much gain-bandwidth to spend, and the design choice is how to allocate it. Same high-frequency counterpart of the gain-versus-headroom trade-off that showed up in Overdrive voltage and MOSFET transconductance.
Deliberately throwing gain away with Source degeneration or Negative feedback doesn’t only buy linearity and predictability, it also buys bandwidth, because the GB you free up by lowering reappears as a larger . The lost gain isn’t wasted, it’s converted.
Reused for the op-amp
The same idea carries straight into the Operational amplifier. An op-amp’s huge Open-loop gain falls off with frequency such that its gain-bandwidth product is constant, quoted on datasheets as the unity-gain frequency , the frequency at which the open-loop gain has dropped to 1. For a closed-loop configuration the bandwidth is then divided by the closed-loop gain, the same GB-is-constant trade applied to a feedback amplifier. One number for the gain-bandwidth budget of any amplifier, transistor stage or op-amp alike.
GB bounds the small-signal bandwidth. It’s distinct from the large-signal Full-power bandwidth, which is limited by Slew rate rather than by GB. An amplifier can sit well within its GB-limited bandwidth and still be slew-rate-limited for large output swings.