gain–bandwidth product (GBW)

Imagine an amplifier has a fixed budget of "speed times strength," and you get to decide how to spend it. You can ask for huge gain, but then the amplifier only keeps that gain over a narrow band of low frequencies; or you can settle for modest gain and enjoy it out to much higher frequencies. You can't have both at once. For most op-amps and single-stage amplifiers, the product of the gain you use and the bandwidth you get is roughly constant — that constant is the gain–bandwidth product, and it sets the ceiling on what the part can do.

The reason is a single dominant pole in the frequency response: above that pole the gain rolls off at a steady 20 dB per decade, meaning every time frequency goes up 10x, the available gain drops 10x. So gain x frequency stays fixed all along that slope. The point where the curve crosses a gain of 1 (0 dB) is the unity-gain frequency, and for a dominant-pole amplifier that crossover frequency is essentially the GBW itself. If a part is spec'd at GBW = 10 MHz and you configure it for a closed-loop gain of 100, your usable bandwidth is only about 10 MHz / 100 = 100 kHz. Want more bandwidth? Use less gain per stage and cascade stages, or pick a faster (higher-GBW) part.

This is why GBW is one of the first numbers you check when picking an amplifier: it's the single figure that tells you the speed-versus-gain trade you're allowed to make. It pairs naturally with slew rate (the large-signal speed limit) — GBW governs how fast small signals can wiggle, slew rate governs how fast big ones can swing.