the gain-bandwidth product
/ GBW or GBP /
An op-amp comes with a fixed speed budget, and the gain-bandwidth product is the size of that budget. Think of it as a fixed amount of money: you can spend it on a lot of gain or on a lot of bandwidth, but not both. Want more gain? You get less bandwidth. Want more bandwidth? Settle for less gain. The two multiply to a constant, and that constant is printed on the datasheet.
Formally, the gain-bandwidth product is the frequency at which the op-amp's open-loop gain falls all the way to 1 (0 dB). Because a compensated op-amp's gain rolls off smoothly at 20 dB per decade, the product of (closed-loop gain) times (bandwidth) stays equal to the GBW at every gain setting. Example: a 1 MHz GBW op-amp set for a gain of 10 gives a bandwidth of 1 MHz / 10 = 100 kHz; set for a gain of 100 it gives only 10 kHz. To get 100 kHz of bandwidth at a gain of 100 you need an op-amp with a GBW of at least 10 MHz.
Why this matters: GBW is the first number to check when you size an op-amp for an AC signal. Pick one whose GBW comfortably exceeds (your gain times your highest signal frequency), with margin to spare since the gain has already sagged before you reach the bandwidth limit. The honest catch: GBW describes only small signals. Large fast signals run into a different, harder wall — the slew rate — so a circuit can have plenty of GBW yet still distort a big waveform.
You need a gain of 50 over a 20 kHz audio band. The product is 50 times 20 kHz = 1 MHz, so a 1 MHz GBW op-amp is exactly on the edge (and the gain is already down 3 dB there). Choose a 5 to 10 MHz part so the gain stays flat across the whole band.
Gain times bandwidth is a constant — choose an op-amp with GBW to spare.
GBW assumes the single-pole roll-off that internal compensation creates. Decompensated op-amps (only stable above some minimum gain) break this simple rule but offer more bandwidth where you can use them.