Output range, bandwidth, and slew rate are separate limits

Start with the allowed DC region

An op amp's supply range, input common-mode range, output swing, output current, and stability requirements are distinct specifications. “Rail-to-rail” needs datasheet conditions and does not imply zero distance from both rails under any load. In this educational example, assume 3.3 V supply and usable output 0.2–3.1 V. With Vref = 1.65 V and gain 11, maximum symmetric output excursion is 1.45 V, corresponding to approximately 131.818 mV at the input.

Small-signal bandwidth

For a suitably compensated, approximately single-pole voltage-feedback op amp, estimate closed-loop bandwidth as GBW divided by noise gain. A 1 MHz GBW and noise gain 11 give approximately 90.909 kHz. This is an approximation, not a universal rule for current-feedback or decompensated amplifiers. An inverting signal gain of −10 has noise gain 11, so using 10 for that estimate is incorrect.

At 10 kHz, a one-pole closed-loop stage with 90.909 kHz bandwidth retains approximately 0.9940 of its low-frequency gain and has about −6.28° phase lag. Further poles, capacitive loading, and layout can change that result. Verify the actual device's stability guidance.

Large-signal speed

A sinusoidal output of peak amplitude Vp requires maximum slope $2\pi fV_p$. At Vp = 1 V and f = 10 kHz, this is 0.062832 V/μs. An assumed slew rate of 0.5 V/μs supports that slope, while 100 kHz would require 0.628319 V/μs and exceed it. A small-signal AC plot does not reveal slew-induced large-signal distortion.

For a 2 V output step, the same slew limit implies at least 4 μs of transition, excluding settling and other dynamics. Check amplitude, bandwidth, and slew rate together; passing one does not pass all three. TI's architecture discussion provides context for the assumptions behind gain-bandwidth relationships. All example limits here are fictional design inputs rather than specifications of a named part.