You designed an op-amp circuit with 10 MHz gain-bandwidth product, verified the small-signal Bode plot, and cranked up the signal. Suddenly a 100 kHz sine wave looks like a triangle wave. Welcome to slew rate limiting — the large-signal cousin of bandwidth that ambushes designers who only think in small-signal terms.

Slew rate (SR) is the maximum rate the output can change, in volts per microsecond. It's set by the internal compensation capacitor C_c and the tail current I_tail of the input differential pair: SR = I_tail / C_c. When the input step is large enough to steer all the tail current into one side, the compensation cap charges at a constant rate — the amplifier becomes an integrator, not a linear system.

The full-power bandwidth formula: for a sine wave V_p·sin(2πft), the peak slope is 2πfV_p. To avoid distortion:

• f_max = SR / (2π · V_p)

Concrete example: the classic LM358 has SR = 0.6 V/μs. You want a 10 V peak-to-peak sine wave (V_p = 5 V) at the output. Maximum undistorted frequency:

• f_max = (0.6 × 10⁶) / (2π × 5) ≈ 19 kHz

Even though the LM358's GBW is 1 MHz, above 19 kHz your 10 Vpp sine wave turns into a lopsided triangle. Drop the amplitude to 100 mV_p and you get back to nearly the full 1 MHz — small signals don't slew-limit.

Practical consequences:

• Audio amplifiers need SR ≥ 2πf_maxV_p. For a 20 V_p output at 20 kHz: SR ≥ 2.5 V/μs. Use ≥ 5 V/μs for margin against harmonic distortion.
• Video and pulse circuits care about rise time. A slew-limited op-amp gives t_r ≈ ΔV / SR, independent of frequency response.
• Comparator misuse: using a slow op-amp as a comparator gives output slew times measured in microseconds, wrecking timing accuracy.
• Slew-induced distortion (SID/TIM): even at frequencies below f_max, transients that momentarily exceed SR cause the feedback loop to open briefly — audible as harsh distortion on percussive material.

Rule of thumb: pick SR at least 3–5× the theoretical minimum. For general-purpose 12 V systems handling signals up to 100 kHz, target 20+ V/μs (LM7171, LT1360, AD8065 territory). For precision DC work you often want a slow op-amp on purpose — high SR usually costs input offset voltage.