Why an amplifier can distort a perfectly clean signal at high frequency — even one well inside its rated bandwidth.
Slew rate is the maximum rate of change an amplifier's output voltage can physically achieve, specified in volts per microsecond (V/µs). It's a hard physical limit set by how much current is available internally to charge the amplifier's own compensation capacitance — and it has nothing to do with the amplifier's small-signal bandwidth or gain-bandwidth product. Ask an amplifier to move its output faster than its slew rate allows, and it simply can't. The output doesn't get quieter or lose a bit of gain — it changes shape entirely.
For a sine wave v(t) = A·sin(2πft), the steepest point on the curve — right as it crosses zero — has a slope of exactly 2πfA. That is the peak rate of change (dV/dt) the amplifier's output must be able to deliver to reproduce that sine faithfully. Notice it depends on boththe amplitude A and the frequency f: doubling either one doubles the required slew rate. As long as 2πfA stays below the amplifier's maximum specified slew rate, the output tracks the sine perfectly. The instant it exceeds that limit, the amplifier's output can no longer keep up with the curve's steepest sections — it slews at its own maximum rate instead, and the once-smooth sine collapses toward a triangular, ramped shape.
Small-signal bandwidth and gain-bandwidth product are measured with a small output swing, where slewing is never an issue — they describe a smooth, amplitude-independent rolloff in gain that never changes the waveform's shape. Slew-rate limiting is a completely different failure mode: an amplitude-dependent, large-signal effect that distorts the waveform's shape outright, turning a sine into a triangle-like ramp. An amplifier can have plenty of gain-bandwidth product to theoretically pass a given frequency — and still badly distort a large-amplitude signal at that same frequency purely because the required slew rate (proportional to amplitude × frequency) exceeds what it can physically deliver. This is exactly why datasheets list slew rate as a separate parameter from gain-bandwidth product, and why full power bandwidth — the highest frequency at which the amplifier can still deliver its full rated output swing without slew-rate distortion — is its own, generally lower, specification than small-signal bandwidth.
Ordinary small-signal bandwidth rolloff comes from a linear RC-like response: past the corner frequency, gain falls off smoothly and the output is still a sine wave — just a smaller one, still recognizably sinusoidal. Slew-rate limiting is a nonlinear, current-starved effect: the amplifier's internal stages simply run out of available current to charge internal (often compensation) capacitance fast enough, so the output ramps at a fixed maximum rate regardless of what the ideal waveform is doing. The two failure modes look completely different on a scope for exactly that reason — one shrinks the sine, the other turns it into a ramp — and they're driven by different variables: bandwidth rolloff cares only about frequency, while slew-rate distortion cares about the product of frequency and amplitude, which is why full power bandwidth (the frequency at which slewing starts to distort the amplifier's full rated output swing) is measured and specified completely separately from, and is typically well below, small-signal bandwidth.
Bandwidth and slew rate are two separate specifications that can fail completely independently of each other, and this misconception collapses them into one. Small-signal bandwidth is typically measured at a low output amplitude, where slewing never enters the picture — it says nothing about what happens at large output swings. A signal sitting comfortably inside an amplifier's rated bandwidth can still come out badly distorted if its amplitude is large enough that the required slew rate — proportional to amplitude × frequency — exceeds the amplifier's maximum slew-rate rating. That's precisely why full power bandwidth exists as its own datasheet specification: it accounts for slew-rate limits at the amplifier's full rated output swing, and it is typically lower than the small-signal bandwidth figure quoted elsewhere on the same datasheet.
Explains why an amplifier's slew rate — the maximum rate of change its output can physically achieve, in volts per microsecond — is a completely separate limit from its small-signal bandwidth, and why a large-amplitude signal at a frequency well within an amplifier's rated bandwidth can still come out visibly distorted, turning from a clean sine into a triangular, ramped waveform.
Bandwidth and slew rate both describe how an amplifier behaves at high frequency, so it's natural to assume that staying within one automatically means staying within the other. They don't move together. Small-signal bandwidth is measured at a low output amplitude where the amplifier is never asked to move quickly in absolute voltage terms, so slewing never enters the picture. Slew rate is a large-signal, amplitude-dependent limit that has nothing to do with the amplifier's gain or small-signal frequency response — a signal can sit well inside an amplifier's bandwidth spec and still exceed its slew-rate capability purely because its amplitude, not its frequency alone, is large.
Slew rate is set by how much current is available internally to charge the amplifier's own compensation (or other internal) capacitance — a hard, current-limited ceiling on dV/dt, expressed in V/µs. For a sine wave v(t) = A·sin(2πft), the steepest instantaneous slope occurs at the zero crossings and equals 2π·f·A. Whenever 2π·f·A stays below the amplifier's rated slew rate, the output tracks the ideal sine exactly. The moment 2π·f·A exceeds that rating, the amplifier can no longer follow the curve's steepest sections; its output instead ramps at its own fixed maximum rate, producing a waveform that looks progressively more triangular as the required rate climbs further past the limit. Because the required rate scales with the product of amplitude and frequency, either one — raised far enough on its own — can push a signal into slew-rate distortion.
This is exactly why op-amp datasheets list slew rate as a parameter entirely separate from gain-bandwidth product, and why full power bandwidth — the highest frequency at which the amplifier can still deliver its full rated output swing without slew-rate distortion — is specified as its own, generally lower, figure than small-signal bandwidth. Designers pushing large-amplitude signals at high frequency (audio power stages, video amplifiers, high-swing signal conditioning) must check full power bandwidth specifically, since checking small-signal bandwidth alone can pass a design that will still visibly distort under real large-signal operating conditions.
Small-signal bandwidth describes a smooth, amplitude-independent reduction in gain at high frequency — the output waveform stays sinusoidal, just smaller. Slew rate is a large-signal, amplitude-dependent hard limit on how fast the output voltage can physically change, set by internal current limits charging internal capacitance. A signal can be well within an amplifier's bandwidth and still get badly distorted in shape if its amplitude makes the required slew rate exceed the amplifier's rating.
Full power bandwidth is the highest frequency at which an amplifier can still deliver its full rated output voltage swing without slew-rate distortion. Because the required slew rate for a sine wave scales with amplitude times frequency, asking for the full rated (large) output swing demands a much higher slew rate at a given frequency than a small-signal test does — so the frequency at which slewing starts to distort a full-swing signal is reached sooner (at a lower frequency) than the frequency where small-signal gain rolls off.
A sine wave whose peaks and zero-crossing regions get replaced by straight, constant-slope ramps, giving the waveform an increasingly triangular appearance as the required slew rate climbs further past the amplifier's rating. This is visually and mechanically distinct from ordinary bandwidth rolloff, which shrinks the sine's amplitude but preserves its curved, sinusoidal shape.
Yes, for a fixed frequency — since the required slew rate is proportional to amplitude, reducing amplitude proportionally reduces the required slew rate. This is also why the same amplifier can pass a small-amplitude high-frequency test signal cleanly while badly distorting a large-amplitude signal at that identical frequency: the required slew rate scales with amplitude, not frequency alone.
No — gain-bandwidth product and slew rate are set by different internal design factors (small-signal loop gain and pole placement versus available bias current and compensation capacitance) and datasheets specify them separately for exactly that reason. It is entirely possible for one amplifier to have a higher gain-bandwidth product but a lower slew rate than another, so both specifications need to be checked independently against a design's actual signal amplitude and frequency requirements.
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