When an Amplifier Cannot Move Its Output Fast Enough
Large Signals Need Slope, Not Just Bandwidth
An amplifier may have enough small-signal bandwidth and still distort a large, fast waveform. The limit can be slew rate: the maximum speed at which the output voltage can change. When a sine wave asks for a steeper slope than the amplifier can provide, the output no longer follows the curve. It begins to look more like a triangle. This matters in op-amp circuits, audio equipment, data acquisition, function generators, and active filters.
A sine wave changes fastest as it crosses zero, not at its positive or negative peak. That maximum slope grows with both frequency and peak voltage. A small signal can therefore work at a frequency where a larger signal distorts. Slew rate is a large-signal limit, while the familiar gain-bandwidth product mainly describes small-signal behavior. A design has to satisfy both. Passing one check does not guarantee the other.
Frequency should be the highest sine-wave frequency that must reach the stated amplitude. Peak voltage is measured from the waveform center to one peak, not peak-to-peak. Available slew rate should come from the correct data-sheet conditions and preferably the guaranteed minimum rather than a typical headline number. Positive and negative slew rates may differ. Supply voltage, output load, temperature, and amplifier configuration can also affect actual performance.
A Twenty-Kilohertz Ten-Volt Peak Output
The working equation is Required slew rate = 2*pi*frequency*peak voltage. Full-power bandwidth = slew rate/(2*pi*peak voltage).
Multiply two pi by frequency in hertz and output peak voltage. The result is volts per second; divide by one million for volts per microsecond. Compare that requirement with the amplifier's minimum specified slew rate. Rearranging the same equation gives full-power bandwidth: available slew rate divided by two pi and peak voltage. Be careful with amplitude definitions. Ten volts peak means twenty volts peak-to-peak, while an RMS value must first be multiplied by the square root of two.
Model limit: Applies to a sine-wave output. Small-signal bandwidth, settling, load current, stability, and output-voltage limits must be checked separately.
Amplitude Changes Full-Power Bandwidth
A 20 kHz sine wave with 10 V peak has maximum slope 2πfVp = 2π×20,000×10 = 1.257×10^6 V/s, or 1.257 V/µs. An amplifier rated at 2 V/µs has an ideal slew margin of 2/1.257 = 1.59. Its slew-limited full-power bandwidth at 10 V peak is 2/(2π×10) = 0.03183 MHz, or 31.83 kHz. The requested 20 kHz lies below that boundary, but the margin is modest if 2 V/µs is typical rather than guaranteed.
Reducing amplitude to 2 V peak raises full-power bandwidth fivefold to about 159 kHz without changing the amplifier. Conversely, interpreting 20 V peak-to-peak as 20 V peak would double the calculated requirement incorrectly. Small-signal gain-bandwidth, output-current capability, settling, common-mode range, and rail swing remain separate constraints. On the bench, increase sine frequency at the required amplitude and watch for straightened slopes and rising distortion. Check both rising and falling edges because positive and negative slew rates can differ. Repeat at the worst expected load and temperature, since the headline data-sheet value may not cover either condition.
Scope Clues and Data-Sheet Limits
The most common error is entering peak-to-peak voltage as peak voltage, which doubles the required result. Another is treating full-power bandwidth as ordinary closed-loop bandwidth. Full-power bandwidth is the sine-wave frequency limit set only by slew rate at a particular amplitude. The circuit may hit its gain-bandwidth, settling-time, output-current, or voltage-swing limit first. Square waves also contain fast edges and many harmonics, so a sine-wave slew calculation does not fully predict their shape.
A margin of one means the ideal sine wave is exactly at the stated limit, which leaves no room for tolerance or changing conditions. More margin reduces the chance of slew-induced distortion, but the appropriate amount depends on the application and data-sheet guarantees. Full-power bandwidth falls when output amplitude rises. If the result is lower than the required operating frequency, reduce the swing, choose a faster amplifier, or reconsider the circuit gain and signal range.
On the bench, drive the circuit with a clean sine wave at the required amplitude and increase frequency while watching the output. Slew limiting often appears as straightened slopes and rising distortion before the amplitude falls dramatically. Check both polarities and the actual load. Use a probe and oscilloscope setup with enough bandwidth so the measurement equipment does not create the shape you are trying to diagnose.
Document signal frequency, peak and peak-to-peak amplitude, required slew rate, the amplifier's guaranteed value, supply rails, load, and closed-loop gain. Then check small-signal bandwidth and settling separately. Keeping large-signal speed distinct from small-signal response prevents a common design surprise: a circuit that looks fine in a bandwidth calculation but cannot reproduce the waveform it was built to handle.