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E3 · op-amp

Slew Rate: The Speed the Output Cannot Keep Up With

GBW was a small-signal limit. Large signals have a different wall. Raise the input frequency yourself and see the slew-rate limit, where the output cannot change faster than a fixed speed and a sine distorts into a triangle.

Raise the frequency and watch the output lag

The faint curve is the input sine and the bold curve is the output. Raise the input frequency. When slow, the output follows the sine faithfully, but when fast the output can only rise and fall at a fixed maximum speed, so the sine distorts into a triangle.

Input frequency f> f_slew
Slope demand and slew rate
2πfA = 2.7 × SR
slew-limited
The frequency is high, so the slope the sine demands far exceeds the slew rate. The output rises and falls only on straight ramps, becoming a triangle.
Slew-limited · triangle

The output cannot change faster than a fixed speed

Inside an op-amp there is a compensation capacitor for stability, and for the output to change this capacitor must be charged or discharged. But the internal current that does this is finite. The rate at which a capacitor’s voltage changes is the current divided by the capacitance, so there is a fixed maximum speed at which the output can change per unit time. This is the slew rate, often written in volts per microsecond. SR = Imax / C.

Too fast and the sine becomes a triangle

A sine is steepest as it crosses zero, and that slope is proportional to the product of amplitude and frequency. When a large amplitude or high frequency pushes this slope past the slew rate, the output has no way to follow the sine’s curve and simply rises and falls on straight ramps at ±slew rate. So the output sine distorts into a triangle. This is an effect that appears only for large signals; at the same frequency a small amplitude demands a smaller slope and follows just fine. It is a different face from the small-signal GBW limit.

And the voltage limit: rail clipping

Large signals have not only a wall of speed but also a wall of height. No matter how hard you push, the output cannot go beyond the supply rails. Raise the amplitude until the peaks reach the positive or negative supply, and everything beyond is sliced off flat. This is the output voltage limit, that is, rail clipping. In sum, an op-amp has two large-signal walls: the slew rate that caps the speed of change per unit time, and the supply rails that cap the height of the amplitude. Add the small-signal GBW to these, and the full boundary of what a real op-amp can do is drawn.

ObserveSR = Imax / C
The slew rate is the internal maximum current over the compensation capacitance.
Chooseslope = 2π f ?
The sine’s steepest slope is amplitude times frequency times 2π.
Fill in2π f A < ?
Only if this slope is below the slew rate does it follow cleanly.
On your ownfmax = SR / (2π ?)
The larger the amplitude, the lower the frequency reachable without slewing.

Back to the first screen

When the frequency was low, the output followed the input sine without a flaw. As you raised the frequency, the slope the sine demanded grew steeper, and past a point the output could no longer keep up and rose and fell only on straight ramps, becoming a triangle. The boundary was whether the sine’s steepest slope exceeded the slew rate. This is a wall of speed that appears only for large-amplitude signals, a different limit from the small-signal GBW. Add to it the wall of height, where the output cannot pass the supply rails, and the true face of the op-amp behind the ideal of infinite gain is revealed.

If GBW (E2) is a small-signal limit, large signals have another wall. The slew rate SR = Imax/C is the maximum speed at which the output can change per unit time. When the input demands a slope steeper than SR (a sine demands 2πfA), the output cannot follow the sine and rises and falls on straight ramps at ±SR, distorting the sine into a triangle (slew distortion). The output also cannot pass the supply rails, so a large amplitude is clipped. The slew rate (max speed) and the rails (max amplitude) are the large-signal limits of an op-amp.

What comes next

You have seen both the ideal and the limits of the op-amp. In the last op-amp unit we shape it into use with RC. Combining the way resistors and capacitors change their impedance with frequency with the op-amp’s large gain makes an active filter that passes only a chosen band of frequencies and presses the rest down. It is a tool for selecting just the part of a signal you want.