# Slew Rate—the op amp speed limit

-June 02, 2013

Slewing behavior of op amps is often misunderstood. It’s a meaty topic so let’s sort it out.

The input circuitry of an op amp circuit generally has a very small voltage between the inputs—ideally zero, right? But a sudden change in the input signal temporarily drives the feedback loop out of balance creating a differential error voltage between the op amp inputs. This causes the output to race off to correct the error. The larger the error, the faster it goes… that is until the differential input voltage is large enough to drive the op amp into slewing.

If the input step is large enough, the accelerator is jammed to the floor. More input will not make the output move faster. Figure 1 shows why in a simple op amp circuit. With a constant input voltage to the closed-loop circuit there is zero voltage between the op amp inputs. The input stage is balanced and the current IS1 splits equally between the two input transistors. With a step function change in Vin, greater than 350mV for this circuit, all the IS1 current is steered to one side of the input transistor pair and that current charges (or discharges) the Miller compensation capacitor, C1. The output slew rate (SR) is the rate at which IS1 charges C1, equal to IS1/C1.

There are variations, of course. Op amps with slew-enhancement add circuitry to detect this overdriven condition and enlist additional current sources to charge C1 faster but they still have a limited slew rate. The positive and negative slew rates may not be perfectly matched. They are close to equal in this simple circuit but this can vary with different op amps. The voltage to slew an input stage (350mV for this design) varies from approximately 100mV to 1V or more, depending on the op amp.

While the output is slewing it can’t respond to incremental changes in the input. The input stage is overdriven and the output rate-of-change is maxed out. But once the output voltage nears its final value the error voltage across the op amp inputs reenters the linear range. Then the rate of change gradually reduces to make a smooth landing at the final value.

There nothing inherently wrong with slewing an op amp—no damage or fines for speeding. But to avoid gross distortion of sine waves, the signal frequency and/or output amplitude must be limited so that the maximum slope does not exceed the amplifier’s slew rate. Figure 2 shows that the maximum slope of a sine wave is proportional to VP and frequency. With 20% less than the required slew rate, output is distorted into a nearly triangle shape.

Large-signal square waves with very fast edges tilt on the rising and falling edges according to the slew rate of the amplifier. The final portion of a rising or falling edge will have rounding as the amplifier reaches its small-signal range as shown in figure 1.

In a non-inverting circuit, a minimum 350mV step is required to make this op amp slew, regardless of gain. Figure 3 shows the slewing behavior for a 1V input step with gains of 1, 2 and 4. The slew rate is the same for each gain. In G=1, the output waveform transitions to small-signal behavior in the final 350mV. In G=2 and G=4 the small-signal portion is proportionally larger because the error signal fed back to the inverting input is attenuated by the feedback network. If connected in a gain greater than 50, this amplifier would be unlikely to slew because a 350mV step would overdrive the output.

Slew rate is usually specified in V/μs, perhaps because early general purpose op amps had slew rates in the range of 1V/μs. Very high speed amplifiers are in the 1000V/μs range, but you would rarely see it written as 1kV/μs or 1V/ns. Likewise, a nanopower op amp might be specified as 0.02V/μs but seldom as 20V/ms or 20mV/μs. There’s just no good reason why for some things; it’s just the way we do it. :-)

I’ve exceeded my word limit yet again! Thanks for hanging in and comments are welcome.

Bruce