# Slew rate

slew rate effect on a square wave: red= desired output, green= actual output

In electronics, slew rate is defined as the maximum rate of change of output voltage per unit of time and is expressed as volt per micro second. Limitations in slew rate capability can give rise to non linear effects in electronic amplifiers. For a sinusoidal waveform not to be subject to slew rate limitation, the slew rate capability (in volts per second) at all points in an amplifier must satisfy the following condition:

$\mathrm{SR} \ge 2\pi f \times V_{\mathrm{pk}},$

where f is the operating frequency, and $V_{\mathrm{pk}}$ is the peak amplitude of the waveform.

In mechanics the slew rate is given in dimensions 1/T and is associated with the change in position over time of an object which orbits around the observer. Slew rate can also be measured in degrees per second.

## Definition

The slew rate of an electronic circuit is defined as the maximum rate of change of the output voltage. Slew rate is usually expressed in units of V/µs.

$\mathrm{SR} = \max\left(\left|\frac{dv_\mathrm{out}(t)}{dt}\right|\right)$

where $v_\mathrm{out}(t)$ is the output produced by the amplifier as a function of time t.

## Measurement

The slew rate can be measured using a function generator (usually square wave) and oscilloscope. The unit of slew rate is typically V/µs. The slew rate is same for both when feedback is considered or not considered.

## Slew rate limiting in amplifiers

There are slight differences between different amplifier designs in how the slewing phenomenon occurs. However, the general principles are the same as in this illustration.

The input stage of modern amplifiers is usually a differential amplifier with a transconductance characteristic. This means the input stage takes a differential input voltage and produces an output current into the second stage.

The transconductance is typically very high — this is where the large open loop gain of the amplifier is generated. This also means that a fairly small input voltage can cause the input stage to saturate. In saturation, the stage produces a nearly constant output current.

The second stage of modern power amplifiers is, among other things, where frequency compensation is accomplished. The low pass characteristic of this stage approximates an integrator. A constant current input will therefore produce a linearly increasing output. If the second stage has an effective input capacitance $C$ and voltage gain $A_{2}$, then slew rate in this example can be expressed as:

$\mathrm{SR} = \frac{I_\mathrm{sat}}{C}A_2$

where $I_\mathrm{sat}$ is the output current of the first stage in saturation.

Slew rate helps us to identify what is the maximum input frequency and amplitude applicable to the amplifier such that the output is not distorted. Thus it becomes imperative to check the datasheet for the device's slew rate before using it for high-frequency applications.