Slew Rate: What is it? (Formula, Units & How To Measure It)

Contents

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Key learnings:

Slew Rate Definition: Slew rate is the maximum speed at which the output voltage of an operational amplifier can change.
Measuring Slew Rate: To measure slew rate, apply a step signal to the amplifier, then observe the rate of voltage change from 10% to 90% of its maximum amplitude using an oscilloscope.
Slew Rate Formula: The formula for calculating slew rate is by dividing the change in output voltage by the change in time, illustrating how quickly the output voltage can change.
Impact on Frequency: Slew rate determines the highest frequency at which the amplifier can function without output distortion, crucial for maintaining clarity in high-frequency applications.
Slew Rate Applications: Slew rate is vital in various applications including audio equipment, signal processing devices, and any electronic system requiring rapid changes in voltage for accurate performance.

What is Slew Rate?

In electronics, slew rate is the maximum rate of output voltage change per unit time. It is written S. That limit sets the largest amplitude and input frequency an operational amplifier (op-amp) can handle before the output waveform is slew-limited.

A higher slew rate allows a larger undistorted output swing at a given frequency. The needed value depends on the peak voltage and the highest frequency in the signal.

Datasheets usually quote slew rate in a unity-gain (+1) test. Closed-loop gain and the size of the input step can change the observed rate.

A general-purpose op-amp may be specified around 10 $V/\mu S$ . That figure means a large input step can move the output by 10 volts in 1 microsecond. Older parts such as the 741 are much slower.

Slew Rate Formula

The slew-rate equation is

$\begin{align*} S = \frac{dV_0}{dt}|_m_a_x_i_m_u_m \,\, Volts/\mu S \end{align*}$

where $V_0$ is the amplifier output as a function of time t.

Slew Rate Units

Slew rate is a voltage change per unit time. Datasheets usually state it in volts per microsecond ( $V/\mu S$ ). The same quantity can be written in volts per second.

How to Measure Slew Rate?

Slew rate is measured by applying a large step to the op-amp and reading the output slope, often between 10% and 90% of the output step. The step must be large enough to drive the input stage into slew. A 1 V step is a common lab choice. Many datasheets use a larger closed-loop step.

From the output waveform:

$\begin{align*} Slew Rate(S) = \frac{dV_0}{dt} = \frac{V_0_(_9_0_\%_) - V_0_(_1_0_\%_)} {t_(_9_0_\%_) - t_(_1_0_\%_)} \end{align*}$

The usual bench tools are an oscilloscope and a function generator.

A typical measurement circuit is shown below.

Slew Rate Measurment Circuit — Slew Rate Measurement Circuit

The input and the slew-limited output are shown below.

Input and Slew Limiting Output Voltage Waveform — Input and Slew Limited Output Voltage Waveform

Slew Rate of OP Amp

Slew rate sets how fast the output can move. That limit also sets the highest full-swing frequency a given op-amp can produce.

If the required dV/dt exceeds the specified slew rate, the output becomes a ramp instead of the intended waveform.

Rising and falling slew rates can differ if the internal current that charges the compensation capacitor is not the same in both directions.

An ideal op-amp would have no slew limit. A practical part such as the IC 741 op-amp is specified at about 0.5 V/µs at 25 °C, unity gain, so it cannot produce a large high-frequency swing without slew limiting.

Slew Rate Limiting in Amplifiers

High Gain at the Input Stage of OP-Amp:

Many operational amplifiers use a high-gain differential input stage with transconductance behaviour: a differential input voltage produces an output current. Transconductance, also called transfer conductance or mutual conductance, is $g_m = \frac {I_o_u_t}{V_i_n}$ .

That transconductance is high, so a small differential voltage can saturate the input stage. In saturation the stage delivers an almost constant output current and behaves as a current source. The output can then change no faster than that current can charge the compensation network. That is the slew-rate limit.

Frequency Compensation at the Second Stage of OP-Amp:

Internal frequency compensation is used to keep the loop stable. The same network that rolls off high-frequency gain also limits how fast the output can move, so it sets much of the slew rate.

The second-stage compensation has a low-pass shape, like an integrator. A constant current into that node then produces a linear output ramp. If the second stage has an effective input capacitance C and voltage gain A₂, the slew rate can be written

$\begin{align*} Slew Rate(S) = \frac {I_c_o_n_s_t_a_n_t}{C} A_2 \end{align*}$

I_constantis the first-stage current once that stage is in saturation.

Temperature:

Slew rate depends on temperature because the charging current and device parameters change with temperature. The positive rate applies to a rising edge. The negative rate applies to a falling edge. Some parts show a higher rate at higher temperature. Check the datasheet curve rather than assuming a universal trend.

Slew Rate vs Bandwidth

Slew Rate

Slew rate is the fastest output slope the amplifier can produce after a sudden input change. If a signal needs a steeper slope, the op-amp clips that slope.

If the required slope of a sine wave, after gain, exceeds the slew rate, the output becomes a straight ramp instead of the curved sinusoidal section. That error is nonlinear, so it changes the waveform shape and adds harmonics.

Bandwidth

Small-signal bandwidth is the frequency range where gain stays nearly constant. Op-amp poles give low-pass-filter behaviour: amplitude falls as frequency rises and phase shift appears. That roll-off is a linear filter effect and does not add the harmonics that slew limiting produces.

A wider small-signal bandwidth keeps gain flatter over the frequencies of interest. Bandwidth is stated in hertz. No real op-amp holds constant gain from 0 Hz to infinite frequency.

Relation Between Slew Rate and Full Power Bandwidth

For a sine-wave input $V_S$ , the highest frequency that still avoids slew limiting is found as follows.

(1) $\begin{equation*} V_S = V_m sin\omega t \end{equation*}$

For a unity-gain non-inverting amplifier, the output equals the input (within the linear range).

$\begin{align*} V_0 = V_m sin\omega t \end{align*}$

Differentiating both sides gives

$\begin{align*} \frac{dV_0}{dt} = \frac{d}{dt} V_m sin\omega t \end{align*}$

(2) $\begin{equation*} \frac{dV_0}{dt} = \omega V_m cos\omega t \end{equation*}$

$\frac{dV_0}{dt}$ is largest when $cos\omegat = 1 (i.e. \omega t=0^0)$ . That peak value of $\frac{dV_0}{dt}$ is the required slew rate S. Substituting into equation (2) gives

(3) $\begin{equation*} S = \frac{dV_0}{dt}|_m_a_x_i_m_u_m = \omega V_m = 2 \pi f_m V_m \,\, V/Sec \end{equation*}$

Where, $f_m$ is the highest signal frequency in Hz that this swing can support

$V_m$ is the peak voltage of the output sine wave

Rearranging equation (3) gives

(4) $\begin{equation*} f_m = \frac{S}{2 \pi V_m} \end{equation*}$

The same $f_m$ is the highest sine frequency at which the amplifier can still produce the chosen peak voltage without slew limiting. When that peak equals the rated full output swing, the result is the full power bandwidth, also called the slew-rate-limited-bandwidth.

Slew Rate Calculation

An op-amp must pass a 5 V peak sine wave at 20 kHz. Find the slew rate required.

Given: $V_m = 5volts$ , $f_m= 20kHz$

$\begin{align*} \begin{split} &S = 2 \pi f_m V_m \\ &= 2 * 3.14 * 20 * 10^3 * 5 \\ &= 628 * 10^3 \\ &S = 628000 V/S \,\, or \,\, 0.628 V/\mu S \end{split} \end{align*}$

Applications of Slew Rate

Slew-rate limits and slew circuits appear in:

Musical instruments, where a controlled slew gives portamento (glide or lag) from one note to the next.
Control-voltage paths that must move from one level to another over a set time.
Other electronics that need a timed output change, using either analog slew circuits or a software slew function.