Slew Rate Calculation

Calculator 1: Required Slew Rate

Calculate the minimum slew rate required to reproduce a signal without distortion.

Hz kHz MHz

Note: Enter Peak Voltage (not Vpp or RMS)

Calculator 2: Measured Slew Rate

Calculate slew rate based on step response measurement (Voltage over Time).

µs (Microseconds) ns (Nanoseconds) ms (Milliseconds)

function calculateFreqSR() { var freqInput = document.getElementById('sr_freq').value; var freqUnit = document.getElementById('sr_freq_unit').value; var vPeakInput = document.getElementById('sr_vpeak').value; var resultBox = document.getElementById('sr_result_freq'); var resultValue = document.getElementById('sr_val_freq'); if (freqInput === "" || vPeakInput === "") { alert("Please enter both Frequency and Peak Voltage."); return; } var f = parseFloat(freqInput) * parseFloat(freqUnit); // Convert to Hz var vp = parseFloat(vPeakInput); // Volts if (isNaN(f) || isNaN(vp)) { resultValue.innerHTML = "Invalid Input"; resultBox.style.display = "block"; return; } // Formula: SR = 2 * pi * f * Vpeak // Result is in Volts per Second var srVoltsPerSecond = 2 * Math.PI * f * vp; // Convert to Volts per Microsecond (V/µs) // 1 V/µs = 1,000,000 V/s var srVoltsPerMicro = srVoltsPerSecond / 1000000; resultValue.innerHTML = srVoltsPerMicro.toFixed(4) + " V/µs"; resultBox.style.display = "block"; } function calculateTimeSR() { var dvInput = document.getElementById('sr_delta_v').value; var dtInput = document.getElementById('sr_delta_t').value; var dtUnit = document.getElementById('sr_time_unit').value; var resultBox = document.getElementById('sr_result_time'); var resultValue = document.getElementById('sr_val_time'); if (dvInput === "" || dtInput === "") { alert("Please enter both Voltage Change and Time Duration."); return; } var dv = parseFloat(dvInput); var dt = parseFloat(dtInput); var unitMultiplier = parseFloat(dtUnit); if (isNaN(dv) || isNaN(dt) || dt === 0) { resultValue.innerHTML = "Invalid Input"; resultBox.style.display = "block"; return; } // Normalize time to Microseconds for the standard V/µs output // Input unit multiplier treats µs as base 1. // ns is 0.001 µs. ms is 1000 µs. var timeInMicroseconds = dt * unitMultiplier; var sr = dv / timeInMicroseconds; resultValue.innerHTML = sr.toFixed(4) + " V/µs"; resultBox.style.display = "block"; }

What is Slew Rate?

Slew Rate (SR) is a critical performance parameter for operational amplifiers (op-amps) and other electronic circuits. It defines the maximum rate at which the output voltage of a device can change in response to a step change in the input. Unlike bandwidth, which represents the frequency response for small signals, slew rate is a large-signal phenomenon limited by the internal currents charging the compensation capacitors within the device.

It is typically expressed in units of Volts per microsecond (V/µs).

Why Slew Rate Matters

If an amplifier is asked to change its output voltage faster than its slew rate limit allows, the output signal will be distorted. This typically manifests as the transformation of a sine wave into a triangular wave, significantly affecting signal integrity, particularly in:

• Audio Amplifiers: Insufficient slew rate causes Transient Intermodulation Distortion (TIM), leading to harsh sound quality.
• Data Acquisition: Slow slew rates prevent the op-amp from tracking rapid changes in sensor data.
• Video Processing: High slew rates are essential for maintaining sharp edges in video signals.

Slew Rate Formulas

There are two primary ways to determine Slew Rate, which correspond to the two calculators above:

1. The Sinusoidal Formula (Full Power Bandwidth)

To reproduce a sinusoidal signal without slew-induced distortion, the amplifier must be able to change voltage faster than the steepest part of the sine wave (the zero crossing). The formula is:

SR = 2 · π · f · V_peak

Where:

• f: The maximum frequency of the signal (Hz).
• V_peak: The maximum peak voltage amplitude (Volts).

2. The Step Response Formula (Measured)

When measuring an op-amp on an oscilloscope, you apply a square wave (step input) and measure the slope of the rising or falling edge.

SR = ΔV / Δt

Where:

• ΔV: The change in output voltage (Volts).
• Δt: The time it takes for that change to occur (typically µs).

Calculation Example

Suppose you are designing an audio pre-amplifier that needs to output a 10V peak signal at 20 kHz (the upper limit of human hearing). What is the minimum slew rate required?

1. Convert frequency to Hz: 20 kHz = 20,000 Hz.
2. Apply the formula: SR = 2 * π * 20,000 * 10.
3. Result: 1,256,637 V/s.
4. Convert to standard units (divide by 10⁶): 1.26 V/µs.

In this scenario, you should choose an op-amp with a slew rate of at least 1.5 V/µs or 2.0 V/µs to provide a safety margin and ensure high fidelity.