What is an active filter?

An active filter uses an op-amp (or other active device) along with resistors and capacitors. It eliminates the need for inductors, provides gain, and offers better performance than passive RC filters.

What is Sallen-Key topology?

Sallen-Key is a popular active filter circuit using a single op-amp with two resistors and two capacitors. At unity gain it is simple and predictable. It creates a second-order (2-pole) response.

What Q value should I use?

Q = 0.707 (1/√2) gives Butterworth (maximally flat) response. Q = 0.5 gives Bessel (linear phase). Q > 0.707 gives peaking at fc. Q < 0.5 gives overdamped response.

What op-amp do I need?

Choose an op-amp with gain-bandwidth product (GBW) at least 100× the filter cutoff frequency. For a 10 kHz filter, use an op-amp with GBW > 1 MHz. Low noise and low offset are important for precision applications.

Active Filter Calculator

Sallen-Key (unity gain)

2nd Order Active

No inductors needed

Sallen-Key Low Pass (2nd Order)

f_c Cutoff Frequency

Q Quality Factor

0.707 = Butterworth (no peaking)

C Choose Capacitor

Pick a standard value; R is calculated

Enter fc, Q and C

Active Filter Components

fc
—
Hz

Q Factor

—

Gain at DC

—

Figure 1: The Sallen-Key topology uses an op-amp with two resistors and two capacitors to create a second-order filter without inductors. Unity-gain feedback keeps the design simple and predictable.

Table of Contents

Fundamentals

What Is a Active Filter?
How It Works

Worked Examples

Sallen-Key Low Pass for Audio
MFB Bandpass for Tone Detection

Deep Dive

Sallen-Key vs MFB Topology
Op-Amp Selection

Reference

Frequently Asked Questions
Related Filter Calculators

What Is a Active Filter?

An active filter uses an operational amplifier (op-amp) with resistors and capacitors to create frequency-selective circuits without inductors. Active filters can provide gain, have excellent buffering, and are easier to tune than passive LC filters. The Sallen-Key and Multiple Feedback (MFB) topologies are the most common. The Filter Cutoff Frequency Calculator covers the fundamental frequency calculation that underpins filter design.

How It Works

The Sallen-Key topology places two RC sections around a unity-gain op-amp. By choosing appropriate R and C values, you control the cutoff frequency and Q factor independently. The op-amp provides buffering so the filter is not affected by load impedance. The RC Filter Calculator covers the passive alternative.

Worked Example — Sallen-Key Low Pass for Audio

Given: fc = 1 kHz, Q = 0.707, C = 10 nF

R₁ = Q/(πfcC) = 0.707/(π×1000×10⁻⁸) = 22.5 kΩ
R₂ = 1/(4πfcCQ) = 11.25 kΩ

The RL Filter Calculator can design the passive equivalent for comparison.

Worked Example — MFB Bandpass for Tone Detection

Given: fc = 5 kHz, Q = 10, C = 1 nF (tone detection)

High Q (10) gives a very narrow bandpass — ideal for detecting a specific DTMF tone frequency.

The LC Filter Calculator explores bandpass configurations in detail.

Sallen-Key vs MFB Topology

Sallen-Key is simple, stable, and works well for Q up to about 10. MFB (multiple feedback) offers better high-frequency performance and inverting gain but is more sensitive to component tolerances. For Q > 10, use state-variable or biquad topologies. The Low Pass Filter Calculator provides the Butterworth coefficients for cascaded stages.

Op-Amp Selection

Choose an op-amp with gain-bandwidth product at least 100× the filter cutoff. Low noise matters for audio; low offset matters for DC-coupled filters. Rail-to-rail output is important for single-supply designs. The High Pass Filter Calculator covers complementary filter designs.

Thevenin Equivalent Calculator: The Thevenin Equivalent Calculator simplifies the source driving the active filter for impedance matching analysis.

Frequently Asked Questions

Do I need a rail-to-rail op-amp?

Only if the signal approaches the supply rails. For dual-supply op-amps (±12V or ±15V) with signals under ±5V, standard op-amps work fine. Single-supply designs benefit from rail-to-rail.

Can I cascade active stages for higher order?

Yes. Cascade two 2nd-order Sallen-Key stages for 4th order. Each stage needs different Q values to maintain overall Butterworth response. The Butterworth Filter Calculator provides the required Q for each stage.

What about noise?

Op-amp noise is amplified by the filter gain. For low-noise designs, choose a low-noise op-amp (e.g. OPA2134 for audio, AD8421 for instrumentation) and keep resistor values low to minimise thermal noise.

Can I adjust Q after building?

In a Sallen-Key, Q depends on the R1/R2 ratio. Replacing one resistor with a trimmer allows Q adjustment. For production designs, use precision resistors instead of trimmers for reliability.

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Last updated: March 2026