Sallen-Key Filter Calculator

Filter response:

Choose the topology you want to analyze from entered component values.

R1:

Enter the first resistor in the frequency-setting network.

R2:

Use the same unit as R1 when you are checking an equal-value prototype.

R3 damping path:

Only used for the band-pass topology and ignored by low-pass/high-pass modes.

C1:

Enter the first capacitor and select its unit.

C2:

Match C1 for a quick equal-component check, or enter the actual schematic value.

Passband gain K: {{ gainValueLabel }}

Slider and exact value both update the Q, chart, checks, and export payload.

V/V

{{ error }}

Input amplitude:

Optional signal level for output swing rows.

Vpp

Op-amp GBW:

Leave the default unless you already know the op-amp gain-bandwidth product.

MHz

Resistor tolerance:

Enter the expected resistor tolerance as a percent.

Capacitor tolerance:

Use the datasheet or measured capacitor tolerance.

Display precision:

Adjust output precision without changing the calculation.

Part	Entered	SI value	Nearest E24	Nearest E96	Copy
{{ row.part }}	{{ row.entered }}	{{ row.si }}	{{ row.e24 }}	{{ row.e96 }}

Check	Current	Reference	Action	Copy
{{ row.check }}	{{ row.current }}	{{ row.reference }}	{{ row.action }}

Frequency	f / f0	Gain	Phase	Copy
{{ row.frequency }}	{{ row.normalized }}	{{ row.gain }}	{{ row.phase }}

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A Sallen-Key filter is a second-order active RC stage that uses an op amp or similar voltage follower to shape a low-pass, high-pass, or band-pass response. The resistors and capacitors set the natural frequency, while the gain and part ratios control damping, quality factor, and peaking.

The topology is common in audio filters, sensor signal conditioning, anti-aliasing stages, tone shaping, and education labs because one active device can produce a useful two-pole response. It is also easy to misread. A neat calculated frequency does not prove that the chosen op amp, supply rails, part tolerances, board parasitics, or output swing can support the circuit.

Sallen-Key RC network feeding an op amp, with feedback shaping Q and the RC path setting f0. — A Sallen-Key second-order stage uses an RC network and amplifier feedback to set natural frequency and Q.

The useful result is not only one frequency. Natural frequency, Q, response shape, gain-bandwidth headroom, tolerance spread, and estimated output swing all affect whether the stage is a reasonable starting point. A Butterworth-like Q near 0.707 gives a flat second-order response, while higher Q creates peaking and tighter sensitivity to real parts.

Treat the calculation as a screening and explanation aid. High-Q or high-frequency stages should still be checked with the selected op amp model, measured component values, supply rails, and layout before a circuit is built.

How to Use This Tool:

Start with the topology and actual part values, then use the checks and curve to decide what needs verification.

Choose Filter response: Low-pass, High-pass, or Band-pass. Band-pass mode adds R3 damping path.
Enter R1, R2, C1, and C2 with their units. Use the schematic values you intend to analyze, not only rounded target values.
Adjust Passband gain K. The exact value field and slider update the summary, Q, chart, and tables together. Keep K between 1.00 and 2.90 V/V.
Open Advanced when you want output swing, op-amp headroom, tolerance spread, or display precision. Input amplitude affects only the output swing estimate, and Display precision changes formatting only.
Read the summary for f0, Q, peak gain, and the response label. If validation appears, fix zero or negative R/C values, out-of-range K, negative input amplitude, invalid GBW, or a non-positive damping result before trusting any output.
Use Component Ledger to compare entered values with nearest E24 and E96 values, then use Design Checks for natural or center frequency, Q profile, feedback ratio, GBW headroom, tolerance span, part ratio spread, and output swing.
Open Gain Response Curve and Sweep Points to inspect gain and phase around f0. Use JSON when you need the same result data for documentation or another calculation.

Interpreting Results:

The headline frequency is the natural frequency for low-pass and high-pass stages, and the center frequency for band-pass mode. For a Butterworth-like second-order section, f0 is close to the familiar -3 dB corner. When Q is much lower or higher, the response curve is the safer place to inspect the usable passband and peaking.

How to read Sallen-Key filter calculator outputs
Output	What to check	Common misread
f0	Natural or center frequency from the entered R and C values.	Assuming it is always the final measured cutoff frequency.
Q profile	Damping and peaking. Near 0.707 is a common flat-response target.	Reading high Q as better filtering without checking tolerance and op-amp limits.
GBW headroom	Screening ratio between entered op-amp GBW and the gain, Q, and frequency demand.	Treating a pass as proof of stability, slew rate, or noise performance.
Tolerance span	Worst-case f0 movement from resistor and capacitor tolerances.	Assuming nominal E-series parts land exactly on the calculated response.
Gain Response Curve	Log-frequency gain curve with f0 and -3 dB reference markers.	Ignoring peak gain when checking supply headroom.

A green-looking headroom number should still lead to a model check for demanding circuits. Verify the chosen op amp's gain-bandwidth product, slew rate, input common-mode range, output swing, load drive, and noise against the real operating point.

When the summary says Damped response, the stage may be intentionally gentle. When it says Peaking response, compare the Output swing estimate with supply rails and rerun the calculation with tighter component tolerances before moving on.

Technical Details:

A Sallen-Key stage can be written as a second-order transfer function with a denominator of 1 + a s + b s^2. The coefficient b sets the time scale, and the coefficient a sets damping. A smaller positive a raises Q; a non-positive a means the ideal pole pair is not safely damped.

Low-pass and high-pass modes use the standard second-order Sallen-Key form. Band-pass mode uses an additional damping resistor and reports bandwidth as f0 divided by Q. The response curve samples the ideal transfer function at logarithmic frequency points, so it shows the arithmetic model rather than an op amp simulation.

Formula Core:

Values are first converted to ohms and farads. The main frequency and Q equations are:

\begin{array}{lcl} f_{0} & = & \frac{1}{2 π \sqrt{b}} \\ Q & = & \frac{\sqrt{b}}{a} \\ BW & = & \frac{f_{0}}{Q} \end{array}

The topology determines a and b:

\begin{array}{lcl} Low-pass b & = & R_{1} R_{2} C_{1} C_{2} \\ Low-pass a & = & C_{2} (R_{1} + R_{2}) + C_{1} R_{1} (1 - K) \\ High-pass b & = & R_{1} R_{2} C_{1} C_{2} \\ High-pass a & = & (1 - K) R_{2} C_{2} + R_{1} C_{2} + R_{1} C_{1} \\ Band-pass b & = & \frac{C_{1} C_{2} R_{1} R_{2}}{1 + \frac{R_{1}}{R_{2}}} \\ Band-pass a & = & C_{2} R_{2} (1 + \frac{R_{1}}{R_{3}} - (K - 1) \frac{R_{1}}{R_{2}}) \end{array}

With equal low-pass or high-pass parts, R1 = R2 = R and C1 = C2 = C, the equations simplify to f0 = 1 / (2*pi*R*C) and Q = 1 / (3 - K). That is why K = 1.586 gives a Butterworth-like Q near 0.707, while values close to 3 become very sensitive.

Sallen-Key design checks and validation boundaries
Check	Rule used	Interpretation
Valid damping	`a > 0` and `b > 0`	Required before frequency, Q, and curve outputs are shown.
Q labels	`Q < 0.55`, `0.64 to 0.78`, and `Q >= 1.2` drive the summary labels.	Use the label as a warning cue, not as a formal filter-family classification.
GBW headroom	`op-amp GBW / (f0 * K * max(1, Q))`	The table treats 20x or more as comfortable for an initial screen.
Tolerance span	Worst-case R and C products are recomputed using the entered tolerances.	Shows how far f0 can move before op amp and layout errors are considered.
Part ratio spread	Largest same-type resistor ratio and capacitor ratio reported separately.	Very large spreads increase leakage, noise, and parasitic sensitivity.
Output swing	Input amplitude times the larger of passband gain or peak curve gain.	Compare against supply rails and load drive limits.

The nearest E24 and E96 values are preferred-value comparisons for part selection. They do not retune the circuit automatically. If you substitute rounded values, rerun the calculation with the values you will actually buy or measure.

Limitations and Privacy:

The calculation is an ideal small-signal estimate. It does not include finite op amp open-loop response, slew rate, output current, rail limits, temperature drift, noise, capacitor voltage coefficient, PCB parasitics, or measured part spread.

Use SPICE or bench measurement for high-Q, high-frequency, high-output-swing, or production-critical stages.
Enter realistic GBW and tolerances before using the checks as a design review aid.
The entered component values are calculated in the browser and are not uploaded for a remote calculation.

Worked Examples:

Equal-part low-pass stage

With Low-pass, R1 = 10 kohm, R2 = 10 kohm, C1 = 10 nF, C2 = 10 nF, and K = 1.586 V/V, the summary reports f0 near 1.592 kHz and Q near 0.707. The Q profile sits near the Butterworth target, so the Gain Response Curve should look flat before the roll-off.

Band-pass damping check

Switching to Band-pass with R1 = R2 = R3 = 10 kohm, C1 = C2 = 10 nF, and K = 1.586 V/V moves the reported center frequency to about 2.251 kHz and gives Q near 0.500. That is a broad, damped passband rather than a narrow resonator.

Non-positive damping recovery

A low-pass entry such as R1 = R2 = 10 kohm, C1 = 100 nF, C2 = 10 nF, and K = 2.90 V/V can trigger the warning that gain and component ratios produce non-positive damping. Lower K or rebalance the capacitor ratio before reading f0, Q, or sweep rows.

FAQ:

Is f0 the same as cutoff frequency?

Not always. For a Butterworth-like second-order low-pass or high-pass stage, f0 is close to the -3 dB point. With other Q values, inspect the Gain Response Curve and -3 dB reference marker.

Why does increasing K raise the risk of peaking?

In Sallen-Key stages, amplifier gain participates in the damping term. Raising K can increase Q, and excessive Q can make the ideal response peak or become invalid for the entered ratios.

Why is R3 shown only for band-pass mode?

The low-pass and high-pass equations use R1, R2, C1, C2, and K. Band-pass mode also uses R3 damping path, so that extra resistor is requested only for that topology.

Do the nearest E24 and E96 columns change the result?

No. They compare entered resistor and capacitor values with common preferred-value series. To see the real effect of a substituted part, enter that chosen value and rerun the calculation.

Can this replace circuit simulation?

No. It gives an ideal Sallen-Key screening result with helpful checks. Use op amp simulation and measurement when GBW, slew rate, supply swing, tolerance, noise, or layout parasitics matter.

Glossary:

Natural frequency: The second-order frequency set by the denominator coefficient b; shown as f0.
Q: Quality factor, a damping measure that controls peaking and bandwidth.
Passband gain K: The non-inverting gain value used by the Sallen-Key stage.
GBW: Gain-bandwidth product, an op amp limit that affects whether the ideal response is realistic.
E24 and E96: Preferred resistor and capacitor value series used for nearest-value comparisons.
Bandwidth: For band-pass mode, the center frequency divided by Q.

References:

Analysis of the Sallen-Key Architecture, Texas Instruments, July 1999 revised September 2002.
Butterworth Sallen-Key Low-Pass Filter Design Tool, Texas Instruments, 2021.
AN-649: Using the Analog Devices Active Filter Design Tool, Analog Devices.
AN-1584: Eight-Pole, Active Low-Pass Filter Optimized for Precision, Low Noise, and High Gain, Analog Devices.
IEC 60063:2015 Preferred number series for resistors and capacitors, International Electrotechnical Commission, 2015.