Formula Used
The calculator uses the common second order Sallen Key low pass model with non-inverting gain K.
Natural angular frequency: ω0 = 1 / √(R1 × R2 × C1 × C2)
Natural frequency: f0 = ω0 / 2π
Quality factor: Q = √(R1 × R2 × C1 × C2) / [C2(R1 + R2) + C1R1(1 - K)]
Magnitude response: |H(jω)| = K / √((1 - u²)² + (u / Q)²), where u = f / f0.
Relative -3 dB point: f-3dB = f0 × √x, where x = [2 - 1/Q² + √((-2 + 1/Q²)² + 4)] / 2.
For equal values, R1 = R2 and C1 = C2. Then f0 = 1 / 2πRC. Also Q = 1 / (3 - K).
How To Use This Calculator
- Enter R1, R2, C1, and C2 with their units.
- Enter the gain K, or select the gain resistor option.
- Add one test frequency to inspect gain and phase.
- Enter part tolerance to estimate the natural frequency range.
- Use the target section to find equal value design suggestions.
- Press Submit to show the result above the form.
- Use CSV or PDF export for records.
Example Data Table
| R1 |
R2 |
C1 |
C2 |
K |
f0 |
Q |
Use Case |
| 10 k ohm |
10 k ohm |
10 nF |
10 nF |
1.000 |
1591.55 Hz |
0.500 |
Soft damped response |
| 10 k ohm |
10 k ohm |
10 nF |
10 nF |
1.586 |
1591.55 Hz |
0.707 |
Butterworth style response |
| 15.9 k ohm |
15.9 k ohm |
10 nF |
10 nF |
1.586 |
1001.03 Hz |
0.707 |
Near 1 kHz section |
| 4.7 k ohm |
4.7 k ohm |
22 nF |
22 nF |
1.200 |
1539.58 Hz |
0.556 |
Moderate damping |
Why This Filter Matters
A Sallen Key low pass filter is a compact active circuit. It passes low frequencies and reduces higher ones. Designers use it before converters, amplifiers, audio stages, and sensor inputs. The calculator helps you study that response before you build hardware. It keeps the math visible, so each part choice has a clear effect.
Design Insight
The cutoff frequency comes from both resistors and both capacitors. Larger values lower the natural frequency. Smaller values raise it. The quality factor shows the damping of the second order section. A low Q gives a soft rolloff. A high Q can create peaking near the corner. Gain also changes Q in the common non inverting Sallen Key form. That makes gain choice important, not just useful.
Practical Component Planning
Real parts have tolerance. A one percent resistor and a five percent capacitor do not create one exact filter. They create a range. This page estimates that range for the natural frequency. It also reports the stability limit for gain. Use those numbers before ordering parts. They can prevent a noisy, ringing, or unstable design.
Testing The Response
The test frequency field checks one point on the curve. It reports gain ratio, decibels, and phase. Try values below cutoff, near cutoff, and far above cutoff. The pattern will show the expected low pass behavior. You can export the result as a CSV file for spreadsheets. You can also make a PDF record for a lab note or design review.
Good Use Cases
This calculator is helpful for analog lessons, audio filters, anti aliasing stages, and sensor smoothing. It is not a replacement for bench testing. Op amp bandwidth, slew rate, output swing, noise, and load effects still matter. After using the tool, simulate the circuit and measure the final board. Use stable, low leakage capacitors where accuracy matters. Keep feedback traces short. Place capacitors close to the amplifier pins. Match paired parts when Q is critical. These habits make the calculated response closer to the real response. For first builds, choose standard values and adjust one pair at a time. Record each trial. Notes make later debugging easier and faster. They help teams compare design choices, before parts are ordered.
FAQs
What is a Sallen Key low pass filter?
It is a second order active filter circuit. It uses an op amp, two resistors, and two capacitors. It passes lower frequencies and reduces higher frequencies.
What does Q mean?
Q is the quality factor. It shows damping near the cutoff region. A higher Q can create peaking. A lower Q creates a smoother transition.
What gain is safe for equal components?
For equal R and C values, ideal stability requires K below 3. A Butterworth style response often uses K near 1.586.
Why is my result unstable?
The damping term may be zero or negative. This usually means the selected gain is too high for the selected component ratio.
Is f0 the same as the -3 dB frequency?
Not always. The -3 dB frequency depends on Q. For some responses, it can differ from the natural frequency.
Can I use this for real hardware?
Yes, for early design and checking. Final hardware should also consider op amp bandwidth, slew rate, noise, output swing, and component tolerance.
Why include a test frequency?
The test frequency shows expected gain and phase at one selected point. It helps you inspect behavior below, near, or above cutoff.
What does the PDF export save?
It saves the visible result summary, frequency response values, stability details, tolerance range, and design helper output into a simple report.