Calculator Inputs
Use design mode to calculate resistor values. Use analyze mode to test existing resistor values.
Example Data Table
These examples use cascaded equal-value high pass and low pass Sallen Key stages.
| Use Case | Lower Cutoff | Upper Cutoff | HP Capacitors | LP Capacitors | Stage Gain | Approximate Result |
|---|---|---|---|---|---|---|
| Voice band cleanup | 300 Hz | 3.4 kHz | 100 nF | 10 nF | 1.586 each | Center near 1.01 kHz |
| Sub audio removal | 20 Hz | 200 Hz | 220 nF | 47 nF | 1.2 each | Center near 63.25 Hz |
| Sensor band isolation | 1 kHz | 10 kHz | 10 nF | 1 nF | 1.586 each | Center near 3.16 kHz |
Formula Used
Equal-value Sallen Key stage cutoff:
fc = 1 / (2πRC)
Equal-value Sallen Key stage quality factor:
Qstage = 1 / (3 - K)
Non-inverting stage gain:
K = 1 + Rf / Rg
Feedback resistor:
Rf = Rg × (K - 1)
Bandpass center frequency:
f0 = √(fL × fH)
Bandwidth:
BW = fH - fL
Approximate band quality factor:
Qband = f0 / BW
Minimum slew rate estimate:
SR = 2π × fH × Vpeak / 1,000,000
How to Use This Calculator
- Select design mode when you want new resistor values.
- Select analyze mode when you already have resistor values.
- Enter the lower cutoff frequency for the high pass stage.
- Enter the upper cutoff frequency for the low pass stage.
- Choose capacitor values that are easy to buy.
- Set stage gain below 3 for equal-value Sallen Key stability.
- Enter signal, source, load, and tolerance values.
- Press calculate and review the results above the form.
- Use the graph to inspect response shape.
- Download CSV or PDF for documentation.
Article: Sallen Key Bandpass Filter Design
Why This Calculator Matters
A Sallen Key bandpass filter is useful when a circuit must pass one signal range and reduce frequencies outside it. Audio tone shaping, sensor cleanup, vibration testing, and lab signal work often need this behavior. This calculator treats the bandpass as two active stages. The first stage is a high pass section. It sets the lower cutoff. The second stage is a low pass section. It sets the upper cutoff. The useful band sits between both cutoffs.
Design Notes
Equal resistor and equal capacitor Sallen Key sections are popular because they are simple to build. The cutoff of each stage depends on one resistor value and one capacitor value. The stage gain changes the damping. It also changes the quality factor of each section. A gain near 1.586 gives about 0.707 Q in the equal value form. That is often used for a smooth Butterworth style response. Higher gain increases Q. Too much gain can make the stage ring or become unstable.
The calculator estimates design resistors from target frequencies and chosen capacitors. It can also analyze existing resistor values. This helps when you already have preferred parts. It reports lower cutoff, upper cutoff, geometric center frequency, bandwidth, approximate band Q, stage Q, feedback resistors, total gain, and useful op amp checks. These values help you judge both the math and the practical build.
Practical Use
Real filters depend on capacitor tolerance, resistor tolerance, op amp bandwidth, loading, and layout. Use one percent resistors when possible. Use stable capacitors for timing parts. Film capacitors are preferred for audio and precision work. Ceramic capacitors can work, but high dielectric types may drift with voltage and temperature.
Keep the source impedance low compared with the filter input network. Keep the next load high compared with the op amp output ability. Check the required slew rate when signal level or frequency is high. Choose an op amp with enough gain bandwidth for the upper cutoff and total gain. After building the circuit, measure the response with a sweep. Then trim values if a tight cutoff or exact center frequency is required. Record values for future troubleshooting and service notes.
FAQs
1. What is a Sallen Key bandpass filter?
It is an active filter arrangement that passes a chosen frequency band. This calculator models it as a cascaded Sallen Key high pass stage and low pass stage.
2. Why does the calculator use two stages?
A practical bandpass response can be formed by placing a high pass section before a low pass section. The high pass stage sets the lower cutoff. The low pass stage sets the upper cutoff.
3. What does stage gain K control?
In an equal-value Sallen Key section, gain affects damping and quality factor. Higher gain raises Q. A gain of 3 or more is not stable in this simplified equal-value model.
4. Why is 1.586 used often?
A gain near 1.586 gives a stage Q close to 0.707 with equal resistors and capacitors. This is commonly used for a smooth Butterworth style response.
5. Can I use preferred resistor values?
Yes. Choose analyze mode and enter your existing resistor values. The calculator will compute the actual lower and upper cutoff frequencies from those parts.
6. Are calculated values exact in real circuits?
No. Real results change with part tolerance, op amp limits, layout, source loading, and output loading. Always test the built filter when accuracy matters.
7. What op amp should I choose?
Choose one with enough gain bandwidth, slew rate, input range, and output drive. The calculator gives simple estimates to help screen unsuitable parts.
8. What capacitors are best for this filter?
Use stable capacitors for timing parts. Film capacitors are strong choices for audio and precision filters. Avoid unstable high dielectric ceramics when drift is important.