What this active filter calculator does
This calculator helps you quickly size resistor values for practical active filters using an op-amp. You can choose low-pass or high-pass behavior, pick 1st-order or 2nd-order response, and estimate gain resistor values for a non-inverting stage. It is designed for fast prototyping, lab work, and sanity checks before simulation.
Core design equations
Cutoff frequency
For equal-value RC sections, the core relationship is: fc = 1 / (2πRC). Rearranged for resistor sizing: R = 1 / (2πfcC).
Non-inverting op-amp gain
For the gain stage, the calculator uses: K = 1 + (Rf / Rg). If you choose a reference Rg, it computes the needed Rf.
Second-order Sallen-Key Q relationship
In the equal-component Sallen-Key form, Q depends on gain: Q = 1 / (3 - K) (valid for K < 3). The calculator includes common alignments:
- Butterworth: Q ≈ 0.707, K ≈ 1.586
- Bessel-like: Q ≈ 0.577, K ≈ 1.268
- Linkwitz-Riley stage: Q = 0.5, K = 1.0
How to use it effectively
Step-by-step workflow
- Pick filter type (low-pass or high-pass).
- Select order based on slope requirement (20 dB/dec or 40 dB/dec).
- Enter your target cutoff frequency.
- Choose a practical capacitor value first (often easiest from available stock).
- Let the calculator solve resistor values and suggest a nearest E12 option.
- Verify in SPICE and adjust for preferred standard values (E24/E96 if needed).
Design tips for real hardware
- Mind op-amp bandwidth: Ensure unity-gain bandwidth is comfortably above your highest passband frequency.
- Use stable capacitors: C0G/NP0 or film caps generally hold value better than high-K ceramics.
- Account for tolerances: 5% parts can noticeably shift cutoff and Q; tighter parts improve repeatability.
- Check output swing: Gain and supply rails can limit dynamic range and introduce clipping.
- Layout matters: Keep high-impedance nodes short and clean to reduce noise pickup.
Quick example
Suppose you need a 1 kHz 2nd-order Butterworth low-pass and choose C = 10 nF. The calculator returns R near 15.9 kΩ (often rounded to 15 kΩ or 16 kΩ), and K ≈ 1.586, so with Rg = 10 kΩ you would target Rf ≈ 5.86 kΩ. After rounding to available values, the actual cutoff shifts slightly—this is normal and shown in the output.
Final note
This tool is intended for fast design estimation. For production circuits, always validate against op-amp limitations, parasitics, and tolerance analysis in simulation and bench measurements.