Free Sallen-Key Bandpass Filter Calculator

Design active second-order bandpass filters. Calculate center frequency (f₀), quality factor (Q), passband gain, component values, and op-amp bandwidth limits.

⚡ Filter Response & Specifications

Filter Topology

Center Frequency (f_0)

Quality Factor (Q)

Q = f_0 / BW (Higher Q = narrower passband).

Midband Passband Gain (A_0)

V/V

Capacitor Baseline (C)

Standard film/C0G capacitor: 10 nF typical.

Filter Bandwidth & Cutoff Limits

200.0 Hz (f_L: 904.9 Hz • f_H: 1104.9 Hz)

Midband Gain: 2.00 V/V (+6.02 dB) at f_0 = 1,000 Hz

Resistor R1 39.8 kΩ Std 1%: 40.2k

Resistor R2 1.73 kΩ Std 1%: 1.74k

Resistor R3 159.2 kΩ Std 1%: 158k

Op-Amp Bandwidth Requirement

≥ 1.00 MHz (GBWP ≥ 20 × Q × f_0)

Ensures internal op-amp phase shift does not cause center frequency drift or self-oscillation.

MFB vs. Sallen-Key: Multiple Feedback (MFB) is preferred for bandpass filters with $Q > 3$ because its sensitivity to op-amp open-loop gain is significantly lower than Sallen-Key. Always use low-temperature coefficient C0G/NP0 ceramic or polypropylene capacitors.

Recommended Tools & Equipment

Tested hardware and components for high reliability

100% Free Tool Zero Sign-Up

Principles of Active Second-Order Bandpass Filters

Active bandpass filters isolate a target band of frequencies while rejecting DC, low-frequency hum, and high-frequency noise without requiring bulky, expensive inductors:

Bandwidth: BW = f_0 / Q
Lower -3dB Cutoff: f_L = f_0 × [ √(1 + 1/(4 Q^2)) - 1/(2 Q) ]
Upper -3dB Cutoff: f_H = f_0 × [ √(1 + 1/(4 Q^2)) + 1/(2 Q) ]

Multiple Feedback (MFB) Sizing Formulas

Setting $C_1 = C_2 = C$:

R1 = Q / (2 × π × f_0 × C × A_0)
R2 = Q / [ (2 × Q^2 - A_0) × 2 × π × f_0 × C ]
R3 = (2 × Q) / (2 × π × f_0 × C)

Note: For real solutions in MFB, the condition $2 Q^2 ge A_0$ must be satisfied.

Frequently Asked Questions

Why does my bandpass filter oscillate when Q is high?

At high Q (e.g. Q > 10), component tolerances shift the filter pole close to the imaginary jw axis. Slight phase lag in the op-amp can cause pole-zero cancellation failure and trigger self-sustaining oscillation. Use an op-amp with GBWP > 50 * Q * f0 and 0.1% precision resistors.

Can I cascade two bandpass stages for steeper roll-off?

Yes! Cascading two identical second-order bandpass stages creates a 4th-order filter with a sharp 40 dB/decade roll-off on either side of the passband.

What capacitor dielectric should I use?

Never use standard X7R or Z5U ceramic capacitors for active filters, as their capacitance shifts wildly with temperature and applied voltage. Use C0G/NP0 ceramics or polyphenylene sulfide (PPS) / metallized polypropylene film capacitors.