Sallen-Key 2nd Order Active Filter Designer
Design active 2nd-order low-pass or high-pass Sallen-Key filters and evaluate Q-factor and frequency response approximation.
Component parameters
Filter Characteristics
Cutoff Frequency (f_c)—
Quality Factor (Q)—
Filter Response Shape:
—
💡 Usage & Formula
Sallen-Key 2nd-Order Cutoff Frequency:
f_c = 1 / (2 × π × sqrt(R₁ × R₂ × C₁ × C₂))
Quality Factor (Q)LP: Q = sqrt(R₁R₂C₁C₂) / (C₂(R₁ + R₂)). This Q-factor determines the shape of the transition band:
- Bessel (Q = 0.577): Best linear phase, minimal pulse overshoot but slow attenuation.
- Butterworth (Q = 0.707): Maximally flat passband response (no ripple) and sharp roll-off.
- Chebyshev (Q > 0.707): Sharpest attenuation slope but introduces amplitude ripples in the passband.
When you need it: Designing a second-order Sallen-Key low- or high-pass stage — ADC anti-aliasing, audio tone shaping, or sensor smoothing — by choosing R and C for a cutoff and Q.
Worked example: A Butterworth (Q = 0.707) low-pass at fc = 1 kHz with equal R = 10 kΩ needs C = 1/(2π × fc × R) ≈ 15.9 nF; the two capacitor values then set the Q.
Tips & gotchas:
- Q sets the peaking: 0.707 is maximally flat (Butterworth); higher Q peaks near fc and rings on transients.
- Cascade identical stages for steeper roll-off (4th order = two 2nd-order sections with the right Qs).
- The op-amp's GBW must comfortably exceed
fc × gain × Q, or the response droops early. - Use 1% resistors and C0G/NP0 capacitors — loose parts move both fc and Q noticeably.