Sallen-Key Cutoff Frequency

fc = 1 / (2π × √(R1×R2×C1×C2))

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Result
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Formula

fc = 1 / (2π × √(R1 × R2 × C1 × C2))

Description

The Sallen-Key topology is the most common second-order active filter structure, using a single op-amp in a non-inverting (voltage follower) configuration with two RC sections. The cutoff frequency depends on the geometric mean of the two RC products. The Q factor (which determines passband peaking) depends on the ratio of component values. With equal R and equal C values (R1=R2, C1=C2), Q = 0.5, giving a Bessel-like response. For Butterworth response (Q = 0.707), specific component ratios are required.

Variables

  • fc — Cutoff frequency (Hz)
  • R1, R2 — Resistors (Ω)
  • C1, C2 — Capacitors (F)

Practical Notes

Advantages of Sallen-Key: unity gain version requires no gain-setting resistors, low sensitivity to op-amp gain, and good performance with single-supply op-amps. Disadvantages: Q is limited to about 10-20 before component sensitivity becomes impractical. For higher Q, use state-variable or biquad topologies. Use 1% resistors and NP0/C0G capacitors for best accuracy.

Related Formulas

RC Low-Pass Filter RC High-Pass Filter Bandpass Bandwidth Filter Rolloff Rate Notch Frequency Butterworth Q Factor

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