Sallen-Key Cutoff Frequency
fc = 1 / (2π × √(R1×R2×C1×C2))
Quick answer
This calculator solves fc = 1 / (2π × √(R1 × R2 × C1 × C2)) for fc. With R1 10 kΩ, R2 22 kΩ, C1 100 nF, C2 0.22 µF, the result is 72.34 Hz.
Calculator
Formula
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 — Resistor (Ω)
- R2 — Resistor (Ω)
- C1 — Capacitor (F)
- C2 — Capacitor (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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| R1 | R1 | kΩ | mΩ, Ω, kΩ, MΩ |
| R2 | R2 | kΩ | mΩ, Ω, kΩ, MΩ |
| C1 | C1 | nF | pF, nF, µF, mF, F |
| C2 | C2 | nF | pF, nF, µF, mF, F |
Step by step
- 1. What you know: R1 10 kΩ, R2 22 kΩ, C1 100 nF, C2 0.22 µF
- 2. The relation: fc = 1 / (2π × √(R1 × R2 × C1 × C2))
- 3. Substitute: R1 = 10 kΩ, R2 = 22 kΩ, C1 = 100 nF, C2 = 0.22 µF
- 4. Result: fc = 72.34 Hz
Worked examples
Minimum range
Given: R1 100 Ω, R2 0.22 kΩ, C1 100 pF, C2 0.22 nF
Result: fc = 7.23 × 10⁶ Hz
Low range
Given: R1 1 kΩ, R2 2.2 kΩ, C1 1 nF, C2 2.2 nF
Result: fc = 72340 Hz
Typical
Given: R1 10 kΩ, R2 22 kΩ, C1 100 nF, C2 0.22 µF
Result: fc = 72.34 Hz
High range
Given: R1 100 kΩ, R2 0.22 MΩ, C1 1 µF, C2 2.2 µF
Result: fc = 0.7234 Hz
Maximum range
Given: R1 1 MΩ, R2 2.2 MΩ, C1 10 µF, C2 22 µF
Result: fc = 0.007234 Hz
How fc changes with R1
| R1 (input) | fc (result) |
|---|---|
| 1 kΩ | 228.8 Hz |
| 2.5 kΩ | 144.7 Hz |
| 5 kΩ | 102.3 Hz |
| 7.5 kΩ | 83.53 Hz |
| 10 kΩ | 72.34 Hz |
| 15 kΩ | 59.07 Hz |
| 20 kΩ | 51.15 Hz |
| 40 kΩ | 36.17 Hz |
| 70 kΩ | 27.34 Hz |
| 100 kΩ | 22.88 Hz |
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<p><a href="https://vbatpower.com/formulas/sallen-key-fc/">Sallen-Key Cutoff Frequency</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Sallen-Key Cutoff Frequency?
Use fc = 1 / (2π × √(R1 × R2 × C1 × C2)). With R1 10 kΩ, R2 22 kΩ, C1 100 nF, C2 0.22 µF, fc works out to 72.34 Hz.
How do you calculate calculate to cutoff frequency in a sallen key filter?
Rearrange for fc: with R1 1 kΩ, R2 2.2 kΩ, C1 1 nF, C2 2.2 nF, fc is 72340 Hz.
How do you calculate cutoff frequency r1 r2 c1?
Rearrange for fc: with R1 10 kΩ, R2 22 kΩ, C1 100 nF, C2 0.22 µF, fc is 72.34 Hz.
What is the formula for Sallen-Key Cutoff Frequency?
The formula is fc = 1 / (2π × √(R1 × R2 × C1 × C2)). 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.
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