Filters Formulas
Filter formulas set the cutoff frequency, bandwidth, and selectivity of passive and active filters. These calculators turn component values into frequency response so you can shape signals precisely. They are fundamental to audio, sensor conditioning, and noise rejection.
Filters Formula Calculators
- RC Low-Pass Filter fc = 1 / (2πRC) Resistance 100 Ω, Capacitance 100 pF → Cutoff Frequency = 15.92 MHz
- RC High-Pass Filter fc = 1 / (2πRC) Resistance 100 Ω, Capacitance 100 pF → Cutoff Frequency = 15.92 MHz
- Bandpass Bandwidth BW = f2 − f1 Lower Cutoff 11 Hz, Upper Cutoff 23.5 Hz → Bandwidth = 12.5 Hz
- Filter Rolloff Rate Rolloff = N × 20 dB/decade Filter Order 0.025 → Rolloff (dB/decade) = 0.5 dB/decade
- Notch Frequency f = 1 / (2π√(LC)) Inductance 100 µH, Capacitance 100 pF → Notch Frequency = 1.592 MHz
- Butterworth Q Factor Q = 1 / (2 × sin(π/(2N))) Filter Order 25 → Q = 7.963
- Sallen-Key Cutoff Frequency fc = 1 / (2π × √(R1×R2×C1×C2)) R1 100 Ω, R2 0.22 kΩ, C1 100 pF, C2 0.22 nF → fc = 7.23 × 10⁶ Hz
- Chebyshev Filter Order N = acosh(√(ε²s/ε²p)) / acosh(fs/fp) Stopband Attenuation (dB) 3 dB, Passband Ripple (dB) 1.41 dB, Stopband Frequency 1 kHz, Passband Frequency 0.47 kHz → N = 0.7607
- Bessel Filter Group Delay τ = R × C Resistance 100 Ω, Capacitance 100 pF → Group Delay = 10 ns
- Active Filter Gain (MFB) Gain = −Rf / Ri Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ → Voltage Gain = -0.4545
- Filter Q to Damping Ratio Q = 1 / (2 × ζ) Damping Ratio ζ 0.055 → Quality Factor = 9.091
- LC Filter Cutoff Frequency fc = 1 / (2π × √(L × C)) Inductance 100 nH, Capacitance 100 nF → Cutoff Frequency = 1.592 MHz
- First-Order Bode Phase φ = −arctan(f/fc) Signal Frequency 5 Hz, Cutoff Frequency 11 Hz → Phase (degrees) = -24.44
- Moving Average Filter Bandwidth f3dB ≈ 0.443 × fs / N Sample Rate 11 Hz, Window Size 0.025 → −3 dB Frequency = 0.1949 kHz
- Switched-Capacitor Filter Cutoff fc = fclk / ratio Clock Frequency 11 Hz, Clock-to-Cutoff Ratio 0.025 → Filter Cutoff = 0.44 kHz
- Pi-Filter Attenuation A = 20 × log10(1/(ω² × L × C)) Frequency 100 Hz, Inductance 100 nH, Capacitance (each) 100 nF → A = 168.1
Worked result for every Filters formula
| Formula | Expression | Worked result |
|---|---|---|
| RC Low-Pass Filter | fc = 1 / (2πRC) | Resistance 100 Ω, Capacitance 100 pF → Cutoff Frequency = 15.92 MHz |
| RC High-Pass Filter | fc = 1 / (2πRC) | Resistance 100 Ω, Capacitance 100 pF → Cutoff Frequency = 15.92 MHz |
| Bandpass Bandwidth | BW = f2 − f1 | Lower Cutoff 11 Hz, Upper Cutoff 23.5 Hz → Bandwidth = 12.5 Hz |
| Filter Rolloff Rate | Rolloff = N × 20 dB/decade | Filter Order 0.025 → Rolloff (dB/decade) = 0.5 dB/decade |
| Notch Frequency | f = 1 / (2π√(LC)) | Inductance 100 µH, Capacitance 100 pF → Notch Frequency = 1.592 MHz |
| Butterworth Q Factor | Q = 1 / (2 × sin(π/(2N))) | Filter Order 25 → Q = 7.963 |
| Sallen-Key Cutoff Frequency | fc = 1 / (2π × √(R1×R2×C1×C2)) | R1 100 Ω, R2 0.22 kΩ, C1 100 pF, C2 0.22 nF → fc = 7.23 × 10⁶ Hz |
| Chebyshev Filter Order | N = acosh(√(ε²s/ε²p)) / acosh(fs/fp) | Stopband Attenuation (dB) 3 dB, Passband Ripple (dB) 1.41 dB, Stopband Frequency 1 kHz, Passband Frequency 0.47 kHz → N = 0.7607 |
| Bessel Filter Group Delay | τ = R × C | Resistance 100 Ω, Capacitance 100 pF → Group Delay = 10 ns |
| Active Filter Gain (MFB) | Gain = −Rf / Ri | Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ → Voltage Gain = -0.4545 |
| Filter Q to Damping Ratio | Q = 1 / (2 × ζ) | Damping Ratio ζ 0.055 → Quality Factor = 9.091 |
| LC Filter Cutoff Frequency | fc = 1 / (2π × √(L × C)) | Inductance 100 nH, Capacitance 100 nF → Cutoff Frequency = 1.592 MHz |
| First-Order Bode Phase | φ = −arctan(f/fc) | Signal Frequency 5 Hz, Cutoff Frequency 11 Hz → Phase (degrees) = -24.44 |
| Moving Average Filter Bandwidth | f3dB ≈ 0.443 × fs / N | Sample Rate 11 Hz, Window Size 0.025 → −3 dB Frequency = 0.1949 kHz |
| Switched-Capacitor Filter Cutoff | fc = fclk / ratio | Clock Frequency 11 Hz, Clock-to-Cutoff Ratio 0.025 → Filter Cutoff = 0.44 kHz |
| Pi-Filter Attenuation | A = 20 × log10(1/(ω² × L × C)) | Frequency 100 Hz, Inductance 100 nH, Capacitance (each) 100 nF → A = 168.1 |
Variables used across Filters formulas
- fc — Cutoff frequency at -3dB point (Hz)
- R — Resistance (Ω)
- C — Capacitance (F)
- BW — Bandwidth (Hz)
- f1 — Lower -3dB cutoff frequency (Hz)
- f2 — Upper -3dB cutoff frequency (Hz)
- N — Filter order (number of poles)
- Rolloff — Asymptotic attenuation rate (dB/decade)
- f — Notch center frequency (Hz)
- L — Inductance (H)
- Q — Quality factor of the highest-Q pole pair
- R1 — Resistor (Ω)
- R2 — Resistor (Ω)
- C1 — Capacitor (F)
- C2 — Capacitor (F)
- Ar — Required stopband attenuation (dB)
- Ap — Allowable passband ripple (dB)
- fs — Stopband edge frequency (Hz)
- fp — Passband edge frequency (Hz)
- τ — Group delay of the filter section (s)
- Gain — Passband voltage gain (negative, indicating inversion)
- Rf — Feedback resistor (Ω)
- Ri — Input resistor (Ω)
- ζ — Damping ratio (dimensionless)
- φ — Phase shift in degrees (negative for low-pass)
- f_3dB — Approximate −3 dB bandwidth (Hz)
- f_clk — Clock frequency (Hz)
- ratio — Clock-to-cutoff frequency ratio (e.g., 50, 100)
Questions people ask about Filters
- Calculate to cutoff frequency in a sallen key filter — Sallen-Key Cutoff Frequency
- Cutoff frequency r1 r2 c1 — Sallen-Key Cutoff Frequency
Related Formula Categories
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