RC Filter Cutoff Frequency & Time Constant Calculator
RC filter -3 dB cutoff: fc = 1/(2πRC). Time constant τ = RC. Works for both low-pass and high-pass single-pole RC filters — enter R in kΩ and C in nF.
RC Filter — Cutoff Frequency & Time Constant
Parameter
Value
Cutoff Frequency fc
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Time Constant τ
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Attenuation @ 10× fc
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Attenuation @ 100× fc
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Formula & Theory
Cutoff frequency: fc = 1 / (2π × R × C)
Time constant: τ = R × C
Attenuation at frequency f: A(f) = −20 log₁₀(√(1 + (f/fc)²)) dB
At 10× fc: A ≈ −20.04 dB (one decade rolloff)
At 100× fc: A ≈ −40.00 dB (two decades rolloff)
The -3 dB point is exact: at f = fc, output voltage = input / √2 = 0.707 × Vin.
Worked Example
Anti-aliasing filter for 10 kSPS ADC (target fc = 1 kHz):
Choose R = 15.9 kΩ (use 16 kΩ), C = 10 nF
fc = 1 / (2π × 16,000 × 10×10⁻⁹) = 995 Hz ≈ 1 kHz
τ = 16,000 × 10×10⁻⁹ = 160 µs
Attenuation at 5 kHz (Nyquist): A = −20 log₁₀(√(1 + (5/1)²)) = −14.2 dB — marginal for high-res ADC; use 2-pole filter for better rejection
Assumptions & Limitations
Single-pole filter only — each additional RC stage adds another -20 dB/decade pole
Ideal components — no capacitor ESR, no resistor parasitic inductance
Source impedance not included — if driven from a non-zero source impedance, R_eff = R_source + R
Load impedance much higher than R — a low-impedance load reduces effective R and shifts fc
Common Mistakes
Ignoring capacitor dielectric absorption: For precision timing circuits, ceramic capacitors have dielectric absorption that causes "soakage" errors. Use film capacitors for RC timing applications requiring better than 1% accuracy.
Forgetting source impedance: If R is driven by a circuit with non-zero output impedance (e.g. an op-amp with Rout, or a DAC with source resistance), the effective cutoff frequency shifts. Add source impedance to R.
Single pole for high-resolution ADC anti-aliasing: A single-pole RC gives only -20 dB/decade. For a 16-bit ADC needing >96 dB alias rejection, a single pole is inadequate — use a multi-pole active filter.
Parts to Consider
Representative part categories — verify specifications match your design requirements before ordering.
Resistors & Capacitors — Component KitsE24 resistor and ceramic cap assortments — useful for prototyping RC filters
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What is the difference between -3 dB cutoff and the time constant?
The time constant τ = RC is the time for the output to reach 63.2% of its final value in response to a step input. The -3 dB cutoff frequency fc = 1/(2πτ) is the frequency where the output power is halved (-3 dB) and the voltage magnitude is 0.707 (-3 dB) of the input. They describe the same filter from time-domain and frequency-domain perspectives.
How many dB does a single-pole RC filter roll off per decade?
A single-pole RC filter rolls off at -20 dB/decade (or -6 dB/octave) above the cutoff frequency. At 10× fc the attenuation is approximately -20 dB. A 2-pole RC filter would give -40 dB/decade, and so on.
How do I design an anti-aliasing filter for an ADC?
Set fc to half the ADC sample rate (Nyquist frequency). For example, a 10 kSPS ADC needs fc ≤ 5 kHz. Choose a component combination that gives this cutoff, then verify the attenuation at the actual sample rate is sufficient for your resolution (e.g. for 12-bit ADC you need >72 dB of attenuation at fs/2).