Calculate cutoff frequency for RC, RL, and RLC filters. Solve for any component value. Frequency response table and filter design.
The cutoff frequency (also called the -3dB frequency or corner frequency) is where a filter's output power drops to half its passband value. For a simple RC low-pass filter, f_c = 1/(2πRC). For an RL filter, f_c = R/(2πL). For an RLC resonant circuit, f₀ = 1/(2π√LC).
At the cutoff frequency, the output voltage is 1/√2 (≈ 70.7%) of the input voltage, corresponding to a -3.01 dB power loss. First-order RC and RL filters roll off at 20 dB per decade (6 dB per octave) beyond the cutoff. Second-order RLC filters have 40 dB/decade roll-off and exhibit resonance characterized by the quality factor Q.
This calculator handles all common passive filter topologies: RC and RL (low-pass and high-pass), and RLC (band-pass and band-stop). It can solve for cutoff frequency, required resistance, capacitance, or inductance given the other values. The frequency response table shows gain across multiple decades. Check the example with realistic values before reporting.
Designing filters requires computing component values from a target frequency, or finding the frequency from given components. The formulas involve π and unit conversions (µF→F, mH→H) that are error-prone by hand.
This calculator provides bidirectional solving (frequency↔components), supports all common passive filter types, shows the complete frequency response, and handles unit conversions automatically. It is essential for electronics design, audio engineering, and RF circuit work.
RC: f_c = 1/(2πRC). RL: f_c = R/(2πL). RLC: f₀ = 1/(2π√LC). Gain at f_c = -3.01 dB = 1/√2. Q = (1/R)√(L/C). BW = f₀/Q.
Result: f_c = 1591.5 Hz, τ = 0.1 ms
f_c = 1/(2π × 1000 × 100×10⁻⁹) = 1/(6.283 × 10⁻⁴) = 1591.5 Hz. Time constant τ = RC = 1000 × 10⁻⁷ = 0.1 ms. At 1591.5 Hz, output is 70.7% of input.
**Low-pass filters** pass frequencies below f_c and attenuate higher frequencies. Used in: audio tone controls, anti-aliasing before ADC, power supply decoupling, and communication channel bandwidth limiting.
**High-pass filters** pass frequencies above f_c and block lower frequencies. Used in: AC coupling (blocking DC), audio bass filtering, and rumble filters in turntable preamplifiers.
**Band-pass filters** pass a range of frequencies centered on f₀ with bandwidth BW = f₀/Q. Used in: radio tuning, audio equalizers, and communication channel selection.
**Band-stop (notch) filters** reject a narrow band around f₀. Used in: eliminating 50/60 Hz mains interference, audio feedback suppression, and harmonic filtering.
Real components have parasitic elements that affect high-frequency behavior. Resistors have stray capacitance (~0.5 pF) and inductance (~10 nH). Capacitors have equivalent series resistance (ESR) and inductance (ESL). These parasitics limit the useful frequency range of passive filters.
For precise filter responses (Butterworth, Chebyshev, Bessel), active filters using op-amps are preferred. The Sallen-Key and multiple-feedback topologies implement second-order sections that can be cascaded for any order. Software tools like FilterPro help design these.
The cutoff frequency and time constant are directly related: f_c = 1/(2πτ). A filter with τ = 1ms has f_c = 159 Hz. The step response of an RC low-pass filter is V(t) = V₀(1 − e^(-t/τ)), reaching 63.2% in one time constant, 95% in three, and 99.3% in five. This means the filter's time response and frequency response are two views of the same behavior, related by the Fourier transform.
-3dB means half power. Since power is proportional to voltage squared, -3dB voltage = 1/√2 ≈ 0.707 of the input. This is the standard definition of the cutoff frequency for all filter types.
For first-order (RC/RL) filters, the cutoff frequency is where gain = -3dB. For second-order RLC circuits, the resonant frequency f₀ = 1/(2π√LC) is where impedance is minimum (series) or maximum (parallel). The -3dB bandwidth depends on Q.
Q = f₀/BW = (1/R)√(L/C) for series RLC. Higher Q means sharper selectivity (narrower bandwidth). Q = 1 is critically damped; Q > 10 gives a sharp resonance peak.
A single reactive element (C or L) creates a single pole in the transfer function. Each pole contributes 20 dB/decade (6 dB/octave) asymptotic roll-off. Second-order (two reactive elements) gives 40 dB/decade.
Yes — two cascaded RC filters give 40 dB/decade roll-off, but the -3dB frequency shifts lower because both stages attenuate. Properly designed active Butterworth/Chebyshev filters give precise characteristics.
For audio (20 Hz–20 kHz): low-pass at 10–15 kHz uses R = 1kΩ, C = 10–15nF. High-pass at 20–100 Hz uses R = 10kΩ, C = 0.1–1µF. Use film capacitors for audio quality.