Cutoff Frequency Calculator (RC/RL/LC)

Cutoff frequency: RC, RL and LC filters

The cutoff frequency f_c is where a filter's output power falls to half (−3 dB) of its passband level. For a first-order RC or RL filter: fc = 1 / (2π · R · C) or fc = R / (2π · L). For an LC resonant filter: fc = 1 / (2π · √(L · C)). The pulse-response equivalent is τ = 1 / (2π · fc). First-order filters roll off at 20 dB/decade; second-order at 40 dB/decade. Sharper responses use Butterworth, Chebyshev or elliptic topologies. Example: R = 10 kΩ, C = 10 nF gives f_c = 1 / (2π · 10 000 · 1e-8) ≈ 1.59 kHz.

Applications: anti-aliasing, audio, power, RF

Cutoff design appears in anti-aliasing filters before an ADC (Nyquist), audio crossovers (woofer/tweeter split), ripple smoothing in switching supplies, RF tuning stages, and biomedical instrumentation (ECG band-pass between roughly 0.5 Hz and 40 Hz).

FAQ

Why −3 dB and not −6 dB? −3 dB corresponds to half power and 1/√2 of voltage — the classic convention for the corner frequency.

Is the LC formula valid with losses? It assumes ideal components; with loss (Q ≪ 10), the actual peak shifts slightly below f_c.

How do I get a steeper roll-off? Cascade filters or use higher-order Butterworth/Chebyshev; each order adds 20 dB/decade.

RC versus RL — when to choose which? RC is cheaper and more common at audio; RL is preferred at RF and in power electronics where inductors handle DC bias better than capacitors.