Lowpass Passive Cutoff⚠ unverified
Electrical / Filters · Compute the cutoff frequency of a passive low-pass filter
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| R | R | — | 1.0 | Resistance |
| C | C | F | 1.0 | Capacitance |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | fc | Hz | Cutoff (-3 dB) frequency, in hertz (Hz) |
The science & history
Understanding the Parameters
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$R$, $C$ set the time constant $\tau = RC$; the cutoff is $f_c = 1/(2\pi RC)$. A "passive" filter can only attenuate (gain $\le 1$) — it has no power source of its own.
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$f_c$ — the half‑power frequency.
Derivation (Approaching a Proof)
The RC divider gives $H(j\omega) = \dfrac{1}{1 + j\omega RC}$, so $|H| = 1/\sqrt{1 + (\omega RC)^2}$. The half‑power condition $|H|^2 = \tfrac12$ requires $\omega RC = 1$, hence
$$f_c = \frac{1}{2\pi R C}.$$
(For the full step‑by‑step voltage‑divider argument see RC Low-Pass Cutoff.) Because a single RC section is first order, its stopband slope is $-20\,$dB/decade; steeper roll‑off needs higher order (cascaded sections or an active design — see Sallen Key Lowpass, Butterworth Cutoff).
History
Passive RC/LC filters predate active designs and remain the default where simplicity, no power supply, and low noise matter (RF front ends, supply decoupling, anti‑alias pre‑filters). The trade‑off is limited selectivity and sensitivity to source/load impedance.
Related Concepts: RC Low-Pass Cutoff, Highpass Passive Cutoff, Filter Order Rolloff, Impedance Capacitor
Notes: Registry calculator lowpass-passive-cutoff (unverified; R is mislabelled dimensionless —
should be ohms). Same formula as RC Low-Pass Cutoff.