Highpass Passive Cutoff⚠ unverified
Electrical / Filters · Compute the cutoff frequency of a passive high-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 $\tau = RC$; the corner is $f_c = 1/(2\pi RC)$ — identical in form to the low‑pass. The series capacitor blocks DC and low frequencies.
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$f_c$ — the half‑power frequency; below it the response falls at $+20\,$dB/decade toward DC.
Derivation (Approaching a Proof)
With $C$ in series and $R$ to ground, $H(j\omega) = \dfrac{j\omega RC}{1 + j\omega RC}$, so $|H| = \dfrac{\omega RC}{\sqrt{1 + (\omega RC)^2}}$. Setting $|H|^2 = \tfrac12$ gives $\omega RC = 1$ and
$$f_c = \frac{1}{2\pi R C}.$$
(See RC High-Pass Cutoff for the detailed divider derivation.) The single RC section is first order, so the transition is a gentle $20\,$dB/decade.
History
Passive high‑pass sections are the classic AC‑coupling element: a series capacitor that blocks a DC bias while passing the signal. They also form the front of differentiators and DC‑blocking interstage couplings throughout analog electronics.
Related Concepts: RC High-Pass Cutoff, Lowpass Passive Cutoff, Filter Order Rolloff, Impedance Capacitor
Notes: Registry calculator highpass-passive-cutoff (unverified; R is mislabelled dimensionless —
should be ohms). Same formula as RC High-Pass Cutoff.