RC High-Pass Cutoff⚠ unverified

Understanding the Parameters

• $R$ and $C$ set the same time constant $\tau = RC$ as the low‑pass; the corner frequency formula is identical. Only the topology (which element is in series) decides whether it is a high‑ or low‑pass.

• $f_c$ — below it the series capacitor's rising impedance attenuates the signal; at DC the capacitor fully blocks.

Derivation (Approaching a Proof)

With $C$ in series and $R$ to ground, the output across $R$ is the voltage‑divider ratio

$$H(j\omega) = \frac{R}{R + 1/(j\omega C)} = \frac{j\omega R C}{1 + j\omega R C},$$

so $|H| = \dfrac{\omega R C}{\sqrt{1 + (\omega R C)^2}}$. The half‑power point $|H|^2 = \tfrac12$ again occurs at $\omega R C = 1$:

$$f_c = \frac{1}{2\pi R C}.$$

The corner is the same $1/(2\pi RC)$ as the low‑pass, but the passband is inverted: $|H|\to 1$ at high frequency and $|H|\to 0$ at DC, with a $+45^\circ$ phase lead at $f_c$.

History

The RC high‑pass is the complement of the RC low‑pass and equally fundamental — used for AC coupling (blocking DC offsets), differentiators, and edge/transient emphasis. Both follow from applying Ohm's law to the capacitor's frequency‑dependent impedance.

Related Concepts: RC Low-Pass Cutoff, Highpass Passive Cutoff, RC Time Constant, Impedance Capacitor

Notes: Registry calculator rc-highpass-cutoff (unverified). Same corner formula as the low‑pass; topology sets the passband.