A high-pass filter calculator like this one helps you design and verify filters that block DC and low frequencies, passing only signals above the cutoff f_c. Like the low-pass cousin, the cutoff is conventionally the −3 dB point: the frequency at which output amplitude has fallen to 1/√2 (≈ 0.707) of the input — half the power. Below f_c the filter is "stopband" (attenuating); above is "passband" (passing); the transition between depends on filter order. The Bode plot is the standard way to visualize this behavior — it graphs magnitude (in dB) and phase (in degrees) against log frequency, making the rolloff slope and phase shift immediately readable.
RC and RL — 1st-order filters
A single resistor + capacitor (RC) or resistor + inductor (RL) makes a 1st-order high-pass with the same f_c = 1 / (2π·τ) formula as low-pass — only the component arrangement differs. For RC: the capacitor goes in series, resistor to ground. For RL: the inductor goes shunt to ground, resistor in series with output. Below f_c the magnitude rolls off at −20 dB/decade (−6 dB/octave) as frequency drops. Phase shifts from +90° at DC (output leads input by a quarter cycle) to 0° at high frequency, passing through +45° at f_c.
Sallen-Key — 2nd-order active filters
The Sallen-Key high-pass topology is the dual of the low-pass: swap the R and C positions. This two-op-amp circuit is the most common active high-pass filter design at audio frequencies. Op-amp + 2 capacitors (in series) + 2 resistors (to ground / feedback) gives a 2nd-order high-pass with −40 dB/decade rolloff below f_c and a tuneable Q factor. The Q-vs-response trade-offs are identical to LP:
- Q = 0.5 (critically damped) — slowest transition, no overshoot in step response.
- Q = 0.577 (Bessel) — maximally-flat group delay. Best pulse fidelity.
- Q = 0.707 (Butterworth) — maximally-flat passband. Standard general-purpose choice.
- Q ≥ 1 (Chebyshev) — sharper rolloff at the cost of passband ripple + step-response ringing.
Practical applications
High-pass filters are everywhere in audio and signal processing. When a single unwanted frequency (rather than an entire low-frequency band) needs targeting, a notch filter is the right tool — it removes a narrow band while leaving the rest of the spectrum intact, unlike a high-pass which attenuates everything below f_c.
- DC blocking — A small series capacitor at the input of an amplifier removes any DC offset from the previous stage. A 1 µF cap into a 10 kΩ input gives f_c = 15.9 Hz, well below audio.
- Rumble / wind filter — Speech/voice work uses f_c = 80–100 Hz to remove HVAC rumble, microphone handling noise, and wind. Most pro mics have built-in switchable HPFs, and the human vocal fundamental rarely falls below 85 Hz, so an 80 Hz HPF passes nearly all intelligibility.
- Subsonic protection — Bass-heavy systems use ~20 Hz HPF to keep speaker cones from over-excursion on signals below the threshold of human hearing.
- RIAA equalization — Phono preamps include a complex HPF as part of the RIAA de-emphasis curve to compensate for the recording side's bass cut.
- Crossover networks — Loudspeaker crossovers apply a high-pass to the tweeter to protect it from low-frequency cone excursion; the HPF cutoff is typically 2–5 kHz at 12 or 24 dB/octave (2nd or 4th order Linkwitz-Riley alignment).
- Anti-aliasing / interpolation in DSP — Often paired with a low-pass to form a band-pass, or used as a pre-filter before analog-to-digital conversion.
Step response — what it tells you
The step response of a high-pass filter is the opposite of a low-pass: it starts at full step amplitude (because the instantaneous edge is "all high frequency") and then decays toward zero (because once the step settles to constant DC, the HPF blocks it). For a 1st-order HP, the decay is a simple exponential reaching ~37% (1/e) at one time constant τ, ~5% at 3τ. For a 2nd-order under-damped (Q > 0.5) HP, the response can swing below zero (undershoot) before settling — the higher the Q, the more pronounced the undershoot and the longer it rings.
Why does a high-pass step response start at 1, not 0?
A unit step has an instantaneous edge at t=0 — that edge contains all frequencies, including the high ones. The HP filter passes the edge through (output = 1 at t=0⁺) then progressively blocks the DC portion that follows, so the output decays back to 0. Mathematically: the step's Laplace transform is 1/s; multiplied by HP transfer function H(s) = s/(s+ωc) for 1st-order, the s in the numerator cancels the 1/s, giving 1/(s+ωc) → exp(−ωc·t). At t=0 that's 1; at t=∞ it's 0. So the HP "blocks DC but passes the edge."
What's the relationship between low-pass and high-pass formulas?
For 1st-order, the magnitudes are complementary: |H_LP|² + |H_HP|² = 1 (at any frequency). They share the same f_c, the same τ, and the same component formulas — just different arrangement. For 2nd-order Sallen-Key, the topology mirrors: where LP has R-R-C-C (series R's with shunt C's), HP has C-C-R-R (series C's with shunt R's). Same Q, same f_c, same op-amp gain calculation.
Why might my high-pass output amplitude be larger than the input?
For 2nd-order Sallen-Key with Q > 0.707, there's gain peaking just above f_c — the same as low-pass but on the other side of the cutoff. At Q = 2 the peak is +6 dB above unity gain, at f_p ≈ f_c·sqrt(1 − 1/(2Q²)) ≈ f_c·0.93. This is sometimes desired (resonant boost for "wah" effects) but usually a problem (clipping, ringing). Reduce Q if you need a flat passband response above f_c.
What capacitor type should I use?
For audio HP filters (10 Hz – 10 kHz cutoffs), use film capacitors (polyester, polypropylene, polycarbonate) for the best linearity and lowest distortion. Electrolytic capacitors have voltage-dependent capacitance and can cause distortion in the signal path — but they're sometimes used because of their large capacitance per dollar, with a low-leakage type required (e.g., NP/bipolar electrolytic). Ceramic Class 1 (NP0/C0G) is fine for small values (≤ 100 nF) but Class 2 (X7R, X5R, Y5V) capacitance varies with voltage and shouldn't be used in audio HP filters where signal flows through the cap.
Does the HP filter affect phase below the cutoff?
Yes. For 1st-order HP: phase is +90° at DC, +45° at f_c, 0° at infinity. Most of the phase shift happens around f_c (a decade above and below). This means HP filters in a signal chain affect bass response phase too — a 50 Hz HPF on a 100 Hz signal shifts that 100 Hz by ~26° even though the magnitude is mostly passed. If you cascade multiple HP filters (e.g., DC-blocking caps at every gain stage) the phase shifts add up and can become audible as a "phasey" character or smearing of transients. Choose f_c well below your lowest signal frequency to minimize this.
Why is RC much more common than RL for high-pass?
Inductors are bulkier, more expensive, less linear, and pick up magnetic noise — capacitors are smaller, cheaper, closer to ideal, and shielded by their own dielectric. RC is the default for audio and most signal-processing. RL high-pass shows up in (a) power supplies where the L is sized for handling DC current, (b) RF circuits where ferrite-core inductors are practical at high frequency, (c) loudspeaker crossover networks where the inductor is the woofer's series impedance protection. For audio signal-path work, use RC.
Can I combine LP and HP to make a band-pass?
Yes — cascade a low-pass with cutoff f_high and a high-pass with cutoff f_low (where f_low < f_high). The passband spans f_low to f_high, with 6 dB/octave rolloff on each side (for 1st-order RC pairs). For dedicated band-pass with sharper edges and selectable bandwidth, use the Band-Pass Filter Calculator (also in this category) which implements multiple-feedback and other topologies designed specifically for band-pass behavior.
What does "−3 dB cutoff frequency" mean in practical terms?
At the −3 dB cutoff frequency f_c, the filter passes a signal at 70.7% of its original amplitude (1/√2). Power is halved (−3 dB on a power scale). In practice that's only a modest attenuation — you may still hear bass bleed through at f_c. For audio work this means an "80 Hz high-pass" doesn't silence the kick drum at 80 Hz; it reduces it by 3 dB there. Significant audible attenuation (−20 dB, one tenth amplitude) only arrives a full decade below f_c for a 1st-order filter, or roughly 3 octaves below for a 2nd-order Butterworth.
What happens when I cascade two identical RC high-pass filters?
Two identical RC high-pass stages in series give a 2nd-order overall response with −40 dB/decade rolloff — faster than a single stage. However, the combined −3 dB frequency shifts: each stage loads the next (because the second stage's R forms a voltage divider with the first's output impedance), so the pair's actual cutoff depends on how the stages are buffered. If you insert a unity-gain buffer (op-amp voltage follower) between stages you get an independent, non-interacting pair with the same f_c, and the result is a 2nd-order response equivalent to a critically-damped (Q = 0.5) filter. The Sallen-Key topology on this calculator provides a proper 2nd-order active design without requiring a separate buffer between passive stages.
How do I choose the right HPF cutoff frequency for vocals or podcasting?
For speech and vocals, a high-pass filter cutoff of 80–120 Hz is the standard starting point. The human vocal fundamental (F0) for a baritone sits around 85–180 Hz; for a soprano, 200–1,000 Hz. A 100 Hz HPF removes rumble, HVAC noise, and mic handling vibration while passing all vocal fundamentals. If the recording is especially boomy or the mic was too close (proximity effect), you can push the cutoff to 150–200 Hz. Roll off too high (above 250 Hz) and you strip warmth from chest voices. Use a 1st-order (−6 dB/octave) to be gentle, or a 2nd-order (−12 dB/octave) Butterworth for stronger rumble rejection without audible coloration in the passband.