How this instrument works
A first-order RC high-pass filter is a voltage divider built the opposite way round from a low-pass one: the capacitor sits in series with the signal path, and the resistor taps the output to ground. A capacitor's opposition to alternating current, its reactance, is 1 ⁄ (2πfC) — enormous near zero frequency and shrinking as frequency climbs. At DC that reactance is effectively infinite, so no current flows and the output sits at zero; as frequency rises the capacitor's opposition falls, more signal reaches the resistor, and above the corner it barely gets in the way at all.
The corner sits exactly where capacitor and resistor present equal opposition, X_C = R, which is why solving 1 ⁄ (2πfC) = R for f returns the same expression, f_c = 1 ⁄ (2πRC), that a low-pass filter built from the identical two parts would use. Swap which component the output is measured across and the whole behavior inverts: what was a low-pass roll-off becomes a high-pass rise, using nothing more than a change in wiring. Below that shared corner, output falls by roughly 6 dB for every octave you move downward, a slope set by a single real pole and nothing sharper.
That blocking is not instantaneous either. Hit the input with a sudden step — a microphone connector unplugging, a sensor's power rail switching on — and the output does not sit quietly at zero; it jumps to the full size of that step and decays back toward zero over roughly five RC intervals, the same interval that governs any first-order network. Anyone wiring AC coupling into an amplifier or an analog-to-digital input has to size that stage to survive the transient without clipping, because for one brief moment right after the disturbance the filter is passing exactly what it was built to block. And because a single RC section offers only one pole, its steady-state roll-off never gets steeper than that fixed 6 dB per octave; cutting deeper into an unwanted low-frequency band means cascading more stages or moving to an active or LC design.
- Enter the series capacitor's value in Capacitance, choosing nF or µF to match the part's printed marking.
- Enter the shunt or load impedance in Resistance, in ohm or kohm — this is what the capacitor's output feeds into.
- Read Cutoff frequency in Hz or kHz: the point where output has fallen to 70.7% of input, 3 dB down.
- Compare your lowest wanted frequency against Cutoff frequency — keep the corner well below it to pass that content cleanly.
- To design a low-pass filter instead, keep the same two values but swap which component the output is taken across.
Worked example — a 10 kΩ, 100 nF stage-rumble filter
A live-sound engineer wants a vocal channel's low-cut filter to strip stage rumble and mic-stand thumps without touching the singer's voice. Building the classic series-capacitor, shunt-resistor stage from a 100 nF capacitor and a 10 kΩ input impedance, enter 10 into Resistance (kΩ) and 100 into Capacitance (nF). Cutoff frequency returns 159.154943092 Hz, from 1 ⁄ (2π × 10,000 Ω × 0.0000001 F) — about 159 Hz in the round numbers a mixing console's knob would show.
That corner sits usefully between a kick drum's thump and a singer's lowest note. One octave above it, near 318 Hz, loss is under 1 dB — essentially inaudible. One octave below, near 80 Hz, output is already down about 7 dB, and a decade below, near 16 Hz, it has fallen close to 20 dB — deep enough to bury stage vibration and HVAC rumble while leaving chest-voice notes above 100 Hz almost untouched.
Questions
What's the actual difference between a high-pass and a low-pass filter here?
Only which component the output is taken across. Keep the same resistor and capacitor, put the capacitor in series and read the output across the shunt resistor, and low frequencies get blocked while highs pass — a high-pass filter. Take the output across the capacitor instead and the behavior flips to low-pass. Both share the identical corner, f_c = 1 ⁄ (2πRC), because that frequency is defined purely by when reactance equals resistance, not by which side you happen to be reading.
Does a high-pass filter block DC completely?
In the ideal model, yes — H(f) goes to exactly zero as f approaches zero, since the capacitor's reactance grows without bound. Real capacitors fall slightly short because of dielectric leakage, which datasheets usually specify as a minimum megohm-microfarad product rather than a flat ohm figure, since leakage current scales with the part's own capacitance. A well-chosen film or ceramic part keeps that shortfall irrelevant for nearly any design; it only turns into a real concern when a large electrolytic is asked to do double duty as both a bulk filter capacitor and a DC block.
How steep is the roll-off below the cutoff frequency?
About 6 dB per octave, or 20 dB per decade, because a single RC stage contributes exactly one real pole. Near the corner the slope is gentler than that asymptote suggests — output is about 7 dB down one octave below cutoff, not 6 — and it only settles onto the full 6 dB/octave rate well away from f_c. A sharper knee needs more poles: cascade RC stages, or move to an active or LC filter design.
Can this filter remove a DC offset from a sensor signal?
Yes, provided the corner sits comfortably below the sensor's lowest frequency of real interest. A vibration sensor reporting content from 5 Hz upward, for instance, wants its cutoff frequency set at 1 Hz or below so the DC bias is stripped without attenuating the signal itself; setting the corner too close to that 5 Hz floor would shave real amplitude off the very content the sensor is meant to capture.
Does a passive high-pass filter add any noise of its own?
A little, and it comes from the resistor rather than the capacitor. Any resistor above absolute zero generates Johnson-Nyquist thermal noise with a voltage spectral density of the square root of 4kTR — for the 10 kΩ shunt in the worked example, that works out to roughly 12.8 nanovolts per root-hertz at room temperature. Against a line-level signal it is irrelevant, but it starts to matter once R climbs into the hundreds of kilohms feeding a sensitive microphone preamp. The capacitor, being purely reactive, contributes none.
Are R and C interchangeable in the formula?
They enter the formula the same way, so doubling either one alone halves the cutoff frequency, and doubling both together quarters it — but they are not interchangeable in the circuit. R and C occupy fixed, different roles: the capacitor must be the series element for high-pass behavior, and the resistor the shunt to ground. Swap their positions, not merely their values, and the filter's pass band flips from high to low.