Electronics
High-pass filter explained
A high-pass filter passes high frequencies and weakens low ones. The simplest is a capacitor in series with the signal and a resistor to ground, with the output taken across the resistor. Its cutoff frequency is fc = 1 ÷ (2π R C), where the output has fallen to 70.7% of the input. Below that, the lower the frequency the less gets through, and steady DC is blocked completely.
A capacitor in the way
A capacitor's reactance, XC = 1 ÷ (2π f C), is huge at low frequencies and tiny at high ones. In a high-pass the capacitor and the resistor form a voltage divider with the output across R. High notes see a small reactance, so nearly all their voltage reaches R. Low notes see a big one, which keeps most of their voltage for itself. At DC the reactance is infinite and nothing passes.
It's the mirror image of a low-pass filter, which takes its output across the capacitor instead.
Live experiment
Sweep a note through a high-pass
A note passes through an RC filter, 1.6 kΩ and 100 nF, with its corner at about 995 Hz. Flip it to high-pass, then slide the note from 20 Hz to 20 kHz: the bass fades and the treble comes through whole, with the output leading the input.
“Low- and high-pass filters” is lesson 4 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 24 before it first.
The cutoff frequency
It's the frequency where XC equals R. There the output is 1 ÷ √2 ≈ 70.7% of the input, −3 dB, and it leads the input by 45°. Below the corner the output falls about 20 dB per decade: a tenth of the cutoff frequency gets through at about a tenth of its size.
Example: a microphone's low-cut filter with 1.6 kΩ and 1 µF.
Rumble at 10 Hz, a decade below, is cut to about −20 dB, while speech at 1 kHz passes almost untouched.
Killing mains hum
A guitar lead picks up 50 Hz hum. Put the cutoff near 500 Hz, a decade above the hum, and the hum drops by about 20 dB. Music at 1 kHz, only twice the cutoff, loses about 1 dB. With a 100 nF capacitor, R = 1 ÷ (2π × 500 × 10⁻⁷) ≈ 3.2 kΩ; the nearest E12 value, 3.3 kΩ, puts the corner at about 480 Hz.
Coupling capacitors
Almost every audio input has a high-pass built in. A coupling capacitor in series with the input, working against the input's own resistance, passes the signal and blocks any steady DC level, so one stage's bias doesn't upset the next. Here the cutoff is set well below 20 Hz, so no music is lost.
A coil can make a high-pass too: put a resistor in series and the coil to ground, and the coil shorts the low frequencies away.
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“Low- and high-pass filters” is lesson 4 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 24 before it first.
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Practice questions
Three quick questions from the lessons. Pick an answer to check it.
Show the answer
Answer: 70.7% of the input. At fc, XC = R and the output is 1 over √2 ≈ 70.7% of the input. That's half the power, since 0.707² = 0.5, which is where the 50% idea comes from.
- Why not “50% of the input”? 50% is half the voltage. At the cutoff it's the power that halves, which leaves 70.7% of the voltage.
- Why not “100% of the input”? The output only gets close to 100% far out in the pass band. At the corner it's already down to 70.7%.
Show the answer
Answer: the capacitor. At high frequencies the capacitor's reactance gets small and drains the signal to ground, so the voltage across it falls. Across the resistor you'd get a high-pass.
- Why not “the resistor”? Taking the output across the resistor gives a high-pass, which passes treble instead of bass.
- Why not “the source”? Across the source you'd just get the input back, unfiltered.
Show the answer
Answer: the same size as the input. A decibel is a ratio. 0 dB is a ratio of 1, the same as the input. Nothing at all would be minus infinity dB, and ten times bigger is +20 dB.
- Why not “ten times the input”? Ten times the input is +20 dB. 0 dB is a ratio of exactly 1.
- Why not “zero”? Decibels compare two things. An output of nothing would be minus infinity dB, not 0 dB.
“Low- and high-pass filters” is lesson 4 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 24 before it first.
Questions people ask
What does a high-pass filter do?
It passes high frequencies and weakens low ones, and blocks steady DC completely. Uses include removing rumble and mains hum, coupling audio between amplifier stages, and the small capacitor in front of a speaker's tweeter.
How do you calculate the cutoff of an RC high-pass filter?
The same way as a low-pass: f_c = 1 ÷ (2π × R × C). With 1.6 kΩ and 1 µF, that's about 100 Hz. At f_c the output is 70.7% of the input, −3 dB, and it leads the input by 45°.
How do I make a high-pass filter from a low-pass?
Swap the two parts. Put the capacitor in series with the signal and the resistor from the output to ground, and take the output across the resistor. The cutoff formula doesn't change.
What is a coupling capacitor?
A capacitor in series with a signal, feeding a stage's input resistance. Together they form a high-pass filter that passes the audio and blocks any DC level. Choose C so the cutoff sits well below the lowest note you care about.
Related topics
- Low-pass filter explainedA resistor and a capacitor that pass the bass and fade the treble, and where the cutoff sits.
- Capacitive and inductive reactance explainedWhy a capacitor passes treble and a coil passes bass: X_C, X_L and Ohm's law for AC.
- How to read a Bode plotGain in decibels against frequency on a log scale: corners, −3 dB and 20 dB per decade.
- RC time constant explainedτ = R × C: how long a capacitor takes to charge through a resistor, and the 63% rule.