How an RC filter works: capacitors and a tone control

What you're hearing

A capacitor passes changes and blocks steady voltage. It's two metal plates with a thin gap between them. No current crosses the gap, but when the voltage on one side changes, charge piles up on one plate and leaves the other, so current flows round the circuit as if it had crossed. A steady voltage stops that flow once the plates are charged. So a capacitor lets fast changes through and blocks slow ones. Its size is in farads; audio circuits use nanofarads (nF), billionths of a farad.

Through a resistor, it takes time to charge. A resistor limits how fast current can fill the capacitor. The time constant is R × C = 10 kΩ × 10 nF = 0.1 ms: in that time the capacitor charges 63% of the way to a new voltage. A sound that changes much slower than that, a low note, gets through almost untouched. A sound that changes much faster, the fizz at the top of a saw, can't fill the capacitor before it reverses, so it's turned down.

The corner is where the two are equal. A capacitor acts like a resistance that falls as the frequency rises: 1/(2πfC). The corner is where that equals R: f = 1/(2πRC) = 1/(2π × 10 kΩ × 10 nF) ≈ 1.59 kHz. There the output is 3 dB down. Above it, each doubling of frequency (an octave) loses about another 6 dB: −7.0 dB at twice the corner, −12.3 dB at four times. Turn the knob up and R grows, so the corner falls and the sound gets darker:

At every setting, the corner is −3 dB, twice the corner −7.0 dB and four times −12.3 dB. Only where the corner sits changes. At the bottom of the knob, the digital version's corner comes out a few percent lower than the formula.

Swap the parts and it's a high-pass. Put the capacitor first and the resistor to ground, and it works the other way round: the capacitor blocks the lows and passes the highs. The corner is the same 1.59 kHz, but now it's twice the corner that's only 1.0 dB down, and half the corner that's 7.0 dB down. The sound goes thin and bright. A capacitor in series like this is also how a pedal blocks a steady voltage at its output.

Two in a row: steeper. A second resistor and capacitor after the first make the treble fall 12 dB per octave far above the corner instead of 6. The second stage loads the first, as a load loads a voltage divider, so it's softer near the corner than two separate filters would be: −9.5 dB at the corner, −16.5 dB at twice it, −25.7 dB at four times. A synth's filter is the same idea taken further: four stages and some feedback make the transistor ladder filter, 24 dB per octave with a resonant peak.

A guitar's tone knob is the same idea, wired differently. There the capacitor goes to ground through the tone pot, and the resistance that sets the corner is mostly the pickup's own. Turning the knob decides how much treble goes to ground rather than moving the corner, and the pickup's coil shapes the curve too. The job is the same: a resistance and a capacitor trading treble for warmth. Either way, a bigger capacitor moves the corner down: double C, and the corner halves.

Try this

• Turn tone from 3.3 kΩ to 100 kΩ while you hold a note. The saw goes from bright and buzzy to dark and soft. The Scope shows its sharp edges rounding off.
• Press "High-pass" and turn it the same way. Now the knob takes away the body instead of the fizz.
• Press "Two in a row". At the same setting it's darker, and the knob's sweep sounds more like a synth filter.
• Open it in SynthMaker to change the parts. Make C1 22n: at tone 10 kΩ, the corner falls to 723 Hz, as if you'd turned the knob to 22 kΩ.

The parts list

circuit Tone  setting tone: 10k, from 3.3k to 100k  R1 in out tone  C1 out gnd 10n  # second stage, for two in a row:  # R2 a out tone  # C2 out gnd 10nend

For two in a row, R1 and C1 end at a new point, a (R1 in a tone, C1 a gnd 10n), and the two lines under them lose their #. For the high-pass, R1 and C1 swap places: C1 in out 10n, R1 out gnd tone.

How we checked it

Checked against ngspice, a standard circuit simulator: within 0.3 dB of ngspice's response from 20 Hz to 5 kHz at the 1× rate it runs at, in all three versions.

Build it step by step

• The lesson: A distortion pedal from six parts (opens in a new tab). Its tone control is this circuit, a resistor and a 10 nF capacitor, and its "offset" step uses a capacitor in series to block a steady voltage.
• The video: This distortion pedal is six lines of text: a real circuit, simulated. It loads only when tapped.

This distortion pedal is six lines of text: a real circuit, simulated

Next and previous

All circuits

Further reading

• The formula, the time constant and the slope: Wikipedia: Low-pass filter (its RC filter section).
• What a capacitor is and how it charges: Wikipedia: Capacitor.
• Why a capacitor acts like a resistance that falls with frequency: Wikipedia: Electrical reactance.
• How a guitar's tone control is wired, and why its pot doesn't move the corner: dr-lex: Guitar electronics (its tone control section).