Op-amp filters
Tone controls and filters built around one op-amp. Turn the knobs on a Baxandall or the Tube Screamer’s tone stage, or enter a frequency and Q for a two-pole filter and get the parts.
Swipe sideways for the whole drawing. Tap a part to jump to its value.
Knobs
Work out the parts
Parts
How op-amp filters work
An op-amp’s gain is very large, so with feedback its output moves to whatever voltage keeps its two inputs equal. Put caps in the feedback or in the network ahead of it, and the gain changes with frequency. The op-amp’s low output resistance drives the next stage without loading the filter.
The Baxandall. The bass network and the treble network each run from the input to the output, with their wipers into the minus input. With a knob at noon its network is balanced, and the gain is 1 at every frequency. Turned toward the input end, more of the signal reaches the minus input than comes back from the output, so that band is boosted. Toward the output end it’s cut. C1 and C2 short the bass pot above the lows, so the bass knob only works down low. C3 and C4 let only the highs into the treble pot. The most boost or cut is set by the resistors on each side of the pots.
The TS tone stage. R7 and C5 cut the treble a little ahead of the op-amp. The Tone pot runs from the plus input to the minus input, and R8 and C6 hang on its wiper. Toward the plus input the branch shunts the treble to ground before the op-amp, a cut. Toward the minus input the branch pulls more treble current through R10, so the op-amp’s gain rises in the treble, a boost. With the knob at noon the stage still cuts the top a little, part of the mid hump the pedal is known for. The same network, with the clipping stage ahead of it, is on the tone stack page.
Two poles. Two caps make two corners, so past the frequency the level falls 12 dB per octave, twice as fast as one resistor and one cap. Q sets the shape around the frequency. At 0.71 (a Butterworth filter) the passband is as flat as it can be, and it’s 3 dB down at the frequency. Under 0.71 the corner is softer. Over it the level rises to a peak first. A band-pass passes a band whose width is the frequency over Q.
Sallen-Key. The op-amp is non-inverting. One part feeds back from the output to the point between the two input parts and lifts the response near the frequency. With unity gain the ratio of the caps sets Q in a low-pass, and the ratio of the resistors in a high-pass. A gain leg (Rf and Rg) raises Q too, and the band-pass needs one. Q climbs fast as the gain nears 3 in the band-pass form, so a 5 % resistor there moves it a lot. With a real op-amp a Sallen-Key low-pass comes back up at high frequencies, because the feedback cap couples the input straight to the output, where the op-amp can no longer hold it down.
Multiple feedback. The op-amp is inverting, with its plus input on ground, and two parts feed back from the output into the network. The gain is set by the parts, −R2 / R1 in a low-pass, −C1 / C2 in a high-pass. It flips the signal upside down, and it holds the high end of a low-pass down better than a Sallen-Key does.
The op-amp’s bandwidth. An op-amp’s own gain falls with frequency. Its gain-bandwidth product is the frequency where that gain is down to 1, about 3 MHz for a TL072 or a JRC4558. Once the gain a filter asks for gets near what the op-amp has left, the response parts from the ideal one. The grey dashed curve is the same parts on an ideal op-amp. For guitar frequencies most op-amps keep up, but a high-Q filter, a high gain or an old part like the 741 can show it.
How this tool works. The response comes from a small-signal solve of the parts, with the op-amp as the bench’s model at small signal: its open-loop gain with one pole at the gain-bandwidth over that gain, its input resistance and its output resistance. The source is ideal and nothing loads the output. Frequency, Q and gain come from the textbook formulas for each form, which assume an ideal op-amp. Stock values are E12 for caps and E24 for resistors. Clipping and slew aren’t in it. For the op-amp stage itself, with its supply and output limits, try the transistor and op-amp stage tool. For one resistor and one cap, try the corner calculator.
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