An op-amp amplifies the difference between its two inputs by an enormous factor (100000x and up). Raw, that gain is useless. You wrap it in negative feedback (route the output back to the inverting input) and the circuit's behaviour becomes set by the resistors around it, not the messy chip. Nearly every preamp, mixer, EQ, active filter, and overdrive pedal is this one block plus a few passives.
+Vs │ V+ (non-inv) ───┤+╲ │ │ ╲│ │ ►──────○ out │ ╱│ V- (inverting) ─┤-╱ │ │ -Vs powered from +Vs / -Vs (studio, eurorack) or +Vs / GND (single-supply pedals)
The ideal op-amp has infinite gain, infinite input impedance, zero output impedance, infinite bandwidth, zero noise, zero offset. Every real-world departure from that list is a spec in Properties, and every one is audible somewhere.
The handful of circuits that make up almost all audio electronics. Each one falls out of the two golden rules.
in ○──────────────┤+╲ │ ╲ │ ►────┬──────○ out │ ╱ │ ┌──────┤-╱ │ │ │ ├────[ Rf ]─────┘ │ [ Rg ] │ Vref Vout = (1 + Rf/Rg) * Vin tie the output straight to V- (drop Rf/Rg) => BUFFER, gain 1, hi-Z in / lo-Z out the workhorse: isolates a delicate hi-Z source (guitar, piezo, the pickup coil) from its load
┌──────[ Rf ]───────┐ │ │ in ○─[Rin]──┴──────┤-╲ │ │ ╲ │ │ ►────────┴──○ out │ ╱ Vref ─────────┤+╱ Vout = -(Rf/Rin) * Vin V- = virtual ground (0 V) V- is a virtual ground, so many input resistors to it do NOT interact: that is a SUMMING MIXER -- the heart of every console. Vout = -(Rf/R1*V1 + Rf/R2*V2 + ...)
| Circuit | Does | Audio use |
|---|---|---|
| Difference / instrumentation | amplifies (V+ - V-), rejects common mode | balanced line receivers, DI boxes, hum rejection |
| Integrator | output = -1/RC times the integral of input | ramp/LFO cores, state-variable filters |
| Sallen-Key filter | 2nd-order lowpass / highpass / bandpass | synth VCFs, active crossovers, tone stacks |
| Precision rectifier | rectifies below Vf (diode in the loop) | envelope detection, meters (see Diodes) |
| Feedback clipper | soft overdrive (diodes across Rf) | Tube Screamer, Klon, most soft-clip pedals |
┌────────[ Rf ]────────┐ │ ┌───►|───┐ │ diodes across the feedback: ├─────┤ ├───────┤ full gain at low level, gain │ └───|◄───┘ │ folds down as the output │ │ passes ±Vf: soft clipping in ○─[Ri]───┴──┤−╲ │ │ ╲ │ │ ►───────────────┴───○ out │ ╱ ref ○───────────┤+╱ this is why the two dives are companions: the op-amp sets the gain + drive, the diode sets the clip
The master table. The ideal value is in parentheses; the real number is the departure that matters, and every departure is audible somewhere.
| Property (ideal) | What it is | Effect on the waveform |
|---|---|---|
| Open-loop gain Aol (inf) | raw gain before feedback, ~100-120 dB, falls with freq | more Aol = more loop gain = more feedback = lower distortion |
| GBW (inf) | gain x bandwidth is constant above the dominant pole | closed-loop BW = GBW/gain; too little rolls off highs and raises HF distortion |
| Slew rate (inf) | fastest the output can move, V/us | caps undistorted output at HF+level; too low = slew/TIM distortion, smeared transients |
| Offset voltage Vos (0) | tiny DC imbalance between inputs | DC at output (x gain): wasted headroom, thumps/clicks on switching |
| Offset drift (0) | how Vos moves with temperature | slow warm-up drift; the op-amp analogue of germanium temp drift |
| Bias current Ib (0) | DC current the inputs actually draw | through a high source R makes offset + noise; matters on hi-Z sources |
| Input impedance (inf) | differential + common-mode input Z | loads the source; hi-Z sources need FET inputs or a buffer |
| Output drive (0 Zout) | how low-Z a load it can swing | headphones/long cable/600 ohm: weak drive = sag + distortion under load |
| CMRR (inf) | common-mode rejection ratio | how well a balanced stage rejects hum/noise common to both inputs |
| PSRR (inf) | power-supply rejection ratio | how much supply ripple/hum leaks into the signal |
| Noise en / in (0) | input-referred voltage + current noise density | the hiss floor; low-noise parts for mic/phono preamps |
| THD+N (0) | total harmonic distortion + noise | the purity when clean, before you overdrive on purpose |
| Supply / Iq | rail span, quiescent current | higher rails = more headroom; Iq sets pedal battery life |
| Output swing | how close output gets to the rails | old parts lose ~1.5 V per rail; rail-to-rail swings almost fully |
Almost all of it yields to a scope, a signal generator, a DMM, and a soundcard running an FFT (REW, Plugin Doctor, or Python). The one rule: your measurement chain must be cleaner than the part under test, or you are measuring your own rig.
| Property | Bench method |
|---|---|
| Offset Vos | build a x100 stage, short the input, measure output DC, divide by gain |
| Offset drift | same, then warm the chip (finger, heat gun) and watch the DC crawl |
| Bias current Ib | 1M in series with an input, measure the offset it creates: Ib = dV / R |
| GBW | sweep a small sine, plot gain vs freq, find -3 dB; GBW = f(-3dB) x gain |
| Slew rate | feed a fast square wave, scope the output edge, measure volts per microsecond |
| Full-power BW | big sine, raise freq until peaks triangle: that onset is slew limiting |
| Noise en | terminate input (low R), gain up a lot, FFT the output, refer to input, divide by root-BW |
| THD+N | clean sine in, FFT out (or notch + AC meter), harmonics/residual vs fundamental |
| CMRR | drive both inputs with the same signal, measure the tiny output, ratio to normal-mode gain |
| PSRR | inject ripple (100 Hz) onto the rail, measure how much appears at the output |
| Output drive | load the output down (600 / 150 / 32 ohm), watch level sag and THD rise |
The input transistor type sets noise, bias current, and impedance, so it decides what the chip is for.
| Input type | Bias current | Voltage noise | Best at | Examples |
|---|---|---|---|---|
| Bipolar (BJT) | higher (nA) | lowest possible | low source-Z: mic pres, phono, line | NE5532/5534, LT1028, AD797 |
| JFET | tiny (pA) | low | high source-Z: guitar, piezo, synth, pedals | TL07x, OPA2134, OPA627 |
| CMOS | tiny | higher | low power, single-supply, rail-to-rail | TLC2262, MCP600x |
Rule of thumb: low source impedance wants a bipolar input (its current noise is irrelevant into a low R and its voltage noise is the lowest); high source impedance wants a FET input (bipolar bias current through a big resistor would make offset and noise). That is why a mic pre is a 5534 and a fuzz input buffer is a TL072.
Studio and eurorack gear runs dual rails (+/-15 V, +/-12 V): signals swing around real 0 V ground. Pedals and battery gear run a single supply (9 V): you fake a "ground" at half the rail (a Vref bias, often 4.5 V) and AC-couple everything with capacitors. The math is identical, you just reference V+ to Vref instead of ground. That is why every pedal schematic is littered with a 4.5 V bias network and coupling caps.
How the section-3 numbers map to what you hear, plus the honest part.
PROPERTY → WHAT YOU HEAR slew rate → HF transients + top end low SR = dull/soft or harsh (TIM), misses fast peaks GBW → bandwidth + HF dist too little = rolled highs, distortion climbs with freq noise (en,in) → the hiss floor the quiet-passage character; the mic-pre spec THD → purity when clean how transparent before you overdrive on purpose offset / drift → DC, thumps, headroom clicks on switching, wasted swing, warm-up drift output drive → behaviour under load headphones/long cable: sag + distortion if weak rails / swing → headroom higher rails + rail-to-rail = more clean level crossover dist → low-level grunge class-B parts (358/324) get ugly near zero
The chips audio gear actually uses, and what each brings.
| Chip | Input | Where it lives | Character |
|---|---|---|---|
| TL071/072/074 | JFET | pedals, synths (Juno, DX7 analog), general | the default: clean, quiet, hi-Z, cheap |
| NE5532 / NE5534 | bipolar | mixing consoles, studio outboard, DIs | the studio workhorse; low noise, drives 600 ohm |
| JRC/NJM4558 | bipolar | Tube Screamer TS808 "magic" chip, cheap combos | 741-class: band-limited, modest slew, softens the OD |
| uA741 | bipolar | historic general-purpose | slow, noisy by modern standards; the teaching classic |
| LM358 / LM324 | bipolar, single-supply | cheap battery gear, non-audio | crossover distortion at low level; cautionary for clean audio |
| OPA2134 / OPA134 | FET | hi-fi, DIY audiophile | very low THD, easy drop-in upgrade |
| OPA627 | FET | premium hi-fi front ends | excellent, expensive |
| LT1028 / AD797 | bipolar | mic preamps, RIAA phono | ultra-low noise, the bottom of the hiss floor |
"Operational amplifier" is older than the chip: it meant an amplifier that performed math operations for analog computers.
inverting gain Vout = -(Rf / Rin) * Vin non-inverting gain Vout = (1 + Rf / Rg) * Vin closed-loop bandwidth f(-3dB) = GBW / gain gain trades directly for bandwidth full-power bandwidth f_max = SR / (2*pi*Vpeak) where slew limiting begins total input noise En = en * sqrt(BW) + source Johnson noise sqrt(4kTR*BW) Sallen-Key cutoff fc = 1 / (2*pi*sqrt(R1*R2*C1*C2)) integrator Vout = -(1/RC) * integral(Vin dt)
For a linear stage, the op-amp circuit is a transfer function you implement directly (bilinear or TPT). The non-ideal behaviours worth adding when you want the character:
overdrive pedal as a gray-box chain (op-amp stage + diodes): in ─► gain ─► 1-pole LPF ─► slew limiter ─► diode f(x) ─► rail clip ─► out Rf/Rin finite GBW |dV/dt| finite GBW = a one-pole lowpass on the ideal response slew limit = a rate limiter (a real nonlinearity: "slew distortion") diode f(x) = the soft-clip curve from the Diodes dive (diodes steal the feedback) rail clip = hard clip at the swing limit (aliases: oversample or ADAA)
| Term | Meaning |
|---|---|
| Virtual ground | the inverting input held at (not wired to) 0 V by feedback |
| Loop gain | the feedback in hand (open-loop minus closed-loop gain) that lowers distortion |
| GBW | gain-bandwidth product; gain x bandwidth is constant above the dominant pole |
| Slew rate | max output dV/dt; sets full-power bandwidth |
| TIM | transient intermodulation, from hitting the slew limit on fast signals |
| Offset / bias current | DC input imbalance / DC current the inputs draw; both make output DC |
| CMRR / PSRR | rejection of common-mode input / power-supply noise, in dB |
| en / in | input-referred voltage / current noise density |
| Rail-to-rail | output (or input) swings to within millivolts of the supplies |
| Compensation | the internal pole that keeps it stable; unity-gain stable = safe at gain 1 |
| Crossover distortion | zero-crossing kink from a class-B output stage at low level |
| Headroom | clean level available before clipping into the rails |
partinfo tl072 # JFET dual, the pedal/synth default partinfo ne5532 # bipolar low-noise studio dual partinfo opa4134 # FET audiophile quad partinfo tle2071 # precision JFET single partinfo search opamp