Compressor and limiter

Try threshold, ratio, knee, attack, release and lookahead on test signals: transfer curve, gain reduction and levels live.

Explanation Tasks

What is happening?

A fader that thinks for itself

Imagine pulling the fader down during a voice recording whenever the speaker gets loud, and pushing it back up afterwards. A compressor does exactly that automatically – faster, more evenly and by fixed rules. It reduces the dynamic range, i.e. the difference between loud and quiet passages. On its own it only makes things quieter – the signal only gets louder through amplification afterwards.

In the diagram “Time history: signal and gain reduction” you see the input (faint) at the top with the output drawn over it, and below it the gain reduction in dB – the reduction the compressor is applying at that moment. The dashed lines “T = …” mark the threshold T. Try it: choose “Sine burst” and press “Play”. As soon as the loud part starts at 0.3 s, gain reduction appears below and the output becomes smaller than the input.

Threshold and ratio: the transfer curve

The threshold T is the level at which the compressor starts to act; below it the signal passes unchanged. The ratio R sets how strongly level increases above it are squeezed: at 4 : 1 the output rises by only 1 dB when the input rises by 4 dB. As a formula (without knee): L_out = T + (L_in − T) / R, with input level L_in and output level L_out.

Worked example with the default settings T = −20 dB and R = 4 : 1: in its loud part the sine burst reaches −6 dBFS, which is 14 dB above the threshold. At the output 14 / 4 = 3.5 dB of this remain, i.e. −16.5 dBFS. The gain reduction is 14 − 3.5 = 10.5 dB; “Maximum gain reduction” shows just under this value.

The “Transfer curve” shows this relation (input level horizontally, output level vertically). Below the threshold (dashed vertical line “T”) the curve lies on the dashed 1 : 1 diagonal, above it the curve is flatter. Push the ratio all the way to the right and it reads ∞ : 1: above the threshold the curve is horizontal and the output does not rise at all – that is a limiter. Try it: choose “Level ramp” (a 100 Hz sine rising from −50 to 0 dBFS in 2 s), set the knee to 0 dB, start playback and follow the dot as it travels along the curve.

Knee and make-up gain

With a hard knee (knee = 0 dB) the compressor switches abruptly from 1 : 1 to the set ratio at the threshold. With a soft knee, compression sets in gradually – over a range of the selected width W that lies half below and half above the threshold and is shaded grey in the transfer curve. Right at the threshold the reduction is already (1 − 1/R) · W / 8: at 4 : 1 and a 12 dB knee that is 0.75 · 12 / 8 ≈ 1.1 dB. Between −26 dB and −14 dB the curve is bent. This sounds less obtrusive because the behaviour never changes suddenly.

Make-up gain raises the output after the gain control by a fixed amount, independent of level. In the transfer curve it shifts the whole curve, including the dashed 1 : 1 line, upwards. To bring the peaks back to their original level you need as much make-up as they were reduced by – statically (1 − 1/R) · (L_peak − T), where L_peak is the peak level at the input, in practice a little less, because the control does not fully catch short peaks.

The control path: measure, compute, smooth

Inside, the compressor works in three steps. The detector measures the level: with “Peak” this is the magnitude of each individual sample, with “RMS” a running RMS value with a 10 ms time constant. For a sine the RMS value is 3 dB below the peak value; that is why the RMS detector reduces the sine burst by only about 8.5 dB instead of 10.5 dB.

The gain computer reads from the transfer curve how much reduction belongs to the measured level. Applied directly, the gain would follow every half-cycle and distort the signal; attack and release therefore smooth the reduction: the attack time sets how quickly it takes hold when the level rises, the release time how quickly it lets go afterwards. Both are time constants τ here: after τ about 63 % of the way is covered, after 2.3 · τ about 90 %. Manufacturers define attack and release differently, so figures from different devices are only roughly comparable.

You can see this lag in the “Transfer curve (ring = target, dot = actual)”: the ring shows where the compressor would operate at this input level once settled, the filled dot where it actually is at the cursor. While the smoothing lags behind, the two are apart and a vertical line connects them.

Attack: let transients through or catch them

Try it: choose the sine burst and the section “Attack” and compare attack 1 ms and 30 ms (threshold −20 dB, ratio 4 : 1). With 1 ms, 90 % of the reduction is in place after just over 3 ms and the first peak reaches only about −12.6 dBFS at the output. With 30 ms this takes about 70 ms (2.3 · 30 ms), and the first cycles pass almost unchecked at about −6.5 dBFS.

This is exactly what is used in the studio: a longer attack time lets the hit of a snare or kick through and only reduces the decay – the drums sound punchier even though they are compressed. A short one catches the peaks but also takes away the bite.

The test signal “Short impulses (0.5 / 2 / 10 / 50 ms)” with 10 ms attack makes this especially clear: the 0.5 ms impulse passes almost unchanged (just over 0.5 dB of reduction during the impulse). Because the detector holds the peak and the smoothing only follows it with the attack time, the reduction keeps building afterwards – almost 9 dB about 30 ms later – and pushes down the quiet 100 Hz tone until it decays with the release time. Only the 50 ms impulse is long enough to be fully compressed itself.

Release: distortion, recovery, pumping

After the loud part the compressor has to let go again. The reduction decays exponentially with the release time constant τ_R, so it takes the time t ≈ τ_R · ln(GR / 1 dB) until it falls from its initial value GR (the gain reduction at the end of the loud part) below 1 dB. With 10.5 dB of reduction and 150 ms release: 150 ms · ln 10.5 ≈ 350 ms. For that long the quiet signal after the loud part is too quiet.

Try it: sine burst, section “Release”, attack 1 ms, then release 5 ms, 50 ms and 300 ms. At 5 ms the compressor already lets go between two half-cycles, because the peak detector sees a small level at every zero crossing of the sine. The reduction then fluctuates by about 1.7 dB in step with the signal and distorts the waveform – about 5 % distortion. With 50 ms about 0.24 dB of fluctuation remains, with 300 ms practically none; in exchange, recovery takes about 12 ms, 120 ms and 0.7 s respectively.

If the recovery time is in the range of the musical rhythm, you hear the gain rise and fall in time with the music: that is pumping. The preset “Fast / pumping” (−30 dB, 8 : 1, attack 1 ms, release 50 ms) shows it on “Drums”: with every hit the gain reduction jumps to more than 20 dB and is almost back at 0 dB before the next one. Release is always a compromise between distortion and pumping on one side and swallowed quiet passages on the other; on buses and the mix bus, release times that match the tempo are often chosen.

Lookahead and limiter

Even with 0.1 ms attack, a control loop can only react to something that has already happened. If a signal starts at full amplitude, the first peak is through before the reduction takes hold. Try it: choose the preset “Limiter” (−12 dB, ∞ : 1, attack 1 ms) with the drums and set lookahead to 0 ms. The kick then overshoots the limit by about 8.5 dB – shown under “Overshoot above limit” and by the dotted line in the time history that marks the output limit when limiting.

Lookahead therefore delays the signal path by a few milliseconds while the detector sees the undelayed level: the reduction starts before the peak reaches the gain stage. With 1 ms of lookahead about 3 dB of overshoot remains in the example, with 5 ms less than 0.1 dB. The price is latency: at a 16 kHz sample rate 5 ms are 80 samples (readout “Latency”). In the DAW, delay compensation makes up for it if the plug-in reports its latency.

So a limiter is a compressor with ∞ : 1, a very short attack time and usually lookahead – at the end of the mastering chain or as clipping protection in broadcasting and sound reinforcement.

Crest factor, loudness and limits

The crest factor is the difference between peak and RMS level; the readout shows it for input and output. Compression can reduce it – provided the control catches the peaks. Try it: choose “Speech-like” (threshold −30 dB, 4 : 1, knee 6 dB, attack 5 ms, release 100 ms) and raise the make-up gain until the peak level at the output matches that of the input again – at about 13.5 dB it is back at about −10.6 dBFS. The RMS level rises from −26.1 to about −22 dBFS, the crest factor falls from 15.4 to about 11.4 dB: at the same peak level the signal is clearly louder. That is why compression and limiting are used in mastering and broadcasting.

A common misconception is: “Compression always makes the peaks smaller.” If the control lets the first peak through while the rest of the level drops, the crest factor even rises. For the drums with a limiter without lookahead it grows from about 14.8 to 19.2 dB, with the preset “Vocals (4 : 1)” and its 5 ms attack even to almost 25 dB. With 5 ms of lookahead the limiter catches the peaks and the crest factor falls to about 11.9 dB.

Limits of the model: it runs at a 16 kHz sample rate with a feed-forward control loop following a common textbook design; real devices differ in detector, curve and colouration. Peak values are measured only at the samples; peaks between the samples (true peak), which real limiters also take into account, are not included here. Levels above 0 dBFS are not cut off but only marked in the transfer curve as the area “above 0 dBFS: clipping”.

Tasks

Practice questions

Questions from studio, stage and mastering – to think about, discuss and check with the module.

1. You compress a snare in parallel (New York compression): the dry and the heavily compressed signal are mixed. The compressor uses 5 ms lookahead. What happens if this latency is not compensated?

Show answer

The compressed branch arrives 5 ms late. Mixing creates a comb filter with dips at 100 Hz, 300 Hz, 500 Hz … (odd multiples of 1 / (2 · 5 ms)), plus a smeared, doubled attack. The DAW compensates this with its delay compensation if the plug-in reports its latency; with hardware inserts or external routing the dry branch must be delayed by hand. Parallel compression only works if both branches are in phase: quiet parts are lifted while the transients of the dry signal are preserved.
2. A bus compressor on the whole mix makes the music pump: with every kick, pads and vocals get quieter too. Why, and what helps?

Show answer

The kick with its low, energetic peaks dominates the detector level and triggers the reduction for the entire mix; with a short to medium release the gain audibly recovers between hits. Remedies: a longer release or one matched to the tempo (at 120 BPM a quarter note lasts 500 ms), less ratio or a higher threshold, or a high-pass filter in the sidechain (around 80–150 Hz) so the bass excites the detector less. Used deliberately, the same effect is sidechain ducking: the kick pushes down the bass, the presenter the music.
3. Streaming platforms normalise tracks to a loudness of about −14 LUFS. Is it worth pushing a song to −8 LUFS with a limiter? And where should the limiter's output ceiling be?

Show answer

A track mastered louder is simply played back quieter by the platform – the loudness advantage disappears, what remains is the smaller crest factor: fewer transients, a flatter sound. A dynamic range that suits the material makes more sense. The ceiling is usually set to about −1 dBTP with a true-peak limiter, because higher peaks can occur between the samples and clip during D/A conversion or encoding to AAC or MP3. This model only measures the samples themselves.

Tasks

Predict first, then try it out, then open the solution. “Load starting point” sets the matching initial values.

1. Tracing the transfer curve

A 100 Hz sine rises from −50 to 0 dBFS within 2 s; threshold −20 dB, ratio 4 : 1, no knee. Start playback and follow the dot on the transfer curve. At which input level does gain reduction start and how large is it at 0 dBFS? Then set the knee to 12 dB.

Load starting point

Show solution

Reduction starts at −20 dB. At 0 dBFS the input is 20 dB above the threshold, but the output rises by only 20 / 4 = 5 dB to −15 dBFS: 15 dB of gain reduction. The readout shows just under 14.7 dB because the control lags slightly behind the rising level. With a 12 dB knee compression already starts at −26 dB and sets in gradually; from −14 dB on the curve is the same again.
2. Attack: letting transients through or catching them

At 0.3 s the sine jumps from −30 to −6 dBFS. Compare attack 1 ms and 30 ms: how high is the output peak level, and how long does it take for the gain reduction curve to nearly reach its final value?

Load starting point

Show solution

With 1 ms the reduction reaches 90 % after about 3 ms, the first peak reaches about −12.6 dBFS. With 30 ms it takes about 70 ms; the first cycles pass almost unchanged at about −6.5 dBFS. Once settled, both end up at about −16.5 dBFS (14 dB above the threshold become 3.5 dB). A long attack time lets transients through.
3. Release: distortion versus recovery

At 1.2 s the level drops back to −30 dBFS. Compare release 5 ms, 50 ms and 300 ms. Watch (also in the “Full” section) the gain reduction curve during the loud part and how quickly it returns to 0 dB afterwards.

Load starting point

Show solution

With 5 ms the compressor already lets go between two half-cycles: the reduction fluctuates by about 1.7 dB with the signal, the waveform is distorted (about 5 % THD). With 50 ms about 0.24 dB of ripple remains, with 300 ms practically none. In return it takes about 12 ms, 120 ms or 0.7 s after the loud part until the reduction falls below 1 dB – for that long the quiet signal is too quiet. Release is always a compromise.
4. Limiter and lookahead

The limiter (∞ : 1, attack 1 ms) should not let any peak above −12 dBFS pass. Read the overshoot. Then increase the lookahead to 1 ms and to 5 ms.

Load starting point

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Without lookahead the kick overshoots the limit by about 8.5 dB despite the 1 ms attack: it starts at full amplitude, and the control can only react once the peak is already there. With 1 ms lookahead about 3 dB remain, with 5 ms less than 0.1 dB, because the reduction starts in time before the peak. The price is a latency of 5 ms (80 samples at 16 kHz).
5. Make-up gain and loudness

Compress the speech-like signal and set the make-up gain so that the output peak level matches the input again. Compare RMS level and crest factor of input and output.

Load starting point

Show solution

At about 13.5 dB make-up the peak is back at about −10.6 dBFS. The RMS level rises from −26.1 to about −22 dBFS (+4 dB), the crest factor drops from 15.4 to about 11.4 dB. At the same peak level the signal is clearly louder – which is why mastering and broadcasting use compression and limiting.

Settings

Sound

Level calibration (dB SPL)

MIDI keyboard

Compressor and limiter