compressors.h

dsp.h's Compressor is the textbook feed-forward design: a detector, a gain computer with a soft knee, a multiplier. Every classic compressor is that diagram with one box replaced by a piece of hardware whose physics is the sound, and "make it sound like an LA-2A" was being answered by turning the textbook's release knob. These are the three gain elements that define the three families, each modelled from what the element does:

OptoCompressor   the LA-2A's T4 cell: an electroluminescent panel driven
                 by the sidechain, lighting a cadmium-sulphide photocell
                 whose resistance sets the gain. The panel is fast; the
                 photocell is not, and its recovery depends on how long
                 and how brightly it was lit. The manufacturer's own
                 figures, which the model reproduces: 10 ms attack, 50%
                 of the release in about 60 ms and the rest in 0.5 to
                 5 seconds, longer after longer compression. Two states
                 -- a fast one and a slow "memory" that fills while the
                 cell is lit -- and the release follows whichever is
                 higher, which is exactly that shape. No ratio control:
                 the T4's own curve is a soft 3:1 in Compress and steeper
                 in Limit, and Peak Reduction sets how hard it is lit.

FetCompressor    the 1176: a FET as the shunt leg of an attenuator, its
                 channel resistance set by the sidechain. Two things the
                 circuit does that a gain computer does not: it is a
                 FEEDBACK compressor (the sidechain reads the OUTPUT), so
                 the ratio buttons set a loop gain and the effective
                 knee and timing are program-dependent; and a FET in its
                 triode region has a channel conductance that depends on
                 the drain voltage -- the signal -- which is where the
                 1176's even-harmonic grain under gain reduction comes
                 from. Attack 20 to 800 microseconds, release 50 to
                 1100 ms, the four ratios and "all buttons in".
                 The loop is SOLVED each sample, not delayed. A digital
                 feedback compressor that feeds back last sample's output
                 has a unit delay in a loop whose gain is 3 to 19, and at
                 a 20 microsecond attack -- one sample -- it limit-cycles;
                 that is why software 1176s quietly lengthen the attack.
                 The output level is the fixed point of "what the
                 detector sees is what the attenuator made", a monotone
                 equation in |y| that bisection finds exactly, the same
                 move zero-delay feedback makes for a filter. Then the
                 FET's signal-dependent conductance makes the sample the
                 root of a quadratic, which has a closed form.

VcaCompressor    the dbx 160 and the SSL bus compressor: a VCA whose gain
                 is exactly exponential in its control voltage, so the
                 ratio is exactly the ratio and the element itself adds
                 nothing -- which is the point of a VCA and the reason
                 this one measures under -60 dB of distortion at 10 dB
                 of gain reduction where the FET measures -40. The dbx
                 detects true RMS through a single time constant (its
                 "program-dependent" feel is the RMS integrator); the
                 SSL detects peaks and offers the two-capacitor auto
                 release, fast then slow. OverEasy is a wide soft knee.

The detector and knee mathematics are Giannoulis, Massberg & Reiss, "Digital Dynamic Range Compressor Design -- A Tutorial and Analysis" (JAES 2012); the time constants and curves are the manufacturers' published specifications; the gain elements are the physics stated above. Every figure quoted is measured in the unit test.

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