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Delta-sigma DAC

Also called sigma-delta, ΔΣ DAC

A delta-sigma DAC converts audio by resampling it to a very high rate with only a few bits, then filtering the result, rather than converting each sample directly. Almost every DAC chip made today works this way, because it achieves very low distortion cheaply.

OversamplingNoise shapingFew-bit DAC+ analog filterPCM samplesmany × ratefew bitsanalog outaudiobandlow-pass filtershaped noise20 kHzfrequencydigitalanalog
A delta-sigma DAC raises the sample rate many times, then a noise-shaping modulator cuts the samples to a few bits and pushes the quantization noise above the 20 kHz audio band. A simple switched DAC turns that stream into a voltage, and an analog low-pass filter removes the ultrasonic noise.

The trick is noise shaping: the quantization noise from the low bit depth is pushed up to ultrasonic frequencies where a filter removes it. ESS, AKM and Cirrus Logic chips all use the technique, and it is why a twenty-dollar dongle can post a SINAD above 100 dB.

The digital filter is part of the design, and many DACs let you choose between filters with slightly different treble behavior. R2R fans argue the approach loses something in the resampling; measurements rarely support an audible loss. DSD is essentially a delta-sigma bitstream stored as a file.

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