IndexDigitalBit Depth & Dynamic Range
Bit Depth & Dynamic Range
Turn word length into signal-to-noise ratio, step size and a visible staircase.
Analogue and hearing figures are typical values, not limits.
Input
Dither trades 4.8 dB of noise for an error that no longer follows the music.
Used only to size one step in volts. 2 V is the usual line level.
How it works
Six decibels per bit
Each extra bit doubles the number of levels, which halves the rounding error. For a full-scale sine wave, the ratio of signal to that rounding noise is
The size of one step for a converter whose full-scale sine is is the peak-to-peak swing divided by the number of levels:
Dither
Without dither the error is tied to the signal, as the red trace shows at low word lengths, and that is heard as distortion. Adding triangular (TPDF) noise two steps wide before rounding makes the error random. The total noise power becomes three times the quantisation noise, a cost of 4.77 dB:
Reading the result
No real converter reaches the 146 dB a 24-bit word allows. Resistor noise limits the analogue side to roughly 120 to 130 dB, about 20 to 21 bits. The spare bits are useful headroom for recording and for digital volume control.