Jitter, Bits, & Sound Quality Peter van Willenswaard in November 1990

Sidebar: Peter van Willenswaard in November 1990 (Vol.13 No.11):

If, in digital audio, one doesn't pay a similar amount of attention to characteristic impedances when connecting two pieces of equipment, jitter will occur....The amount of jitter caused by impedance mismatching is admittedly small, but some simple arithmetic may clarify the situation. If, in the final digital/analog conversion, we do not tolerate more than 0.5 LSB of amplitude error (vertical axis), neither should we accept a greater error along the horizontal axis (time)....Vertically there are 65,535 steps in a 16-bit system. The highest audio frequency (within the CD format, that is) is 20kHz; each period is sampled twice (every 22µs, to be precise). So for a similar horizontal accuracy at the D/A conversion there should not be more time error (=jitter) than 22/(65535*0.5)µs=0.17ns (170ps). That is for one 16-bit mono channel. The AES/EBU and S/PDIF busses, however, transport two channels of 20-bit audio plus 12 supplementary bits in each channel, which adds up to a total of 64 bits every 22µs. This is four times as much, so jitter at the receiving end's digital interface should be less than 0.04ns (40ps). This is a monstrous demand, as such timing accuracy requires not too disastrous behavior well into the Gigahertz region.

Fortunately, all digital AES/EBU and S/PDIF inputs are followed by a piece of electronic circuitry (a phase-locked loop or PLL) that synchronizes with the incoming bitstream in order to filter the clock signal. The jitter-reduction efficiency of such a "filter" varies between 30x (for a normal, general-purpose PLL) to something like 100x (for a quartz-controlled PLL). If we assume 50x as a mean value for our calculation, the permissible jitter at the input jumps up to a more relaxed but still tough value of 0.04 x 50ns=2ns. Still tough, because this is about only 0.5% of the basic 0.35µs repetition time (2.8MHz cell clock rate) of the digital signal.

Which demonstrates that we have to be very, very careful if we want the transitions to remain exactly where they were. (One could argue that for a lower audio frequency than 20kHz, demands become progressively less stringent, which is true; but our hearing's peak sensitivity occurs around 5kHz, implying an 8ns maximum for jitter, which is an only marginally less severe requirement.)—Peter van Willenswaard

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