[BC] CD vs LP

[RichardBJohnson at comcast.net]

Bob,
As a further amplification, I can show how the 93.3 dB
taught by Dunn is wrong and where it came from.
It was incorrectly assumed that a 16-bit number has
65536 codes, i.e., 0 to 65535.

65536 codes * .707 (for sine-wave crest-factor) =  4633.952
20 * log10 (4633.952) = 93.31 dB  That’s Dunn’s magic number.

That is how it was obtained. The problem is that an
alternating voltage of this type would require + and – 65535
and that is NOT a 16-bit number. That requires 17 bits,
not 16 bits.

Sixteen bit AC converters have 16 bits, not 17 bits. They
are essentially 16-bit DC converters, auto-biased to mid
reference with that bias subtracted from their output.

The lack of much headroom is why many audio consoles
use 18 to 24 bits. That said, the 16-bit codes in the ".wav"
file, the original thread, are precisely a 16-bit signed number
that can only have 32767 codes in either direction. That means
that, there are 32768 levels, including zero.

32768 * .707 = 23167 (for sine-wave crest factor)

20 * log10 (23167) = 87.3 dB

This is all you get. There just isn't any more!

--
Cheers,
Richard B. Johnson
Read about my book
http://www.LymanSchool.org