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010010100011101000110110
h
ow
daC
S
work
A DAC is a circuit that converts
digital measures of audio amplitude
in discrete steps into a continuous analog
electrical equivalent of the sound to be reproduced. The
amplitude is a digital number (like a 16 bit word) and the
steps occur based on the sampling rate (like 48,000 times per
second). This process is very much like an endless conveyer
belt with empty one gallon jugs on it, moving by a filling
station. The size of the jug is fixed, the rate they pass by is
determined by the sampling rate. The goal of the DAC is to
fill each jug to exactly the right level specified by the music.
There are three techniques used to accomplish this; Delta
Sigma, Ladder, and the MSB Sign Magnitude Ladder.
Line speed
is like Sampling
Rate (48,000 per second)
A “one bit” measuring cup is either
full or empty. With 64 times over-
sampling, the cup is only 1/64th
the volume of the jug. This rather
crude cup does not
come close to
being accurate
enough. The cup
would need to be
1/16,777,216th
the volume of the jug
to be accurate.
Each sample or jug is
filled to the right level
with many measuring
cups, poured to reach
the target level.
By keeping a running tally of the error and by going a little over
and a little under in many many samples, a very accurate average is
reached, but only with an aggressive filter applied to the output.
D
elta
S
igma
DaC
S
(S
ingle
B
it
)
A ladder DAC is different
in that instead of a single
measuring cup (or bit), a
whole array of cups are
available, from very
small to very large.
Any combination of cups
can be used to fill each jug
to exactly the right level.
No filtering
is required but
the accuracy is
defined by the
cumulative error of
all the cups used.
The MSB Sign Magnitude
Ladder DAC is like a Ladder
DAC but refined in two ways.
Because the jars are
typically 1/2 full when
finished, we start
with very accurately
1/2 filled containers
instead of empty ones.
From there, we again
use the wide range of
measuring cups to either add
or take away from each jar.
Again each jar is filled exactly so no
filtering is needed, but because we only had to add or subtract a little bit
our accuracy is higher. Because our hearing is most sensitive to low level
sound (sound near the 1/2 full zero crossing) our DAC is most accurate
near 1/2 full where we use the smallest and most accurate measuring cups.
mSB S
ign
m
agnituDe
l
aDDer
DaC
l
aDDer
DaC
t
he
MSB d
iaMond
daC
No commercial DAC is available with the level of accuracy
we wanted without filtering, so we produce our own using
discrete logic and resistors in a DAC module. MSB is unique
in this respect. The result is a signal-to-noise rating of up to
160 db and THD+Noise ratings near the theoretical limit of
a 24 bit source.
w
hat
aBout
J
itter
?
Jitter is a variation in the speed of the conveyer belt.
With a Delta Sigma DAC, the quantity of water ending
up in the jug is dramatically affected by the speed
change because the whole cycle is occupied with the
application of many small scoops of water. With either
Ladder DAC method, all the water is placed in the jug
at the same time, and even if the jug is a little ahead
or behind in the conveyer belt, the quantity is still
accurate. That is why we never heard much about jitter
until the first Delta Sigma DACs arrived on the scene.
w
hat
aBout
u
pSaMpLing
?
Synchronous Upsampling like MSB does just means adding more
jars between the existing jars and moving them faster down the line.
By looking at many jars before and after the new empty one, we
calculate how full to make it. The result is smaller steps as shown in
the waveform.
THE DAC STORY
