of Microprocessors

DIGITAL-TO-ANALOG AND ANALOG-TO-DIGITAL CONVERSION 371
Sign-Magnitude Coding
Looking again at the curves in Fig. 12-2, it is seen that the maximum
SiN ratio of 96 dB for a 16-bit DAC occurs right at the point of overload. In
a real listening situation, this would correspond to the peak of the loudest
crescendo in the piece. At the ear-shattering volume this might represent,
one is highly unlikely to notice a noise level scarcely louder than a heartbeat.
On the other hand, duting extremely quiet passages when the noise would be
noticed most, the noise level remains unchanged meaning that the SiN ratio
has degraded.
It would be nice ifsome of the excess SiN at high signal levels could be
traded off for a cheaper DAC without affecting or even improving the SiN at
lower signal levels. This, in fact, is possible and can be accomplished in at
least three different ways.
Although not specifically mentioned previously, an audio DAC must
be connected so that both positive and negative voltages can be produced.
Normally, this is accomplished by offset binary coding and shifting the
normally unipolar DAC output down by exactly one-half of full scale. In
audio applications, a de blocking capacitor is sufficient for the level shifting.
Low signal levels imply that the net DAC output hovers around zero.
An offset binary DAC, however, sees this as one-half scale. In Chapter 7, it
was determined that the most significant bit of the DAC had the greatest
accuracy requirement; therefore, it is logical to assume that the greatest
linearity error would occur when the MSB switches. Unfortunately, this
occurs at half scale also so this kind of DAC imperfection would directly
subtract from the SiN ratio at low signal levels as well as high. Thus, with
offset binary coding, one must use a highly linear DAC.
The sign-magnitude method of obtaining a bipolar DAC output does
not suffer from this problem. Using the basic circuit configuration that was
shown in Fig. 7-17, small signal levels will only exercise the lesser
significant DAC bits, thus eliminating the noise caused by errors in the most
significant bits. As a side effect, the sign-bit amplifier provides the
equivalent of one additional bit of resolution making a 16-bit DAC act like a
17-bitter!
The significance of all this is that inexpensive DACs with 16 bits of
resolution but only 13 or so bits of linearity are available. When linearity is
less than resolution it means that the most significant bits are off enough to
make the DAC nonlinear at the points where the affected bits change. A
16-bit DAC with 13-bit linearity could have nearly an eight-step gap or
backtrack right at 1/2 scale, lesser errors at 1/4 and 3/4 scale, and an even
smaller error at 1/8, 3/8, 5/8, and 718 scale. If connected in an offset binary
circuit, it would perform no better than a 13-bit DAC. But when connected
in a sign-magnitude circuit, we have just the tradeoff that we have been
looking for as the curve in Fig. 12-3 shows.