of Microprocessors

374 MUSICAL ApPLICATIONS OF MICROPROCESSORS
90
80
16-BIT DAe
12-BIT FLOATI~~
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20
10
o
-BO -70 -60 -50 -40 -30 -20 -10 0 +/0 +20
SIGNAL LEVEL RELATIVE TO OVERLOAD (dB)
Fig. 12-5. Floating-point DAC performance
amplifier, which the DAC drives. Low signal levels are created by programming
the amplifier for a low gain rather than reducing the digital
sample values going to the DAC. Thus, the DAC's noise is also reduced and
the resulting SiN ratio tends to be constant at low signal levels.
Let us assume for a moment that the programmable gain amplifier has
eight possible gain settings, each a factor of two apart. Thus, gains of 1.0,
0.5, 0.25, ... ,0.0078 are possible. The corresponding SiN ratio graph for
the system is shown in Fig. 12-5. The maximum SiN ratio is no more than
that of an ordinary 12-bit DAC, but at low signal levels it is actually better
than a true 16-bit unit! Furthermore, only 15 bits are used for the samples.
Note that these are theoretical figures, since retaining a noise level 115 dB
below the overload point in subsequent circuitry is quite a feat indeed.
Since the gain data are carried along with the signal data in each
sample, there is no problem in handling transients as there is in an analog
audio system. The data format is actually very much like the floating point
number format in computer arithmetic. The 12 bits going to the DAC are
the "fraction" part, while the 3 bits going to the gain control circuit are the
"exponent." The base of 2 is set by the design of the gain control circuit.
A floating-point DAC can also be viewed as having a variable step size.
In the region close to zero, the step size is quite small, which minimizes
quantization noise. As the signal level increases, the step size becomes twice
as large, four times, etc., until at levels near overload the steps are 128 times
larger than at low levels. Of course, every time the step size is doubled the