of Microprocessors

DIGITAL-TO-ANALOG AND ANALOG-TO-DIGITAL CONVERSION 375
quantization noise increases by 6 dB, but the signal has also increased by 6
dB; thus, the SiN ratio is nearly constant.
One problem in using this setup is that the sample data must be
converted from their typical 16-bit signed integer format into the floating
point format, which can be time consuming. A relatively simple hardware
translator, however, can be placed between the computer and the DAC to
accomplish this on the fly. Essentially, the translator must determine which
of several "ranges" each sample lies in. The range determination then controls
the amplifier and a parallel shifter, which insures that the most significant
12 bits in the particular sample are sent to the DAC. Operation would
be as follows:
Digital sample values
000D-07FF
080D-OFFF
100Q--.1FFF
2000-3FFF
4000-7FFF
Bits to DAC
0-11
1-12
2-13
3-14
4-15
Gain selection
0.0625
0.125
0.25
0.5
1.0
A similar table can be constructed for negative sample values. Note
that the lowest gain used is 0.0625. If the input samples are normal 16-bit
integers, it is not possible to get the extra dynamic range that floating-point
format allows.
Aside from the parallel shifter, constructing a floating-point DAC is
fairly simple. For the DAC part, one would use a standard 12-bit DAC
module set up for offset binary coding with an inverter in the most significant
bit to make it twos complement. The gain-controlled amplifier must be
accurate, at least to the 0.012% level to retain 12-bit performance. If the
gains are not accurate, there can be a nonlinearity at points where the gain
switches such as in Fig. 12-6. Simple analog switches with precision gainsetting
resistors can be used for the amplifier. A multiplying DAC could also
be used if it can accept a bipolar reference. The main DAC output would be
connected to the reference input of the multiplying DAC. The 3-bit "exponent"
would be sent to a 1-of-8 decoder whose outputs would be connected
to the most significant 8 bits of the MDAC. The MDAC output then
becomes the final system output.
Exponential DACs
Just as exponential control voltages in analog synthesizers allow accurate,
noise-free representation ofparameters having a wide range, exponential
DACs, which are also called companding DACs, can increase audio dynamic
range with a limited number ofsample bits. For use with audio signals, which
are inherently linear, one would first take the logarithm of the sample value.