of Microprocessors

228 MUSICAL ApPLICATIONS OF MICROPROCESSORS
3-8
7
DECODER 6
rC 5
4 TO CORRESPONDING
DIGITAL
B 3 ANALOG SWITCH
INPUT
2
A I
LSB
0
R
R
R
R
R
R
R
Fig. 7-4. Resistor string DAC
The most significant advantage is that all of the resistors are of the same
value, and each resistor corresponds to one and only one step in the input
code-output voltage graph in Fig. 7-1. Differential linearity can be made
very good even with fairly inaccurate resistors. For example, if 5%-tolerance
resistors were used, the worst differential linearity error would be only onetenth
of the step size-very good performance indeed. Better yet, this level of
differential linearity can be maintained even at very high resolutions of 12
bits and more using the same 5%-tolerance resistors, just a whole lot more of
them.
Integral linearity can be a problem, however. Imagine building one of
these DACs at the 8-bit level. For the 255 resistors required, you would buy
three bags of 100 5% resistors and connect them in the series string using all
of the resistors from one bag before going to the next. Although all of the
resistors are within 5% of their marked value and will be fairly randomly
distributed throughout this range, it is entirely possible that bag 1 might
average a couple of percent lower than bags 2 and 3 because they were made
on a Monday. When the DAC is complete and tested, it will be found that
the first 100 steps will be a couple of percent smaller than the others on the
average, which makes the overall stair-step curve bow down and to the right
very significantly. Of course, in a real manufacturing situation or on a chip,