of Microprocessors

DIGITAL-TO-ANALOG AND ANALOG-TO-DIGITAL CONVERTERS 227
of the rectangular wave into the filter is the clock frequency divided by the
number of counter states, which is equivalent to the resolution of the DAC.
Thus, a 4096 level (12-bit) resolution would give a frequency of 10 MHzI
4096 or 2,441 Hz, which is a period of about 410 f.1-sec.
The output ofthe low-pass filter will have some ripple superimposed on
top of the average dc level, since its cutoff is not infinitely sharp. It would be
reasonable to desire a ripple amplitude of less than one-half the least
significant bit. With the· simple RC filter shown, the cutoff frequency would
have to be roughly 1/8,000 of the rectangular wave input frequency to have
an acceptable ripple. The cutofffrequency in this example then would have to
be around 0.3 Hz, which is equivalent to an RC time constant of over 0.5
sec. Even though this sounds slow, the worst-case settling time of the filter to
one-half LSB would be roughly nine times the time constant or nearly 5 sec!
Adding a bit of resolution to this DAC would multiply the settling time by
slightly greater than four. Although more complex filters and switching
sequences may reduce the response time to tens ofmilliseconds, this clearly is
not a high-speed technique. Differential linearity, however, is essentially
perfect regardless of resolution, and integral linearity is limited only by the
regulation of the reference voltage under a varying load. Accuracy can also be
excellent, limited primarily by the reference and the difference between
switch turn-on and turn-off times.
Resistor String DAC
Another approach to D-to-A conversion that is inherently much faster
is to use various combinations of resistors and switches along with a stable
reference voltage. The idea is to use the digital code to operate the switches
such that the resistors are connected in various configurations to produce the
desired fraction of the reference voltage at the output.
Conceptually, the simplest arrangement of switches and resistors is
shown in Fig. 7-4. This 3-bit example uses seven equal-value resistors
connected in series between the reference voltage source and ground. Eight
analog switches, only one of which is on at a time, select the desired fraction
of the reference voltage according to the 3-bit digital input to the 3-to-8
decoder and connects it to the analog output. One drawback to the circuit
should be immediately clear; for every added bit of resolution, the number of
resistors and switches doubles. An 8-bit converter, therefore, would require
255 resistors and 256 switches! In the past, such a circuit was completely
impractical beyond 4 or 5 bits. Its advantages, however, actually make it
attractive in integrated form where the repeated resistor-switch chain
structure can be laid out inexpensively on a chip. National Semiconductor,
for example, has a line of D-to-A and A-to-D converters that use this
structure at the 8-bit level. Another drawback is that the output must be
buffered by an op-amp voltage follower. Connecting a finite load resistance to
the output will greatly affect the circuit's linearity because its output
impedance changes with the digital code.