of Microprocessors

DIGITAL-TO-ANALOG AND ANALOG-TO-DIGITAL CONVERTERS 229
the errors are likely to be more evenly distributed, but, when they are not,
the unit will have to be rejected. The point is that, with any DAC circuit
using resistors and switches, overall linearity and accuracy cannot be better
than the accuracy of the components.
Resistive Divider
The most common technique and the one on which nearly all commercial
DACs are based is the resistive divider technique. Figure 7-5 shows a
simple 2-bit resistive divider type of DAC. Each switch is controlled by a bit
of the digital input. If a bit is a one, the switch is up connecting its resistor
to the reference voltage; for zero bits it is down and the resistor is grounded.
It is instructive to calculate the output voltage for each of the four possible
combinations of 2 bits. Clearly, 00 would give zero output and 11 would
give Vre/. The case of 10 gives an R-2R voltage divider, which results in
2/3 Vrif output, while 01 gives a 2R-R divider and 1/3 Vre/. Once again the
circuit is a multiplying DAC with an output proportional to the product of a
reference voltage and a binary fraction input.
The scheme is readily expanded to more bits by adding one switch and
resistor for each new bit. The third bit, for example, would use a resistor
value of 4R and the new voltage levels would be from 017 Vref to 717 Vre/ in
steps of 1I7Vre/. Each new bit would use a resistor twice as large as the
previous bit. Note that the output range stays the same (0 to Vrej) but that
each added bit halves the size of the steps.
This network is often called a weighted resistor voltage output network
because the value of each resistor is weighted in inverse proportion to the
significance of the bit controlling it, and the output IS inherently a voltage
level. The performance of the circuit is, in general, good. Differential linearity
is determined largely by the accuracy of the resistors used. If the resistors
are not in the proper ratio and the resolution is high, grossly unequal step
sizes or even nonmonotonic behavior is possible. As an example, assume an
8-bit converter with perfect lR, 2R, ... 128R resistors but the lR resistor
is 1% too large, that is, 1.01R. The table below shows the voltage output of
the network for some possible digital inputs:
I
t R MSB LSB OUTPUT
! MSB
0
0 0 0
)00""'
v,ef 0 1/3 V,ef
I
t 2R 0 2/3 V,ef
I LSB 1 V,ef
0
Fig. 7-5. Weighted resistor DAC