Page 226 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Unit 12: A/D and D/A Converters

a Thevenin equivalent circuit for the output of the ladder. The resistance looking back into the Notes
ladder is clearly R = 1000W. Thus the Thevenin equivalent is as shown in Figure. 12.11. From this
figure, the output voltage is
2R
V = +9.6875 * 2R + R = +6.4583
A
The operational amplifier (OA) shown in Figure. 12.12a is connected as a unity-gain non-inverting
amplifier. It is thus a good buffer amplifier for connection to the output of a resistive ladder. It
will not load down the ladder and thus will not disturb the ladder output voltage V ; V will
A
A
then appear at the output of the OA.
Figure 12.11: Example 12.7

Connecting an OA with a feedback resistor R as shown in Figure 12.12b results in an amplifier
that acts as an inverting current-to-voltage amplifier. That is, the output voltage V is equal to
A
the negative of the input current l multiplied by R. The input impedance to this amplifier is
essentially 0W; thus, when it is connected to an R-2R ladder, the connecting point is virtually
at ground potential. In this configuration, the R-2R ladder will produce a current output. It is
a binary weighted sum of the input digital levels. For instance, the MSB produces a current of
V/2R. The second MSB produces a current of V/4V, and so on. But the OA multiplies these
currents by -R, and thus V is
A  V V  V V

V = (−R )   + + ...... =− − − ...
A   2 R 4 R    2 4
This is exactly the same expression given in Eq. (12.2) and (12.3) except for the sign. Thus the D/A
converter in Figure 12.12a and b will provide the same output voltage V A
Figure 12.12: D/A Converter

2 0 2 n–1 2 n
+15 Vdc
2R 2R 2R –
OA
+
2R R R V A
V A –15 Vdc
()
a

2 0 2 n–1 2 n
2R 2R 2R I
+15 Vdc
–
2R R R OA
+
V= –RI
Virtual R –15 Vdc A
ground
()
b
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