Page 222 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Unit 12: A/D and D/A Converters

Notes
Figure 12.6: Binary Ladder

The total resistance looking out toward the 2 input is also 2R. These two resistors can be combined
0
to form an equivalent resistor of value R as shown in Figure 12.7a.
Now, moving to node B, we see that the total resistance looking into the branch toward node A
is 2R, as is the total resistance looking out toward the 2 input. These resistors can be combined
1
to simplify the network as shown in Figure 12.7b.
From Figure 12.7b, it can be seen that the total resistance looking from node C down the branch
toward node B or out the branch toward the 2 input is still 2R. The circuit in Figure 12.7b can
2
then be reduced to the equivalent as shown in Figure 12.7c.
From this equivalent circuit, it is clear that the resistance looking back toward node C is 2R, as is
the resistance looking out toward the 2 input.
3
From the preceding discussion, we can conclude that the total resistance looking from any node
back toward the terminating resistor or out toward the digital input is 2R. Notice that this is true
regardless of whether the digital inputs are at ground or + V. The justification for this statement
is the fact that the internal impedance of an ideal voltage source is 0 Ω, and we are assuming that
the digital inputs are ideal voltage sources.

We can use the resistance characteristics of the ladder to determine the output voltages for the
various digital inputs. First, assume that the digital input signal is 1000.

Figure 12.7: Total Resistance
2 1 2 2 2 3

2R 2R 2R
R R R R
V A
A B C D
a
()

2 2 2 3 2 3

2R 2R 2R
R R R R R
V V
B C D A C D A
() ()
b
c

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