Page 234 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Unit 12: A/D and D/A Converters

Solution: Notes
The LSB of an 11-bit system has a resolution of 1/2048. This would provide a resolution at the
output of 1/2048 * (+10) = +5 mV.
It is important to realize that resolution and accuracy in a system should be compatible. For
example, in the 4-bit system previously discussed, the resolution was found to be 1 V. Clearly it
would be unjustifiable to construct such a system to an accuracy of 0. 1%. This would mean that the
system would be accurate to 16 mV but would be capable of distinguishing only to the nearest 1 V.
Similarly, it would be wasteful to construct the 11-bit system described in Example 12.11 to an
accuracy of only 1 percent. This would mean that the output voltage would be accurate only to
100 mV, whereas it is capable of distinguishing to the nearest 5 mV.

12.5 A/D Converter—Simultaneous Conversion

The process of converting an analog voltage into an equivalent digital signal is known as analog-
to-digital (A/D) conversion. This operation is somewhat more complicated than the converse
operation of D/A conversion. A number of different methods have been developed, the simplest
of which is probably the simultaneous method.

The simultaneous method of A/D conversion is based on the use of a number of comparator
circuits. One such system using three comparator circuits is shown in Figure 12.19 on the next
page. The analog signal to be digitized serves as one of the inputs to each comparator. The second
input is a standard reference voltage. The reference voltages used are +V/4, +V/2, and +3V/4.
The system is then capable of accepting an analog input voltage between 0 and +V.
Figure 12.19: Simultaneous A/D Conversion—(a) Logic Diagram,
(b) Comparator Outputs for Input Voltage Ranges

C
Ref. voltage Comp. 3
+3V/4
Comparator output
Analog input Input voltage
voltage0to C 2 Comparator C 1 C 2 C 3
V volts Rev. voltage Comp. outputs 0to +V/4 Low Low Low
+V/2
+V/4 to +V/2 High Low Low
+V/2 to +3V/4 High High Low
C +3V/4 to +V High High High
Rev. voltage Comp. 1
+V/4
b
a
() ()
If the analog input signal exceeds the reference voltage to any comparator, that comparator turns
on. (Let us assume that this means that the output of the comparator goes high.) Now, if all the
comparators are off, the analog input signal must be between 0 and +V/4. If C1 is high (comparator
C1 is on) and C2 and C3 are low, the input must be between +V/4 and +V/2 V. If C1 and C2
are high while C3 is low, the input must be between +V/2 and +3V/4. Finally, if all comparator
outputs are high, the input signal must be between +3V/4 and +V. The comparator output levels
for the various ranges of input voltages are summarized in Figure 12.19b.

Examination of Figure 12.19 reveals that there are four voltage ranges that can be detected by this
converter. Four ranges can be effectively discerned by two binary digits (bits). The three comparator
outputs can then be fed into a coding network to provide 2 bits which are equivalent to the input
analog voltage. The bits of the coding network can then be entered into a flip-flop register for
storage. The complete block diagram for such an A/D converter is shown in Figure 12.20.
In order to gain a clear understanding of the operation of the simultaneous A/D converter, let us
investigate the 3-bit converter shown in Figure 12.21a. Notice that in order to convert the input

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