Page 233 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Digital Circuits and Logic Design

Notes 5. Two simple but important tests that can be performed to check the proper operation of the
D/A converter are the steady-state accuracy test and the monotonicity test.
(a) True (b) False

12.4 D/A Accuracy and Resolution

Two very important aspects of the D/A converter are the resolution and the accuracy of the
conversion. There is a definite distinction between the two, and you should clearly understand
the differences.
The accuracy of the D/A converter is primarily a function of the accuracy of the precision resistors
used in the ladder and the precision of the reference voltage supply used. Accuracy is a measure
of how close the actual output voltage is to the theoretical output value.

For example, suppose that the theoretical output voltage for a particular input should be +10 V.
An accuracy of 10% means that the actual output voltage must be somewhere between +9 and
+ 11 V. Similarly, if the actual output voltage were somewhere between +9.9 and +10.1 V, this
would imply an accuracy of 1%.

Resolution, on the other hand, defines the smallest increment in voltage that can be discerned.
Resolution is primarily a function of the number of bits in the digital input signal; that is, the
smallest increment in output voltage is determined by the LSB.
In a 4-bit system using a ladder, for example, the LSB has a weight of 1s. This means that the
smallest increment in output voltage is of the input voltage. To make the arithmetic easy, let us
assume that this 4-bit system has input voltage levels of + 16 V. Since the LSB has a weight of
1s a change in the LSB results in a change of 1 V in the output. Thus the output voltage changes
in steps (or increments) of 1 V. The output voltage of this converter is then the staircase shown
in Figure 12.16 and ranges from 0 to + 15 V in 1-V increments. This converter can be used to
represent analog voltages from 0 to + 15 V, but it cannot resolve voltages into increments smaller
than 1 V. If we desired to produce +4.2 V using this converter, therefore, the actual output voltage
would be +4.0 V. Similarly, if we desired a voltage of +7.8 V, the actual output voltage would be
+8.0 V. It is clear that this converter is not capable of distinguishing voltages finer than 1 V, which
is the resolution of the converter.
If we wanted to represent voltages to a finer resolution, we would have to use a converter with
more input bits. As an example, the LSB of a 10-bit converter has a weight of 1/1024. Thus the
smallest incremental change in the output of this converter is approximately 1/1000 of the full-
scale voltage. If this converter has a + 10-V full-scale output, the resolution is approximately
+ 10 * 1/l000 = 10 mV. This converter is then capable of representing voltages to within 10 mV.

12.10: What is the resolution of a 9-bit D/A converter which uses a ladder network?
What is this resolution expressed as a percent? If the full-scale output voltage of this converter is
+ 5 V, what is the resolution in volts?
Solution:
The LSB in a 9-bit system has a weight of 1/512. Thus this converter has a resolution of 1 part in
512. The resolution expressed as a percentage is 1/512 * 100% ≡ 0.2%. The voltage resolution is
obtained by multiplying the weight of the LSB by the full-scale output voltage. Thus the resolution
in volts is 1/512 * 5 ≡ 10 mV.
12.11: How many bits are required at the input of a converter if it is necessary

to resolve voltages to 5 mV and the ladder has +10 V full scales?

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