Page 122 - Embedded Microprocessor Systems Real World Design

If the supply voltage is used as a reference and the supply voltage is 5V, mea-
suring a 3V input would produce the following result:
Digital word = (Vin/Vref) x 255 = (3V/5V) x 255 = 15310 = 9g16

However, the result depends on the value of the 5V supply. If the supply voltage is
high by 1 percent, it has a value of 5.05V. Now the value of the A/D conversion will be:

(3V/5.05V) x 255 = 15110 = 97,,
So a 1 percent change in the supply voltage causes the conversion result to change
by two counts. Typical power supplies can vary by 2 or 3 percent, so power supply
variations can have a significant effect on the results. The power supply output can
vary with loading, especially if there is any significant drop in the cabling that con-
nects the power supply to the microprocessor board. Thus, if your design needs all
the analog inputs and cannot use an external reference, be sure power supply vari-
ations will not cause accuracy problems. One way to minimize such errors is to
power the measured signal from the microcontroller supply.

Resolution
The resolution of an ADC or DAC is determined by the reference input and by the word
width. The resolution defines the smallest voltage change that can be converted. As
mentioned earlier, the resolution is the same as the smallest step size and can be cal-
culated by dividing the reference voltage by the number of possible conversion values.
For the example we’ve been using so far, an &bit ADC with a 5V reference, the
resolution is .0195V (19.5mV). This means that any input voltage below 19.5mV
will result in an output of zero. Input voltages between 19.5 mV and 39 mVwill result
in an output of 1. Between 39 mV and 58.6 mV, the output will be 3.
Resolution can be improved by reducing the reference input. Changing from
5V to 2.5V gives a resolution of 2.5/256, or 9.7mV. However, the maximum voltage
that can be measured is now 2.5V instead of 5V.
The only way to increase resolution without changing the reference is to use an
ADC with more bits. A 10-bit ADC using a 5V reference has 21°, or 1024 possible
output codes. Thus, the resolution is 5\3/1024, or 4.88mV.
The resolution also has implications for system design, especially in the area of
noise. A O-to-5V, 10-bit ADC with 4.88mV resolution will respond to 4.88mV
of noise just like it will to a DC input of 4.88mV. If your input signal has lOmV of
noise, you will not get anything like 10 bits of precision unless you take a number
of samples and average them. This means you either have to insure a very quiet
input or allow time for multiple samples.

Cumulative Accuracy
The accuracy of your ADC or DAC system is the cumulative accuracy of all the parts.
This means that the accuracy of your measurements (for an ADC) or output voltage

104 Embedded Microprocessor Systems