Question

A temperature in the range of -40° C to 55° C is to be measured with a resolution of 0.1° C. The minimum number of ADC bits required to get a matching dynamic range of the temperature sensor is
1. 8
2. 10
3. 12
4. 14

Answer 1

Correct Answer - Option 2 : 10

Concept:

• Analog-to-Digital Converters (ADCs) transform an analog voltage to a binary number (a series of 1’s and 0’s).
• Then eventually to a digital number (base 10) for reading on a meter, monitor, or chart.
• The ADC resolution depends upon the number of bits used to represent the digit number. 
• As the number of bits increases the resolution of an Analog to Digital Converter improves and the quantization error decreases.

 

Resolution for n – bit A/D converter  will be:

\(R= \frac{V_{FS} \ \times \ (2^ib^i)}{{{2^n} - 1}}\)

Where 

R = Resolution

VFS is reference voltage 'or' Full-scale voltage

n = number of bits

2ibi gives output voltage value.

Calculation:

Given that,

Resolution = 0.1° C

Final temp = 55° C

Initial temp  = 40° C

calculating the range of temperature

Range of temperature = (Final temp - Initial temp)

= 55° - (-40 °) = 95° C 

No of points required = Range of temp/ resolution

= 95/0.1 = 950

The number of bits (n) for ADC is given by

2ⁿ > No. of points required

n > log₂(No. of points required)

n > 9.891

n = 10

Hence option (2) is correct