Electronic
Digital display thermometer
Take 15 minutes to prepare this exercise.
Then, if you lack ideas to begin, look at the given clue and start searching for the solution.
A detailed solution is then proposed to you.
If you have more questions, feel free to ask them on the forum.
The principle of a digital display thermometer is :
The temperature probe is a platinum resistor, whose resistance varies with temperature according to the law :
Where is the temperature expressed in , the coefficient of temperature of the resistivity ( ), the resistance in at the temperature and the resistance in at ( ).
This sensor is placed in one arm of a measuring bridge (Wheatstone bridge) fed by an ideal generator of direct current ( ).
Resistances , , and are assumed to be independent of temperature.
Question
Determining the voltage as a function of , , , and .
Hint
Solution
The KVL applied to the loop defined in the figure above gives :
Yet, according to the rule of the current divider :
And :
Referring in expression of , we finally obtain :
Question
What value does it give to if the bridge is in equilibrium at , that is to say at that temperature ?
Keep this value for the following exercises.
Hint
Solution
So that the bridge is in equilibrium at the temperature of , it is necessary that :
So :
Question
The temperature may vary between and , determine in terms of temperature .
Make the numerical application for , , , , and .
Does linearly vary with temperature ?
Hint
Solution
At any temperature (in ), platinum resistance can be expressed as :
The voltage can then be written :
Consequently, using the equilibrium condition of the bridge at :
Numerically, we get :
With in and in .
The voltage values for the conditions suggested in the statement are listed in the table below :
Température 






Voltage (V) 






It is found that in the range of considered temperatures, and that, therefore, : the voltage varies linearly with temperature.
Question
The signal delivered is small, it is amplified. Which amplifier circuit do you use ? After amplification and shaping, the tension is obtained :
With in °C and in .
Hint
Solution
A simple amplifier circuit can, for example, be a noninverting amplifier circuit, made of an ideal operational amplifier and whose schema is recalled in the figure below, for which :
As part of this exercise, the affine variation between and is :
With in and in .
Question
The voltage is applied to an analogdigital converter (ADC) successive approximation  bits  scale (  ).
The ADC can encode the analog voltage into a number of binary digits ( bits).
The transfer characteristic is given in the figure below.
Why do we use the base not base ? How many digital values ADC can it distinguish ?
What is the minimum variation of so that the numerical value in base is changed by one unit, that is to say the most significant bit ?
Deduce the minimum temperature variation that can be enjoyed with this arrangement.
Hint
Solution

The base is used here because it is, in general, used in electronic logic.
The number of digits, which can be equal to or . Therefore, may take values.

The minimum voltage variation that can be indicated will be given by :
Which corresponds to a minimum change in temperature equal to :