# PRÁCTICA 3. TAT (2017)

Pràctica InglésUniversidad | Universidad Politécnica de Cataluña (UPC) |

Grado | Ingeniería de Aeronavegación - 3º curso |

Asignatura | Aviónica |

Año del apunte | 2017 |

Páginas | 12 |

Fecha de subida | 24/06/2017 |

Descargas | 2 |

Subido por | areig |

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Alba Martín, Anna Reig
ADC TEMPERATURE MEASUREMENT
Simulation with Lab View software
OBJECTIVES
•
•
•
•
•
•
•
Learn how to design a temperature sensor
Learn how to get temperature values from a sensor by using a simple conditioning circuit
Apply mathematical equations to transform voltage data obtained into temperature
Learn how to use the NTC thermistor from EPSOX/TDX
Learn how to calibrate a nonlinear temperature sensor and how to measure its transitory response
Demonstrate there is no need to arrive to the final temperature value to know it
Demonstrate that in avionics, the acquiring temperature system does not need an amplifier
1. Introduction
The main aim of this project is to design the temperature sensor of the Air Data Computer system for a
commercial aircraft. To do so, a NTC thermistor sensor from EPSOX/TDX will be used.

First, in a theoretical way, the exponential model of the thermistor is analysed to be aware of its behaviour
Thus, using the characteristic values from the manufacturer specifications, for a temperature margin, the
corresponding sensor resistance has been computed as well as the committed error and the resolution of the
measure. Secondly, a tension divider is used as conditioning circuit where the analogue input is delivered
firstly by a simple NTC sensor to check the system works as expected and then by the NTC prepared to be
submitted to the practice experiments.

So, in a practical way, using this conditioning system and heating the encapsulated NTC sensor until 100ºC,
its transitory response has been obtained and compared it with the expected one. Furthermore, the
calibration of the sensor has been done by obtaining the temperature behaviour at three different values
which has led to determinate the noise, the resolution and the accuracy of the sensor. Finally, a simple
mathematical equation is obtained so to determine the final temperature value without having to wait to
arrive to it.

2. Technical specifications
The sensor used in this project is B57164K from EPSOX/TDX which is a leaded NTC thermistor with 5mm lead
spacing. Some general technical data needed to develop the design is specified below.

NTC Thermistor B57164K
Manufacturer resistance (𝑹𝟎 = 𝑹𝟐𝟓)
Manufacturer resistance tolerance
𝜷
𝜷 tolerance
Dissipation factor
2200 Ω
±5%
3900
±3%
7.5 mW/K
Table 1 B57164K NTC characteristics [1]
1
Alba Martín, Anna Reig
The exponential model of the sensor corresponds to the exponential of its variable resistance involving the
parameters specified above.

𝑅(𝑇) = 𝑅0 𝑒
1 1
𝛽( − )
𝑇 𝑇0
Known this model, let’s give some characteristic temperature values to it to have an idea of the order of
magnitude of the corresponding resistance. As seen below, when increasing temperature, the resistance
diminishes exponentially as expected.

•
•
•
•
For 𝑇 = −55 ℃; 𝑅−55 = 268 kΩ
For 𝑇 = 0 ℃; 𝑅0 = 7.29 kΩ
For 𝑇 = 25 ℃; 𝑅25 = 2200 Ω
For 𝑇 = 60 ℃; 𝑅60 = 555.95 Ω
3. Conditioning circuit
As explained in the introduction, the conditioning circuit used to obtain the voltage input given by the sensor
is a tension divider that can be modelled by a simple equation.

𝑉 = 𝑉𝑖𝑛 ·
𝑅(𝑇)
𝑅(𝑇) + 𝑅25
Knowing that the output is 5V and the associated resistance obtained above,
the voltage of the sensor for different temperatures has been computed:
• For 𝑇 = −55 ℃; 𝑉−55 = 4.96 V
• For 𝑇 = 0 ℃; 𝑉0 = 3.84 V
• For 𝑇 = 25 ℃; 𝑉25 = 2.5 V
Figure 1 System measurement circuit
• For 𝑇 = 60 ℃; 𝑉60 = 1 V
The negative correlation is due to the relation between the temperature and the resistance for an NTC, when
increasing temperature, the resistance and the voltage decreases.

4. System error
System error must be considered if one wants to design a reliable sensor as accurate as possible. The
mentioned error, evaluated for the four temperatures used in the previous sections, can be due to either the
tolerance of the resistance and of β or to the self-heating of the sensor. Below, some values have been
obtained for these two cases.

•
Error caused by the tolerance due to 𝑅0 (5%) and 𝛽 (3%)
Δ𝑅0
1 1
Δ𝛽
Δ𝑅(𝑇) = 𝑅(𝑇) (
) + 𝛽 ( − ) · ( ) · 𝑅(𝑇)
𝑅0
𝑇 𝑇0
𝛽
o
o
o
o
For 𝑇 = −55 ℃; Δ𝑅−55 = 51992Ω (19.4 %)
For 𝑇 = 0 ℃; Δ𝑅0 = 626.94Ω (8.6 %)
For 𝑇 = 25 ℃; Δ𝑅25 = 100Ω (5 %)
For 𝑇 = 60 ℃; Δ𝑅60 = 4.4476Ω (0.8 %)
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Alba Martín, Anna Reig
•
Error caused by the self-heating of the sensor
2
𝑃
𝐼 2 𝑅(𝑇)
𝑉𝑖𝑛
𝑅(𝑇)
Δ𝑇 =
=
=
𝛿𝑡ℎ 7.5 · 10−3 7.5 · 10−3 · (𝑅(𝑇) + 𝑅25 )2
o
o
o
o
For 𝑇 = −55 ℃; Δ𝑇−55 = 0.0122K
For 𝑇 = 0 ℃; Δ𝑇0 = 0.269K
For 𝑇 = 25 ℃; Δ𝑇25 = 0.3786K
For 𝑇 = 60 ℃; Δ𝑇60 = 0.2426K
5. Data acquisition
Once analysed all the theoretical parameters and having considered the system error, it is time to act. The
tension divider is mounted as shown in Figure 1. In this figure, the box represents the data acquisition card
which supplies 5V to the circuit and at the same time processes the temperature data generated firstly by a
simple NTC temperature sensor and then by the NTC prepared to be submitted to the practice experiments.

Besides, between the analogue input and the output, there is a resistance of 2200Ω. So, now to manipulate
the generated data, it has been developed a simple software on Lab View able to get the data from the sensor
and save it on an excel file as it can be appreciated below. The measurement of the temperature is developed
by transforming the voltage obtained by the sensor into resistance that is directly related to temperature by
the characteristic equation shown in previous sections.

Figure 2 Temperature measurement: LabView software
Before acquiring definitive temperature data, as said before, the developed LabView software is checked by
the use of a simple NTC sensor which changes as a function of its surrounding temperature. Experimentally,
in this step of the design, it has been observed that in the display of the software it is shown the temperature
of the room where the practice has been developed and when the sensor has been heated by our fingers, this
temperature has increased slightly.

6. Time response variation with and without encapsulation
Once approved the system of data acquisition and generation, the NTC sensor has been swap with the one
encapsulated leading to calculate experimentally the time response variation of the studied encapsulated
sensor which means obtaining the characteristic time constant. Subsequently, knowing the response with
encapsulation, it is compared with the time constant without encapsulation. This is the way the influence of
the encapsulation is going to be tested.

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Alba Martín, Anna Reig
One can think that the real response time should be the one achieved by the sensor without any physical
package involving it, however in real avionics sensors it is not possible. All sensors used by the aircraft must
be protected from any damage that could cause its breakage or could develop a bad use of its measures. That
is why it has been considered the encapsulation of the sensor in an unknown material that reduces the
measurement time, making thus the sensor response becoming slower and less sensitive to rapid changes.

This experiment is about heating the encapsulated NTC sensor
up to 100ºC using a water boiling machine. That is having an
initial temperature approximatively of 28ºC (classroom
temperature when the practice was done) and a final
temperature of 100ºC theoretically. Besides, in the B57164K NTC
DataSheet, it is specified that the time constant when cooling or
heating the sensor itself is approximately 20 seconds. Hence, it
is possible now to obtain the theoretical equation that should Figure 3. NTC Sensor with yellow encapsulation
follow the NTC sensor without encapsulation.

𝑇 = 𝑇𝑓𝑖𝑛𝑎𝑙 + (𝑇𝑖𝑛𝑖𝑡𝑖𝑎𝑙 − 𝑇𝑓𝑖𝑛𝑎𝑙 ) · 𝑒 −
𝑇 = 100 + (28 − 100) · 𝑒 −
𝑡𝑖𝑚𝑒
20
𝑡𝑖𝑚𝑒
𝜏
= 100 + (−72) · 𝑒 −
𝑡𝑖𝑚𝑒
20
After having carried out the experiment, the experimental data has been analysed so to get the time constant
associated to the time response variation for the encapsulated sensor. This experimental time constant has
been obtained assuming that the thermal time constant is the time required for a thermistor to change 63%
of the total difference between its initial and final body temperature when subjected to a step function change
in temperature. As it can be seen in the table below, it is obtained a lower value for the time constant; this is
caused by the fact explained above.

DataSheet theoretical value
Encapsulated experimental value
20 seconds (approx.)
17. 32 seconds
Table 2 Time constant difference
In the next figure, it can be appreciated the data obtained experimentally with encapsulation compared to the
one obtained theoretically without encapsulation.

Time response variation of the sensor
Temperature (ºC)
120
100
80
60
40
20
0
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
Time (s)
Encapsulated
Non Encapsulated
Figure 4. Time response variation of the encapsulated and non-encapsulated sensor
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Alba Martín, Anna Reig
This figure reinforces the fact that when having an encapsulated sensor, the time response tends to be slower
approaching the final value in a more progressive way; that is why the experimental time constant is smaller
than the theoretical one. Noticing that, it can be said that when selecting a device for a given time constant,
both the construction and the test methodology must be considered to ensure there are no surprises later (i.e.

during the time before reaching the final value) when using the sensor which should be displaying the correct
temperature.

7. Calibration of the system
Once determined the time response variation of the encapsulated NTC, it is time to calibrated it taking out
the encapsulation. Hence, the sensor can be calibrated with the help of a climatic chamber, where the error
between the desired temperature and the delivered by the chamber should be very small, not as for the
encapsulated sensor. However, when introducing the sensor into the climatic chamber, the sensor does not
fit into it correctly, making impossible to have the sensor touching the heating part of the chamber which
leads obviously to an initial error before starting taking measures. Thus, this error is due to the fact that the
sensor is influenced by the ambient temperature and the chamber temperature.

By introducing the sensor in the camera for three reference points which are 0ºC, 25ºC and 60ºC, one can
know the difference between the measured temperature and the true temperature. Below, it can be observed
the obtained data along the experiment as well as the normal distribution of each temperature tested.

Normal Distribution of the Temperature at 0ºC
Probability Density
Function
Temperature (ºC)
Temperature Calibration at 0ºC
11,300
11,200
11,100
8
6
4
2
Figure 5 Temperature measurements
for 0ºC
11,000
10,900
0
1
2
3
4
5
6
7
8
9
0
10,91
10,97
10
11,03
11,09
11,15
11,21
11,27
Temperature (ºC)
Time (s)
Figure 5 Temperature measurement for 0 ºC and the corresponding normal distribution
Normal Distribution of the Temperature at 25ºC
25,05
Probability Density Function
Temperature (ºC)
Temperature Calibration at 25ºC
24,95
24,85
24,75
24,65
0
1
2
3
4
5
6
7
8
9 10 11 12 13
Time (s)
8
6
4
2
0
24,678
24,738
24,798
24,858 24,918
Temperature (ºC)
Figure 6 Temperature measurement for 25 ºC and the corresponding normal distribution
5
24,978
25,038
Alba Martín, Anna Reig
Normal Distribution of the Temperature at 60ºC
Probability Density Function
Temperature (ºC)
Temperature Calibration at 60ºC
45,6
45,4
45,2
45
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51
Time (s)
3,5
3
2,5
2
1,5
1
0,5
0
45,1045,1645,2245,2845,3445,4045,4645,5245,5845,6445,70
Temperature (ºC)
Figure 7 Temperature measurement for 60 ºC and the corresponding normal distribution
With the help of Excel, the normal distribution is plotted above, next to each temperature variation plot to get
visually a better idea of the error committed due to the thermal drift in each case. As seen for the first two
cases, the normal distribution is not centred, being for the first case shifted to the right and for the second
case shifted a little bit to the left, meaning that there is an error which is not systematic caused by the
temperature when using semiconductors. However, for the third studied case, there is no thermal drift
appreciable.

When looking at the left plots, it can be noticed that the temperature is not very variant apparently for the
three cases. Nevertheless, let’s obtain the standard deviation, the maximum and minimum acceptable values
as well as the resolution of the measures to see if the temperature variations obtained are acceptable or not.

These parameters are computed as follows:
•
•
Resolution: obtained directly by subtracting two adjacent points having the minimal variation
Standard deviation: computed using the following formula
2
•
∑(𝑋 − 𝑋)
𝑆𝑇𝐷 = √
𝑁
Where: 𝑋 corresponds to each value in the data set, 𝑋 to the mean of all values in the data set and
𝑁 to the number of values in the data set
Acceptable error: computed multiplying by 4 the standard deviation value, as for z=4 the
probability of getting a correct value is close to 1. (See Annex to have a better understanding)
Applying these criteria, the parameters are the next ones for the studied cases.

Temperature
0 ºC
25 ºC
60 ºC
Mean temperature
value
11,13 ºC
24,85 ºC
45,39 ºC
Resolution
0,0894 ºC
0,0888 ºC
0,1199 ºC
Table 3 Computed parameters for calibration
6
Standard
deviation
0,069
0,0683
0,1239
Acceptable
error
±0,2764 ºC
±0,2733 ºC
±0,4957 ºC
Alba Martín, Anna Reig
Let’s check by plotting the acceptable error range, if the values obtained are within it. As seen below, all the
values for the three cases are within the limits, thus validating the generated measures.

Temperature (ºC)
Temperature Calibration at 0ºC
11,500
11,400
11,300
11,200
11,100
11,000
10,900
10,800
Temperature Values
Maximum Accepted
Temperature Values
Minimum Accepted
Temperature Values
0
1
2
3
4
5
6
7
8
9
10
Time (s)
Figure 8 Limits of accepted temperature values for 0ºC
Temperature (ºC)
Temperature Calibration at 25ºC
25,2
25,1
25
24,9
24,8
24,7
24,6
24,5
Temperature Values
Maximum Accepted
Temperature Values
Minimum Accepted
Temperature Values
0
1
2
3
4
5
6
7
8
9
10 11 12 13
Time (s)
Figure 9 Limits of the accepted temperature values for 25ºC
Temperature Calibration at 60ºC
Temperature (ºC)
46
Temperature
Values
45,8
45,6
45,4
45,2
45
44,8
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51
Time (s)
Figure 10 Limits of the accepted temperature values for 60ºC
7
Maximum
Accepted
Temperature
Values
Minimum
Accepted
Temperature
Values
Alba Martín, Anna Reig
Hence, from the experimental mean temperature values and the associated theoretical ones, the calibrating
curve can be acquired as it follows as well as the tendency of the curve which corresponds to the dotted line
with the corresponding equation at the top left.

Experimental Mean Temperature Value
(ºC)
Calibration Curve
70
60
60,00
y =-0.0017x^3+0.1342x^2-1.2833x
50
40
25,00
30
20
10
0,00
0
11,1254
24,8470
45,3873
Theoretical Temperature Value (ºC)
Figure 11 Calibration equation representation
As seen above, the equation corresponding to this curve can be approximated by a third polynomial equation:
𝑇𝑐𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛 = −0.0017𝑇 3 + 0.1342𝑇 2 − 1.2833𝑇
Finally, applying the calibration to the plots of the initial measurements, it is possible to calibrate the values
and thus obtain the correct ones.

Temperature Calibration at 0ºC
12,000
Temperature (ºC)
10,000
8,000
6,000
4,000
2,000
0,000
-2,000
0
1
2
3
4
5
6
7
8
Time (s)
Temperature Values
Calibrated Temperature Values
Figure 12 Calibrated temperature for 0ºC
8
9
10
Alba Martín, Anna Reig
Temperature (ºC)
Temperature Calibration at 25ºC
25,4
25,3
25,2
25,1
25
24,9
24,8
24,7
24,6
24,5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Time (s)
Temperature Values
Temperature Calibrated Values
Figure 13 Calibrated temperature for 25ºC
Temperature Calibration at 60ºC
Temperature (ºC)
60,00
56,00
52,00
48,00
44,00
0
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
51
Time (s)
Temperature Values
Calibrated Temperature Values
Figure 14 Calibrated temperature for 60ºC
As can be seen, the final values are much more accurate than initially were, corresponding to the expected
temperature values. There is still some variations and obviously the calibrated temperature values move in a
certain range. It can be noticed that the calibration for 0 ºC and 60 ºC is less accurate than for 25ºC, as the
calibration does not reach the corresponding theoretical temperature. This can be explained by the fact that
for these two cases, the experimental values are further from the expected ones than for the case of 25ºC
which is the typical temperature in a room, being easier to get it. Therefore, this makes the variations of the
temperature to be less visible in the previous plots for the extreme cases than for the case of 25ºC.

9
Alba Martín, Anna Reig
As it seen before, the calibration is not perfectly equal to the theoretical values meaning on the one hand that
there are random errors which cannot been solved and should be taken into account when implementing this
temperature sensor in a determinate system and on the other hand that the calibration should be done in a
more accurate way to get accurate results.

8. Make it simple
In that section, it is desired to reduce the complexity of the initial equation for the temperature acquisition
that consists on an exponential as well as to know the final value of the exponential without having to wait to
arrive to it. A basic processor would not be able to perform these operations, that is why reducing the equation
to one based on operations such as addition, subtraction, multiplication and division from the measurement
of the minimum possible values would facility its processing.

The idea is to determine the temperature final value by knowing three initial points of the time response
variation of the sensor, which are:
•
•
•
T0, first (initial) temperature with its corresponding time, t0
T1, second temperature with its corresponding time, t1
T2, third temperature with its corresponding time, t2
The clue is to consider that between t0 and t1 and between t1 and t2 there is the same time difference, Δt.

Therefore, reducing the complexity starts with the “problematic” exponential equation.

𝑇 = 𝑇𝑓𝑖𝑛𝑎𝑙 + (𝑇𝑖𝑛𝑖𝑡𝑖𝑎𝑙 − 𝑇𝑓𝑖𝑛𝑎𝑙 ) · 𝑒 −
𝑡𝑖𝑚𝑒
𝜏
𝑇 = 𝑇𝑓𝑖𝑛𝑎𝑙 + (𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙 ) · 𝑒 −
𝑡𝑖𝑚𝑒
𝜏
𝑇 − 𝑇𝑓𝑖𝑛𝑎𝑙 = (𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙 ) · 𝑒 −
𝑡𝑖𝑚𝑒
𝜏
Let’s particularize for To, T1 and T2:
𝑡0
𝑇0 → 𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙 = (𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙 ) · 𝑒 − 𝜏 →
𝑡0
𝑡0
𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙
= 𝑒− 𝜏 → 1 = 𝑒 𝜏
𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑡1
𝑡1
𝑡1
𝑇1 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙
= 𝑒− 𝜏 →
=𝑒𝜏
𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑇1 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑡2
𝑡2
𝑡2
𝑇2 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙
= 𝑒− 𝜏 →
=𝑒𝜏
𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑇2 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑇1 → 𝑇1 − 𝑇𝑓𝑖𝑛𝑎𝑙 = (𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙 ) · 𝑒 − 𝜏 →
𝑇2 → 𝑇2 − 𝑇𝑓𝑖𝑛𝑎𝑙 = (𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙 ) · 𝑒 − 𝜏 →
Dividing the equation of T1 over T0 and T2 over T1 and applying the clue of the problem:
𝑡1−𝑡0
Δ𝑡
𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙
=𝑒 𝜏 →
=𝑒𝜏
𝑇1 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑇1 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑡2−𝑡1
Δ𝑡
𝑇1 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑇2 − 𝑇𝑓𝑖𝑛𝑎𝑙
=𝑒 𝜏 →
=𝑒𝜏
𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑇2 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑇1 − 𝑇𝑓𝑖𝑛𝑎𝑙
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Alba Martín, Anna Reig
Now, let’s equal both equations.

𝑇1 − 𝑇𝑓𝑖𝑛𝑎𝑙 𝑇0 − 𝑇𝑓𝑖𝑛𝑎𝑙
𝑇0 𝑇2 − 𝑇12
=
→ 𝑖𝑠𝑜𝑙𝑎𝑡𝑖𝑛𝑔 𝑇𝑓𝑖𝑛𝑎𝑙 → 𝑇𝑓𝑖𝑛𝑎𝑙 =
𝑇2 − 𝑇𝑓𝑖𝑛𝑎𝑙 𝑇1 − 𝑇𝑓𝑖𝑛𝑎𝑙
−2𝑇1 + 𝑇0 + 𝑇3
For a basic processor, that is:
𝑇𝑓𝑖𝑛𝑎𝑙 =
𝑇0 𝑇2 − 𝑇1 𝑇1
−2𝑇1 + 𝑇0 + 𝑇3
This deduced equation has no longer exponentials and is composed by only arithmetic operations easily
interpretable by a processor. This is a useful way to determine in advance the final temperature value.

9. Conclusions
Through all this project, it has been developed a temperature sensor in order to model the ones used in
aircrafts avionics.

Firstly, the characteristics and some important parameters as the equivalent voltage, tolerance and error of
the system has been computed to have a better idea of what was needed. Secondly, the sensor was
implemented within a conditioning circuit used to obtain the measured values and study its time response.

Once obtained all the parameters, as always, the measures have been calibrated so as to obtain the most
accurate values to the reals as possible.

However, after doing all these steps, the accuracy can still be improved and must be if this sensor is placed in
a system which requires a high reliability on it. Besides, it demonstrates that good calibrations are not easy
jobs to do but are the base for any system generating data. These facts also justify the cost of some
calibrations.

Finally, to make all the computations easier and after having calibrated the system, a simpler equation is
extracted to determine final values of stabilized temperature from three initial values. This simple equation
perfectly comprehensible for a processor is also a way of making a prediction of the future, anticipating
possible actions that could improve the performance of the system or could avoid some issues for instance.

10. References
[1]. NTC Thermistors for temperature measurement. Leaded NTC B57164K. March 2013.

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Alba Martín, Anna Reig
ANNEX
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