PRÁCTICA 3. TAT (2017)Pràctica Inglés
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Alba Martín, Anna Reig
ADC TEMPERATURE MEASUREMENT
Simulation with Lab View software
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
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 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 %) 2 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.
3 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 4 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 10 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 . NTC Thermistors for temperature measurement. Leaded NTC B57164K. March 2013.
11 Alba Martín, Anna Reig ANNEX 12 ...