Calibration of ESI Temperature Sensors
Jim Burrous, Carol Harper, Terry Mast
May 1998
We have compared the readings from a set of 26 RTD sensors read by a Hewlett-Packard controller and a set of 19 LM35 sensors read by Galil controllers. Assuming that the average of the RTD readings are equal to temperature in oC, we establish linear relationships between the Galil readings and temperature.
Readings were taken in "cold", "cool", and "warm" environments ( ~0 oC, ~10 oC, and ~20 oC)
We had two purposes:
1. inter compare the RTD sensors readings
2. establish the relationship between reading and temperature for the LM35 sensors.
No absolute temperature reference was used, so we assume the average reading of the RTD / HP controller system is the temperature of the environment.
We describe in turn the HP system results and then the Galil system results.
RTD Sensors / HP Controller
The RTD sensors are embedded in an aluminum block (Figure 1). The LM35 sensors are soldered to a connector in open air. We assume that thermal equilibrium has been achieved for each test and all sensors are at the same temperature.
Figure 1
Thirty RTD sensors (R.T.D. Company, RS2P-463) were used in the positions indicated in Figure 1. Sensors 106 - 109 were not embedded in holes like the others and were held to the block's top surface with a metal clip. Thermal conducting grease (Wakefield Engineering Inc., Thermal Grease #122) was applied to sensors 106 and 107. The readings of these four sensors did not track the remainder, indicating a different rate of thermal equilibration. We have eliminated them from the analysis below. The sensors were read using a Hewlett-Packard controller (Hewlett-Packard, HP34970A Data Acquisition / Switch, with three HP34901A 20-channel Armature Multiplexer cards, 10 sensors per card).
The results are given in Spreadsheet No. 1. Configuration changes were only made to the LM35 / Galil system (config 1,2,3), and none were made to the RTD/HP system. Readings were taken on 15 and 18 May at the times indicated.
There is no evidence of a difference between the inner and outer rows in the block (Figures 2,3,4). This is evidence that there is good thermal communication within the aluminum block.
We assume the block temperature (oC) equals the average of the 26 sensor readings. The sensor-to-sensor rms variation is 0.04 oC to 0.06 oC. The average reading and the rms deviation about the mean are repeated below from Spreadsheet No. 1.
config |
environ |
AVE |
stdev |
|
1 |
cold |
0.5596 |
0.0456 |
|
2 |
cold |
0.3734 |
0.0436 |
|
3 |
cold |
0.5564 |
0.0429 |
|
1 |
cool |
9.6191 |
0.0460 |
|
2 |
cool |
9.4124 |
0.0434 |
|
3 |
cool |
9.5080 |
0.0430 |
|
1 |
warm |
23.8424 |
0.0647 |
|
2 |
warm |
23.7910 |
0.0644 |
|
3 |
warm |
23.7299 |
0.0646 |
For each individual sensor we have fit its readings to establish a linear relation between readings and temperature (based on the average of 26).
temperature(isensor) = slope(isensor) * reading(isensor) + intercept(isensor)
The values of the fitted slope and intercept are given in Spreadsheet No. 1. The rms residuals to the fits are extremely small. Averaged in quadrature over all readings and all sensors, the rms residual = 0.0068 oC.
The sensor-to-sensor rms variation in
slope = 0.0027 oC / reading unit and
intercept = 0.0442 oC.
At the end of spreadsheet No 1 we calculate the effect of not making any slope intercept corrections. If simply interpret the reading as the temperature in degrees C, we achieve an accuracy better than 0.05 oC.
CONCLUSION. Since this is adequate for the application (these sensors will be used on DEIMOS), we recommend that the reading be used directly as temperature. This will save any further calibration, bookkeeping, and software.
LM35 Sensors / Galil Controller
Eight LM35 sensors (National Semiconductor LM35 CZ/54AV) are soldered to each connector. Connectors A, B, C were used on analog boards #4, #5,#6 (24-bit analog input card, EL1230). Two Galil controllers (Galil DMC-1580, controller #0 S/N KK1666, controller #1 S/N KK1049 ) were used to read the sensors. The measurements were made at the environments "cold" , "cool", and "warm." The test configurations were as follows.
environment |
test |
board |
controller |
board |
controller |
||
cold |
1 |
4 |
0 |
5 |
1 |
||
cold |
2 |
6 |
0 |
4 |
1 |
||
cold |
3 |
5 |
0 |
6 |
1 |
||
cool |
1 |
4 |
0 |
5 |
1 |
||
cool |
2 |
6 |
0 |
4 |
1 |
||
cool |
3 |
5 |
0 |
6 |
1 |
||
warm |
1 |
4 |
0 |
5 |
1 |
||
warm |
2 |
6 |
0 |
4 |
1 |
||
warm |
3 |
5 |
0 |
6 |
1 |
The readings and analysis are given in Spreadsheet No. 2. The temperature of each test is given in the row TREF; the temperatures determined from the RTD / HP controller data described above.
Inspection of the "cool" readings versus temperature shows the cool readings change by much larger amounts (~4 oC) from test to test than the HP readings (~ 0.2 C). This suggests that the block and the air were not in equilibrium. The variations are much closer for the "cold" and "warm" data. We conclude that the "cool" data are not useful and we eliminated them from further analysis.
This eliminates our check of linearity that we would have had with three separated temperatures. With only two temperature environments we assume linearity. (Future measurements can be made taking readings say 10 minutes apart for each of the cold, cool, warm environments would allow us to determine whether the system has stabilized.)
For each sensor we have used the two points to determine a slope and intercept in the relation
temperature(isensor,board,controller) = slope(isensor,board,controller) * reading(isensor,board,controller) + intercept(isensor,board,controller)
The intercept and slopes are given in Spreadsheet #2. Figures 5 and 6 show the intercepts and slopes versus sensor for the different boards and controllers. There are variations from board to board and controller to controller. There are no dominant and easily parameterized variations. To use these calibrations we will use the appropriate intercept/slope pair for each particular sensor-board-controller configuration.
At the bottom of spreadsheet No. 2, we calculate the effect of using the average slope and intercept to convert all readings to temperature.
Temperature(isensor,board,controller) [oC] = 10.268 * reading(isensor,board,controller) - 0.607
The error made by this approximation has a range of ± 1.1oC. Since this is adequate for our goals for ESI, we recommend using this equation. This saves any further calibrations, bookkeeping, and software.