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Changes for page Sensor Module

Last modified by Heimir Thordarson on 2026/07/05 12:56
From version 56.3
edited by Heimir Thordarson
on 2026/02/09 19:51
Change comment: There is no comment for this version
To version 57.1
edited by Heimir Thordarson
on 2026/02/09 19:52
Change comment: There is no comment for this version

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... ... @@ -167,4 +167,37 @@
167 167  
168 168  [[image:Oil_Temp_schematic.png||height="271" width="632"]]
169 169  
170 -Knowing the beta constant of the thermistor, the
170 +Knowing the beta constant of the thermistor, the equation for the temperature based on the voltage measured by the ADC inside microcontroller can be derived.
171 +(% style="font-size: 1.5em;" %)
172 +(((
173 +{{mathjax}}
174 +$$
175 +R_T = R_f \frac{V_{out}}{V_{in} - V_{out}}
176 +$$
177 +{{/mathjax}}
178 +)))
179 +
180 +Where:
181 +
182 +* {{mathjax}}\(R_f\){{/mathjax}} = The upper resistor in the voltage divider which stays fixed, which in this case is 4.7k {{mathjax}}\(\Omega\){{/mathjax}}
183 +* {{mathjax}}\(V_{out}\){{/mathjax}} = The voltage over the thermistor, and the voltage that the microcontroller will measure.
184 +* {{mathjax}}\(V_{in}\){{/mathjax}} = The supply voltage of the voltage divider, which in this case is a constant 3.3 {{mathjax}}\(V\){{/mathjax}}
185 +* {{mathjax}}\(R_T\){{/mathjax}} = Resistance of the thermistor
186 +
187 +Knowing this, the resistance of the thermistor can be added into the following equation. This will determine the temperature of the thermistor based on the known resistance and the beta value of the thermistor.
188 +
189 +(% style="font-size: 1.5em;" %)
190 +(((
191 +{{mathjax}}
192 +$$
193 +T = \frac{1}{\frac{1}{T_0} + \frac{1}{\beta} \ln\left(\frac{R_T}{R_0}\right)}
194 +$$
195 +{{/mathjax}}
196 +)))
197 +
198 +where:
199 +
200 +* {{mathjax}}\(\beta\){{/mathjax}} = material constant that defines the steepness of its resistance-temperature curve between two temperature points, usually 25/85 degrees celsius. In this case it is 3694 //**K.**//
201 +* {{mathjax}}\(T_0\){{/mathjax}} = The test temperature at which the thermistor is 10k {{mathjax}}\(\Omega\){{/mathjax}}, which in this case is 25 degrees celsius.
202 +* {{mathjax}}\(R_0\){{/mathjax}} = The resistance of the thermistor when it is 25 degrees celsius.
203 +* {{mathjax}}\(R_T\){{/mathjax}} = The current resistance of the thermistor.