# Thermistor

## Theory

A thermistor is a type of resistor which resistance varies with temperature. There are two types of thermistors: positive temperature coefficient of resistance and negative temperature coefficient of resistance. The resistance of thermistors with positive temperature coefficient of resistance is increasing when the temperature grows and with negative the resistance decreases. The respective abbreviations are PTC (positive temperature coefficient) and NTC (negative temperature coefficient).

The thermistors resistances' dependence of the temperature is not linear and this complicates the usage of it. For accurate temperature measurements in wider temperature flotation the Steinhart-Hart third-order exponential equation is used as the thermistors resistance is linear only in small temperature range. The following simplified Steinhart-Hart equation with B-parameter exists for NTC thermistors:

where:

• T0 - nominal temperature, usually 25 °C.
• R0 - resistance at nominal temperature.
• B - parameter B.

Parameter B is a coefficient, which is usually given in the datasheet of the thermistor. But it is stable enough constant only in a certain ranges of temperature, for example at ranges 25–50 °C or 25–85 °C. If the temperature range measured is wider , the data sheet should be used for retrieving the equation.

Usually a voltage-divider is used for measuring the resistance of a thermistor, where one resistor is replaced with a thermistor and the input voltage is constant. The output voltage of the voltage-divider is measured, which changes according to the change of the resistance of the thermistor. If the voltage is applied, current goes through the thermistor which heats up the thermistor due to thermistors resistance and therefore alters again the resistance. The fault caused by heating up of the thermistor can be compensated with calculations, but it is easier to use a thermistor that has higher resistance and therefore heats up less.

With restricted resources and with less demands on accuracy, previously calculated charts and tables for temperatures are used. Generally the tables have ranges of temperatures and respective values of resistance, voltage or analogue-digital converters. All exponential calculations are already done and the user needs to only find the correct row and read the temperature given.

## Practice

The Sensor module of the HomeLab is equipped with a NTC type thermistor which has 10 kΩ nominal resistance. At temperatures 25-50 °C the parameter B of the thermistor is 3900. One pin of the thermistor is connected to supply and the other one is connected to the analogue-digital converter (HomeLab II channel 2 and HomeLab III channel 14). A typical 10 kΩ resistor is also connected with the same pin of the microcontroller and earth and together with the thermistor forms a voltage divider. Since we are dealing with a NTC thermistor, which resistance decreases as the temperature grows; the output voltage of the voltage divider is increasing repectively with growing temperature.

While using the AVR it is practical to use a conversion table of values of temperature and analogue-digital converter to find the correct temperature. It is wise to find corresponding value of analogue-digital converter for each temperature degree of desired range of temperature because reverse table will be too large due to the amount of 10 bit ADC values. It is recommended to use any kind of spreadsheet program (MS Excel, LibreOffice Calc, etc.) to make the table. Steinhart-Hart formula which is customized for the mentioned NTC thermistors able's to find the resistance of the thermistor which corresponds to the temperature. Derived from the resistance, is possible to calculate the output voltage of the voltage divider and using this output voltage to calculate the value of the ADC. Calculated values can be inserted to the program as follows:

```// Table for converting temperature values to ADC values
// Every element of the array marks one Celsius degree
// Elements begin from -20 degree and end at 100 degree
// There are 121 elements in the array
const signed short min_temp = -20;
const signed short max_temp = 100;

const unsigned short conversion_table[] =
{
91,96,102,107,113,119,125,132,139,146,153,
160,168,176,184,192,201,210,219,228,238,247,
257,267,277,288,298,309,319,330,341,352,364,
375,386,398,409,421,432,444,455,467,478,489,
501,512,523,534,545,556,567,578,588,599,609,
619,629,639,649,658,667,677,685,694,703,711,
720,728,736,743,751,758,766,773,780,786,793,
799,805,811,817,823,829,834,839,844,849,854,
859,863,868,872,876,880,884,888,892,896,899,
903,906,909,912,915,918,921,924,927,929,932,
934,937,939,941,943,945,947,949,951,953,955
};```

Following algorithm may be used to find the temperature which corresponds to the parameters of the ADC:

```// Converting the ADC values to Celsius degrees:
{
signed short celsius;

// Covering the table backwards:
for (celsius = max_temp - min_temp; celsius >= 0; celsius--)
{
// If the value in the table is the same or higher than measured
// value, then the temperature is at least as high as the
// temperature corresponding to the element
{
// Since the table begins with 0 but values of the elements
// from -20, the value must be shifted
return celsius + min_temp;
}
}

// If the value was not found the minimal temperature is returned
return min_temp;
}```

The algorithm searches range from the table where the ADC value is and acquires the lower ranking number of this range. The ranking number marks degrees, adding the primary temperature to this a temperature with accuracy of 1 degree is reached.

This conversion table and function are already in the library of the HomeLab, therefore there is no need to write them for this exercise. In the library the conversion function is named thermistor_calculate_celsius. Must be considered, that the conversion is valid only when used on the thermistor on the Sensors module of the HomeLab. For using other thermistors, a conversion table needs to be created and more complex function described in the manual of the library must be used. Example program of this exercise is a thermometer, which measures temperature in Celsius scale and displays it on an alphabetical LCD.

```// Example program of the thermistor of Sensors module
// The temperature is displayed on the LCD
#include <stdio.h>
#include <homelab/module/sensors.h>
#include <homelab/module/lcd_gfx.h>
#include <homelab/delay.h>

// Robotic Homelab II

// Robotic Homelab III

// Main program
int main(void)
{
unsigned short value;
signed short temperature;
char text;

// Initialization of LCD
lcd_gfx_init();

// Clearing the LCD and setting backlight
lcd_gfx_clear();
lcd_gfx_backlight(true);

// Name of the program
lcd_gfx_goto_char_xy(1, 1);
lcd_gfx_write_string("Thermometer");

// Endless loop
while (true)
{
// Reading the 4 times rounded values of the voltage of the
// thermistor

// Converting the values of ADC into celsius scale
temperature = thermistor_calculate_celsius(value);

// Converting the temperature in to text
// To display the degree sign, the octal variable is 56
sprintf(text, "%d\56C   ", temperature);

// Displaying the text in the beginning of the third row of the LCD
lcd_gfx_goto_char_xy(5, 3);
lcd_gfx_write_string(text);

hw_delay_ms(1000);
}
return 0;
}``` 