# Thermistor

RS 10K Thermistor
typical temperature sawtooth of "bang-bang" heated bed temperature controller, (measured by a Mendel Parts thermistor)

# Thermistors

In most RepRaps, a thermistor senses the temperature of the Hot End. Often a second thermistor senses the temperature of the Heated Bed.

Thermistors are resistors that change of resistance with a change in temperature. Good qualities of thermistors are a predictable, accurately known resistance value at every temperature in its operating range. The lowering, or rise, depends on the type of thermistor per degree Kelvin (or Celcius, if you prefer), this is called its coefficient. Positive thermal coefficient (PTC) will increase in resistance with an increase in temperature, negative ones (NTC) will decrease. But the formula in practice is not linear, so sometimes an accurate table of measurements is better than the linear formula. These measurements can usually be found in the datasheet that accompanies the thermistor.

### Theory

You cannot directly measure resistance. To test the resistance, you can put a voltage on a wire and see how much current will run. Another alternative is to use it together with another resistor of a known value, and measure the potential (or voltage) between the resistors. This is what a multimeter does to be able to show you the (deduced) resistance. Remember that there usually is a dial on a multimeter, this allows you to select a range to measure in. This is because the value of the known resistor has to be varied to have the potential (voltage) be in a range that can be measured accurately.

This can best be explained by example: You have two resistors between 0 and 5V. The two resistors are R2=4.7K Ohm at the 5V side and R1=1K Ohm at the ground side. The two resistors act as what is known as a voltage divider. Between the resistors, the voltage is based on the ratio of the two resistances. If you have the 5V power source (Vcc) turned on, this means that the voltage will be: 5V - 5V * 4700/(4700+1000) = ~ 0.88 V. This is also the voltage you would measure at the R2 + R1 junction with a multimeter/voltmeter. If you add a resistor to the mix that changes strongly with a change in temperature, this will affect the value of the voltage divider and the resulting voltage in between. This is because two parallel resistors of which one changes resistance, the total resistance of the total resistance will change as well.

If the thermistor Rth is connected between the ground (0 Volts) and the middle of the two resistors, the value of resistance between the middle junction and the ground will be based on the following formula:

Rpair = 1 / (1/R1 + 1/Rth) = 1 / (1/1000 + 1/Rth) = Rpair

Rpair is the resistance between 0 V and the middle junction. If Rpair is known, based on the calculation of the voltage divider, you can deduce the resistance of the thermistor (Rth).

Through algebraic manipulation you get the formula for Rth: Rth = 1 / (1/1000 - 1/Rpair)

In voltage terms, the voltage at the junction Vout is:

``` Vout = Vcc*Rpair/(R2+Rpair)
```

The ADC in reprap hardware measures Vout as the fractional voltage between its reference voltage Vref (commonly Vref=Vcc) and 0V, expressed as a count of steps (commonly 0 to 1023) at the resolution of the ADC (commonly 1024 or 10 bits.)

As a ratio, the voltage difference is:

``` Vout/Vcc = Rpair/(R2+Rpair)
```

``` ADC_count = 1024*Vout/Vref = 1024*Rpair/(R2+Rpair)
```

ADC_count is limited to the range (0,...,1023) and the device may be damaged with Vout below 0 or above Vref.

Reprap firmware typically uses a table of values mapping an ADC voltage count to a temperature in Celcius (see example below). One could create this table manually by measuring the temperature of the sensor and reading the count from the ADC, or by measuring the temperatures and corresponding voltages (Vout) and calculating the 1024*Vout/Vref, or one could use a program to do these calculations for you.

Note that the tables below refer to a broken link, and that the tables were likely generated with a modified copy of createTemperatureLookup.py.

Note also that several of the tables below for 100Kohm thermistors indicate a R1=0, which, to the createTemperatureLookup.py program, indicates a non-existent R1 (R1 is an open circuit or an infinite resistance). The higher resistance thermistors do not commonly require an R1 to be stable at the operating temperatures. A non existent R1 simplifies the above equations in that Rpair = Rtherm, and the basic ADC count as read by the electronics is:

``` ADC_count = 1024*Vout/Vref = 1024* Rth /(R2+Rth)  # for 100K thermistors without R1.
```

I suspect the best resistor selection -- given some thermistor, the resistor values that give the best sensitivity to temperature at some desired temperature -- is to choose R2 the same resistance as the thermistor at the desired temperature, and to leave out R1 ("infinity"). (In other words, R2 is *not* the room-temperature resistance of the thermistor, unless you really want to optimize for room temperature). Given the desired temperature Td and a nearby temperature Td + 1 Kelvin, those resistor values are the ones that give the greatest difference in output voltage between those temperatures. I thought that would imply that the maximum in the pink graphs on the Gen7 Research#Selecting the Thermistor Voltage Divider page would occur at exactly the point where the output voltage (the green graph) crossed half the supply voltage. I see that the maximum of the pink graph is very close to, but not exactly equal to that half-way point -- am I reading the graphs incorrectly, or is my intuition a bit off? --DavidCary (talk) 11:32, 3 March 2014 (PST)

## Thermistors vs thermocouples

main article: Thermocouple vs Thermistor.

A thermistor is usually more accurate than a thermocouple, but thermocouples can handle higher temperatures and are linear. A thermocouple gives a really small voltage (Type K produces 8.138mV @200C) that can be calibrated and conditioned by an IC (AD595A Amplifier, MAX6675 SPI, or MAX31855 SPI) into a form readable by the electronics. Thermocouples can be more sensitive to noise because of the low voltage. The thermocouple is technically the junction between the two wires so the measurement area and form factor are smaller.

## RepRap Thermistors

Each thermistor has a variety of special values such as Beta and Rz value. A variety of thermistors you may encounter when building a RepRap are listed below, along with the appropriate information. These tables were calculated using this Python script. The resistors are labeled as in Temperature_Sensor_2_0#Schematic. shown on the right.

EPCOS also has data for R/T curves for all of their products in this web-utility.

For comparison to thermocouples see Thermocouple vs Thermistor.

### EPCOS 100K Thermistor (B57540G0104F000)

 Supplier Part Number Digi-Key 495-2125-ND Mouser 871-B57540G104F
• Rz: 348394
• Temperature rating: -55 degC ~ +250 degC (according to datasheet)

(Apparently the same as EPCOS B57540G1104F000 ?)

```// EPCOS 100K Thermistor (B57540G0104F000)
// Thermistor lookup table for RepRap Temperature Sensor Boards (http://make.rrrf.org/ts)
// ./createTemperatureLookup.py --r0=100000 --t0=25 --r1=0 --r2=4700 --beta=4066 --max-adc=1023
// r0: 100000
// t0: 25
// r1: 0
// r2: 4700
// beta: 4066
#define NUMTEMPS 20
short temptable[NUMTEMPS][2] = {
{1, 841},
{54, 255},
{107, 209},
{160, 184},
{213, 166},
{266, 153},
{319, 142},
{372, 132},
{425, 124},
{478, 116},
{531, 108},
{584, 101},
{637, 93},
{690, 86},
{743, 78},
{796, 70},
{849, 61},
{902, 50},
{955, 34},
{1008, 3}
};
```

### EPCOS 100K Thermistor (B57560G1104F)

 Supplier Part Number Farnell 1791917 Mouser 871-B57560G1104F000
• Temperature rating: -55 degC ~ +300 degC (according to datasheet)
```// EPCOS 100K Thermistor (B57560G1104F)
// ./createTemperatureLookup.py --r0=100000 --t0=25 --r1=0 --r2=4700 --beta=4092 --max-adc=1023
// r0: 100000
// t0: 25
// r1: 0
// r2: 4700
// beta: 4092
#define NUMTEMPS 20
short temptable[NUMTEMPS][2] = {
{1, 821},
{54, 252},
{107, 207},
{160, 182},
{213, 165},
{266, 152},
{319, 141},
{372, 131},
{425, 123},
{478, 115},
{531, 107},
{584, 100},
{637, 93},
{690, 86},
{743, 78},
{796, 70},
{849, 60},
{902, 49},
{955, 34},
{1008, 3}
};
```

### EPCOS 100K Thermistor (B57560G104F)

 Supplier Part Number Farnell 3878697
```// EPCOS 100K Thermistor #3(B57560G104F)
// ./createTemperatureLookup.py --r0=100000 --t0=25 --r1=0 --r2=4700 --beta=4036 --max-adc=1023
// r0: 100000
// t0: 25
// r1: 0
// r2: 4700
// beta: 4036
#define NUMTEMPS 20
// {ADC, temp }, // temp
uint16_t temptable[NUMTEMPS][2] PROGMEM = {
{1, 864}, // 864.165363324 C
{54, 258}, // 258.53991594 C
{107, 211}, // 211.310066205 C
{160, 185}, // 185.861725716 C
{213, 168}, // 168.31793816 C
{266, 154}, // 154.754297589 C
{319, 143}, // 143.52544406 C
{372, 133}, // 133.784751118 C
{425, 125}, // 125.033500921 C
{478, 116}, // 116.945124847 C
{531, 109}, // 109.283980973 C
{584, 101}, // 101.861768746 C
{637, 94}, // 94.5095302806 C
{690, 87}, // 87.0542728805 C
{743, 79}, // 79.2915563492 C
{796, 70}, // 70.9409729952 C
{849, 61}, // 61.5523326183 C
{902, 50}, // 50.25271896 C
{955, 34}, // 34.7815846664 C
{1008, 2} // 2.86606331838 C
};
```

### RRRF 100K Thermistor

 Supplier Part Number RS 198-961
• Rz: 337254
```// Thermistor lookup table for RepRap Temperature Sensor Boards (http://make.rrrf.org/ts)
// ./createTemperatureLookup.py --r0=100000 --t0=25 --r1=0 --r2=4700 --beta=3960 --max-adc=1023
// r0: 100000
// t0: 25
// r1: 0
// r2: 4700
// beta: 3960
#define NUMTEMPS 20
short temptable[NUMTEMPS][2] = {
{1, 929},
{54, 266},
{107, 217},
{160, 190},
{213, 172},
{266, 158},
{319, 146},
{372, 136},
{425, 127},
{478, 119},
{531, 111},
{584, 103},
{637, 96},
{690, 88},
{743, 80},
{796, 71},
{849, 62},
{902, 50},
{955, 34},
{1008, 2}
};
```

### RRRF 10K Thermistor

• Rz: 29000
```// Thermistor lookup table for RepRap Temperature Sensor Boards (http://make.rrrf.org/ts)
// ./createTemperatureLookup.py --r0=10000 --t0=25 --r1=680 --r2=1600 --beta=3964 --max-adc=305
// r0: 10000
// t0: 25
// r1: 680
// r2: 1600
// beta: 3964
#define NUMTEMPS 19
short temptable[NUMTEMPS][2] = {
{1, 601},
{17, 260},
{33, 213},
{49, 187},
{65, 170},
{81, 156},
{97, 144},
{113, 134},
{129, 125},
{145, 117},
{161, 109},
{177, 101},
{193, 94},
{209, 86},
{225, 78},
{241, 69},
{257, 59},
{273, 46},
{289, 28}
};
```

### RS 10K Thermistor

• Beta: 3480
• Rz: 29000
```// Thermistor lookup table for RepRap Temperature Sensor Boards (http://make.rrrf.org/ts)
// ./createTemperatureLookup.py --r0=10000 --t0=25 --r1=680 --r2=1600 --beta=3480 --max-adc=315
// r0: 10000
// t0: 25
// r1: 680
// r2: 1600
// beta: 3480
#define NUMTEMPS 20
short temptable[NUMTEMPS][2] = {
{1, 922},
{17, 327},
{33, 260},
{49, 225},
{65, 202},
{81, 184},
{97, 169},
{113, 156},
{129, 145},
{145, 134},
{161, 125},
{177, 115},
{193, 106},
{209, 96},
{225, 87},
{241, 76},
{257, 64},
{273, 50},
{289, 29},
{305, -45}
};
```

### Honeywell 100K Thermistor (135-104LAG-J01)

 Supplier Part Number Farnell 1383986 Mouser 785-135-104LAG-J01 RS 2508333162 Digi-Key 480-3135-ND
• Temperature rating: -60 degC ~ +300 degC
```// Honeywell 100K Thermistor (135-104LAG-J01)
// ./createTemperatureLookup.py --r0=100000 --t0=25 --r1=0 --r2=4700 --beta=3974 --max-adc=1023
// r0: 100000
// t0: 25
// r1: 0
// r2: 4700
// beta: 3974
#define NUMTEMPS 20
short temptable[NUMTEMPS][2] = {
{1, 916},
{54, 265},
{107, 216},
{160, 189},
{213, 171},
{266, 157},
{319, 146},
{372, 136},
{425, 127},
{478, 118},
{531, 110},
{584, 103},
{637, 95},
{690, 88},
{743, 80},
{796, 71},
{849, 62},
{902, 50},
{955, 34},
{1008, 2}
};
```

```// Honeywell 100K Thermistor (135-104LAG-J01)
// ./createTemperatureLookup.py --r0=100000 --t0=25 --r1=0 --r2=4700 --beta=3974 --max-adc=1023
// r0: 100000
// t0: 25
// r1: 0
// r2: 4700
// beta: 3974
#define NUMTEMPS 20
short temptable[NUMTEMPS][2] = {
{1, 916},
{54, 265},
{107, 216},
{160, 189},
{213, 171},
{266, 157},
{319, 146},
{372, 136},
{425, 127},
{478, 118},
{531, 110},
{584, 103},
{637, 95},
{690, 88},
{743, 80},
{796, 71},
{849, 62},
{902, 50},
{955, 34},
{1008, 2}
};
```

### ATC Semitec 104GT-2

 Supplier Part Number Rapid Electronics 61-0452
```// /usr/local/bin/createTemperatureLookup.py --r0=100000 --t0=25 --r1=0 --r2=4700 --beta=4267 --max-adc=1023
// r0: 100000
// t0: 25
// r1: 0
// r2: 4700
// beta: 4267
#define NUMTEMPS 20
short temptable[NUMTEMPS][2] = {
{1, 713},
{54, 236},
{107, 195},
{160, 172},
{213, 157},
{266, 144},
{319, 134},
{372, 125},
{425, 117},
{478, 110},
{531, 103},
{584, 96},
{637, 89},
{690, 83},
{743, 75},
{796, 68},
{849, 59},
{902, 48},
{955, 34},
{1008, 3}
};
```

### PT1000 (Cyntec - same for other suppliers???) (1kOhm)

Requires modification of board and disconnecting voltage from Vref pin of CPU and adding 100nF capacitor instead. Vref = 1,1V is available internally in CPU. Advantages are good availability and extreme temperature range (more than 500C) and is fairly linear and quite accurate.
r2 = 8k2
Vref = 1,1V

```#define NUMTEMPS 15
short temptable[NUMTEMPS][2] = {
{505, 0},
{547, 25},
{591, 50},
{632, 75},
{672, 100},
{711, 125},
{749, 150},
{785, 175},
{821, 200},
{856, 225},
{890, 250},
{923, 275},
{955, 300},
{987, 325},
{1018, 350},
};
```

### KTY82-210 (Philips) (2kOhm SMD)

Requires modification of board and disconnecting voltage from Vref pin of CPU and adding 100nF capacitor instead. Vref = 1,1V is available internally in CPU.
r2 = 15k
Vref = 1,1V

```#define NUMTEMPS 15
short temptable[NUMTEMPS][2] = {
{456, 0},
{491, 10},
{528, 20},
{566, 30},
{605, 40},
{645, 50},
{686, 60},
{728, 70},
{771, 80},
{814, 90},
{858, 100},
{901, 110},
{943, 120},
{980, 130},
{1011, 140},
};
```

## Thermistor Calculations

Do bear in mind that the PIC will not correctly calculate temperature if the resistance drops below 1K so if yours does, stick a small resistor in series with the thermistor to ensure that the overall resistance remains above 1K.

If you are writing firmware to calculate temperatures, please consider:

Even though ABS melts below 200 degrees Celcius, many people are driving their hot end over 260 degrees Celcius to get faster ABS flow (see Hotend theory). So please use something larger than a BYTE so you can store temperatures above 260 degrees Celcius.

Even though many people use low-cost thermistors and bias it with a low-cost 5% resistors and so are lucky if their hardware indicates temperatures within 2 degrees of the actual temperature, PID temperature control seems to work better with values that are more precise than 1 degree. There are apparently 3 approaches to PID calculation control that take advantage of a precision better than 1 degree Celcius:

• Use integer units that are some fraction of a degree Celcius (the Teensy Breadboard#Thermistor_Table firmware uses units of 1/4 of a degree Celcius; there are rumours of firmware using units of 1/10 of a degree Celcius)
• Use a reverse-lookup to convert the desired temperature in Celcius to ADC values, then run the PID loop using the raw integer ADC values.
• Use a `float` degrees Celcius.

If you are using a non-standard thermistor or you simply want more information on how they work, check these pages out:

### Thermistor Workings Illustrated

Generation 7 Electronics Research shows how thermistors behave and how the surrounding parts can be calculated.

### Calculating Thermistor Beta / Rz Values

This is how you calculate the Beta and Rz values for a thermistor. You will need these if you plan on using a non-standard thermistor. The following page contains a javascript calculator to help make things easy.

### Calculating PIC Temperatures

The PIC uses a capacitor and charges it through the thermistor. It sends the temperature back to the host as a timer reading. This page describes how it is calculated and how to choose the right capacitor.