# Steinharts-Hart equation: Calculating the coefficients marathon

• 71GA
In summary, the extended Steinhart-Hart's equation is a mathematical equation used to calculate the temperature of an NTC thermistor based on its resistance. The equation involves four coefficients - A, B, C, and D - which can be determined by solving a system of linear algebraic equations using specific temperature and resistance pairs. The process of calculating these coefficients may be challenging and may require double checking for errors. However, once the equations are correctly inputted, the coefficients can be calculated accurately and used in programming languages such as C.
71GA
Homework Statement
I would like to calculate coefficients for the Steinharts-Hart equation but it is alarge system...
Relevant Equations
Steinharts-Hart equation
I read about the Steinharts-Hart's equation here and I decided to try and calculate the four coefficients of the extended Steinharts-Hart's equation:

$$\frac{1}{T} = A + B \ln(R) + C \cdot (\ln(R))^2 + D\cdot (\ln(R))^3$$

Where T is a temperature and R is a resistance of the e.g. NTC thermistor. On the supplied website it is written that:

Sometimes calculation of coefficients is done using special temperature values. Inserting four value pairs in the range of interest into the extended Steinhart-Hart poylonm leads to a system of linear algebraic equations (Three value pairs for the standard Steinhart-Hart polynom). Temperatures typically used are for example 0° C, 15° C, 25° C and 70° C. By solving this system the values for A, B, C and D can be determined.

Well I have chosen my NTC thermistor, found the documentation and took four of the temperature - resistance pairs. Then I tried to calculate the first coefficient, but it is a marathon (attachment)!

I would need someone to quick check for errors. I am not sure my substitutions were made corectly... Do you think I am even on the right track?

#### Attachments

• calculation-003.pdf
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At this point I managed to calculate all the coefficients, but probably they are wrong. Here is the entire calculation. If anyone spots any errors please let me know.

#### Attachments

• calculation--003.pdf
210.2 KB · Views: 288
As it turned out. Al lthe equations were correct, but I inputed the wrong numerical values in my calculator. At the end I inserted equatioins in C programming language and it calculated everything perfectly.

## What is the Steinharts-Hart equation?

The Steinharts-Hart equation is an empirical formula used to describe the relationship between temperature and resistance in a thermistor. It is commonly used in thermistor calibration and temperature measurement.

## How is the Steinharts-Hart equation calculated?

The Steinharts-Hart equation is calculated by taking the natural logarithm of the resistance at three known temperatures and using the resulting values to solve for the coefficients A, B, and C.

## What are the coefficients in the Steinharts-Hart equation used for?

The coefficients in the Steinharts-Hart equation are used to determine the temperature from the resistance of a thermistor. They are unique to each thermistor and are determined through calibration.

## Why is the Steinharts-Hart equation important in marathon running?

The Steinharts-Hart equation is important in marathon running because it allows for accurate temperature measurements, which are crucial for monitoring the health and performance of runners. It also helps in calculating the ideal pace for runners based on the temperature.

## Can the Steinharts-Hart equation be used for other types of sensors?

Yes, the Steinharts-Hart equation can be used for other types of sensors, such as thermocouples and resistance temperature detectors (RTDs). It is a versatile equation that can be applied to various types of temperature sensors.

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