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# Steinhart-Hart equation

The Steinhart-Hart equation is a model of the resistance of a semiconductor at different temperatures. The equation is:

${1 \over T} = A + B \ln(R) + C (\ln(R))^3 \,$

where:

• T is the temperature (in kelvins)
• R is the resistance at T (in ohms)
• A, B, C, and D are the Steinhart-Hart coefficients which vary depending on the type and model of thermistor and the temperature range of interest. The D coefficient is frequently neglected because it is typically much smaller than the other coefficients.

#### Uses of the equation

The equation is often used to derive a precise temperature of a thermistor since it provides a closer approximation to actual temperature than simpler equations, and is useful over the entire working temperature range of the sensor. Steinhart-Hart coefficients are usually published by thermistor manufacturers.

Where Steinhart-Hart coefficients are not available, but three accurate measures of resistance are made at precise temperatures, then the coefficients may be derived by solving three simultaneous equations.

#### Developers of the equation

The equation is named after John S. Steinhart and Stanley R. Hart who first published the relationship in 1968[1]. Professor Steinhart (1929-2003), a fellow of the American Geophysical Union and of the American Association for the Advancement of Science, was a member of the faculty of University of Wisconsin-Madison from 1969-1991[1]. Dr. Hart, a Senior Scientist at Woods Hole Oceanographic Institution since 1989 and fellow of the Geological Society of America, the American Geophysical Union, the Geochemical Society and the European Association of Geochemistry, [2] was associated with Professor Steinhart at the Carnegie Institution of Washington when the equation was developed.

## References

1. ^ Steinhart, J. S. and S. R. Hart, "Calibration curves for thermistors", Deep Sea Res., 15, 497-503 (1968).