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, they can be derived. Three accurate measures of resistance are made at precise temperatures, then the coefficients are derived by solving three simultaneous equations.
Inverse of the equation
To find the resistance of a semiconductor at a given temperature, the inverse of the Steinhart–Hart equation must be used. See the , "A, B, C Coefficients for Steinhart–Hart Equation". where
Steinhart–Hart coefficients
To find the coefficients of Steinhart–Hart, we need to know at-least three operating points. For this, we use three values of resistance data for three known temperatures. With, and values of resistance at the temperatures, and, one can express, and :
The most general form of the equation can be derived from extending the B parameter equation to an infinite series: is a reference resistance value. The Steinhart–Hart equation assumes is 1 ohm. The curve fit is much less accurate when it is assumed and a different value of such as 1 kΩ is used. However, using the full set of coefficients avoids this problem as it simply results in shifted parameters. In the original paper, Steinhart and Hart remark that allowing degraded the fit. This is surprising as allowing more freedom would usually improve the fit. It may be because the authors fitted instead of, and thus the error in increased from the extra freedom. Subsequent papers have found great benefit in allowing. The equation was developed through trial-and-error testing of numerous equations, and selected due to its simple form and good fit. However, in its original form, the Steinhart–Hart equation is not sufficiently accurate for modern scientific measurements. For interpolation using a small number of measurements, the series expansion with has been found to be accurate within 1 mK over the calibrated range. Some authors recommend using. If there are many data points, standard polynomial regression can also generate accurate curvefits. Some manufacturers have begun providing regression coefficients as an alternative to Steinhart–Hart coefficients.
