Editing Thermistor (section)

==Steinhart–Hart equation==
{{main article|Steinhart–Hart equation}}
In practical devices, the linear approximation model (above) is accurate only over a limited temperature range. Over wider temperature ranges, a more complex resistance–temperature [[transfer function]] provides a more faithful characterization of the performance. The [[Steinhart–Hart equation]] is a widely used third-order approximation:
: <math>\frac{1}{T} = a + b \ln R + c\, (\ln R)^3,</math>
where ''a'', ''b'' and ''c'' are called the Steinhart–Hart parameters and must be specified for each device. ''T'' is the [[absolute temperature]], and ''R'' is the resistance. The equation is not dimensionally correct, since a change in the units of R results in an equation with a different form, containing a <math>(\ln R)^2</math> term. In practice, the equation gives good numerical results for resistances expressed in, for example, [[ohm]]s (Ω) or kiloohms, but the coefficients a, b, and c must be stated with reference to that particular unit.<ref>{{cite journal |last1=Matus |first1=Michael |title=Temperature measurement in dimensional metrology - Why the Steinhart-Hart equation works so well |journal=MacroScale |date=2011 |url=https://oar.ptb.de/files/download/810.20130620D.pdf|archive-url=https://web.archive.org/web/20240603204130/https://oar.ptb.de/files/download/810.20130620D.pdf|archive-date=2024-06-03}}</ref>  To give resistance as a function of temperature, the above cubic equation in <math> \ln R </math> can be solved, the real root of which is given by
:<math> \ln R = \frac{b}{3 c \, x^{1/3}} -x^{1/3} </math>
where
:<math>\begin{align}
  y &= \frac{1}{2c} \left(a - \frac{1}{T}\right), \\
  x &= y + \sqrt{\left(\frac{b}{3c}\right)^3 + y^2}.
\end{align}</math>

The error in the Steinhart–Hart equation is generally less than 0.02&nbsp;°C in the measurement of temperature over a 200&nbsp;°C range.<ref>[http://literature.cdn.keysight.com/litweb/pdf/5965-7822E.pdf "Practical Temperature Measurements"]. Agilent Application Note. Agilent Semiconductor.</ref> As an example, typical values for a thermistor with a resistance of 3&nbsp;kΩ at room temperature (25&nbsp;°C = 298.15&nbsp;K, R in Ω) are:
:<math>\begin{align}
  a &= 1.40 \times 10^{-3}, \\
  b &= 2.37 \times 10^{-4}, \\
  c &= 9.90 \times 10^{-8}.
\end{align}</math>