StienHart-Hart Equation?

[MikeMl]

Usually found as 1/T = f(R,A,B,C).

Does any body have it transposed, i.e. R=f(T,A,B,C)?

Added:

Never mind, I found it here.

 

[MrAl]

Hi Mike,

Yes, and many times C is taken to be equal to zero so that greatly simplifies the solution:
R=e^(1/(B*T)-A/B)
and this works out pretty well in practice. In fact, the value of C is not usually published, only A and B.

If you do in fact need C, then here is another solution which only requires taking the third root one time:
x=sqrt(((27*A^2*C+4*B^3)*T^2-54*A*C*T+27*C)/(108*C^3*T^2))+1/(2*C*T)-A/(2*C)
y=x^(1/3)
R=e^(y-B/(3*C*y))

You should check any of the solutions you intend to use over the expected range of operation however.

 

[ericgibbs]

There is this calculator.
Steinhart-Hart Thermistor Calculator

 

[MrAl]

Hello again,

This formula comes in handy because the published value of B and R0 are given on many manufacturers data sheets:
R=R0*e^(B*(1/T-1/T0))
where
R is the resistance at temperature T, and
R0 is the resistance at temperature T0 also given on the data sheet, and
T is the temperature in K, and
T0 is the temperature in K at which R0 was measured (also given on the data sheet), and
B is the B constant given on many manufacturers data sheets.

For example, a typical value for B is 4000 and a typical value of R0 is 10k at 25 deg C, and that indicates that the thermistor measured 10k at temperature 25+273 K and measuring R at other temperatures had shown that B came out to be 4000.
This means we can get R0, T0, and B from the data sheet and that allows a quick calculation of R knowing the new T.
Note all values of T and T0 are in K not degrees C. To convert from C to K add 273.
Note also that the values in the SH equations are different, but related to these values also (for example B(SH)=1/B).

Just in case anyone wants to be bothered with the four constant SH equation, here is a solution for R given A,B,C, and D:

x=sqrt((27*A^2*D^2+(4*B^3-18*A*B*C)*D+4*A*C^3-B^2*C^2)*T^2+(-54*A*D^2+18*B*C*D-4*C^3)*T+27*D^2)/(6*sqrt(3)*D^2*T)-(27*A*D^2*T-9*B*C*D*T+2*C^3*T-27*D^2)/(54*D^3*T)
y=x^(1/3)
z=y-(3*B*D-C^2)/(9*D^2*y)-C/(3*D)
R=RT*e^z