A easy passive interface for NTC thermistors

Given their usually low price, small measurement, strong building, accuracy, versatility, and sensitivity, it’s no marvel that fundamental detrimental temperature coefficient (NTC) thermistors charge among the many hottest temperature sensors accessible. Nonetheless, their temperature response perform is extremely nonlinear (actually exponential), making excitation and sign digitization and processing fascinating design workouts.

The standard NTC thermistor’s datasheet (e.g., Molex 2152723605) summarizes thermo-electric properties with 4 parameters (Equations 1 via 5), proven in Determine 1 (numbers borrowed from 2152723605 knowledge):

To = rated/calibration temperature (25°C = 298.15 Ok)          (1)
Ro = resistance at To (10k ±1%)                                               (2)
b = beta (3892 Ok)                                                                         (3)
Dissipation (self-heating) issue (1.5 mW/°C)                       (4)

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Then thermistor resistance (Rt) as a perform of temperature (T) in Kelvin is predicted by:

Rt = Ro exp(b(T^-1 – To^-1))                                                           (5)

Making use of the traditional KISS precept, we see in Determine 1 a candidate for the only attainable circuit to wheedle a sign from a thermistor, and a few fundamental math to winnow a temperature measurement from its output and parameters 1, 2, and three from above.

Determine 1 Fundamental thermistor passive excitation circuit: Cx = non-obligatory noise discount, maybe 100 nF; Rx = excitation resistor; Rt = Rx(V/Vref)/(1 – V/Vref); T = (Ln(Rt/Rx)/b + Tx^-1)^-1.

Aside from the (very uncritical) Cx and the thermistor itself, the one element in Determine 1 is Rx. How greatest to decide on its worth?

Instinct suggests and math confirms that the optimum (at the least practically so) selection is to make Rx equal to the thermistor’s on the center of the span of temperature measurement required by the applying. Mentioned mid-point temperature (name it Tx) will then output V = Vref/2 and thus distribute ADC decision symmetrically over the vary of measurement. Equation. 5 tells us find out how to get there.

Suppose we select a measurement vary of 0^oC to 100^oC, then Tx = 50^oC = 323.15 Ok and Equation 5’s arithmetic tells us (utilizing the 2152723605’s numbers):

Rx = Ro exp(b(Tx^-1 – To^-1))
Rx = 10000 exp(3892(323.15^-1 – 298.15^-1))
Rx = 3643 (closest commonplace 1% worth = 3650)

Now, if we conveniently select Vref = 5V for each enter to Rx and to the reference enter of the ADC (since it is a ratiometric measurement, absolutely the worth of Vref is comparatively unimportant) we are able to set:

X = ADC/2^N = V/Vref
Then,
T = (Ln(X/(1 – X))/b + Tx^-1)^-1
oC = (Ln(X/(1 – X))/3892 + 0.003095)^-1– 273.15

 And the job is finished! 

Or is it? What about that dissipation (self-heating) issue (1.5 mW/°C)? 

We clearly don’t need thermistor self-heating to considerably intervene with the temperature measurement. An inexpensive restrict for self-heating error could be half a level and within the case of the 2152723803’s 1.5 mW/°C, this may dictate limiting most dissipation to not more than:

Pmax = (1.5 mW)/2 = 0.75 mW

Dissipation maxes out to Vref²/4/Rx when Rt = Rx and on this case of Vref = 5 V will due to this fact be:

Pmax  = Vref²/4/Rx
= 25/4/3650
= 1.7 mW
= 1.1°C

Yikes! That’s greater than twice the stipulated most self-heating error. What to do? To not fear, an answer is usually recommended by Determine 2.

Determine 2 Rvdd limits max thermistor self-heating to Pmax: Pmax = Vdd²/4/(Rx + Rvdd); Rvdd = Vdd²/4/Pmax – Rx if  > zero, else Rvdd = 0; (Vdd Rx/(Rvdd + Rx)) < Vref  < Vdd.

Dipping once more into the 2152723605 numbers and holding Vdd = 5 V:

Rvdd = 25/4/(0.75 mW) – 3650
Rvdd = 8333 – 3650 = 4.7k
Pmax = 0.749 mW
2.8 V < Vref  <  5 V

Word that if the Determine 2 math yields a zero or detrimental worth for Rvdd, then no Rvdd is required, and the unique Determine 1 circuit will work simply tremendous.

Though Vref will range with Rt and due to this fact temperature, external-reference monolithic ADCs are sometimes very tolerant of Vref variations inside the vary proven and can carry out correct ratiometric conversions regardless of them.

And now the job is achieved! We simply needed to maintain pondering constructive.

Stephen Woodward’s relationship with EDN’s DI column goes again fairly a good distance. Over 100 submissions have been accepted since his first contribution again in 1974.

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