Negative Temperature Coefficient Thermistors for Temperature ...

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2 Thermistors Ln R A B T C D T2 T3 Since the deviation is primarily cubic, some approximations neglect the squared term. Equation (3) is messy to invert, but it can be inverted approximately to get an equation of similar form 1 T a b Ln R c Ln 2 R d Ln 3 R The expected error in using the full third order model, equation (3), is less than 1/100°C over a 200°C span within the range of 0° to 260°C. 0.01°C is less than the usual measurement uncertainty for typical thermistor applications. Self Heating In an electrical circuit a thermistor functions like a temperaturevariable resistor, as such it dissipates power, which in turn heats it up, affecting the temperature measurement. The rate at which a thermistor dissipates power is given approximately by P A T Θ Where (Θ) is the casetoambient thermal resistance, and (T) is the difference between the thermistor’s case temperature and the ambient temperature. The units of thermal resistance are typically degrees Kelvin per Watt. The value of (Θ) is quite variable, for small isolated electronic components it can exceed 100°K/W, whereas well heatsunk components may be under 1°K/W. Some of the energy input to the thermistor is absorbed as the thermistor heats up, here is the equation P T C T C t In this equation (PT ) is the power absorbed by the thermistor, (TC ) is the thermistor’s case temperature, and (C) is the heat capacity of the thermistor. The units of heat capacity are typically Joule/°K Let (P) be the electrical power input to the thermistor, conservation of energy requires that P PA PT T Θ C TC t This is a first order differential equation which can be solved for T, the result is T P Θ 1 t C Θ From (8) it can be seen that the asymptotic temperature rise is the expected (PΘ ). The thermal time constant is (CΘ ). Since many manufactures do not publish values for (C), it often must be estimated in house. For thermistors that are fairly homogeneous this can done by weighing them and using the published specific heats for similar materials. Both (Θ) and (C) can also be measured by means of equation (8). For many applications the selfheating affect is unimportant. For some applications the thermistor power can be pulsed on only during measurements to reduce dissipation. A Case Study In this example application a NTC thermistor is used to measure outside temperature yearround. Assuming a moderate climate, the expected temperature range is from −40° C to +80°C. (3) (4) (5) (6) (7) (8)
Thermistors 3 Here is the electrical circuit diagram for the sensor 1 C1 10k 25C b RT1 Off Board T 10.0k R1 0.1 C2 ADC Figure 1 The thermistor (RT1) is connected to the positive supply. The positions of RT1 and R1 could have as easily been reversed and RT1 connected to the negative supply, but the positive connection has the advantage of producing an output voltage that increases with temperature. Also, if the Analog to Digital Converter (ADC) has a fairly consistent input impedance, its effect on R1 can be included as a simple parallel sum. The parameters given for RT1 (Β = 3750 and R0 = 10k Ohms) are the manufacture’s typical values. There are usually several tolerance grades available with ±10% being the least expensive. 5% tolerance units are very common, while 1% or better units begin to cost a lot more. The repeatability of a given unit is usually very good. Even a unit with a 10% manufacturing tolerance can be calibrated to measure with an accuracy better than 0.1°C over a wide temperature range. The long term stability of a thermistor sensor is usually determined by the packaging. Hermetic glass bead packages have good long term stability, as do some glasscoated surface mount units. Referring to Fig.1, capacitor C2 is a radio frequency interference filter. C2 may not be required for many applications. Capacitor C1 acts as a low pass filter, it not only reduces high frequency noise, it also reduces errors due to ADC charge injection. For many applications C1 could be reduced or eliminated. The thermistor’s own thermal time constant is often several seconds, which tends to be the limiting factor on signal bandwidth. Selecting the value of R1 is an interesting problem. Different values for R1 produce different curvatures in the circuit’s temperature to voltage relationship. For temperature controllers operating at a fixed temperature, R1 is usually selected to give the greatest sensitivity at the operating temperature. For measuring instruments, like this one, a common choice is to pick R1 so that the sensitivity is equal at the extremes of the measurement range. This constraint is easy to express analytically, and it tends to reduce the nonlinearity of the voltage vs temperature relationship over the range of interest.
Page 1: Negative Temperature Coefficient Th
Page 5 and 6: Thermistors 5 Intuitively, the best
Page 7 and 8: Thermistors 7 Error° K 1.25 1 0.75
Page 9 and 10: Thermistors 9 T ° K 340 320 300 28
Page 11 and 12: Thermistors 11 R5% R5% Β2% Β2% Er

Negative Temperature Coefficient Thermistors for Temperature ...

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