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where: RT1
RT2 T1
= resistance at temperature 1 = resistance at temperature 2
= temperature 1 (K); T2 = temperature 2 (K) The data sheet for the thermistor normally lists the beta
value for two cases: the two temperatures at 25°C and 50°C, and 25°C and 85°C. The user chooses the value closest to the design’s temperature range. Higher-accuracy thermistors and end solutions use
Figure 7: A thermistor ratiometric confi guration measurement
the Steinhart-Hart equation to convert from resistance to degrees Celsius. From Equation 2, three constants are needed (A, B and C), which are provided by the sensor manufacturer. As the coefficients for the equation are generated using three temperature points, the resulting equation minimises the error introduced due to linearisation – typically 0.02°C.
A, B and C are constants derived from three
temperature test points, R = thermistor’s resistance in Ω and T = temperature in degrees K.
Figure 8: Multiple thermistors’ analogue input confi guration measurements
depends on the temperature range being measured, the required accuracy, the application environment, and the thermistor’s long-term stability.
Linearisation: Beta vs. Steinhart-Hart Equation To convert from resistance to degrees Celsius, a beta value is commonly used. It is determined by knowing two temperature points and the corresponding resistance at each temperature point:
Current/voltage excitation Figure 3 shows current excitation of the sensor. An excitation current is applied to the thermistor and to a precision resistor, with the precision resistor being used as measurement reference. This resistor must have a value equal or greater than the highest resistance value of the thermistor – dependent on the system’s minimum temperature being measured. When selecting this current, the thermistor’s maximum resistance must be considered, to ensure that the voltage generated across the sensor and reference resistor is always suitable for the design’s electronics. Excitation current sources require some headroom or output compliance. If the thermistor has a large resistance at the minimum temperature being measured, this leads to a very low excitation current value. Therefore, the voltage generated across the thermistor at hot temperatures is small. To optimise the measurement of these low-level signals, a programmable gain stage should be used; however, the gain needs to be programmed dynamically as the signal level from the thermistor changes signifi cantly over temperature.
Another option is to set the gain but use a dynamic
excitation current. So, as the signal level from the thermistor changes, the excitation current value is changed dynamically so that the voltage generated across the thermistor is within the electronics’ specifi ed input range. All this requires a high degree of control, continuously monitoring the voltage across the thermistor, to ensure that
08 February 2024
www.electronicsworld.co.uk
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