Instrumentation & Measurement Magazine 26-2 - 13

Research on the Adaptability of
Thermistor Calibration Equations
Aiju Li, Haitao Wang, Liang Dong, Qiang Han, Meng Wen, and Xiaodong Wen
F
our different equations are used to fit the resistance-temperature
relationship for negative
temperature coefficient thermistor sensor in the range
of 273.15~373.15 K. In order to obtain more general results,
thermistors produced by four different manufacturers are
selected for experiments. The fitting results by Hoge-2 and
Hoge-3 equations are more consistent with the experimental
results than S-H and R-C equations. As the amount of experiment
data decreases, the fitting results of Hoge-3 equation
gradually deviate from the experimental results, but it has little
effect on the fitting results of Hoge-2 equation. In addition,
the expression of the Hoge-2 equation is simpler than that of
the Hoge-3 equation, so the Hoge-2 equation is recommended
as the calibration equation for thermistors fitting.
Study of Thermistors
Negative temperature coefficient thermistor sensors (NTCs)
have drawn considerable attention in automotive electronics,
household appliances, and other fields for their high-temperature
coefficient of resistance, sensitive response and excellent
stability [1]-[3]. However, the application of NTCs in the fields
that require high measurement accuracy is limited due to their
highly nonlinear characteristics. Thus, a suitable equation for
the resistance-temperature relationship is needed. At present
the Steinhart-Hart (S-H equation) is the most widely used calibration
equation. Rudtsch and von Rohden proposed that the
S-H equation showed a poor performance, and the number of
parameters in the interpolation equation could have a considerable
influence on the interpolation error [4]. Liu evaluated
nine approximate calibration equations for the resistance-temperature
relationship of MF501 NTCs at the range of 278.15
~328.15 K, and the research confirmed that the Hoge-2 equation
was the best calibration equation of the equations for
high-precision temperature measurement.[5] Chen selected
seven calibration equations to evaluate the fitting results of the
resistance-temperature relationship and estimated the parameters
of these calibration equations by least squares method.
The results of this study indicated that Hoge-3 equation was
the best for seven equations [6]. Chung and Oh introduced an
April 2023
approach to calibrate NTCs using the residual compensation
method that increased the temperature accuracy of the basic
equation [7].
The results of these studies are inconsistent because most
studies only focus on the resistance-temperature relationship
of one or several types of thermistors. The preparation
process and the types of additives in the thermistors affect resistance-temperature
relationship seriously, and as a result,
thermistors produced by different manufacturers have different
resistance-temperature relationships. It is necessary to
study the resistance-temperature relationship of thermistors
produced by different manufacturers. Herein, we use four
different approximate calibration equations to study thermistors
produced by different manufacturers and find a modified
equation that is widely applicable and easy to use.
Experiments
Methods and Materials
Four thermistors were purchased from the United States, Europe,
and China. Their details are listed in Table 1. The sensor
chips were assembled in hermetically sealed stainless steel
housing with 4-wire insulated cables, and a special shielding
wire for the precision sensor produced by OMEGA was used.
Before the experiment, all samples were aged at 120 °C for
100 h. The test range of thermistors was 0~100 °C.
The residual compensation method was used to fit the
resistance-temperature relationship of thermistors. The constant
temperature tanks of HTS100 and HXT100 (produced by
Table 1 - Information of thermistors
Type
MF5802
44007
55104
P60BA
Producer
China
America (OMEGA)
Europe (TE)
Europe (Amphenol)
IEEE Instrumentation & Measurement Magazine
1094-6969/23/$25.00©2023IEEE
Claimed
Resistance Value
5 kΩ (at 0 °C)
5 kΩ (at 25 °C)
5 kΩ (at 25 °C)
5 kΩ (at 25 °C)
13
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