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大学物理实验, 2026, 39(3): 6-12     https://doi.org/10.14139/j.cnki.cn22-1228.2026.03.002
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非平衡电桥测温实验的非线性修正与不确定度评定#br#
高 磊
中国石油大学( 北京) 理学院,北京 102249
Nonlinearity Compensation and Uncertainty Evaluation in an Unbalanced-Bridge Temperature Measurement Experiment#br#
GAO Lei
College of Science,China University of Petroleum( Beijing) ,Beijing 102249,China
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摘要  非平衡直流电桥法是非电量电测技术的重要基础,广泛应用于高校物理实验教学与工程测量实践。针对传统实验中采用线性近似公式测量 NTC 热敏电阻( 如 MF51 型) 时,在宽温区( 尤其高温端) 引入显著原理性误差的问题,提出了基于精确模型的改进方法,并进行了规范化的不确定度评定。研究依据 JJF 1059.1—2012《测量不确定度评定与表示》规范,建立了基于戴维宁定理的电压输出法精确数学反演模型,有效消除了线性近似引入的方法误差,并采用 GUM( 测量不确定度表示指南) 方法合成评定了 A 类与 B 类不确定度。此外,通过对比 1.5 V 低压与 5.0 V 常规供电条件,定量分析并验证了低压供电抑制自热效应引起系统误差的必要性。实验结果表明,在 25~65 ℃温区内,采用非线性反演模型并配合 1.5 V 低压供电,有效消除了传统线性近似法在高温端引入的超过 40%的原理性偏差,并将自热效应误差控制在 1%以内。不确定度评定显示,改进后的电测系统本身相对扩展不确定度仅为 0.12%;在引入 K 型热电偶的测温不确定度后,测量系统的总不确定度主要受限于温度采集环节。本研究量化了从“模型修正”到“硬件瓶颈”的精度层级,为非平衡电桥实验中的非线性误差处理与系统级不确定度评定提供了具有操作性的教学示范。
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高 磊
关键词:     非平衡直流电桥  NTC 热敏电阻  非线性模型修正  不确定度评定  自热效应  电压输出法    
Abstract: The unbalanced DC bridge method is an important foundation for non-electrical quantity measurement technology and is widely used in university physics experimental teaching and engineering measurement practice. Addressing the issue that the traditional experimental method using a linear approximation formula for NTC thermistors( such as the MF51type) introduces significant principle errors overa wide temperature range( especially at the high-temperature end) ,this paper proposes an improved method based on an accurate model and carries out a standardized uncertainty evaluation.Based on the JJF 1059.1—2012Evaluation and Expression of Uncertainty in Measurement specification,an accurate mathematical
inversion model for the voltage output method based on Thevenin' s theorem was established,effectively
eliminating the method errors introduced by linear approximation.The combined standard uncertainty arising
from Type A and Type B evaluations was determined using the GUM method.Furthermore,by comparing 1.5 V
low-voltage supply with 5. 0 V conventional supply conditions,the impact of the self-heating effect was
quantitatively analyzed,verifying the necessity of low-voltage supply in suppressing systematic errors. The
experimental results show that in the temperature range of 25.0 ℃ to 65.0 ℃,after adopting the nonlinear
inversion model,the relative expanded uncertainty of the measurement system is stable within the range of
0.12% to 0.13%( Note: this evaluation excludes the uncertainty of temperature measurement) ; in contrast,the
systematic deviation produced by the traditional linear approximation method exceeds 40% at 65.0 ℃. The
material constant of the thermistor obtained based on the improved model is 3 946 K,with a relative deviation
from the nominal value of only -0.1%.This study provides an operable teaching demonstration for nonlinear
model correction and standardized uncertainty processing in unbalanced bridge experiments.
Key words:       unbalanced DC bridge    NTC thermistor    nonlinear model correction    uncertainty evaluation    self-heating effect    voltage output method
                    发布日期:  2026-06-25     
ZTFLH:  O 4-34  
基金资助:  北京高等教育学会教改课题( ms2025210) ; 教育部高等学校大学物理课程教学指导委员会大中物理教育衔接工作委员会
教学研究课题( wx202517) 资助
引用本文:    
高 磊. 非平衡电桥测温实验的非线性修正与不确定度评定#br#[J]. 大学物理实验, 2026, 39(3): 6-12.
GAO Lei. Nonlinearity Compensation and Uncertainty Evaluation in an Unbalanced-Bridge Temperature Measurement Experiment#br#. Physical Experiment of College, 2026, 39(3): 6-12.
链接本文:  
https://dawushiyan.jlict.edu.cn/CN/10.14139/j.cnki.cn22-1228.2026.03.002  或          https://dawushiyan.jlict.edu.cn/CN/Y2026/V39/I3/6
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