高精度多参考阻值比率测温系统

高精度多参考阻值比率测温系统 High-precision multi-reference ratiometric temperature measurement system 1 2 3 first-author 辛世杰（1994-），男，河北秦皇岛人，博士研究生，2016年于电子科技大学获得学士学位，主要从事低噪声信息获取与处理方面的研究。E-mail：sh_jie@163.com http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850102&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850106&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850104&type= 22.01333618 32.00402451 辛世杰 （1994-），男，河北秦皇岛人，博士研究生，2016年于电子科技大学获得学士学位，主要从事低噪声信息获取与处理方面的研究。E-mail： sh_jie@163.com sh_jie@163.com 1 3 corresp E-mail： leiding@mail.sitp.ac.cn E-mail： leiding@mail.sitp.ac.cn 丁　雷（1968-），男，上海人，博士，教授，研究员，现任中国科学院上海技术物理研究所所长、博士生导师，主要从事航天光学遥感仪器的研制以及光学遥感成像技术、高精度辐射定标技术的研究。E-mail： leiding@mail.sitp.ac.cn http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850108&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850112&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850110&type= 22.01333618 32.00402832 丁　雷 （1968-），男，上海人，博士，教授，研究员，现任中国科学院上海技术物理研究所所长、博士生导师，主要从事航天光学遥感仪器的研制以及光学遥感成像技术、高精度辐射定标技术的研究。E-mail： leiding@mail.sitp.ac.cn leiding@mail.sitp.ac.cn 中国科学院 上海技术物理研究所，上海 200083 中国科学院 上海技术物理研究所，上海 200083 Shanghai Institute of Technical Physics， Chinese Academy of Sciences， Shanghai 200083， China Shanghai Institute of Technical Physics， Chinese Academy of Sciences， Shanghai 200083， China 中国科学院大学，北京 100049 中国科学院大学，北京 100049 University of Chinese Academy of Sciences， Beijing 100049， China University of Chinese Academy of Sciences， Beijing 100049， China 中国科学院 红外探测与成像技术重点实验室，上海 200083 中国科学院 红外探测与成像技术重点实验室，上海 200083 Key Laboratory of Infrared System Detection and Imaging Technology， Chinese Academy of Sciences， Shanghai 200083， China Key Laboratory of Infrared System Detection and Imaging Technology， Chinese Academy of Sciences， Shanghai 200083， China 单参考阻值比率测温系统是一种目前常用的高精度测温方法，可以有效削弱恒流源长期漂移、放大器增益漂移、热电势等因素对测量结果所造成的影响，但测量性能会随着测量阻值远离参考电阻阻值而变差。为了解决该问题，本文首先分析了基于恒流源的铂电阻、参考电阻比率测温方法，引入非线性因子，理论分析了测量性能会随着测量阻值远离参考电阻阻值而变差的原因，并由此提出了多参考阻值比率测温方法，进行了硬件系统的设计。对多参考阻值比率测温系统进行了长期稳定性、分辨能力、不同环境温度所造成非线性标定劣化的等效实验，验证了本文理论推导部分的正确性。实验结果表明，在 - 38.8~64.6 ℃的温度测量范围内，高精度多参考阻值比率测温系统的测量稳定性优于0.002 5 ℃/5 day，测量分辨能力优于0.001 25 ℃，在5~45 ℃环境温度下的测量稳定性优于0.004 ℃。基本满足长期、环境温度变化较大的温度测量应用需求。 The single-reference resistance ratio temperature measurement system is a commonly used method for high-precision temperature measurement， which can effectively weaken the effect of constant current source long-term drift， amplifier gain drift， thermoelectric potential， and other factors on the measurement results. However， the performance worsens when the value of the measured resistance is far away from the reference resistance. To solve this problem， we analyze the platinum resistance and a single-reference resistance ratio temperature measurement method based on a constant current source， introduce a nonlinear factor， and analyze why the measurement performance will deteriorate as the value of the measured resistance moves far away from the reference resistance. Moreover， based on this， a multi-reference resistance ratio temperature measurement method is proposed and the hardware system is designed. The multi-reference resistance ratio temperature measurement system was tested by performing equivalent experiments to determine the long-term stability， resolution ability， and nonlinear calibration degradation caused by different ambient temperatures， which verifies the correctness of the theoretical derivation part of this study. The experimental results showed that， in the temperature measurement range of approximately - 38.8~64.6 ℃， the measurement stability of the high-precision multi-reference resistance ratio temperature measurement system is better than 0.0025 ℃/5 d， the measurement resolution is better than 0.00125 ℃， and the measurement stability at an ambient temperature range of 5 to 45 ℃ is better than 0.004 ℃. It basically meets the long-term temperature measurement application requirements with large environmental temperature changes. 温度测量 比率测温 铂电阻 多参考 非线性 temperature measurements ratio temperature measurements platinum resistance multi-reference nonlinear 1 引　言 1 随着航天红外遥感技术的发展，待解决的各种科学问题对红外载荷观测水平提出了更高要求。而星载定标黑体辐射源作为保持红外载荷高精度观测水平的重要组成部分 ［ 1 1 - 4 4 1-4 ］ ，其评价参数包括空腔的轴向温度均匀性、稳定性、黑体辐射温度等，这些参数均需要稳定且高精度的温度测量电路来获得并溯源 ［ 5 5 ］ 。因此，高精度的温度测量电路的性能会影响红外载荷黑体的溯源水平。 恒流源激励的四线制铂电阻测温方法作为一种高精度测温手段，其优点在于可完全消除导线电阻对测量结果的影响，精确获取铂电阻的微小变化信息，应用十分广泛。然而恒流源长期漂移、放大器增益漂移、热电势等因素依旧会对该电路结构下的测量结果产生影响，导致该方法在长期及环境温度变化较大的应用中受到了很大的限制。 为解决该问题，文献［ 6 6 - 8 8 6-8 ］等使用了基于恒流源的铂电阻、参考电阻比率测温方法，通过控制电压采集单元分别对铂电阻及参考电阻进行采集处理，消除了恒流源长期漂移、温差电势以及电压测量中零点误差、灵敏度误差等引起的测温误差，提高了测量结果的稳定性。然而这种测量方法在铂电阻阻值远离参考电阻阻值时会存在非线性及测温性能劣化的问题。例如Fluke公司的超级电阻测温仪1 595 A也是采用这种测温方法，当电阻比率在0.95~1.05范围内时，其不确定度为 <math id="M1"><mn mathvariant="normal">6</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">8</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850116&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850114&type= 13.20800018 3.04800010 ，然而当电阻比率在0.25~0.5或2.0~4.0范围内时，其不确定度劣化为 <math id="M2"><mn mathvariant="normal">5</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">7</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850122&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850119&type= 13.20800018 3.04800010 。 普通测温电路为解决非线性问题，常通过多测温点的数据采集，得到测量结果关于真实结果的拟合函数关系式，并将其固化在系统中的微处理器或微控制器中 ［ 9 9 - 11 11 9-11 ］ 。但由于放大器、有源滤波器、模数转换器等器件的非线性会随温度变化而变化，且长期使用会产生漂移，导致这种方法具有时效性及温度敏感的缺点，不适用于长期应用及环境温度变化较大的场合。 针对上述问题，本文对基于恒流源的铂电阻、参考电阻比率测温方法的原理进行了分析，给出了测温结果非线性及性能劣化原因的解释；针对测温结果非线性的问题，给出了一种多参考阻值的改进比率测温方法。最终实现了一种可满足长期及环境温度变化较大场合应用需求的高精度测温系统。 2 铂电阻、参考电阻比率测温法局限性 1 基于恒流源的铂电阻、参考电阻比率测温电路结构如 图1 图1 所示。其中 <math id="M3"><msub><mrow><mi>I</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850198&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850195&type= 2.62466669 3.72533321 为方向可控恒定电流源； <math id="M4"><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850130&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850128&type= 1.52400005 2.79399991 为导线电阻； <math id="M5"><mi>E</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850134&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850132&type= 2.62466669 2.79399991 为电流激励回路上的热电势； <math id="M6"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850382&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850379&type= 3.47133350 3.72533321 为铂电阻； <math id="M7"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850330&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850328&type= 3.55599999 3.72533321 为参考电阻； <math id="M8"><msub><mrow><mi>V</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850147&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850145&type= 5.16466665 3.80999994 为铂电阻两端产生的电势差； <math id="M9"><msub><mrow><mi>V</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850151&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850149&type= 5.24933338 3.80999994 为参考电阻两端产生的电势差； <math id="M10"><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850155&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850153&type= 3.38666677 3.72533321 ， <math id="M11"><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850159&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850157&type= 3.47133350 3.72533321 分别为铂电阻、参考电阻测量回路上的热电势。 由于后级的电压测量模块的内阻一般为 <math id="M12"><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mn mathvariant="normal">9</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850169&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850167&type= 4.82600021 3.04800010 Ω级别，远大于铂电阻及参考电阻的阻值，意味着测量导线上通过的电流约为几nA，导线电阻所带来的电压波动约为 <math id="M13"><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">9</mn></mrow></msup><mtext> </mtext><mi mathvariant="normal">V</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850174&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850171&type= 10.83733368 3.13266683 ，故导线电阻对测温结果的影响可忽略不计。通过开关切换恒流源方向和后级电压测量模块的测量对象，可得方程组： <math display="block" id="M14"><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>=</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><mfenced separators="|"><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo>+</mo><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></mrow></mfenced><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>U</mi></mtd></mtr><mtr><mtd><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub><mo>=</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><mfenced separators="|"><mrow><mo>-</mo><msub><mrow><mi>I</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo>+</mo><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></mrow></mfenced><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>U</mi></mtd></mtr><mtr><mtd><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>=</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><mfenced separators="|"><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub><mo>+</mo><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub></mrow></mfenced><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>U</mi></mtd></mtr><mtr><mtd><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub><mo>=</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><mfenced separators="|"><mrow><mo>-</mo><msub><mrow><mi>I</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub><mo>+</mo><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub></mrow></mfenced><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>U</mi></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850180&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850177&type= 65.53199768 25.65399933 ， 其中： <math id="M15"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850486&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850485&type= 1.94733346 2.79399991 为放大器增益漂移误差； <math id="M16"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850488&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850487&type= 2.87866688 2.79399991 为放大器增益倍数； <math id="M17"><msub><mrow><mi>I</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850198&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850195&type= 2.62466669 3.72533321 为恒流源电流； <math id="M18"><mi mathvariant="normal">Δ</mi><mi>U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850490&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850489&type= 5.50333309 2.79399991 为放大器输出失调电压。由此可得铂电阻阻值 <math id="M19"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850382&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850379&type= 3.47133350 3.72533321 ： <math display="block" id="M20"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub><mo>×</mo><mfrac><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub></mrow><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850215&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850213&type= 36.06800079 8.46666718 . 这便消除了电路中恒流源的长期漂移、放大器增益漂移、导线电阻及热电势等因素对测量结果所带来的影响。 但由于电路元件并非理想，温度测量系统中放大器、有源滤波器及模数转换器等对输入电压 <math id="M21"><mi>U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850220&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850217&type= 3.04800010 2.79399991 的响应存在非线性的问题，且该非线性会受到电路元件温度 <math id="M22"><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850376&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850375&type= 2.53999996 2.79399991 影响，因此引入非线性响应因子 <math id="M23"><mi>β</mi><mfenced separators="|"><mrow><mi>U</mi><mo>,</mo><mi>T</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850232&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850229&type= 12.78466606 4.23333359 ，将上述方程组改写为： <math display="block" id="M24"><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfenced><mo>×</mo><mfenced open="[" close="]" separators="|"><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><mfenced separators="|"><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo>+</mo><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></mrow></mfenced><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>U</mi></mrow></mfenced></mtd></mtr><mtr><mtd><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfenced><mo>×</mo><mfenced open="[" close="]" separators="|"><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><mfenced separators="|"><mrow><mo>-</mo><msub><mrow><mi>I</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo>+</mo><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></mrow></mfenced><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>U</mi></mrow></mfenced></mtd></mtr><mtr><mtd><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfenced><mo>×</mo><mfenced open="[" close="]" separators="|"><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><mfenced separators="|"><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub><mo>+</mo><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub></mrow></mfenced><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>U</mi></mrow></mfenced></mtd></mtr><mtr><mtd><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfenced><mo>×</mo><mfenced open="[" close="]" separators="|"><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><mfenced separators="|"><mrow><mo>-</mo><msub><mrow><mi>I</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub><mo>+</mo><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub></mrow></mfenced><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>U</mi></mrow></mfenced></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850237&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850235&type= 100.07599640 28.70199966 ， 其中： <math id="M25"><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850243&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850240&type= 17.10266685 4.91066647 ， <math id="M26"><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850249&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850246&type= 17.10266685 4.82600021 ， <math id="M27"><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850255&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850252&type= 17.86466599 4.91066647 ， <math id="M28"><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850261&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850258&type= 17.86466599 4.82600021 分别为电路在 <math id="M29"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850266&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850263&type= 3.72533321 3.72533321 温度下对铂电阻正电压测量、铂电阻负电压测量、参考电阻正电压测量、参考电阻负电压测量的非线性响应因子。化简可得： <math display="block" id="M30"><mfrac><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub></mrow><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mfenced open="{" close="}" separators="|"><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><msub><mrow><mi>I</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo>×</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">2</mn><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfenced><mo>+</mo><mfenced open="[" close="]" separators="|"><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>U</mi></mrow></mfenced><mo>×</mo><mfenced open="[" close="]" separators="|"><mrow><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>-</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfenced></mrow></mfenced></mrow><mrow><mfenced open="{" close="}" separators="|"><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><msub><mrow><mi>I</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub><mo>×</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">2</mn><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfenced><mo>+</mo><mfenced open="[" close="]" separators="|"><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>U</mi></mrow></mfenced><mo>×</mo><mfenced open="[" close="]" separators="|"><mrow><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>-</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfenced></mrow></mfenced></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850272&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850269&type= 181.94866943 13.80066681 . 在实际应用中，由于 式（4） 式（4） 中 <math id="M31"><mfenced open="[" close="]" separators="|"><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>U</mi></mrow></mfenced><mfenced open="[" close="]" separators="|"><mrow><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>-</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850278&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850275&type= 71.45866394 5.67266655 及 <math id="M32"><mfenced open="[" close="]" separators="|"><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>α</mi></mrow></mfenced><mi>A</mi><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>U</mi></mrow></mfenced><mfenced open="[" close="]" separators="|"><mrow><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>-</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850285&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850281&type= 73.06733704 5.67266655 项的存在，使得恒流源的长短期漂移、放大器增益漂移、噪声及热电势等因素继续影响着测量结果的不确定度。从原理上分析可得，除非放大器、有源滤波器、模数转换器等器件的正负电压响应理想对称，否则这种电路结构仅能削弱上述因素对测温结果的影响，无法完全消除。 为探讨电路非线性对测温结果的影响，将 式（4） 式（4） 化简，忽略高阶项，可得： <math display="block" id="M33"><mtable><mtr><mtd><mfrac><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub></mrow><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub></mrow></mfrac><mo>≈</mo></mtd></mtr><mtr><mtd><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">2</mn><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfenced></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">2</mn><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfenced></mrow></mfrac></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850291&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850288&type= 55.03333664 22.69066620 . 令 <math id="M34"><mi>K</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850333&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850331&type= 2.79399991 2.79399991 为电路的非线性误差系数： <math display="block" id="M35"><mi>K</mi><mo>=</mo><mfrac><mrow><mn mathvariant="normal">2</mn><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850301&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850300&type= 56.55733109 10.83733368 . 由于当 <math id="M36"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850382&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850379&type= 3.47133350 3.72533321 与 <math id="M37"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850330&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850328&type= 3.55599999 3.72533321 的值接近时，电路的非线性响应因子也接近，从而 <math id="M38"><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>≈</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850314&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850312&type= 39.36999893 4.91066647 ， <math id="M39"><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>≈</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850318&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850316&type= 40.30133438 4.82600021 ，得到铂电阻阻值计算公式： <math display="block" id="M40"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo>≈</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub><mo>×</mo><mfrac><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub></mrow><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mo>-</mo></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850322&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850320&type= 36.06800079 8.46666718 . 但当铂电阻的阻值 <math id="M41"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850382&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850379&type= 3.47133350 3.72533321 偏离参考电阻的阻值 <math id="M42"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850330&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850328&type= 3.55599999 3.72533321 时，式中的非线性误差系数 <math id="M43"><mi>K</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850333&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850331&type= 2.79399991 2.79399991 不为1，这便是电路的非线性对测温结果所造成的偏移。 3 高精度多参考阻值比率测温系统 1 高精度多参考阻值比率测温系统由三个电路部分组成：高精度多参考阻值比率测温电路、基于LTC6655恒压基准芯片的高稳定性恒流源和时分复用式高精度电压采样与处理电路。其中，高精度多参考阻值比率测温电路吸取了铂电阻、参考电阻比率测温电路的优点，同时为测温系统提供了抑制非线性所带来性能劣化的解决方案；基于LTC6655恒压基准芯片的高稳定性恒流源为测温系统提供了短期稳定性能出色的恒流源；时分复用式高精度电压采样与处理电路提供了较高的电压分辨能力，保障了测温公式中扰动项的一致性。 3.1　高精度多参考阻值比率测温电路原理 2 为继续削弱恒流源的长短期漂移、放大器增益漂移、噪声及热电势等因素对测温结果的影响，减小测温结果的非线性问题，本文采取了如 图 2 图 2 所示的测温方法。 本文采用铂电阻PT1000来进行温度测量，即铂电阻在0 ℃时的阻值为1 000 Ω，令 <math id="M44"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">900</mn><mtext>  </mtext><mi mathvariant="normal">Ω</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850345&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850342&type= 17.94933319 3.72533321 ， <math id="M45"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">1</mn><mtext> </mtext><mn mathvariant="normal">000</mn><mtext>  </mtext><mi mathvariant="normal">Ω</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850349&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850347&type= 20.40466690 3.72533321 ， <math id="M46"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">1</mn><mtext> </mtext><mn mathvariant="normal">100</mn><mtext>  </mtext><mi mathvariant="normal">Ω</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850353&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850351&type= 20.40466690 3.72533321 ， <math id="M47"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">1</mn><mtext> </mtext><mn mathvariant="normal">200</mn><mtext>  </mtext><mi mathvariant="normal">Ω</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850357&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850355&type= 20.40466690 3.72533321 。电路在电流方向为正、负时的非线性响应因子分别为 <math id="M48"><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>+</mo></mrow></msub><mo>,</mo><mi>T</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850362&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850359&type= 17.27199936 4.91066647 ， <math id="M49"><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>-</mo></mrow></msub><mo>,</mo><mi>T</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850369&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850365&type= 17.27199936 4.91066647 ，其中 <math id="M50"><mi>i</mi><mo>=</mo><mn mathvariant="normal">1,2</mn><mo>,</mo><mn mathvariant="normal">3,4</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850372&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850371&type= 18.88066673 3.21733332 ； <math id="M51"><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850376&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850375&type= 2.53999996 2.79399991 为当前温度。工作过程为：设置恒流源方向为正、负方向，分别对铂电阻 <math id="M52"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850382&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850379&type= 3.47133350 3.72533321 两端的正、负电压进行测量；同样地，对参考电阻 <math id="M53"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850386&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850384&type= 3.80999994 3.72533321 ， <math id="M54"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850390&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850388&type= 3.80999994 3.72533321 ， <math id="M55"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850394&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850392&type= 3.80999994 3.72533321 及 <math id="M56"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850398&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850396&type= 3.80999994 3.72533321 两端的正、负电压进行测量；最后根据下文给出的铂电阻计算公式得到铂电阻阻值，从而确定被测目标温度。 为了简化说明过程，假设电路的非线性响应因子随阻值增加是单调变化的，易证： <math display="block" id="M57"><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mfenced open="{" close="}" separators="|"><mrow><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>,</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">t</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced></mrow></mfenced><mo>=</mo><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">1</mn><mo>,</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">t</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo><</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mfenced separators="|"><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfenced></mtd></mtr><mtr><mtd><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">2</mn><mo>,</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">t</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced><mo>,</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mfenced separators="|"><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfenced><mo>≤</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo><</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mfenced separators="|"><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></mrow></mfenced></mtd></mtr><mtr><mtd><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">3</mn><mo>,</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">t</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced><mo>,</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mfenced separators="|"><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></mrow></mfenced><mo>≤</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo><</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mfenced separators="|"><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></mrow></mfenced></mtd></mtr><mtr><mtd><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">4</mn><mo>,</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">t</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced><mo>,</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mfenced separators="|"><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></mrow></mfenced><mo>≤</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></mtd></mtr></mtable></mrow></mfenced><mo>,</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850402&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850400&type= 106.42600250 36.06800079 <math display="block" id="M58"><mi>i</mi><mo>=</mo><mn mathvariant="normal">1,2</mn><mo>,</mo><mn mathvariant="normal">3,4</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850406&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850404&type= 18.88066673 3.21733332 ， 其中： <math display="block" id="M59"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>,</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">t</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn mathvariant="normal">2</mn><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced><mo>+</mo><mi>β</mi><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>-</mo></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850410&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850408&type= 62.73799896 10.92199993 . 这意味着铂电阻和与其阻值最接近的参考电阻作比率测温所得结果的非线性误差最小。但这种方法在切换参考电阻时，会导致测温结果不连续的问题。例如当铂电阻阻值从小于 <math id="M60"><mfenced separators="|"><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfenced><mo>/</mo><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850415&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850413&type= 19.38866615 4.82600021 变为大于 <math id="M61"><mfenced separators="|"><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfenced><mo>/</mo><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850419&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850417&type= 19.38866615 4.82600021 时，由于 <math id="M62"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">1</mn><mo>,</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850423&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850421&type= 8.21266651 3.72533321 与 <math id="M63"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">2</mn><mo>,</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850427&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850425&type= 8.21266651 3.72533321 并不相同，导致铂电阻阻值反推结果不连续。 为此，引入与阻值相关的调节因子 <math id="M64"><mi>a</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850430&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850429&type= 1.86266661 2.79399991 ， <math id="M65"><mi>b</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850435&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850433&type= 1.86266661 2.79399991 ： <math display="block" id="M66"><mi>a</mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850437&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850436&type= 23.11400032 8.55133343 ， <math display="block" id="M67"><mi>b</mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850439&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850438&type= 23.02933502 8.55133343 . 给出此时的铂电阻阻值计算公式为： <math display="block" id="M68"><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo>≈</mo><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>×</mo><mfrac><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub></mrow><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">1</mn><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">1</mn><mo>-</mo></mrow></msub></mrow></mfrac><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo><</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mtd></mtr><mtr><mtd><mfrac><mrow><mfenced separators="|"><mrow><mi>a</mi><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><mi>b</mi><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfenced><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub></mrow></mfenced></mrow><mrow><mi>a</mi><mo>×</mo><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>-</mo></mrow></msub></mrow></mfenced><mo>+</mo><mi>b</mi><mo>×</mo><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn><mo>-</mo></mrow></msub></mrow></mfenced></mrow></mfrac><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>×</mo><mfrac><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub></mrow><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">4</mn><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">4</mn><mo>-</mo></mrow></msub></mrow></mfrac><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>≤</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></mtd></mtr></mtable></mrow></mfenced></mtd></mtr><mtr><mtd><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>≤</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo><</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mi>i</mi><mo>=</mo><mn mathvariant="normal">1,2</mn><mo>,</mo><mn mathvariant="normal">3</mn></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850441&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850440&type= 73.49066925 38.52333450 ， <math id="M69"><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>+</mo></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850443&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850442&type= 7.36600018 3.72533321 与 <math id="M70"><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>-</mo></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850445&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850444&type= 7.36600018 3.72533321 分别代表第 <math id="M71"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850447&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850446&type= 1.10066664 2.79399991 个参考电阻在电流正向流过、反向流过所测得的电压结果（ <math id="M72"><mi>i</mi><mo>=</mo><mn mathvariant="normal">1,2</mn><mo>,</mo><mn mathvariant="normal">3,4</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850449&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850448&type= 18.54199982 3.21733332 ）。由于调节因子 <math id="M73"><mi>a</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850451&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850450&type= 1.86266661 2.79399991 、 <math id="M74"><mi>b</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850453&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850452&type= 1.86266661 2.79399991 中存在未知数 <math id="M75"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850455&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850454&type= 3.47133350 3.72533321 ，在 公式（12） 公式（12） 中代入 公式（10） 公式（10） 和 公式（11） 公式（11） 并化简后，得到： <math display="block" id="M76"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo>≈</mo><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>×</mo><mfrac><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub></mrow><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">1</mn><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">1</mn><mo>-</mo></mrow></msub></mrow></mfrac><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo><</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mtd></mtr><mtr><mtd><mfrac><mrow><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub></mrow></mfenced><mfenced separators="|"><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn><mo>-</mo></mrow></msub></mrow></mfenced><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>-</mo></mrow></msub></mrow></mfenced></mrow><mrow><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn><mo>-</mo></mrow></msub></mrow></mfenced><mo>-</mo><mfenced separators="|"><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi>i</mi><mo>-</mo></mrow></msub></mrow></mfenced></mrow></mfrac><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>≤</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo><</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mi>i</mi><mo>=</mo><mn mathvariant="normal">1,2</mn><mo>,</mo><mn mathvariant="normal">3</mn></mtd></mtr><mtr><mtd><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>×</mo><mfrac><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub></mrow><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">4</mn><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">4</mn><mo>-</mo></mrow></msub></mrow></mfrac><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>≤</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850458&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850457&type= 157.73399353 32.25799942 . 这种多参考阻值比率测温电路实质上将铂电阻与参考电阻的比率限定在较小的范围内，减小了当铂电阻阻值远离参考电阻阻值时，电路非线性对测温结果所造成的影响，因此这种多参考阻值比率测温电路的测量结果在全温度测量范围内所引入的非线性误差要优于单参考阻值比率测温电路。同时，由于多测温点拟合函数曲线的非线性校正方法只能对当前温度下电路的非线性进行校正，而放大器、有源滤波器、模数转换器等器件的非线性会随着温度变化而变化，且在长期使用过程中也会产生非线性的变化，当电路非线性发生改变时该非线性校正方法便失去效果，因此本文方法的非线性校正性能在长期及环境温度变化较大的应用中也要优于多测温点拟合函数曲线的非线性校正性能。 3.2　基于LTC6655恒压基准芯片的高稳定性恒流源 2 本文采用的测温电阻为PT1000铂电阻，其无自热效应的最大测温电流为0.5 mA ［ 12 12 ］ ，恒流源的设计应按照该电流大小进行设计。由于本文设计的测温电路已从原理上削弱了恒流源长期漂移对测温结果所带来的误差干扰，测温精度仅与恒流源短期稳定性有关，因此在元器件的选择中应考虑选取低温漂、低噪声的器件，从而保证恒流源的短期稳定性。最终设计的高稳定性恒流源如 图3 图3 所示。 由于基准电压参考的长期稳定性、温漂、噪声等指标直接影响恒流源精度，故选用Analog Devices公司的超低噪声3 V输出的LTC6655芯片，其最大输出电压误差为 <math id="M77"><mo>±</mo><mn mathvariant="normal">0.025</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850464&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850462&type= 16.08666801 3.47133350 ，0.1 Hz~10 Hz的低频噪声峰峰值为 <math id="M78"><mn mathvariant="normal">2.5</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">7</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850467&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850466&type= 16.34066582 3.04800010 ，10 Hz~10 kHz的噪声有效值为 <math id="M79"><mn mathvariant="normal">2.1</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">7</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850469&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850468&type= 16.25600052 3.04800010 ，最大温漂为 <math id="M80"><mn mathvariant="normal">2</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">6</mn></mrow></msup><mtext> </mtext><mo>℃</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850506&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850503&type= 17.61066628 3.13266683 ，可让输出电流噪声尽可能的降低。参考电阻 <math id="M81"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850474&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850472&type= 4.99533367 3.72533321 的长期稳定性、温漂也会直接影响恒流源精度，这里选用七一八友晟电子有限公司的RJ711型有可靠性指标的精密合金箔固定电阻器，其阻值允许偏差为 <math id="M82"><mo>±</mo><mn mathvariant="normal">0.01</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850478&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850476&type= 14.22399998 3.47133350 ，最大温漂可达 <math id="M83"><mn mathvariant="normal">2</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">6</mn></mrow></msup><mtext> </mtext><mo>℃</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850506&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850503&type= 17.61066628 3.13266683 ，满足设计精度需要。运算放大器选用Analog Devices公司的ADA4522芯片，其最大失调电压为5 μV，失调漂移为22 nV/℃，输入偏置电流50 pA，电压噪声低至 <math id="M84"><mn mathvariant="normal">5.8</mn><mtext> </mtext><mi mathvariant="normal">n</mi><mi mathvariant="normal">V</mi><mo>/</mo><mroot><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850482&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850481&type= 20.23533440 4.06400013 ，从而尽可能的降低运算放大器对恒流源精度的影响。 将设计的0.5 mA恒流源流过七一八友晟电子有限公司的RJ711型号的3 kΩ标准电阻，通过Agilent3458A数字万用表采集该电阻两端的电压值。在约70 min的时间段中，共采集了10 000组电压数据，由GB/T 27418-2017测量不确定度评定和表示的国家标准，标准不确定度的A类评定可根据统计分析的方法来进行。统计分析可知，该恒流源输出电流在10 s内的标准不确定度为0.43 nA，最大相对不确定度为 <math id="M85"><mn mathvariant="normal">8.67</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">7</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850484&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850483&type= 18.11866570 3.04800010 ，满足铂电阻测温的精度需求。 3.3　时分复用式高精度电压采样与处理电路 2 为了保证 公式（13） 公式（13） 中测量各个直流电压时放大器增益漂移误差 <math id="M86"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850486&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850485&type= 1.94733346 2.79399991 、放大器增益倍数 <math id="M87"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850488&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850487&type= 2.87866688 2.79399991 、放大器输出失调电压 <math id="M88"><mi mathvariant="normal">Δ</mi><mi>U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850490&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850489&type= 5.50333309 2.79399991 的一致性，需采用同一个电压采样与处理电路对这些直流电压进行测量。时分复用式高精度电压采样与处理电路组成框图如 图 4 图 4 所示。通过数字信号处理芯片DSP控制的测量对象切换器来切换所需测量的铂电阻、参考电阻等测量目标，然后通过仪表放大器对微弱信号变化进行放大，低通滤波器对其进行滤波降噪，再经由模数转换器输出到DSP中进行铂电阻阻值计算，最终输出温度的测量值。 由于一个温度测量周期时间越长，恒流源的短期漂移越大，从而大幅降低测温精度，所以该电压采样与处理电路不仅需要很高的测量精度，还需要较快目标切换速度及电压响应速度。综合考虑后，选取International Rectifier公司的PVT422光伏继电器作为测量对象切换器的组成部分，相较于市面上一般的信号继电器而言，其2 ms的最大开启/关闭时间、 <math id="M89"><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msup><mtext> </mtext><mi mathvariant="normal">Ω</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850495&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850494&type= 9.22866726 3.04800010 的隔离阻抗可以满足切换速度和阻抗的需求。 由于铂电阻的阻值随温度变化较小，不易由模数转换器直接采集，因此应设计放大电路将其进行放大，同时对电路中耦合的共模干扰进行削弱。与普通运算放大器相比，仪表放大器具有极高的共模抑制比，可同时抑制两个输入端共有的任何信号，从而放大两个输入信号电压之间微弱的差值，其超高的输入阻抗可将测量回路的电流降到最低，从而抑制测量回路上阻抗变化对测量结果的影响。本文采用Analog Devices公司的AD8422型精密仪表放大器，其具有150 dB的共模抑制比，输入阻抗为200 GΩ，0.001%精度的建立时间可达到 <math id="M90"><mn mathvariant="normal">15</mn><mtext> </mtext><mi mathvariant="normal">μ</mi><mi mathvariant="normal">s</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850497&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850496&type= 7.87400007 3.64066648 ，且其在1 kHz时最大输入电压噪声为 <math id="M91"><mn mathvariant="normal">8</mn><mtext> </mtext><mi mathvariant="normal">n</mi><mi mathvariant="normal">V</mi><mo>/</mo><mroot><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850499&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850498&type= 17.35666656 4.06400013 ，非线性度为 <math id="M92"><mn mathvariant="normal">5</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">7</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850501&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850500&type= 13.37733269 3.04800010 ，增益误差优于0.04%，可满足铂电阻测温信号放大的精度和速度需求。此外，采用RJ711型号的标准电阻来设定AD8422的放大倍数，其温漂系数仅为 <math id="M93"><mn mathvariant="normal">2</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">6</mn></mrow></msup><mtext> </mtext><mo>℃</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850506&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850503&type= 17.61066628 3.13266683 ，可有效提高放大电路的增益稳定性。 为了减小放大器在通带内的噪声，削弱所测直流电压信号中存在的50 Hz工频干扰及高频噪声，采用低通滤波器对放大后的信号进一步滤波。Analog Devices公司的滤波器设计软件可以方便快捷的设计出所需的滤波器，考虑测温速度及测温精度后设计了七阶Butterworth-Bessel低通滤波器，其截止频率为15 Hz，在50 Hz处的衰减可达到 - 55 dB。利用LTSpice软件对其进行仿真，可知该滤波器在260 ms之内的幅值稳定性可达到 <math id="M94"><mn mathvariant="normal">2</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">5</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850509&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850507&type= 13.46199989 3.04800010 ，满足高精度测温的需要。 为了减小模拟电路中存在的热噪声、散粒噪声及高频干扰等各种噪声，常通过DSP对ADC采集的数据进行均值滤波，但由于二者之间通讯时间的限制，这种操作会加长测温周期，从而加剧恒流源短期漂移对测温结果的影响。为此，本文选取了Analog Devices公司的LTC2368芯片，其分辨位数为24位，典型非线性为 <math id="M95"><mn mathvariant="normal">1</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">6</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850513&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850511&type= 13.29266548 3.04800010 ，自带集成型数字平均滤波器，能对1至65 536个转换结果进行实时平均，可将输入信号的动态范围从101 dB（1.5 MSa/s）改善至145 dB（30.5 Sa/s）。 数字信号处理器DSP的功能主要为：控制恒流源方向的切换；控制分时复用式电压采样与处理电路的电压测量对象；控制LTC2368在电压测量对象改变后的260 ms之后做10 000个转换结果的实时均值滤波，再传输给DSP；根据 公式（13） 公式（13） 求解铂电阻阻值；通过铂电阻阻值与温度的计算公式，得到当前温度。 4 实验与结果 1 鉴于实验室条件下难以对铂电阻阻值进行高稳定性、高分辨率的控制，本文首先通过设计等效实验来考察多参考阻值比率测温系统的测量稳定性和有效分辨能力；通过电阻箱来模拟铂电阻测温结果的非线性标定过程，在不同的环境温度下对比多参考阻值比率测温系统和单参考比率测温系统的非线性标定劣化程度；最终对铂电阻元件进行标定，得到阻值—温度关系，通过校准实验，考察多参考阻值比率测温系统的测量准确性。 4.1　多参考阻值切换调节因子作用效果实验 2 根据前文所述，普通参考电阻切换方法下测得的铂电阻阻值为： <math display="block" id="M96"><msub><mrow><mi>R</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>×</mo><mfrac><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">t</mi><mo>-</mo></mrow></msub></mrow><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">1</mn><mo>+</mo></mrow></msub><mo>-</mo><msub><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mn mathvariant="normal">1</mn><mo>-</mo></mrow></msub></mrow></mfrac><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">t</mi></mrow></msub><mo>≤</mo><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mtd></mtr><mtr><mtd><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>×</mo><mfrac><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi 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40.21666718 . 因此，选取1 150 Ω作为普通参考电阻切换方法下的铂电阻阻值跨越点，利用ZX74D型直流电阻箱来模拟铂电阻从小于1 150 Ω至大于1 150 Ω的过程；同样地，根据 公式（13） 公式（13） ，选取1 100 Ω作为铂电阻阻值跨越点。普通参考电阻切换方法测量结果及引入了调节因子的多参考阻值切换方法测量结果分别如 图5 图5 ~ 图6 图6 所示。 可以看出，普通参考电阻切换方法在切换电阻区间时会产生如 图5 图5 所示的断层，引入了约1 Ω的误差，等效温度误差约为0.26 ℃；而引入了调节因子的多参考阻值切换方法在切换电阻区间时并不会产生断层，如 图6 图6 所示，铂电阻阻值在不同阻值区间的过渡过程较为流畅。 4.2　测量稳定性等效实验 2 采用七一八友晟电子有限公司的RJ711型有可靠性指标的精密合金箔固定电阻器模拟恒温条件下的铂电阻，其温漂系数为 <math id="M97"><mn mathvariant="normal">2</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">6</mn></mrow></msup><mo>/</mo><mo>℃</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850539&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850537&type= 18.62666702 3.47133350 ，满足测温稳定性等效实验的需要。本测温系统的温度测量范围为 - 38.8~64.6 ℃，等距取4个温度点作为测试目标，以每次测试结果的均值变化及不确定度来衡量测温结果的稳定性，其中测试结果的均值变化程度表征测温系统在时间尺度上的示值漂移程度。在为期3天、每天连续1小时室温环境下的测试中，同时考察了多参考阻值比率测温、单参考阻值比率测温及普通四线制测温系统的稳定性，实验结果如 表1 表1 所示。 2 Date 2 Temperature setpoint 2 Multi-reference method 2 Single-reference method 2 Normal method Mean hange Uncertainty Mean hange Uncertainty Mean hange Uncertainty 4 05/11 -25.974 0 -0.001 5 0.000 3 -0.001 6 0.000 3 -0.013 9 0.000 7 0.000 0 -0.000 1 0.000 3 0.000 2 0.000 3 -0.003 5 0.000 5 25.974 0 -0.000 2 0.000 3 -0.000 2 0.000 5 -0.004 1 0.001 5 51.948 1 0.000 1 0.000 3 -0.000 5 0.000 7 -0.011 1 0.001 2 4 07/11 -25.974 0 -0.000 2 0.000 3 -0.000 2 0.000 3 -0.007 6 0.001 2 0.000 0 -0.002 5 0.000 4 -0.002 5 0.000 4 -0.028 6 0.002 6 25.974 0 -0.000 7 0.000 5 -0.000 6 0.000 4 -0.022 8 0.003 3 51.948 1 0.000 2 0.000 3 -0.000 2 0.000 5 -0.023 8 0.002 7 4 09/11 -25.974 0 -0.001 1 0.000 4 -0.001 8 0.000 4 -0.023 6 0.001 1 0.000 0 -0.000 1 0.000 3 0.000 4 0.000 3 -0.009 8 0.000 6 25.974 0 0.000 1 0.000 5 -0.000 8 0.000 7 -0.017 2 0.003 3 51.948 1 0.000 0 0.000 3 -0.000 2 0.000 5 -0.026 2 0.000 8 ℃ 可以看出，本文设计的多参考阻值比率测温系统的各个测温点的均值变化最大值为0.002 5 ℃，略小于单参考阻值比率测温系统，远小于普通四线制测温系统。而多参考阻值比率测温系统的各个测温点的测量不确定度约为0.000 5 ℃，略优于单参考阻值比率测温系统，远优于普通四线制测温系统。 因此，本文设计的高精度多参考阻值比率测温系统在长期使用中的测量稳定性要略优于目前的单参考阻值比率测温系统，远优于普通四线制测温系统。 4.3　测量分辨能力等效实验 2 在 - 38.8~64.6 ℃的温度测量范围内等距选取4个温度点，通过利用ZX74D型直流电阻箱来模拟铂电阻阻值的微小变化，从而测试多参考阻值比率测温系统在全温度测量范围内的等效温度分辨能力。ZX74D的最小阻值步进为0.001 Ω，等效为PT-1000型铂电阻的0.000 25 ℃最小温度步进。 图7 图7 为多参考阻值比率测温系统在不同温度点等效测温分辨能力的实验结果，易知，本文设计的测温系统在全温度测量范围（ - 38.8~64.6 ℃）内的分辨能力均优于0.001 25 ℃。 4.4　非线性标定劣化实验 2 将多参考阻值比率测温系统及单参考阻值比率测温系统置于恒温箱内，设定恒温箱温度为25 ℃。为避免温度变化对参考电阻产生影响，将参考电阻用四线制接法引出恒温箱。待热环境稳定后，对ZX74D直流电阻箱进行阻值测量，利用标准铂电阻温度计算公式，标定这两个测温系统的阻值—温度关系。 调整电阻箱阻值分别为 - 25.974 ℃，0 ℃，25.974 0 ℃，51.948 1 ℃对应的等效阻值，将其作为测量目标，分别通过在5 ℃，15 ℃，25 ℃，35 ℃，45 ℃环境温度下的多参考阻值比率测温系统及单参考阻值比率测温系统进行采集，利用阻值—温度标定公式换算为等效温度，与实际等效温度相减后取绝对值，最终得到这两种测量方法在不同环境温度下测量误差的绝对值，结果如 图8 图8 ~ 图9 图9 所示。 从 图8 图8 可以看出，随着环境温度逐渐远离标定环境温度（25 ℃）、测量温度等效阻值逐渐远离参考电阻阻值，单参考阻值比率测温系统的测量误差逐渐增大，最大测量误差约为0.03 ℃，这种变化趋势与理论预测的结果基本一致。从 图9 图9 可以看出，随着环境温度逐渐远离标定环境温度（25 ℃），多参考阻值比率测温系统的测量误差总体上是逐渐增大的，最大测量误差约为0.004 ℃。多参考阻值比率测温系统的测量误差普遍小于单参考阻值比率测温系统，说明其在环境温度变化剧烈场合中的非线性标定劣化程度更小，更加适合环境温度变化剧烈的应用场景。 4.5　测温系统的校准与检定 2 KEYSIGHT公司3458A型号的八位半数字万用表在1 kΩ档的分辨率为100 μΩ，在工作环境温度保持（25±1）℃的情况下可达到 <math id="M98"><mn mathvariant="normal">2.2</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">6</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850565&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850563&type= 16.34066582 3.04800010 /24 h， <math id="M99"><mn mathvariant="normal">8.5</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">6</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850569&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850567&type= 16.34066582 3.04800010 /90 d， <math id="M100"><mn mathvariant="normal">3.1</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">6</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850573&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850571&type= 16.25600052 3.04800010 /℃的测量精度，完全可以满足对本文所设计测温系统的校准精度需求，因此设计了如下校准实验：采用xxx级薄膜铂电阻制作了两个小型铂电阻探头放置于恒温箱中，其中一个铂电阻探头与KEYSIGHT公司的3458A数字万用表四线制相连，另一个铂电阻探头与多参考阻值比率测温系统相连。保持工作环境温度为（25±1）℃，3458A数字万用表测得的铂电阻阻值通过标准铂电阻—温度转化公式换算成温度，将该温度其视为实际温度，对多参考阻值比率测温系统的测温结果进行标定。由于计算精度的限制，将测量数据进行中心化及尺度变换后得到的拟合函数结果更好，因此对多参考阻值比率测温系统的测量结果进行中心化及尺度变换操作： <math display="block" id="M101"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub><mfenced separators="|"><mrow><mi>i</mi></mrow></mfenced><mo>=</mo><mfrac><mrow><mi>R</mi><mfenced separators="|"><mrow><mi>i</mi></mrow></mfenced><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>m</mi></mrow></mfrac><mstyle displaystyle="true"><munderover><mo 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separators="|"><mrow><mi>n</mi></mrow></mfenced></mrow></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mrow><mrow/></mroot></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850577&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850575&type= 62.48400116 20.99733353 ， 其中： <math id="M102"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub><mfenced separators="|"><mrow><mi>i</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850582&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850580&type= 8.63599968 4.06400013 为进行中心化及尺度变换后的第 <math id="M103"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850594&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850592&type= 1.10066664 2.79399991 个测量结果； <math id="M104"><mi>R</mi><mfenced separators="|"><mrow><mi>i</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850590&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850588&type= 7.02733374 3.97933316 为第 <math id="M105"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850594&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850592&type= 1.10066664 2.79399991 个原始测量结果； <math id="M106"><mi>m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850598&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850596&type= 2.79399991 2.79399991 为测量点个数，本实验共有10个温度点，故 <math id="M107"><mi>m</mi><mo>=</mo><mn mathvariant="normal">10</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850602&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850600&type= 11.43000031 2.79399991 。经标定，多参考阻值比率测温系统所测阻值与温度之间的函数关系为： <math display="block" id="M108"><mi>t</mi><mo>=</mo><mo>-</mo><mn mathvariant="normal">0.243</mn><mtext> </mtext><mn mathvariant="normal">6</mn><msup><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mn mathvariant="normal">30.52</mn><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub><mo>+</mo><mn mathvariant="normal">15.49</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850604&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850603&type= 57.31933212 4.06400013 ， <math display="block" id="M109"><mtable columnalign="left"><mtr><mtd><mi>t</mi><mo>=</mo><mn mathvariant="normal">0.111</mn><mtext> </mtext><mn mathvariant="normal">5</mn><msup><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub></mrow><mrow><mn 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columnalign="left"><mtr><mtd><mi>t</mi><mo>=</mo><mn mathvariant="normal">0.215</mn><mtext> </mtext><mn mathvariant="normal">5</mn><msup><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msup><mo>+</mo><mn mathvariant="normal">0.189</mn><mtext> </mtext><mn mathvariant="normal">4</mn><msup><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msup><mo>-</mo><mn mathvariant="normal">0.614</mn><mtext> </mtext><mn mathvariant="normal">4</mn><msup><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msup><mo>-</mo></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.630</mn><mtext> </mtext><mn mathvariant="normal">5</mn><msup><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msup><mo>+</mo><mn mathvariant="normal">0.092</mn><mtext> </mtext><mn mathvariant="normal">65</mn><msup><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mn mathvariant="normal">30.96</mn><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub><mo>+</mo><mn mathvariant="normal">15.49</mn></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850608&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850607&type= 71.03533173 8.80533314 ， 其中式（16）~ 式（18） 式（18） 分别为多参考阻值比率测温系统阻值—温度的二次、四次、六次拟合多项式。 对高精度多参考阻值比率测温系统的校准检定结果如 表2 表2 所示。表中第1列为3458A所测实际温度值，第2~4列分别为多参考阻值比率测温系统二次、四次、六次拟合函数关系测得的温度值。 Real temperature Quadratic polynomials value Quartic polynomial value Sixth degree polynomial value -30.198 8 -30.209 5 -30.208 8 -30.194 8 -20.000 0 -20.015 2 -19.975 7 -19.999 7 -9.818 3 -9.918 0 -9.867 0 -9.807 1 0.140 7 0.195 7 0.145 7 0.123 9 10.279 2 10.439 1 10.338 9 10.303 9 20.338 9 20.299 2 20.285 8 20.319 8 30.363 6 30.229 2 30.342 8 30.373 7 40.479 9 40.463 5 40.532 7 40.476 4 50.555 2 50.513 3 50.528 3 50.554 4 60.592 8 60.543 3 60.601 0 60.590 6 根据校准结果分析可知，采用二次、四次、六次拟合函数的多参考阻值比率测温系统的测量不确定度分别为0.079 4 ℃，0.036 7 ℃，0.012 3 ℃， <math id="M111"><mi>k</mi><mo>=</mo><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850612&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=16850611&type= 8.38199997 2.79399991 。可以看出，随着拟合函数最高次幂的增加，该测温系统校准后的测量值越接近真实值，校准结果越好，这是由于测温系统内部非线性和校准温度点比较多所共同造成的。在实际使用时应综合考虑测温系统的计算量及测温精度来确定拟合函数的最高次幂。 值得注意的是，这里设计的标定实验仅是为了验证该测温系统经标定程序后的实测性能，测量结果与真实温度值之间存在偏差，该偏差可通过计量院的温度标定实验来消除。 5 结　论 1 本文分析了基于恒流源的铂电阻、参考电阻阻值比率测温系统的测量性能会随着远离参考电阻阻值而变差的原因，并由此提出了多参考阻值比率测温方法，采用高稳定性的恒流源设计来削弱恒流源漂移对测温结果的影响，采用时分复用高精度电压采样与处理电路来降低电压测量噪声及漂移对测温结果的影响，设计并实现了高精度多参考阻值比率测温电路。实验结果表明，在 - 38.8~64.6 ℃的温度测量范围内，高精度多参考阻值比率测温系统的测量稳定性优于0.002 5 ℃/5 d，测量分辨能力优于0.001 25 ℃，在5~45 ℃环境温度下的测量稳定性优于0.004 ℃，可满足长期应用，且对环境温度变化较不敏感，减小了遥感载荷为保证测温结果稳定的热控成本。 参考文献 郭玲玲 ， 赵其昌 ， 杨勇 ， 等 . 傅里叶变换光谱仪的红外探测器非线性校正 ［J］. 光学学报 ， 2020 ， 40 （ 5 ）： 214 - 221 . 傅里叶变换光谱仪的红外探测器非线性校正 GUO L L ， ZHAO Q CH ， YANG Y ， et al . 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