电阻式温度计 - 铂电阻温度计 - PT100_pt100的相对介电常数

Resistance thermometer 电阻温度计

翻译自：Resistance thermometer - Wikipedia

全文人工翻译，欢迎指出错误或不准确的表达。

Resistance thermometers, also called resistance temperature detectors (RTDs), are sensors used to measure temperature. Many RTD elements consist of a length of fine wire wrapped around a ceramic or glass core but other constructions are also used. The RTD wire is a pure material, typically platinum, nickel, or copper. The material has an accurate resistance/temperature relationship which is used to provide an indication of temperature. As RTD elements are fragile, they are often housed in protective probes.

RTDs, which have higher accuracy and repeatability, are slowly replacing thermocouples in industrial applications below 600 °C.[1]

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电阻温度计是一种用于测量温度的传感器，又被称为电阻温度监测器（RTD）。许多RTD 元件由两部分组成——一个陶瓷或玻璃的核心和一段绕在核心上面的细导线，除此之外也存在其他构造。RTD 导线是一种纯的金属，通常是铂、镍或者铜。这些材料具有精确的电阻-温度特性，因而被用于提供温度指示。RTD 元件十分脆弱，所以通常都被包裹在保护性的探头外壳中。

相比热电偶，RTD 通常拥有更高的精度和可重复性，因而在600°C 以下的工业应用中，前者正在被RTD 缓慢替换。

Resistance/temperature relationship of metals 金属的电阻-温度特性

Common RTD sensing elements constructed of platinum, copper or nickel have a repeatable resistance versus temperature relationship (R vs T) and operating temperature range. The R vs T relationship is defined as the amount of resistance change of the sensor per degree of temperature change.[1] The relative change in resistance (temperature coefficient of resistance) varies only slightly over the useful range of the sensor.

Platinum was proposed by Sir William Siemens as an element for a resistance temperature detector at the Bakerian lecture in 1871:[2] it is a noble metal and has the most stable resistance–temperature relationship over the largest temperature range. Nickel elements have a limited temperature range because the amount of change in resistance per degree of change in temperature becomes very non-linear at temperatures over 300 °C (572 °F). Copper has a very linear resistance–temperature relationship; however, copper oxidizes at moderate temperatures and cannot be used over 150 °C (302 °F).

The significant characteristic of metals used as resistive elements is the linear approximation of the resistance versus temperature relationship between 0 and 100 °C. This temperature coefficient of resistance is denoted by α and is usually given in units of Ω/(Ω·°C):

where:

$R_0$ is the resistance of the sensor at 0 °C,

$R_{100}$ is the resistance of the sensor at 100 °C.

Pure platinum has α = 0.003925 Ω/(Ω·°C) in the 0 to 100 °C range and is used in the construction of laboratory-grade RTDs. Conversely, two widely recognized standards for industrial RTDs IEC 60751 and ASTM E-1137 specify α = 0.00385 Ω/(Ω·°C). Before these standards were widely adopted, several different α values were used. It is still possible to find older probes that are made with platinum that have α = 0.003916 Ω/(Ω·°C) and 0.003902 Ω/(Ω·°C).

These different α values for platinum are achieved by doping – carefully introducing impurities, which become embedded in the lattice structure of the platinum and result in a different R vs. T curve and hence α value.[citation needed]

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一般由铂、镍或铜构成的RTD 元件具有可重复的电阻-温度特性（R-T）和可用温度范围。R-T 特性用温度变化导致元件电阻的变化量来定义。在元件的整个可用温度区间上，电阻的相对变化量（电阻的温度因数）只有轻微的变化。注：意思是线性很好

使用铂作为电阻温度检测器的想法由Sir William Siemens 于1871 年在Bakerian lecture 提出。铂是一种贵金属，它具有最大的使用温度范围，以及在这个范围上最稳定的R-T 特性。镍元件的使用温度相对受限，在300°C 以上，镍的R-T 特性会变得很不线性。铜的线性很好，但是铜在常温下就会氧化，而且铜不能被用在大于150°C 的场合。

对于要用作电阻性敏感元件的金属，它的特征参数是对0 到100 °C 的R-T 特性的线性近似。这个温度因数记作$\alpha$ ，单位是Ω/(Ω⋅°C)， 由下式计算：
$$\alpha =\frac{R_{100}-R_0}{100°C\cdot R_0}$$
其中，

$R_0$ 是元件0°C 的电阻，

$R_{100}$ 是元件在100°C 的电阻。

纯的铂在0 到100°C 范围， $\alpha =0.003925\Omega /(\Omega \cdot °C)$ ，它被用于制造实验室等级的RTD。不同的是，在IEC 60751 和ASTM E-1137 这两个被广为接受的标准中，对于工业用RTD，规定$\alpha =0.00385\Omega /(\Omega \cdot °C)$。在这两个标准被广泛采用之前，还有其他不同的数值被使用。比方说，仍然有可能找到一些旧的使用了铂的探头，他们的数值是$\alpha =0.003916\Omega /(\Omega \cdot °C)$ 或$\alpha =0.003902\Omega /(\Omega \cdot °C)$。

这些不同的铂α 值可通过掺杂实现，即小心的引入杂质。这些杂质会嵌入铂的晶格结构中，产生不同的R-T 特性以及α 值。

Calibration 校准

To characterize the R vs T relationship of any RTD over a temperature range that represents the planned range of use, calibration must be performed at temperatures other than 0 °C and 100 °C. This is necessary to meet calibration requirements. Although RTDs are considered to be linear in operation, it must be proven that they are accurate with regard to the temperatures with which they will actually be used (see details in Comparison calibration option). Two common calibration methods are the fixed-point method and the comparison method.[citation needed]

• Fixed point calibration

  is used for the highest-accuracy calibrations by national metrology laboratories.[3] It uses the triple point, freezing point or melting point of pure substances such as water, zinc, tin, and argon to generate a known and repeatable temperature. These cells allow the user to reproduce actual conditions of the ITS-90 temperature scale. Fixed-point calibrations provide extremely accurate calibrations (within ±0.001 °C). A common fixed-point calibration method for industrial-grade probes is the ice bath. The equipment is inexpensive, easy to use, and can accommodate several sensors at once. The ice point is designated as a secondary standard because its accuracy is ±0.005 °C (±0.009 °F), compared to ±0.001 °C (±0.0018 °F) for primary fixed points.

• Comparison calibrations

  is commonly used with secondary SPRTs and industrial RTDs.[4] The thermometers being calibrated are compared to calibrated thermometers by means of a bath whose temperature is uniformly stable. Unlike fixed-point calibrations, comparisons can be made at any temperature between −100 °C and 500 °C (−148 °F to 932 °F). This method might be more cost-effective, since several sensors can be calibrated simultaneously with automated equipment. These electrically heated and well-stirred baths use silicone oils and molten salts as the medium for the various calibration temperatures.

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在计划使用的温度范围中，为了表征一个代表性的范围里RTD 的R-T 特性，必须在0 到100°C 以外的温度上进行校准。为了满足校准要求，这一点是必要的。虽然一般认为RTD 在使用中是线性的，但是仍需证明在实际使用的温度上，它是精确的（详情参见比较校准法）。一般使用的校准方法有两种：固定温度校准法和比较校准法。

• 定点校准法

  这是在国家级计量实验室中使用的最高精度的校准方法。它利用了纯的相变材料的三相点，即凝固点或熔点，从而产生一个已知且可重复的测试温度。这些相变材料一般有水、锌、锡或氩。这种措施令测试者可以重复ITS-90 温标的条件。定点校准法能提供极高的精度（±0.001 °C）。工业级探头的一种常用定点校准法是冰浴法。这种测试设备廉价易用，并且能一次性测试多个传感器。冰点是二级测试标准，它的精度是±0.005 °C，相比之下，一级定点的精度是±0.001 °C。

• 比较校准法

  这种方法通常用于二级的标准铂电阻温度计（SPRT）和工业RTD。需要校准的温度计在液浴的稳定温度中与已被校准的温度计做比较。与定点校准法不同，比较校准法的测试温度可在−100 °C至 500 °C 之间任选。这种方法的性价比可能更高，因为多个传感器可以在自动化设备上同时校准。一般使用硅油或熔盐作为介质进行不同温度的校准。液浴介质使用电加热，并被搅拌均匀。

Element types 元件类型

The three main categories of RTD sensors are thin-film, wire-wound, and coiled elements. While these types are the ones most widely used in industry, other more exotic shapes are used; for example, carbon resistors are used at ultra-low temperatures (−273 °C to −173 °C).[5]

• Carbon resistor elements

  are cheap and widely used. They have very reproducible results at low temperatures. They are the most reliable form at extremely low temperatures. They generally do not suffer from significant hysteresis or strain gauge effects.

• Strain-free elements

  use a wire coil minimally supported within a sealed housing filled with an inert gas. These sensors work up to 961.78 °C and are used in the SPRTs that define ITS-90. They consist of platinum wire loosely coiled over a support structure, so the element is free to expand and contract with temperature. They are very susceptible to shock and vibration, as the loops of platinum can sway back and forth, causing deformation.

Thin-film PRT

• Thin-film elements

  have a sensing element that is formed by depositing a very thin layer of resistive material, normally platinum, on a ceramic substrate (plating). This layer is usually just 10 to 100 ångströms (1 to 10 nanometers) thick.[6] This film is then coated with an epoxy or glass that helps protect the deposited film and also acts as a strain relief for the external lead wires. Disadvantages of this type are that they are not as stable as their wire-wound or coiled counterparts. They also can only be used over a limited temperature range due to the different expansion rates of the substrate and resistive deposited giving a “strain gauge” effect that can be seen in the resistive temperature coefficient. These elements work with temperatures to 300 °C (572 °F) without further packaging, but can operate up to 600 °C (1,112 °F) when suitably encapsulated in glass or ceramic. Special high-temperature RTD elements can be used up to 900 °C (1,652 °F) with the right encapsulation.

Wire-wound PRT

• Wire-wound elements

  can have greater accuracy, especially for wide temperature ranges. The coil diameter provides a compromise between mechanical stability and allowing expansion of the wire to minimize strain and consequential drift. The sensing wire is wrapped around an insulating mandrel or core. The winding core can be round or flat, but must be an electrical insulator. The coefficient of thermal expansion of the winding core material is matched to the sensing wire to minimize any mechanical strain. This strain on the element wire will result in a thermal measurement error. The sensing wire is connected to a larger wire, usually referred to as the element lead or wire. This wire is selected to be compatible with the sensing wire, so that the combination does not generate an emf that would distort the thermal measurement. These elements work with temperatures to 660 °C.

Coil-element PRT

• Coiled elements

  have largely replaced wire-wound elements in industry. This design has a wire coil that can expand freely over temperature, held in place by some mechanical support, which lets the coil keep its shape. This “strain free” design allows the sensing wire to expand and contract free of influence from other materials; in this respect it is similar to the SPRT, the primary standard upon which ITS-90 is based, while providing the durability necessary for industrial use. The basis of the sensing element is a small coil of platinum sensing wire. This coil resembles a filament in an incandescent light bulb. The housing or mandrel is a hard fired ceramic oxide tube with equally spaced bores that run transverse to the axes. The coil is inserted in the bores of the mandrel and then packed with a very finely ground ceramic powder. This permits the sensing wire to move, while still remaining in good thermal contact with the process. These elements work with temperatures to 850 °C.

The current international standard that specifies tolerance and the temperature-to-electrical resistance relationship for platinum resistance thermometers (PRTs) is IEC 60751:2008; ASTM E1137 is also used in the United States. By far the most common devices used in industry have a nominal resistance of 100 ohms at 0 °C and are called Pt100 sensors (“Pt” is the symbol for platinum, “100” for the resistance in ohms at 0 °C). It is also possible to get Pt1000 sensors, where 1000 is for the resistance in ohms at 0 °C. The sensitivity of a standard 100 Ω sensor is a nominal 0.385 Ω/°C. RTDs with a sensitivity of 0.375 and 0.392 Ω/°C, as well as a variety of others, are also available.

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RTD 元件主要有三种类型，分别是薄膜式、线绕式、线圈式。这三种在工业中应用最为广泛，亦有其他不同风味的传感器形式，比如在极低温度下（−273 °C to −173 °C ），碳电阻常被使用。

• 碳电阻

  碳电阻价格低廉，也被广泛使用。在低温下碳电阻测量结果的可重复性很好。在极低温度下，碳电阻是最可靠的元件。碳电阻一般没有显著的回差和应变片效应。

• 无应变元件

  这种元件内有封装在密封壳体中的线圈，线圈只被松散的支撑，壳体内充入惰性气体。这种元件可在最高961.78°C 下工作。它被用在SPRT 中，以此为基础定义了ITS-90 标准。它由铂制导线制成，导线松散的在支撑结构上缠绕成线圈，所以元件可以自由的热胀冷缩。它容易受到冲击和震动影响，因为铂线圈可以自由的前后摆动，这会导致变形。

• 薄膜元件

  这种元件的电阻材料通常是铂，通过在陶瓷基体上沉积一层薄膜制成。这层薄膜一般只有1 到10 纳米后。薄膜上会涂附一层环氧树脂或玻璃用以提供保护，并且可以释放外部引线的应力。这种类型的元件不如线绕式或线圈式稳定。它的使用温度较为受限，因为元件内部陶瓷基体和沉积薄膜的热胀冷缩率存在差异，这会导致应变计效应，对电阻-温度特性产生可观的影响。这类元件无更多封装时可在300°C 下工作，使用合适的玻璃或陶瓷封装可以提高操作温度到600°C 。正确封装的特殊高温RTD 可在900°C 下使用。

• 线绕元件

  具有更高的精度，尤其是在宽温度范围上。具有一定直径的线圈是一种折衷的方案，它在机械稳定性与允许导线热胀冷缩的空间上做了取舍，从而最小化导线应力，以及随之而来的特性漂移。感温导线绕在一个绝缘的芯轴或者芯料上。线芯形状可以是圆柱或平板，其材质必须是电气绝缘体。线芯的热胀冷缩率与感温导线匹配，从而尽量消除机械应力，而作用在元件导线上的机械应力会导致测量误差。感温导线会与更粗的导线连接，即元件的引脚或引线。这种导线经过挑选，使其与感温导线兼容，避免在接合处产生电动势扰乱测量结果。这类元件可在660°C 下工作。

• 线圈元件

  这类元件在工业领域已大量替代了线绕元件。这种设计中，线圈可以自由的热胀冷缩，又有支持结构把线圈固定在原地，避免变形。这种“无应力”设计使得可以不受其他结构影响的自由热胀冷缩，在这方面它和SPRT 类似，同时又提供了工业用途所必须的耐久性。元件的基本结构是一段微小的铂制感温线圈，和白炽灯中的灯丝类似。元件的外壳或芯轴是坚硬的烧结陶瓷氧化物管，沿着轴线，横向等距打孔。线圈塞入这些芯轴上的孔中，然后填充入非常精细研磨的陶瓷粉。这能在保证良好热传导的同时，允许感温导线发生移动。这类元件可在850°C 下工作。

目前，国际标准IEC 60751:2008 定义了铂电阻温度计（PRT）的公差和温度-电阻特性，而在美国，ASTM E1137 也被采用。现在工业领域使用最广泛的元件0°C 标称电阻是100Ω，因而被称作“PT100” 传感器，“PT” 是铂的元素符号。同样的，也有0°C 标称电阻为1000Ω 的“PT1000” 传感器。PT100 的标称敏感度是0.385 Ω/°C。具有0.375 Ω/°C、0.392 Ω/°C 或其他敏感度类型的RTD 亦可获得。

Function 功能

Resistance thermometers are constructed in a number of forms and offer greater stability, accuracy and repeatability in some cases than thermocouples. While thermocouples use the Seebeck effect to generate a voltage, resistance thermometers use electrical resistance and require a power source to operate. The resistance ideally varies nearly linearly with temperature per the Callendar–Van Dusen equation.

The platinum detecting wire needs to be kept free of contamination to remain stable. A platinum wire or film is supported on a former in such a way that it gets minimal differential expansion or other strains from its former, yet is reasonably resistant to vibration. RTD assemblies made from iron or copper are also used in some applications. Commercial platinum grades exhibit a temperature coefficient of resistance 0.00385/°C (0.385%/°C) (European Fundamental Interval).[7] The sensor is usually made to have a resistance of 100 Ω at 0 °C. This is defined in BS EN 60751:1996 (taken from IEC 60751:1995). The American Fundamental Interval is 0.00392/°C,[8] based on using a purer grade of platinum than the European standard. The American standard is from the Scientific Apparatus Manufacturers Association (SAMA), who are no longer in this standards field. As a result, the “American standard” is hardly the standard even in the US.

Lead-wire resistance can also be a factor; adopting three- and four-wire, instead of two-wire, connections can eliminate connection-lead resistance effects from measurements (see below); three-wire connection is sufficient for most purposes and is an almost universal industrial practice. Four-wire connections are used for the most precise applications.

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电阻式温度计具有很多构造形式，在一些场合，相较于热电偶，能提供更高的稳定性、精度和重复性。电阻式温度计基于电阻值，要有电源才能操作，而热电偶基于塞贝克效应，可以独立产生电压。根据 Callendar-Van Dusen 方程，电阻在理想情况下几乎随温度呈线性变化。

铂制感温导线要保证不被污染，从而维持性能稳定。铂制导线或薄膜以特定方式获得支撑，这要最小化它与支撑件膨胀率的差异，以及其他会因支撑导致应力的因素，又要保证对震动有足够的抵抗力。在一些应用中，铁或铜制的RTD 也被采用。商业等级的铂的电阻-温度系数为 0.00385Ω/°C （European Fundamental Interval）。铂制传感器通常做成在0°C 具有100Ω 电阻的特性，这在BS EN 60751：1996 标准中定义，而它又是从IEC 60751：1995 标准中借来的。美国标准（American Fundamental Interval）中，基于比欧洲标准更纯等级的铂，传感器的温度系数是0.00392Ω/°C。这个标准来自Scientific Apparatus Manufacturers Association（SAMA），而它在这个标准的领域已经不存在了。因此，这个美国标准即便在美国也很难算的上是标准。

传感器引线的电阻也是个影响因素。相比于两线法，使用三线或四线法测量可以消除连接线的影响。三线式在几乎所有工业实践中已经足够，四线式则用于最高精度的应用中。

Advantages and limitations 优势和限制

The advantages of platinum resistance thermometers include:

• High accuracy
• Low drift
• Wide operating range
• Suitability for precision applications.

Limitations:

RTDs in industrial applications are rarely used above 660 °C. At temperatures above 660 °C it becomes increasingly difficult to prevent the platinum from becoming contaminated by impurities from the metal sheath of the thermometer. This is why laboratory standard thermometers replace the metal sheath with a glass construction. At very low temperatures, say below −270 °C (3 K), because there are very few phonons, the resistance of an RTD is mainly determined by impurities and boundary scattering and thus basically independent of temperature. As a result, the sensitivity of the RTD is essentially zero and therefore not useful.[citation needed]

Compared to thermistors, platinum RTDs are less sensitive to small temperature changes and have a slower response time. However, thermistors have a smaller temperature range and stability.

RTDs vs thermocouples

The two most common ways of measuring temperatures for industrial applications are with resistance temperature detectors (RTDs) and thermocouples. The choice between them is typically determined by four factors.

• Temperature

  If process temperatures are between −200 and 500 °C (−328.0 and 932.0 °F), an industrial RTD is the preferred option. Thermocouples have a range of −180 to 2,320 °C (−292.0 to 4,208.0 °F),[9] so for temperatures above 500 °C (932 °F) it is the contact temperature measurement device commonly found in physics laboratories.

• Response time

  If the process requires a very fast response to temperature changes (fractions of a second as opposed to seconds), then a thermocouple is the best choice. Time response is measured by immersing the sensor in water moving at 1 m/s (3.3 ft/s) with a 63.2% step change.

• Size

  A standard RTD sheath is 3.175 to 6.35 mm (0.1250 to 0.2500 in) in diameter; sheath diameters for thermocouples can be less than 1.6 mm (0.063 in).

• Accuracy and stability requirements

  If a tolerance of 2 °C is acceptable and the highest level of repeatability is not required, a thermocouple will serve. RTDs are capable of higher accuracy and can maintain stability for many years, while thermocouples can drift within the first few hours of use.

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铂电阻温度计具有如下优点：

• 高精度
• 低漂移
• 宽温度范围
• 适合高精度应用

限制：

在工业应用中，RTD 很少会用在超过660°C 的场合。大于660°C h时，很难避免铂受到杂质的污染，而杂质则来自温度计的金属外壳。这就是为什么实验室标准的温度计要用玻璃结构替换金属外壳。在极低温度下，比如-270°C，由于声子变得极少，RTD 的电阻主要由杂质和边界散射决定，而这些基本上与温度无关。这样一来，RTD 的敏感度就变成了零，于是失去了测量作用。

相比热敏电阻，铂制RTD 对微小温度变化不敏感，它的响应时间更慢。然而，热敏电阻的稳定性和可用温度范围较差。

RTD 与热电偶

在工业应用中，两种最常用的测温方法就是RTD 和热电偶。要选择用那种，取决于以下四个因素：

• 温度

  如果操作温度在-200°C 到500°C 之间，工业级RTD 更值得青睐。热电偶的温度范围在-180°C 到2320°C，所以当温度大于500°C时，热电偶就成为了物理实验室的常用测温设备。

• 响应时间

  如果需要对温度变化有很快的响应，比如几分之一秒而不是数秒，那么热电偶会是最好的选择。时间响应是将传感器浸入以 1 m/s流动的水中测量的，水温阶跃式变化，幅度为63.2%。

• 尺寸

  一个标准的RTD 护套直径在3.175 到6.35 mm 之间，而热电偶的直径可以小到1.6 mm。

• 精度和稳定性需求

  如果2°C 的公差可以接受，高水平的重复性也不必要，那么热电偶足矣。RTD 具有更高的精度，并且能在数年间保持稳定性能，而热电偶则会在初次使用的几个小时间发生漂移。

Construction 结构

These elements nearly always require insulated leads attached. PVC, silicone rubber or PTFE insulators are used at temperatures below about 250 °C. Above this, glass fibre or ceramic are used. The measuring point, and usually most of the leads, require a housing or protective sleeve, often made of a metal alloy that is chemically inert to the process being monitored. Selecting and designing protection sheaths can require more care than the actual sensor, as the sheath must withstand chemical or physical attack and provide convenient attachment points.

The RTD construction design may be enhanced to handle shock and vibration by including compacted magnesium oxide (MgO) power inside the sheath. MgO is used to isolate the conductors from the external sheath and from each other. MgO is used due to its dielectric constant, rounded grain structure, high-temperature capability, and its chemical inertness.

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这类元件几乎总是需要连接绝缘的引线。低于250°C 时，PVC，硅橡胶或PTFE 可以用作绝缘材料。超过这个温度时会采用玻璃纤维或陶瓷。元件的测温点以及大部分引线都需要一个外壳或者保护性的外套。这些结构通常是由化学上相对惰性的合金制成，不会干扰要检测的对象。相比传感器方面的工作，选择或者设计一个保护性外壳的过程可能要投入更多精力。因为这个外壳一定要能经受的了化学或物理性的考验，又要提供一个方便的接口。

RTD 的结构设计中，可以在外壳中加入压实的氧化镁粉末以增强应对冲击和振动的能力。氧化镁用于将内部的导体与外壳相互隔离，使用 MgO 是考虑到它的介电常数、圆形晶粒结构、高温性能和化学惰性。

Wiring configurations 接线方式

Two-wire configuration

The simplest resistance-thermometer configuration uses two wires. It is only used when high accuracy is not required, as the resistance of the connecting wires is added to that of the sensor, leading to errors of measurement. This configuration allows use of 100 meters of cable. This applies equally to balanced bridge and fixed bridge system.

For a balanced bridge usual setting is with R2 = R1, and R3 around the middle of the range of the RTD. So for example, if we are going to measure between 0 and 100 °C (32 and 212 °F), RTD resistance will range from 100 Ω to 138.5 Ω. We would choose R1 = 120 Ω. In that way we get a small measured voltage in the bridge.

Three-wire configuration

In order to minimize the effects of the lead resistances, a three-wire configuration can be used. The suggested setting for the configuration shown, is with R1 = R2, and R3 around the middle of the range of the RTD. Looking at the Wheatstone bridge circuit shown, the voltage drop on the lower left hand side is V_rtd + V_lead, and on the lower right hand size is V_R3 + V_lead, therefore the bridge voltage (V_b) is the difference, V_rtd - V_R3. The voltage drop due to the lead resistance has been cancelled out. This always applies if R1=R2, and R1, R2 >> RTD, R3. R1 and R2 can serve the use of limiting the current through the RTD, for example for a PT100, limiting to 1mA, and 5V, would suggest a limiting resistance of approximately R1 = R2 = 5/0.001 = 5,000 Ohms.

Four-wire configuration

The four-wire resistance configuration increases the accuracy of measurement of resistance. Four-terminal sensing eliminates voltage drop in the measuring leads as a contribution to error. To increase accuracy further, any residual thermoelectric voltages generated by different wire types or screwed connections are eliminated by reversal of the direction of the 1 mA current and the leads to the DVM (digital voltmeter). The thermoelectric voltages will be produced in one direction only. By averaging the reversed measurements, the thermoelectric error voltages are cancelled out.[citation needed]

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两线式

两线式是最简单的电阻式温度计接线方式。只有不追求高精度时才使用它，因为连接线的阻值会加在传感器的阻值上，导致测量误差。这种接线方式允许使用100 米的连接线，平衡式或非平衡式电桥也一样。

对于平衡电桥来说，通常设置R2 = R1，R3 取值约为RTD 阻值范围的一半。举例而言，如果要测量的温度范围是0 - 100°C，RTD 的阻值范围是100 - 138.5Ω，R1可以取120Ω。这样一来就可以从电桥获得一个小的测量电压。 注：120Ω 的应该是R3。电路图参考上面的原文，下同。

三线式

要减少导线电阻的影响，可以采用三线式接法。如图所示的电路中，推荐的取值是R1 = R2, R3 取RTD 阻值范围的一半。查看图中的惠斯通电桥，左下部分的电压是RTD 电压加导线电压$V_{rtd}+V_{lead}$，而右下部分的电压是R3 电压加导线电压$V_{r3}+V_{lead}$，因此电桥的输出电压$V_b$ 就是其差值$V_{rtd}-V_{r3}$。导线上的电压被剔除了。当R1 = R2, 并且R1, R2 >> RTD, R3 时，这个结果总是适用。R1 和R2 可用于限制经过RTD 的电流，以PT100 为例，限制电流为1mA，以5V 供电，则限流电阻可取 R1 = R2 = 5 / 0.001 = 5kΩ。

四线式

四线接法可用来进一步提高电阻的测量精度。四线法能消除引起误差的测量线路上的压降。为了提高精度，1mA 测试电流的方向以及电压表测量线的极性被反转，从而消除由不同类型导线或接线螺丝引起的残余热电势。热电势只会在一个方向上产生。通过平均多次不同方向的测量，就能消除热电势导致的误差。

注：主要就是用恒流源驱动电阻，测量线上没有电流，消除了电流压降。因为热电势的极性只和材料组合有关，所以变换电流和测量方向可以将其剔除。

Classifications of RTDs - RTD 的分级

The highest-accuracy of all PRTs are the Ultra Precise Platinum Resistance Thermometers (UPRTs). This accuracy is achieved at the expense of durability and cost. The UPRT elements are wound from reference-grade platinum wire. Internal lead wires are usually made from platinum, while internal supports are made from quartz or fused silica. The sheaths are usually made from quartz or sometimes Inconel, depending on temperature range. Larger-diameter platinum wire is used, which drives up the cost and results in a lower resistance for the probe (typically 25.5 Ω). UPRTs have a wide temperature range (−200 °C to 1000 °C) and are approximately accurate to ±0.001 °C over the temperature range. UPRTs are only appropriate for laboratory use.

Another classification of laboratory PRTs is Standard Platinum Resistance Thermometers (Standard SPRTs). They are constructed like the UPRT, but the materials are more cost-effective. SPRTs commonly use reference-grade, high-purity smaller-diameter platinum wire, metal sheaths and ceramic type insulators. Internal lead wires are usually a nickel-based alloy. Standard PRTs are more limited in temperature range (−200 °C to 500 °C) and are approximately accurate to ±0.03 °C over the temperature range.

Industrial PRTs are designed to withstand industrial environments. They can be almost as durable as a thermocouple. Depending on the application, industrial PRTs can use thin-film or coil-wound elements. The internal lead wires can range from PTFE-insulated stranded nickel-plated copper to silver wire, depending on the sensor size and application. Sheath material is typically stainless steel; higher-temperature applications may demand Inconel. Other materials are used for specialized applications.

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最高等级的铂电阻温度计（PRT）被称为究极准铂电阻温度计（UPRT）。这个精确性是用耐久性和高成本换来的。UPRT 的元件使用参考等级的铂导线绕制。内部的引线通常由铂制成，支撑材料是石英或熔融石英玻璃。护套通常由石英制成，取决于预定的温度范围，有时也用铬镍铁合金。元件采用了较大直径的铂导线，这拉高了成本，但能降低传感器的阻值（一般25.5Ω）。UPRT 的工作温度范围很宽，可达-200 到1000 °C，并且在这个范围上具有约 ±0.001°C 的精度。UPRT 是唯一适用于实验室的等级。

另一种实验室等级的PRT 是标准铂电阻温度计（SPRT）。它的结构类似UPRT，但材料的成本较低。SPRT 多使用参考等级，高纯度，小直径的铂导线，采用金属护套和陶瓷绝缘结构。内部引线通常是镍基合金。SPRT 的使用温度较为受限（-200 到500°C），精度约为 ±0.03°C.

工业PRT 设计用来耐受工业使用环境。它的耐久度可与热电偶相当。根据不同应用场景，工业PRT 可使用薄膜或线圈元件。内部引线的选择范围可从PTEE 绝缘的镀镍铜线到银线，取决于传感器尺寸和用途要求。护套材料一般是不锈钢，用于较高温度时可能需要铬镍铁合金。对于更特殊的场景也会使用其他护套材料。注：不锈钢基本就是铁镍合金或铁镍铬合金，可能差别在碳含量。

History 历史

The application of the tendency of electrical conductors to increase their electrical resistance with rising temperature was first described by Sir William Siemens at the Bakerian Lecture of 1871 before the Royal Society of Great Britain. The necessary methods of construction were established by Callendar, Griffiths, Holborn and Wein between 1885 and 1900.

The Space Shuttle made extensive use of platinum resistance thermometers. The only in-flight shutdown of a Space Shuttle Main Engine — mission STS-51F — was caused by multiple failures of RTDs which had become brittle and unreliable due to multiple heat-and-cool cycles. (The failures of the sensors falsely suggested that a fuel pump was critically overheating, and the engine was automatically shut down.) Following the engine failure incident, the RTDs were replaced with thermocouples. [10]

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Sir William Siemens在1871年英国皇家学会举办的Bakerian Lecture上首次描述了电导体的电阻有随温度上升而增加的趋势，及其应用。1885年至1900年期间，Callendar、Griffiths、Holborn和Wein开发出了制造的方法。

航天飞机项目广泛使用了铂电阻温度计。而在STS-51F 任务中，唯一一次航天飞机主发动机飞行中关机的故障就是由多个RTD 失效导致的，经历多次冷热循环后，这些RTD 变脆并不再可靠。失效的传感器错误发出燃料泵严重过热的信号，于是发动机被自动关闭。在这次事故后，RTD 被热电偶替代。

Standard resistance thermometer data 标准电阻-温度数据

Temperature sensors are usually supplied with thin-film elements. The resistance elements are rated in accordance with BS EN 60751:2008 as:

Tolerance class	Valid range
F 0.3	−50 to +500 °C
F 0.15	−30 to +300 °C
F 0.1	0 to +150 °C

Resistance-thermometer elements functioning up to 1000 °C can be supplied. The relation between temperature and resistance is given by the Callendar-Van Dusen equation:

Here $R_T$ is the resistance at temperature T, $R_0$ is the resistance at 0 °C, and the constants (for an α = 0.00385 platinum RTD) are:

Since the B and C coefficients are relatively small, the resistance changes almost linearly with the temperature.

For positive temperature, solution of the quadratic equation yields the following relationship between temperature and resistance:

Then for a four-wire configuration with a 1 mA precision current source[11] the relationship between temperature and measured voltage $V_T$ is

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温度传感器通常使用薄膜元件。参照BS EN 60751：2008 标准，这类电阻元件的额定值为：

市面上有最高可在1000°C 下工作的电阻式温度计元件。温度与电阻值的关系可由Callendar-Van Dusen 方程计算：
R T = { R 0 ⋅ [ 1 + A T + B T 2 + C T 3 ( T − 100 ) ] , ( − 200 ° C < T < 0 ° C ) R 0 ⋅ [ 1 + A T + B T 2 ] , ( 0 ° C ≤ T < 850 ° C ) R_T =

$$\begin{cases} R_0 \cdot [ 1 + AT + BT^2 + CT^3(T - 100) ] , \quad (-200°C < T < 0°C) \\ R_0 \cdot [1 + AT + BT^2], \quad (0°C \le T \lt 850°C) \end{cases}$$ RT​={R0​⋅[1+AT+BT2+CT3(T−100)],(−200°C<T<0°C)R0​⋅[1+AT+BT2],(0°C≤T<850°C)​
其中，

$R_T$ 是温度T 时的电阻值，

$R_0$ 是0°C 时的电阻值，

A、B、C 是常量，对于 α = 0.00385 的铂RTD 来说：

$A=3.9083\times 10^{-3}°C^{-1}$，

$B=-5.775\times 10^{-7}°C^{-2}$，

$C=-4.183\times 10^{-12}°C^{-4}$。

因数B ，C 相对来说很小，所以电阻值对温度的变化几乎是线性的。

在正温度时，由二次方程的解可得出如下关于温度和电阻的关系：
$$T=\frac{-A+\sqrt{A^2-4B(1-\frac{R_T}{R_0})}}{2B}$$

使用四线式接法和1mA 的精密恒流源时，温度与测量的电压$V_T$ 的关系是：
$$T=\frac{-A+\sqrt{A^2-40B(0.1-V_T)}}{2B}$$

Temperature-dependent resistances for various popular resistance thermometers 几种常用电阻温度计的R-T 数据表

Temperature in °C	Resistance in Ω
ITS-90 Pt100[12]	Pt100 Typ: 404	Pt1000 Typ: 501	PTC Typ: 201	NTC Typ: 101	NTC Typ: 102	NTC Typ: 103	NTC Typ: 104	NTC Typ: 105
−50	79.901192	80.31	803.1	1032
−45	81.925089	82.29	822.9	1084
−40	83.945642	84.27	842.7	1135			50475
−35	85.962913	86.25	862.5	1191			36405
−30	87.976963	88.22	882.2	1246			26550
−25	89.987844	90.19	901.9	1306		26083	19560
−20	91.995602	92.16	921.6	1366		19414	14560
−15	94.000276	94.12	941.2	1430		14596	10943
−10	96.001893	96.09	960.9	1493		11066	8299
−5	98.000470	98.04	980.4	1561	31389	8466
0	99.996012	100.00	1000.0	1628	23868	6536
5	101.988430	101.95	1019.5	1700	18299	5078
10	103.977803	103.90	1039.0	1771	14130	3986
15	105.964137	105.85	1058.5	1847	10998
20	107.947437	107.79	1077.9	1922	8618
25	109.927708	109.73	1097.3	2000	6800			15000
30	111.904954	111.67	1116.7	2080	5401			11933
35	113.879179	113.61	1136.1	2162	4317			9522
40	115.850387	115.54	1155.4	2244	3471			7657
45	117.818581	117.47	1174.7	2330				6194
50	119.783766	119.40	1194.0	2415				5039
55	121.745943	121.32	1213.2	2505				4299	27475
60	123.705116	123.24	1232.4	2595				3756	22590
65	125.661289	125.16	1251.6	2689					18668
70	127.614463	127.07	1270.7	2782					15052
75	129.564642	128.98	1289.8	2880					12932
80	131.511828	130.89	1308.9	2977					10837
85	133.456024	132.80	1328.0	3079					9121
90	135.397232	134.70	1347.0	3180					7708
95	137.335456	136.60	1366.0	3285					6539
100	139.270697	138.50	1385.0	3390
105	141.202958	140.39	1403.9
110	143.132242	142.29	1422.9
150	158.459633	157.31	1573.1
200	177.353177	175.84	1758.4

后记

所以说相较百度百科，维基也不能免俗，车轱辘话翻来覆去的说。好在还是有干货的。

另外，用于测温的装置一般还有：

• thermostat 温控开关：输出的开关量，一般是基于双金属片受热变形分离的原理，空开、机械式启辉器里有类似的东西；
• thermistor 热敏电阻：热敏电阻有NTC 的也有PTC，这篇讲的RTD 侧重于高温测量场合基于金属的PTC。
• thermocouple 热电偶：上文对比过。日常用的热电偶一般就是一根绝缘线，头部裸露，内部导线点焊起来形成热电耦合。可以做到很长，又细又软，非常灵活。