Resistance thermometer

Resistance thermometers are electrical components that use the temperature dependence of the electrical resistance of an electrical conductor to measure the temperature .

Pure metals are preferably suitable as resistance material. They show greater changes in resistance than alloys. They also have an almost linear relationship between resistance and temperature. Corrosion-resistant platinum is preferably used for reliable measurements , since it shows particularly little aging and since it can be used to manufacture thermometers with low error limits .

The temperature-sensitive sensor, the measuring resistor, can also consist of ceramics (sintered metal oxides) or semiconductors, with which much higher temperature coefficients than with metals and thus much higher sensitivities can be achieved, but with less accuracy and considerable temperature dependence of the temperature coefficient itself. refers to these resistors as thermistors , said thermistor (NTC resistors) used in the measurement rather than cold conductor (PTC).

Two individual measuring resistors;
Examples from a wide variety of types

Measuring insert with connection socket; the temperature-sensitive measuring resistor is in the area framed on the right

Industrial resistance thermometer in protective tube with connection head

Platinum resistance thermometers for industrial use consist of a measuring insert in a fitting that protects against corrosion. The wiring of the measuring insert is often done in a connection head, from where the thermometer can be connected to an external electrical measuring device via cable. The measuring insert is an easily exchangeable unit, mostly with a ceramic or stainless steel jacket and a connection base; this insert contains one or more platinum measuring resistors at its end. In addition to the clamping screws for the wiring, the measuring insert shown in the picture also contains two spring-loaded mounting screws in the connection base, which provide the necessary pressure for good thermal contact with the protective tube.

Conventional thermometers measure the temperature based on the change in length or volume of a substance and are only suitable as indicating measuring devices. The advantage of resistance thermometers is that they deliver an electrical signal and are suitable for use in industrial measurement technology .

Parameters and limit deviations

The formula can often be used within small temperature ranges

${\displaystyle R_{t}=R_{20}\cdot (1+\alpha _{20}\cdot (t-20\;^{\circ }\mathrm {C} ))}$

be applied. If the resistance belonging to the Celsius temperature , the resistance belonging to 20 ° C and the temperature coefficient related to 20 ° C are known, the temperature can be calculated as follows: ${\displaystyle t}$ ${\displaystyle R_{t}=R(t)}$ ${\displaystyle R_{20}}$ ${\displaystyle \alpha _{20}}$

${\displaystyle t=20\;^{\circ }\mathrm {C} +{\frac {R_{t}-R_{20}}{R_{20}\cdot \alpha _{20}}}}$

The temperature coefficient is viewed as a material constant that indicates the relative change in resistance per change in temperature ${\displaystyle \Delta R/R_{20}}$ ${\displaystyle \Delta t}$

${\displaystyle \alpha _{20}={\frac {1}{R_{20}}}{\frac {\Delta R}{\Delta t}}}$

A prerequisite for such a simple calculation is a restricted measuring range or a constant temperature coefficient. The latter is only approximately the case with metals and silicon; This approximation is not given for thermistors made of barium titanate .

platinum

Characteristic curve of a platinum measuring resistor Pt100

For the platinum resistance thermometers widely used in industrial measurement technology and the measuring resistors used in them, there is a standard in which additional summands are specified for the function behind the linear element ${\displaystyle R_{t}=R(t)}$

• for the area : ${\displaystyle t=0\ldots 850\ ^{\circ }\mathrm {C} }$

${\displaystyle R_{t}=R(t)=R_{0}\;(1+At+Bt^{2})}$,

• for the area : ${\displaystyle t=-200\ldots 0\ ^{\circ }\mathrm {C} }$

${\displaystyle R_{t}=R(t)=R_{0}\;(1+At+Bt^{2}+C(t-100\,^{\circ }\mathrm {C} )t^{3})}$,

with ; ; . ${\displaystyle A=3{,}9083\cdot 10^{-3}\ ^{\circ }\mathrm {C} ^{-1}}$ ${\displaystyle B=-5{,}775\cdot 10^{-7}\ ^{\circ }\mathrm {C} ^{-2}}$ ${\displaystyle C=-4{,}183\cdot 10^{-12}\ ^{\circ }\mathrm {C} ^{-4}}$

The nominal value is given, i.e. the resistance at 0 ° C. Resistors with a nominal value of 100 Ω are preferably used; these sensors are called Pt100. Other common nominal values ​​are 500 Ω and 1000 Ω. Details are given under the heading platinum measuring resistor . The values in the table below are calculated using these equations. ${\displaystyle R_{0}=R(0)}$

The definition range says nothing about the temperature up to which a measuring resistor or measuring insert can actually be used; the permissible range of application depends on the total materials used and is specified by the manufacturer in the catalog. Platinum resistance thermometers can be used for significantly smaller ranges or, with the appropriate design, extrapolated the characteristic curve down to −250 ° C or +1000 ° C.

A platinum thermometer should be assigned to an accuracy class by the manufacturer . In the specified standard, the maximum permissible measurement deviations ( limit deviations ) are specified for each class :

class	Scope		Limit deviation
	Wire wound resistors	Sheet resistors
AA	0−50 ... +250 ° C	−00… +150 ° C	0.1 0 ° C + 0.0017 ∙ ${\displaystyle |t|}$
A.	−100 ... +450 ° C	−30 ... +300 ° C	0.15 ° C + 0.002 0∙ ${\displaystyle |t|}$
B.	−196 ... +600 ° C	−50 ... +500 ° C	0.3 0 ° C + 0.005 0∙ ${\displaystyle |t|}$
C.	−196 ... +600 ° C	−50 ... +600 ° C	0.6 0 ° C + 0.01 00∙ ${\displaystyle |t|}$

Example of the preferably used class B: At 500 ° C, deviations of the measured value are permissible up to ± 2.8 ° C.

The temperature coefficient of the resistance is specified in the standard somewhat differently than often (and also above) than

${\displaystyle \alpha _{0}={\frac {\Delta R/R_{0}}{\Delta t}}}$ ,

i.e. at the reference temperature of 0 ° C instead of 20 ° C. The mean temperature coefficient over the range 0 ... 100 ° C results from and is used as a characterizing value . With the linear approximation ${\displaystyle \alpha _{0}=3{,}85\cdot 10^{-3}\ ^{\circ }\mathrm {C} ^{-1}}$

${\displaystyle R_{t}=R(t)=R_{0}\;(1+\alpha _{0}t)}$

if the deviation is in the range of −20… +120 ° C, the amount is less than 0.4 ° C. They are not greater than the limit deviations specified above (error limits due to production fluctuations) in class B.

Usually measurements are taken and the temperature is searched. The resolution ("inversion") according to or the linearization (generation of an output signal that is linearly linked not with the resistance but with the temperature) is partly carried out by a transmitter integrated in the measuring insert, see below for measuring circuits . ${\displaystyle R_{t}}$ ${\displaystyle t}$ ${\displaystyle t}$

nickel

Compared to platinum, nickel is more sensitive; it provides a greater change in relative resistance for the same change in temperature. However, this material has been removed from the standardization. The equation for the temperature curve in the range from −60 ° C to +250 ° C was:

${\displaystyle R_{t}=R(t)=R_{0}\cdot (1+At+Bt^{2}+Ct^{4}+Dt^{6})}$

with the temperature in ° C; the resistance rating at 0 ° C; . ${\displaystyle t}$ ${\displaystyle R_{0}}$ ${\displaystyle A=5{,}485\cdot 10^{-3}\ ^{\circ }\mathrm {C} ^{-1};\ B=6{,}65\cdot 10^{-6}\ ^{\circ }\mathrm {C} ^{-2};\ C=2{,}805\cdot 10^{-11}\ ^{\circ }\mathrm {C} ^{-4};\ D=-2\cdot 10^{-17}\ ^{\circ }\mathrm {C} ^{-6}}$

In addition to the Ni100 with = 100 Ω, the versions Ni500 with 500 Ω and Ni1000 with 1000 Ω were in use. ${\displaystyle R_{0}}$

According to DIN 43760, which was last only applied to nickel measuring resistors and has been withdrawn since April 1994, the limit deviations were:

Scope	Limit deviation
−60… 000 ° C	0.4 ° C + 0.028 ∙ ${\displaystyle |t|}$
−00 ... 250 ° C	0.4 ° C + 0.007 ${\displaystyle t}$

Disadvantages compared to the platinum measuring resistor are the smaller temperature range (−60… +250 ° C) and the larger limit deviation, especially in the range below 0 ° C.

silicon

Silicon measuring resistors can be used in the range of −50… +150 ° C. According to the data sheet, the equation applies to their temperature response in the range −30 ... +130 ° C:

${\displaystyle R_{t}=R(t)=R_{25}\cdot (1+A(t-t_{25})+B(t-t_{25})^{2})}$

with the temperature in degrees Celsius; the temperature 25 ° C; the nominal resistance value at 25 ° C; . ${\displaystyle t}$ ${\displaystyle t_{25}}$ ${\displaystyle R_{25}}$ ${\displaystyle A=7{,}88\cdot 10^{-3}\ ^{\circ }\mathrm {C} ^{-1};\ B=1{,}937\cdot 10^{-5}\ ^{\circ }\mathrm {C} ^{-2}}$

In the data sheet mentioned, nominal values ​​are given for 1000 Ω and 2000 Ω at a measuring current of 1 mA with limit deviations of 1… 3%. ${\displaystyle R_{25}}$

There are also integrated circuits for the same temperature range with a linearized output signal, for example with a nominal 1 μA / K or 10 mV / K with a supply voltage of 4 ... 30 V; for example.

Thermistor

NTC thermistors show a highly non-linear relationship between resistance and temperature. The following function is used as a useful approximation of the temperature-dependent resistance, which has the absolute temperature as an argument : ${\displaystyle T}$

${\displaystyle R_{T}=R(T)=A\cdot \mathrm {e} ^{^{\frac {B}{T}}}=R_{R}\cdot \mathrm {e} ^{B\left({\frac {1}{T}}-{\frac {1}{T_{R}}}\right)}}$

Here, the reference temperature (usually 298.15 K = 25 ° C) and the resistance at the reference temperature (usually as written). The size is a material-dependent constant, which is usually between  = 2500… 5000 K. ${\displaystyle T_{R}}$ ${\displaystyle R_{R}}$ ${\displaystyle R_{25}}$ ${\displaystyle B}$ ${\displaystyle B}$

The usual tolerances of are 5 or 10%, of 3%. ${\displaystyle R_{R}}$ ${\displaystyle B}$

The temperature coefficient is defined somewhat differently here and results in the limit case to be differentially smaller temperature changes

${\displaystyle \alpha _{T}={\frac {1}{R_{T}}}\,{\frac {\mathrm {d} R}{\mathrm {d} T}}\Rightarrow -{\frac {B}{T^{2}}}}$

It decreases quadratically with increasing absolute temperature. In the usual permitted working range between −50 ° C and +125 ° C, this can change by a factor of around 3.

Example : With = 3600 K and = 300 K the result is = ${\displaystyle B}$ ${\displaystyle T}$ ${\displaystyle \alpha _{T}}$ -40e^-3 K⁻¹. That isaround ten times the amountcomparedto platinum. ${\displaystyle \alpha _{0}}$

NTC thermistors show poor long-term constancy, change their resistance due to moisture, have a certain memory (resistance depends on the previous history), so that they are not very suitable for measurement purposes. They are used for non-critical temperature monitoring as well as for simple temperature measurements with accuracy requirements of 1… 3 K (example: microcontroller boards, battery temperatures / sensor temperatures in cameras). In these cases, linearization is usually carried out using stored lookup tables.

Depending on the version, NTC thermistors can range between about −55 ° C and max. +250 ° C can be used. They are made in the form of rods, discs or pearls, some of which are encased in glass.

Measuring circuits

Measuring circuits for resistance thermometers

A constant current must flow through the resistor to measure the resistance. The applied voltage is an easily measurable signal proportional to the resistance. Often, however, one does not measure this voltage, but only its change compared to an initial value by means of a differential circuit ( Wheatstone bridge ). In order to keep the error due to self-heating to a minimum, the measuring current must be as low as possible, typically not higher than one milliampere for Pt100.

In industrial systems, larger distances between the sensor and the transmitter often have to be bridged with correspondingly long supply lines. In order to avoid influences of the resistance of the lines on the measured value, platinum resistance sensors are also manufactured with three or four wire connections . This enables the measuring current to be fed in separately or the feed line error can be compensated . In outdoor areas, installation with three or four ladders is strongly recommended. Alternatively, a first transmitter is already housed in the connection head.

Bridge circuit

The principle applies to the almost balanced Wheatstone bridge (with a small detuning)

${\displaystyle U\sim \Delta R=R_{t}-R_{1}}$

Two-wire circuit

${\displaystyle U\sim R_{t}+2\cdot R_{\mathrm {Ltg} }+R_{\mathrm {Abgl} }-R_{1}}$

${\displaystyle U\sim R_{t}+2\cdot R_{\mathrm {Ltg} }-\mathrm {konst} }$

One is indistinguishable from one . Standardized may be up to 10 Ω. If the line resistance is lower, a balancing resistance to 10 Ω is added. Since the copper cables have roughly the same temperature coefficient as a Pt100, any temperature change in the cable of up to 10% is roughly noticeable like a temperature change at the measuring point; fluctuations of 50… 70 K are realistic in overhead lines. ${\displaystyle \Delta R_{\mathrm {Ltg} }}$ ${\displaystyle \Delta R_{t}}$ ${\displaystyle 2\cdot R_{\mathrm {Ltg} }}$

Three-wire circuit

${\displaystyle U\sim (R_{t}+R_{\mathrm {Ltg3} })-(R_{1}+R_{\mathrm {Ltg2} })}$

${\displaystyle U\sim R_{t}-R_{1}\ .}$

If the lines are the same it falls out A balancing resistor is then superfluous. acts like a source resistance of the supply voltage and is practically not noticeable. ${\displaystyle R_{\mathrm {Ltg} }}$ ${\displaystyle R_{\mathrm {Ltg1} }}$

Four-wire circuit

Using an electronically stabilized constant current source is independent of and from in the feed lines. If an electronic voltmeter with a high input resistance is used, (no noticeable current branching) and (no noticeable voltage drop in the test leads); so is ${\displaystyle I}$ ${\displaystyle R_{t}}$ ${\displaystyle R_{\mathrm {Ltg} }}$ ${\displaystyle I_{U}\ll I}$ ${\displaystyle I_{U}\cdot R_{\mathrm {Ltg} }\ll I\cdot R_{t}}$

${\displaystyle U=I\cdot R_{t}\;;\quad U\sim R_{t}\;.}$

Two conductors with transmitter

A resistance thermometer with an integrated measuring transducer, sometimes referred to as a "current transmitter", allows a current to flow through it that is linearly related to the temperature. With a current interface that works with a standard signal, the current is independent. Furthermore, digital technology are fieldbus Transmitter available. A two-wire line handles both the energy and the signal transmission. With a constant dependent on the measuring range , the result is ${\displaystyle R_{\mathrm {Ltg} }}$ ${\displaystyle t_{0}}$

${\displaystyle I\sim t-t_{0}\;.}$

Sources of error

As with all contact thermometers , static and retarding heat conduction influences must be observed. In the case of resistance thermometers, the influence of the resistance of the measuring lines can also be considered as a source of error:

Insufficient insulation resistance

A deficient insulation resistance can be viewed electrically as a parasitic parallel resistance to the measuring resistor. It therefore leads to the fact that the evaluating components show a temperature that is too low. It usually arises during the production of the sensors due to the penetration of moisture into the measuring insert, especially where mineral-insulated sheathed cables with hygroscopic insulation material such as magnesium or aluminum oxide powder are used. For platinum measuring resistors according to, an insulation resistance of ≥100 MΩ with a direct voltage of at least 100 V at room temperature is prescribed, but only ≥0.5 MΩ at 500 ° C and 10 V.

Parasitic thermal voltages

They are caused by the thermoelectric effect and result from the use of different materials for the connection conductors and the platinum sensor itself. Thus, several parasitic thermal voltage sources are formed in a measuring insert that uses nickel feed lines and a platinum chip sensor with palladium connection wires . Since the thermal voltages arise on both the supply line and the return line, it can usually be assumed that they cancel each other out. In unfavorable cases, however, due to irregular heat transfers, thermal voltages occur which the evaluating electronics can only distinguish from the voltage drop across the measuring resistor if it reverses the polarity for each measurement.

Self-heating

The measuring current generates a power loss at the measuring resistor, which is converted into heat and is dependent on the basic value, the measuring temperature, the design and the heat conduction and capacity. Since a measurement current of 1 mA is generally not exceeded, this power loss with a Pt100 is in the range of a few tenths of a milliwatt and normally does not generate any significant measurement errors. Self-heating only has to be taken into account in rare cases and determined for the respective application under operating conditions.

Hysteresis

The hysteresis is noticeable in that the thermometer no longer measures the same value as before after large temperature changes. It can be traced back to mechanical stresses in the sensor element, which are caused by different expansion coefficients of the platinum and the carrier material, or in the case of glass sensors, the casing. For platinum measuring resistors, this deviation caused by the pretreatment must not be greater than the limit deviation at the test temperature for the respective accuracy class in accordance with a test procedure specified in the associated standard.

table

Resistance values ​​for various common resistance thermometers (in Ω )

Temperature in ° C	Pt100	Pt1000	PTC	NTC
	Type: 404	Type: 501	Type: 201	Type: 101	Type: 102	Type: 103	Type: 104	Type: 105
−200	18.52	185.2
−100	60.26	602.6
−50	80.31	803.1	1032
−45	82.29	822.9	1084
−40	84.27	842.7	1135			50475
−35	86.25	862.5	1191			36405
−30	88.22	882.2	1246			26550
−25	90.19	901.9	1306		26083	19560
−20	92.16	921.6	1366		19414	14560
−15	94.12	941.2	1430		14596	10943
−10	96.09	960.9	1493		11066	8299
−5	98.04	980.4	1561	31389	8466
± 0	100.00	1000.0	1628	23868	6536
+5	101.95	1019.5	1700	18299	5078
10	103.90	1039.0	1771	14130	3986
15th	105.85	1058.5	1847	10998
20th	107.79	1077.9	1922	8618
25th	109.73	1097.3	2000	6800			15000
30th	111.67	1116.7	2080	5401			11933
35	113.61	1136.1	2162	4317			9522
40	115.54	1155.4	2244	3471			7657
45	117.47	1174.7	2330				6194
50	119.40	1194.0	2415				5039
55	121.32	1213.2	2505				4299	27475
60	123.24	1232.4	2595				3756	22590
65	125.16	1251.6	2689					18668
70	127.08	1270.7	2782					15052
75	128.99	1289.9	2880					12932
80	130.90	1309.0	2977					10837
85	132.80	1328.0	3079					9121
90	134.71	1347.1	3180					7708
95	136.61	1366.1	3285					6539
100	138.51	1385.1	3390
110	142.29	1422.9
150	157.33	1573.3
200	175.86	1758.6
250	194.10	1941.0
300	212.05	2120.5
400	247.09	2470.9
500	280.98	2809.8
600	313.71	3137.1
700	345.28	3452.8
800	375.70	3757.0

Web links

• Matthias Nau: Electrical temperature measurement 2007 pdf
• Resistance thermometers / thermocouples
• Formulas and online calculator (by Andreas Hofmeier)
• Michael Vogel: Noble metal for hot measurements . Sensors with platinum resistors make it possible to determine high temperatures reliably and precisely. In: Physics Journal . tape 15 , no. 09 , 2016, p. 76-77 .

Individual evidence

1. ↑ ^{a b c} DIN EN 60751: 2009-5 Industrial platinum resistance thermometers and platinum temperature sensors (in accordance with IEC 60751: 2008)
2. ↑ http://www.datasheetcatalog.org/datasheet/infineon/1-kt.pdf
3. ↑ http://www.analog.com/static/imported-files/data_sheets/AD590.pdf
4. ↑ http://www.ti.com/lit/ds/symlink/lm35.pdf
5. ↑ ^{a b} https://de-de.wika.de/upload/DS_TE9101_de_de_1887.pdf
6. ↑ https://www.jumo.net/attachments/JUMO/attachmentdownload?productgroup=707030&language=de
7. ↑ https://www.de.endress.com/de/messgeraete-fuer-die-prozesstechnik/produktfinder?filter.business-area%5B%5D=temperature&filter.product-family-external%5B%5D=itemp&filter.text = TMT71