Temperature-dependent resistor

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Platinum measuring resistor

A platinum measuring resistor is a resistance thermometer used to measure temperature. The most commonly applied platinum resistance thermometers are Pt100 and Pt1000. The designations Pt100/Pt1000 describe the resistor material involved, in this case platinum, and its nominal resistance R₀ at a temperature of 0 °C. (R_0,Pt100 = 100 Ω / R_0,Pt1000 = 1 kΩ). Usually Pt100 and Pt1000 are used, although other resistance values are possible.

Resistance thermometers: Design

A platinum resistance thermometer consists of an electrical resistance of platinum. Platinum is often used for temperature changes due to its constant electrical properties. The resistor is connected to the connecting wires by an electrical conductor. The components are protected against external influences by a protective housing and appropriate insulation.

Resistance thermometers: How they work

A constant current flows via the connecting cables through the resistance thermometer. An electrical voltage is measured between the two connecting cables which depends on the platinum resistance. The linear correlation between the electrical resistance of the platinum conductor and the temperature is used to measure the temperature. If the temperature rises, so too does the electrical resistance. As a result, a different voltage is also measured between the conductors, which is used to calculate the temperature.

The structure of a platinum measuring resistor — The design of a platinum measuring resistor:
A: Connection ends, B: Resistor; C: Cable

Converting Pt100/Pt1000 resistance into temperature

The change to resistance of an electrical resistance depends on the temperature difference and the temperature coefficient of the material involved. The nominal resistance at 0°C is 100 Ω for Pt100 and 1 kΩ for Pt1000. The temperature coefficients for platinum A = 3,91 · 10⁻³ K^-1 and B = -0,588 · 10⁻⁶ K^-2 (K stands for Kelvin).

The general formula for calculating temperature-dependent resistance is as follows:

$R (ϑ) = R_{ϑ 0} \cdot (1 + A \cdot (ϑ - ϑ_{0}) + B \cdot (ϑ - ϑ_{0})^{2})$	$R (ϑ) :$	Temperature-dependent resistance [Ω]
	$R_{0} :$	Electrical nominal resistance at 0°C [Ω]
	$ϑ :$	Temperature [°C]
	$ϑ_{0} :$	Reference temperature [°C]
	$A :$	Linear temperature coefficient [K^-1]
	$B :$	Quadratic temperature coefficient [K^-2]

The temperature range from 0 °C to 100 °C can be described with a very good linear approximation equation. To do so, ϑ₀ = 0 °C is selected as the reference temperature. The coefficients A and B are replaced by the mean coefficient α = 3,91 · 10⁻³ K^-1.

$R (ϑ) = R_{0} \cdot (1 + α \cdot ϑ)$	$R (ϑ) :$	Temperature-dependent resistance [Ω]
	$R_{0} :$	Electrical nominal resistance at 0°C [Ω]
	$ϑ :$	Temperature [°C]
	$α :$	Mean temperature coefficient [K^-1]

Conversion of the formula allows you to convert the measured resistance into temperature:

$ϑ (R) = \frac{R - R_{0}}{R_{0} \cdot α}$			$ϑ (R) :$	Resistance-dependent temperature [°C]
or also			$α :$	Mean temperature coefficient [K^-1]
$ϑ (R) = \frac{Δ R}{R_{0} \cdot α}$	with	$Δ R = R - R_{0}$	$R :$	Measured resistance of the Pt sensor [Ω]
			$R_{0} :$	Electrical nominal resistance at 0°C [Ω]
			$Δ R :$	Measured change to resistance [Ω]

Converting Pt100/Pt1000 resistance into temperature

The change to resistance of an electrical resistance depends on the temperature difference and the temperature coefficient of the material involved. The nominal resistance at 0°C is 100 Ω for Pt100 and 1 kΩ for Pt1000. The temperature coefficients for platinum
A = 3,91 · 10⁻³ K^-1 und B = -0,588 · 10⁻⁶ K^-2 (K stands for Kelvin).

The general formula for calculating temperature-dependent resistance is as follows:

$R (ϑ) = R_{ϑ 0} \cdot (1 + A \cdot (ϑ - ϑ_{0}) + B \cdot (ϑ - ϑ_{0})^{2})$
$R (ϑ) :$	Temperature-dependent resistance [Ω]
$R_{0} :$	Electrical nominal resistance at 0°C [Ω]
$ϑ :$	Temperature [°C]
$ϑ_{0} :$	Reference temperature [°C]
$A :$	Linear temperature coefficient [K^-1]
$B :$	Quadratic temperature coefficient [K^-2]

$R (ϑ) = R_{0} \cdot (1 + α \cdot ϑ)$
$R (ϑ) :$	Temperature-dependent resistance [Ω]
$R_{0} :$	Electrical nominal resistance at 0°C [Ω]
$ϑ :$	Temperature [°C]
$α :$	Mean temperature coefficient [K^-1]

Conversion of the formula allows you to convert the measured resistance into temperature:

$ϑ (R) = \frac{R - R_{0}}{R_{0} \cdot α}$
or also
$ϑ (R) = \frac{Δ R}{R_{0} \cdot α}$
with
$Δ R = R - R_{0}$
$ϑ (R) :$	Resistance-dependent temperature °C
$α :$	Mean temperature coefficient [K^-1]
$R :$	Measured resistance of the Pt sensor [Ω]
$R_{0} :$	Electrical nominal resistance at 0°C [Ω]
$Δ R :$	Measured change to resistance [Ω]

The linear correlation between the electrical resistance of the platinum conductor and the temperature is used to measure the temperature.
Patrick Targonski, Product Manager at autosen

Resistance thermometer characteristic curve

he characteristic curve shows the linear relationship between electrical resistance and temperature. Exact values for Pt100 and Pt1000 can be determined graphically from the Pt100 characteristic curves / Pt1000 characteristic curves or read directly from the Pt100 table / Pt1000 table. Platinum is highly suitable as a material due to its high long-term stability and particularly constant electrical properties at high temperatures. Thus, the characteristic curve for platinum resistors is very linear even at high temperatures. By adding other impurities to platinum, even better results are achieved in this respect.

Pt100 Kennlinie

Pt100 characteristic curve

Show/Hide Pt100 table

Temperature	Resistance	Tolerance class B	Tolerance class A
°C	Ω	in ± °C / in ± Ω	in ± °C / in ± Ω
-40	84,27	0,5 / 0,2	0,23 / 0,09
-30	88,22	0,45 / 0,18	0,21 / 0,08
-20	92,16	0,4 / 0,16	0,19 / 0,07
-10	96,09	0,35 / 0,14	0,17 / 0,07
0	100	0,3 / 0,12	0,15 / 0,06
10	103,9	0,35 / 0,14	0,17 / 0,07
20	107,79	0,4 / 0,16	0,19 / 0,07
30	111,67	0,45 / 0,17	0,21 / 0,08
40	115,54	0,5 / 0,19	0,23 / 0,09
50	119,4	0,55 / 0,21	0,25 / 0,1
60	123,24	0,6 / 0,23	0,27 / 0,1
70	127,08	0,65 / 0,25	0,29 / 0,11
80	130,9	0,7 / 0,27	0,31 / 0,12
90	134,71	0,75 / 0,29	0,33 / 0,13
100	138,51	0,8 / 0,3	0,35 / 0,13
110	142,29	0,85 / 0,32	0,37 / 0,14
120	146,07	0,9 / 0,34	0,39 / 0,15
130	149,83	0,95 / 0,36	0,41 / 0,15
140	153,58	1 / 0,37	0,43 / 0,16
150	157,33	1,05 / 0,39	0,45 / 0,17
160	161,05	1,1 / 0,41	0,47 / 0,17
170	164,77	1,15 / 0,43	0,49 / 0,18
180	168,48	1,2 / 0,44	0,51 / 0,19
190	172,17	1,25 / 0,46	0,53 / 0,2
200	175,86	1,3 / 0,48	0,55 / 0,2
210	179,53	1,35 / 0,49	0,57 / 0,21
220	183,19	1,4 / 0,51	0,59 / 0,22
230	186,84	1,45 / 0,53	0,61 / 0,22
240	190,47	1,5 / 0,54	0,63 / 0,23
250	194,1	1,55 / 0,56	0,65 / 0,24
260	197,71	1,6 / 0,58	0,67 / 0,24
270	201,31	1,65 / 0,59	0,69 / 0,25
280	204,9	1,7 / 0,61	0,71 / 0,25
290	208,48	1,75 / 0,63	0,73 / 0,26
300	212,05	1,8 / 0,64	0,75 / 0,27
310	215,61	1,85 / 0,66	0,77 / 0,27
320	219,15	1,9 / 0,67	0,79 / 0,28
330	222,68	1,95 / 0,69	0,81 / 0,29
340	226,21	2 / 0,7	0,83 / 0,29
350	229,72	2,05 / 0,72	0,85 / 0,3
360	233,21	2,1 / 0,73	0,87 / 0,3
370	236,7	2,15 / 0,75	0,89 / 0,31
380	240,18	2,2 / 0,76	0,91 / 0,32
390	243,64	2,25 / 0,78	0,93 / 0,32
400	247,09	2,3 / 0,79	0,95 / 0,33
410	250,53	2,35 / 0,81	0,97 / 0,33
420	253,96	2,4 / 0,82	0,99 / 0,34
430	257,38	2,45 / 0,84	1,01 / 0,34
440	260,78	2,5 / 0,85	1,03 / 0,35
450	264,18	2,55 / 0,86	1,05 / 0,36
460	267,56	2,6 / 0,88	1,07 / 0,36
470	270,93	2,65 / 0,89	1,09 / 0,37
480	274,29	2,7 / 0,91	1,11 / 0,37
490	277,64	2,75 / 0,92	1,13 / 0,38
500	280,98	2,8 / 0,93	1,15 / 0,38
510	284,3	2,85 / 0,95	1,17 / 0,39
520	287,62	2,9 / 0,96	1,19 / 0,39
530	290,92	2,95 / 0,97	1,21 / 0,4
540	294,21	3 / 0,98	1,23 / 0,4
550	297,49	3,05 / 1	1,25 / 0,41

Pt1000 characteristic curve

Resistance table Pt1000

Show/Hide Pt1000 table

Temperature	Resistance	Tolerance class B	TTolerance class A
°C	Ω	in ± °C / in ± Ω	in ± °C / in ± Ω
-40	842,47	0,5 / 1,99	0,23 / 0,91
-30	882,11	0,45 / 1,78	0,21 / 0,83
-20	921,57	0,4 / 1,57	0,19 / 0,75
-10	960,86	0,35 / 1,37	0,17 / 0,67
0	1000	0,3 / 1,17	0,15 / 0,59
10	1039,03	0,35 / 1,36	0,17 / 0,66
20	1077,94	0,4 / 1,55	0,19 / 0,74
30	1116,73	0,45 / 1,74	0,21 / 0,81
40	1155,41	0,5 / 1,93	0,23 / 0,89
50	1193,97	0,55 / 2,12	0,25 / 0,96
60	1232,42	0,6 / 2,3	0,27 / 1,04
70	1270,75	0,65 / 2,49	0,29 / 1,11
80	1308,97	0,7 / 2,67	0,31 / 1,18
90	1347,07	0,75 / 2,85	0,33 / 1,26
100	1385,06	0,8 / 3,03	0,35 / 1,33
110	1422,93	0,85 / 3,21	0,37 / 1,4
120	1460,68	0,9 / 3,39	0,39 / 1,47
130	1498,32	0,95 / 3,57	0,41 / 1,54
140	1535,84	1 / 3,75	0,43 / 1,61
150	1573,25	1,05 / 3,92	0,45 / 1,68
160	1610,54	1,1 / 4,1	0,47 / 1,75
170	1647,72	1,15 / 4,27	0,49 / 1,82
180	1684,78	1,2 / 4,44	0,51 / 1,89
190	1721,73	1,25 / 4,61	0,53 / 1,95
200	1758,56	1,3 / 4,78	0,55 / 2,02
210	1795,28	1,35 / 4,95	0,57 / 2,09
220	1831,88	1,4 / 5,11	0,59 / 2,16
230	1868,36	1,45 / 5,28	0,61 / 2,22
240	1904,73	1,5 / 5,45	0,63 / 2,29
250	1940,98	1,55 / 5,61	0,65 / 2,35
260	1977,12	1,6 / 5,77	0,67 / 2,42
270	2013,14	1,65 / 5,93	0,69 / 2,48
280	2049,05	1,7 / 6,09	0,71 / 2,54
290	2084,84	1,75 / 6,25	0,73 / 2,61
300	2120,52	1,8 / 6,41	0,75 / 2,67
310	2156,08	1,85 / 6,57	0,77 / 2,73
320	2191,52	1,9 / 6,72	0,79 / 2,8
330	2226,85	1,95 / 6,88	0,81 / 2,86
340	2262,06	2 / 7,03	0,83 / 2,92
350	2297,16	2,05 / 7,18	0,85 / 2,98
360	2332,14	2,1 / 7,33	0,87 / 3,04
370	2367,01	2,15 / 7,48	0,89 / 3,1
380	2401,76	2,2 / 7,63	0,91 / 3,16
390	2436,4	2,25 / 7,78	0,93 / 3,22
400	2470,92	2,3 / 7,92	0,95 / 3,27
410	2505,33	2,35 / 8,07	0,97 / 3,33
420	2539,62	2,4 / 8,21	0,99 / 3,39
430	2573,79	2,45 / 8,36	1,01 / 3,45
440	2607,85	2,5 / 8,5	1,03 / 3,5
450	2641,79	2,55 / 8,64	1,05 / 3,56
460	2675,62	2,6 / 8,78	1,07 / 3,61
470	2709,33	2,65 / 8,91	1,09 / 3,67
480	2742,93	2,7 / 9,05	1,11 / 3,72
490	2776,41	2,75 / 9,19	1,13 / 3,78
500	2809,78	2,8 / 9,32	1,15 / 3,83
510	2843,03	2,85 / 9,46	1,17 / 3,88
520	2876,16	2,9 / 9,59	1,19 / 3,94
530	2909,18	2,95 / 9,72	1,21 / 3,99
540	2942,08	3 / 9,85	1,23 / 4,04
550	2974,87	3,05 / 9,98	1,25 / 4,09

Diagramm der Toleranzklassen — Tolerance classes:
A: Tolerance class A; B: Tolerance class B;
y: Tolerance in °C; x: Temperature in °C

Accuracy classes

We offer cable temperature sensors in two tolerance classes. Tolerance class A is, however, more accurate than tolerance class B:

Deviations tolerance class A:	$in K = \pm (0,15 + 0,002 \| t \| *)$
Deviations tolerance class B:	$in K = \pm (0,3 + 0,005 \| t \| *)$
* Temperature value in °C

Accuracy classes

We offer cable temperature sensors in two tolerance classes. Tolerance class A is, however, more accurate than tolerance class B:

Deviations tolerance class A:
$in K = \pm (0,15 + 0,002 \| t \| *)$
Deviations tolerance class B:
$in K = \pm (0,3 + 0,005 \| t \| *)$
* Temperature value in °C

Which is more accurate? Pt100 or Pt1000?

The platinum resistors Pt100 and Pt1000 are offered in both tolerance class A and tolerance class B. This raises the question of which temperature sensor is more accurate. Tolerance class A is more accurate than tolerance class B. However, a Pt100 measuring resistor boasts similar measuring accuracy to a Pt1000 sensor of the same tolerance class. Nonetheless, both temperature sensors have different susceptibility to measuring errors, which is discussed in the following sections.

Influence of conductor resistance on accuracy

The temperature measurement with Pt100/Pt1000 is achieved through a change in electrical resistance. Other electrical resistances, such as the resistivity of connecting cables, have a negative impact on the measuring accuracy of the temperature measurement. The resistance depends on the material (usually copper), the length and the cross-section of the cable. The order of magnitude of the measuring error is shown using the example of a 50 m cable with 2-wire measurement.

Example: Calculation of conductor resistance for a 50 m cable

Specific Resistance

at 20°C

$ρ = 0,01786 \frac{Ω \cdot {mm}^{2}}{m}$

Cable length 50 m

Length out and back

$l = 100 m$

Conductor cross-section

d: Diameter

$A = 0,34 {mm}^{2}$

with

$A = \frac{1}{4} π d^{2}$

Formula:

$R = ρ \cdot \frac{l}{A}$

⟶

$R = 0,01786 \frac{Ω \cdot {mm}^{2}}{m} \cdot \frac{100 m}{{0,34 mm}^{2}}$

$= 5,25 Ω$

Example: Calculation of conductor resistance for a 50 m cable

Specific Resistance

at 20°C

$ρ = 0,01786 \frac{Ω \cdot {mm}^{2}}{m}$

Cable length 50 m

Length out and back

$l = 100 m$

Conductor cross-section

d: Diameter

$A = 0,34 {mm}^{2}$

with

$A = \frac{1}{4} π d^{2}$

Formula:

$R = ρ \cdot \frac{l}{A}$
$R = 0,01786 \frac{Ω \cdot {mm}^{2}}{m} \cdot \frac{100 m}{{0,34 mm}^{2}}$	$= 5,25 Ω$

If a Pt100 sensor is connected to the electronic measuring equipment via a 50 m cable, the actual measured resistance is 5.25 Ohm higher due to the conductor resistance, which obviously affects the temperature measurement. Each ohm of resistivity results in a measuring error of approx. 2.5 Kelvin. This results in a measuring error of approx. 13 °C. The resistance of a Pt1000 resistor is ten times greater than that of a Pt100 sensor, meaning the influence of the electrical conductor is ten times smaller. As explained in the example, the measuring error can be calculated and deducted from the actual measurement result. Alternatively, another measuring circuit can be used to compensate for the error.

Rule of thumb: “Each ohm of resistivity results in a measuring error of approx. 2.5 Kelvin.”

Patrick Targonski

Product Manager at autosen

2, 3 or 4-wire measurement?

There are several ways to connect a Pt resistance thermometer to the electronic measuring equipment. A distinction is made between 2, 3 and 4-wire measurements. With 2-wire measurement, the resistivity falsifies the measurement result. 3-wire and 4-wire measurements compensate the conductor resistance and provide a more accurate measurement result.

2-wire technology

The 2-wire circuit corresponds to the example given. The resistance and the resistivity are not distinguished by the electronic measuring equipment. The resistivity is included in the measurement as an error.

3-wire technology

The influence of the conductor resistance is to a large degree compensated in a 3-wire measurement. The prerequisite is that the resistivities are identical, something which can be assumed for 3-wire cables. The voltage error between the lines is measured and subtracted from the total voltage, thereby compensating for the resistivity.

4-wire technology

4-wire measurement is the ideal solution. Due to the symmetrical design, the resistivities are completely compensated.