RTD

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Latest revision as of 22:14, 16 July 2008

RTD = Resistive Temperature Device

Common type of RTD is Pt-100, which is a temperature sensor made from platinum. Resistance varies with temperature. 100Ω at 0 °C.

Pt-100

Temperature	Resistance
Temperature	Pt-100 α=0.003750 °C^-1	Pt-100 α=0.003850 °C^-1
°C	Ω	Ω
-200	19.9	18.5
-100	61.2	60.3
0	100	100
100	138	139
200	174	176
300	209	212
400	243	247
500	275	281
600	307	314
700	337	345
800	366	376
850	380	390

Callendar-Van Dusen Equation

Given from RTD manufacturer:

Alpha, α
Delta, δ
Beta, β

Calculated from α, δ & β:

A = <math>\alpha + \frac{\alpha \times \delta}{100}</math>

B = <math>-\frac{\alpha \times \delta}{100^2}</math>

C = <math>-\frac{\alpha \times \beta}{100^4}</math>

Given:

R_T = Resistance (Ω) at T°C
R₀ = Resistance (Ω) at 0°C (100 Ω for Pt-100)
T = Temperature in °C

Temperature according to ITS-90 (International Temperature Scale of 1990.

Calculated

R_T = R₀ x (1 + A x T + B x T² + (T-100 °C) x C x T³)	for T < 0 °C
R_T = R₀ x (1 + A x T + B x T²)	for T > 0 °C

Callendar-Van Dusen Constants

Constants

The purity of the metal will determine the constants.

Given			Calculated
Alpha, α	Delta, δ	Beta, β	A	B	C
°C^-1	°C	°C	°C^-1	°C^-2	°C^-4
0.003750	1.605	0.16	0.381 x 10^-3	-6.02 x 10^-7	-6.0 x 10^-12
0.003850	1.4999	0.10863	3.908 x 10^-3	-5.775 x 10^-7	-4.183 x 10^-12
0.003902	1.52	0.11	3.96 x 10^-3	-5.93 x 10^-7	-4.3 x 10^-12
0.003911			3.9692 × 10^-3	–5.8495 × 10^-7	–4.233 × 10^-12
0.003916			3.9739 × 10^-3	–5.870 × 10^-7	–4.4 × 10^-12
0.003920			3.9787 × 10^-3	–5.8686 × 10^-7	–4.167 × 10^-12
0.003928			3.9888 × 10^-3	–5.915 × 10^-7	–3.85 × 10^-12

Alpha, α, is sometimes known as TCR

0.003850 is according to IEC 751-2 standard. Made from 99.99% pure platinum.

Typical data

Standard	Typical data
Standard	α	Tolerance	R₀
BS EN 60751 1996	0.003850 °C^-1	±0.05%, ±0.03%, ±0.02%, ±0.01%	100 Ω
DIN 43760 1980	0.003850 °C^-1	±0.05% (1/2 DIN B), ±0.03% (1/3 DIN B), ±0.02% (1/5 DIN B), ±0.01% (1/10 DIN B)	100 Ω
IEC 60751:1995	0.003850 °C^-1	±0.05%, ±0.03%, ±0.02%, ±0.01%	100 Ω
JIS C1604 - 1981 (Japanese Industrial Standard)	0.003916 °C^-1	±0.15ºC, ±0.2ºC, ±0.5ºC	100 Ω or 50 Ω
US Standard Curve	0.003916 °C^-1	±0.1 ohms	100 Ω or 50 Ω
BS 2G 148 (British Aircraft Industry)	0.003900 °C^-1	±0.1% (at 0ºC)	130 Ω

Graph

Temperature vs Resistance

Non linearity

This graph shows the affect of B & C in the Callendar-Van Dusen equation. Percentage error if the RTD would have been assumed to be linear.

Standards

IEC 60751:1995
BS EN 60751 1996
DIN 43760 1980
BS 2G 148

Sources

Contributors

Joakim Ögren

@@ Line 8: / Line 8: @@
 ! rowspan="2" | Temperature  !! colspan="2" | Resistance
 |-
-                 ! Pt-100<br/>0.003750                     !! Pt-100<br/>0.003850
+                 ! Pt-100<br/>&alpha;=0.003750 °C<sup>-1</sup> !! Pt-100<br/>&alpha;=0.003850 °C<sup>-1</sup>
 |-
 ! °C           !! &Omega;                                 !! &Omega;
@@ Line 33: / Line 33: @@
 |-
 | 800          || <rtd>800 100 0.003750 1.605 0.16</rtd> || <rtd>800 100 0.003850 1.4999 0.10863</rtd>
+|-
+| 850          || <rtd>850 100 0.003750 1.605 0.16</rtd> || <rtd>850 100 0.003850 1.4999 0.10863</rtd>
 |}
@@ Line 56: / Line 58: @@
 R<sub>0</sub> = Resistance (&Omega;) at 0°C (100 &Omega; for Pt-100)<br/>
 T = Temperature in °C
+''Temperature according to ITS-90 (International Temperature Scale of 1990.''
 '''Calculated'''
@@ Line 91: / Line 95: @@
 |}
-''Alpha, &alpha, is sometimes known as TCR''
+''Alpha, &alpha;, is sometimes known as TCR''
-''0.003850 is according to IEC 751-2 (ITS90) standard. Made from 99.99% pure platinum.''
+''0.003850 is according to IEC 751-2 standard. Made from 99.99% pure platinum.''
 === Typical data ===
@@ Line 100: / Line 104: @@
 ! rowspan="2" | Standard                          !! colspan="3" | Typical data
 |-
-                                                    ! &alpha;                  !! Tolerance                      !! R<sub>0</sub>
+                                                    ! &alpha;                   !! Tolerance                      !! R<sub>0</sub>
 |-
-| BS EN 60751 1996                                || 0.003850 °C<sup>-1</sup> || ±0.05%, ±0.03%, ±0.02%, ±0.01% || 100 &Omega;
+| BS EN 60751 1996                                || 0.003850 °C<sup>-1</sup>  || ±0.05%, ±0.03%, ±0.02%, ±0.01% || 100 &Omega;
 |-
-| DIN 43760 1980                                  || 0.003850 °C<sup>-1</sup> || ±0.05% (1/2 DIN B), ±0.03% (1/3 DIN B), ±0.02% (1/5 DIN B), ±0.01% (1/10 DIN B) || 100 &Omega;
+| DIN 43760 1980                                  || 0.003850 °C<sup>-1</sup>  || ±0.05% (1/2 DIN B), ±0.03% (1/3 DIN B), ±0.02% (1/5 DIN B), ±0.01% (1/10 DIN B) || 100 &Omega;
 |-
-| IEC 751 1995                                    || 0.003850 °C<sup>-1</sup> || ±0.05%, ±0.03%, ±0.02%, ±0.01% || 100 &Omega;
+| IEC 60751:1995                                  || 0.003850 °C<sup>-1</sup>  || ±0.05%, ±0.03%, ±0.02%, ±0.01% || 100 &Omega;
 |-
-| JIS C1604 - 1981 (Japanese Industrial Standard) || 0.003916 °C<sup>-1</sup> || ±0.15ºC, ±0.2ºC, ±0.5ºC        || 100 &Omega; or 50 &Omega;
+| JIS C1604 - 1981 (Japanese Industrial Standard) || 0.003916 °C<sup>-1</sup>  || ±0.15ºC, ±0.2ºC, ±0.5ºC        || 100 &Omega; or 50 &Omega;
 |-
-| US Standard Curve                               || 0.003916 °C<sup>-1</sup> || ±0.1 ohms                      || 100 &Omega; or 50 &Omega;
+| US Standard Curve                               || 0.003916 °C<sup>-1</sup>  || ±0.1 ohms                      || 100 &Omega; or 50 &Omega;
 |-
-| BS 2G 148 (British Aircraft Industry)           || 0.003900 °C<sup>-1</sup> || ±0.1% (at 0ºC)                 || 130 &Omega;
+| BS 2G 148 (British Aircraft Industry)           || 0.003900 °C<sup>-1</sup>  || ±0.1% (at 0ºC)                 || 130 &Omega;
 |}
@@ Line 162: / Line 166: @@
     set ytics 0,1
     set xtics 50
-   alpha = 0.003750
-   delta = 1.605
-   beta = 0.16
     R0 = 100
-    A = alpha + (alpha * delta)/100
-    B = -(alpha * delta)/(100**2)
+   alpha1 = 0.003750
-    C = -(alpha*beta)/(100**4)
+   delta1 = 1.605
-    CParam(T) = T>0 ? 0 : (T-100)*C*(T**3)
+   beta1 = 0.16
-    dev(T) = ((1 + A*T)/(1 + A*T + B*(T**2) + CParam(T)))*100-100
+    A1 = alpha1 + (alpha1*delta1)/100
-    plot [x=-200:850] dev(x) title "Pt-100 (0.003750)"
+    B1 = -(alpha1*delta1)/(100**2)
+    C1 = -(alpha1*beta1)/(100**4)
+    C1Param(T) = T>0 ? 0 : (T-100)*C1*(T**3)
+    dev1(T) = ((1 + A1*T)/(1 + A1*T + B1*(T**2) + C1Param(T)))*100-100
+   alpha2 = 0.003850
+   delta2 = 1.4999
+   beta2 = 0.10863
+   A2 = alpha2 + (alpha2*delta2)/100
+   B2 = -(alpha2*delta2)/(100**2)
+   C2 = -(alpha2*beta2)/(100**4)
+   C2Param(T) = T>0 ? 0 : (T-100)*C2*(T**3)
+   dev2(T) = ((1 + A2*T)/(1 + A2*T + B2*(T**2) + C2Param(T)))*100-100
+    plot [x=-200:850] dev1(x) title "Pt-100 (0.003750)",dev2(x) title "Pt-100 (0.003850)"
 </gnuplot>
 == Standards ==
-* IEC 751:1995
+* IEC 60751:1995
 * BS EN 60751 1996
 * DIN 43760 1980
@@ Line 181: / Line 198: @@
 == Sources ==
-* [http://www.t-d-i.co.uk/pdfs/tdi-cat.pdf Thermal Developments International Ltd.: Hand made platinum resistance
+* [http://www.t-d-i.co.uk/pdfs/tdi-cat.pdf Thermal Developments International Ltd.: Hand made platinum resistance temperature detectors]
-temperature detectors]
 * [http://content.honeywell.com/sensing/prodinfo/temperature/technical/c15_136.pdf Honeywell - Sensing and Control: Reference and Application Data - Temperature Sensors Platinum RTDs]
 * [http://www.pentronic.se/eng/katalog/pdf/4/4_1-7.pdf Pentronic: Platinum resistance thermometers]

RTD