RTD basic concept for Instrumentation and Electrical

RTD

1. Created by:
M.Dije
RTD (Resitance
Temperature
Detector)

2. ??????

3. RTD Characteristic
??????
??????=??????
01+�??????−??????
0+�??????−??????
0+ …
??????
??????=??????
��+????????????−??????
�

4. ??????
??????=??????
��+????????????−??????
�
0
50
100
150
200
250
300
350
400
-400 -200 0 200 400 600 800
Resistance (ohm)
Temperature (°C)
Resistance V Temperature -PT 100
??????
0=0°?????? →??????=100 ??????ℎ??????
100
138.5
??????=100°?????? →??????=138.5 ??????ℎ??????
Based on linear equation and boundary value
problems, we have
138.5=1001+??????100−0
??????=�.��??????????????????
Linear behavior
∴??????=
??????−���
�.??????????????????

5. Resistance Temperature tableAccuracy of the
various
approximation
Source :
https://realpars.com/pt100/
Source :
http://www.mosaic-
industries.com/embedded-
systems/microcontroller-
projects/temperature-
measurement/platinum-rtd-
sensors/resistance-calibration-table#excel-
spreadsheet-for-rtd-resistancetemperature-
computations

6. Construction of a RTD

7. Wheatstone Bridge
G
±
R1 R2
Rx R4
a
b c??????
1−?????? ??????
2−4
??????=??????
1−??????+??????
2−4
??????
1 and ??????
?????? are connected in series.
The value of ??????
1−?????? is given by:
??????
2 and ??????
4 are connected in series.
The value of ??????
2−4 is given by:
??????
1−??????=
??????
??????
1+??????
??????
V
??????
2−4=
??????
??????
2+??????
4
The change in voltage from node b
to node a is given by
??????
�−??????
�=??????
1−????????????
1=
??????
??????
1+??????
??????
??????
1 ??????
�−??????
�=??????
2−4??????
2=
??????
??????
2+??????
4
??????
2
The different voltage between b and c.
??????=??????
�−??????
�=??????
�−??????
�−??????
�−??????
�
The change in voltage from node c
to node a is given by
??????=
V
??????
2+??????
4
??????
2−
??????
??????
1+??????
??????
??????
1
??????=
??????
2??????
1+??????
??????−??????
1??????
2+??????
4
??????
1+??????
????????????
2+??????
4
?????? ??????=
??????
2??????
??????−??????
1??????
4
??????
1+??????
????????????
2+??????
4
??????

8. Wheatstone Bridge
G
±
R1 R2
Rx R4
a
b c??????
1−?????? ??????
2−4 V
??????=
??????
2??????
??????−??????
1??????
4
??????
1+??????
????????????
2+??????
4
??????
When this happen the parallel network is said to be unbalanced as the
voltage at point b is at different value to the voltage at point c.
Something else equally as important is that the voltage difference between
pointband pointcwill be zero volts as both points are at the same value.
When this happens, both sides of the parallel bridge network are said to
bebalanced.
In balanced condition the numerator of the function equal to zero.
??????
2??????
??????−??????
1??????
4=0
??????
2??????
??????=??????
1??????
4
??????
1
??????
3
=
??????
2
??????
4

9. 2 Wire RTD
G
±
R1 R2
Rx R4
a
b c??????
1−?????? ??????
2−4 V

10. 2 Wire RTD
G
±
R1 R2
Rx R4
a
b c??????
1−?????? ??????
2−4 V

11. 2 Wire RTD
G
±
R1 R2
R4
a
b
c??????
1−?????? ??????
2−4 V
Rx
RL1
RL2
??????
??????????????????=??????
??????1+??????
??????+??????
??????2
Let ??????
1, ??????
2, ??????
4 are equal value so that ??????
1=??????
2=??????
4=??????
Consider ??????
?????? changes based on temperature so that
??????
??????=??????+∆??????
Based on unbalanced wheatstone circuit equation.
Now circuit shown consist of 3 resistors, ??????
??????1, ??????
??????2, and
??????
?????? connected together in series, we have
??????=
??????
2??????
??????????????????−??????
1??????
4
??????
1+??????
????????????????????????
2+??????
4
??????
??????=
????????????
??????1+??????
??????+??????
??????2−????????????
??????+??????
??????1+??????
??????+??????
??????2??????+??????
??????
??????=
????????????
??????1+??????
??????+??????
??????2−??????
??????+??????
??????1+??????
??????+??????
??????22??????
??????
??????=
??????
??????1+??????+∆??????+??????
??????2−??????
??????+??????
??????1+??????+∆??????+??????
??????22
??????
??????=
??????
??????1+∆??????+??????
??????2
4??????+2??????
??????1+∆??????+??????
??????2
??????

12. 2 Wire RTD
G
±
R1 R2
R4
a
b
c??????
1−?????? ??????
2−4 V
Rx
RL1
RL2
??????
??????????????????=??????
??????1+??????
??????+??????
??????2
??????=
??????
??????1+∆??????+??????
??????2
4??????+2??????
??????1+∆??????+??????
??????2
??????
Suppose that ??????
??????1=??????
??????2=??????
??????
??????=
∆??????+2??????
??????
4??????+22??????
??????+∆??????
??????

13. 3 Wire RTD
±
G
R1 R2
R4
a
b
c
V
Rx
RL1
RL2
RL3
Let ??????
1, ??????
2, ??????
4 are equal value so that ??????
1=??????
2=??????
4=??????
Consider ??????
?????? changes based on temperature so that
??????
??????=??????+∆??????
The different voltage between b and c.
??????=??????
�−??????
�=??????
�−??????
�−??????
�−??????
�
•Using voltage divider, the voltage
change from node c to node a is
given by:
??????
�−??????
�=
??????
2
??????
2+??????
4
??????
??????
�−??????
�=
??????
??????+??????
??????
??????
�−??????
�=
1
2
??????

14. 3 Wire RTD
±
G
R1 R2
R4
a
b
c
V
Rx
RL1
RL2
RL3
??????
1=??????
2=??????
4=??????
??????
??????=??????+∆??????
??????=??????
�−??????
�=??????
�−??????
�−??????
�−??????
�
??????
�−??????
�=
1
2
??????
•Look in the picture below, the
voltage change from node b to
node a is given by:
a
b c
R1
RL1
Rx
RL2

15. THANKS