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Signal Conditioning and Linearization of RTD
Sensors Collin Wells
Texas Instruments
HPA Precision Linear Applications
9/24/11
Introduction
• Primary Support
– 4-20mA Loop Drivers (XTRXXX)
– Gamma Buffers (BUFXXXXX)
• Other Support
– Temperature Sensors (TMP)
– IR Temperature Sensors (TMP006)
– OPA Stability
– Instrument Amplifiers
• Applications (Other)
– Industrial – Programmable Logic Controllers (PLC)
– RTD
– Reference Designs
Contents
•RTD Overview
•RTD Nonlinearity
•Analog Linearization
•Digital Acquisition and Linearization
What is an RTD?
• Resistive Temperature Detector
• Sensor with a predictable resistance vs. temperature
• Measure the resistance and calculate temperature based on the
Resistance vs. Temperature characteristics of the RTD material
200 100 0 100 200 300 400 500 600 700 8000
40
80
120
160
200
240
280
320
360
400
RTD Resistance vs. Temperature
Temperature (C)
Res
ista
nce
(O
hm
s)
RTD (Temp)PT100
α = 0.00385
RTDR
How does an RTD work?
• The product n*u decreases over temperature, therefore resistance
increases over temperature (PTC)
Resistance R L
A
Resistivity p1
e n
• Linear Model of Conductor Resistivity Change vs. Temperature
• L = Wire Length
• A = Wire Area
• e = Electron Charge
(1.6e-19 Coulombs)
• n = Electron Density
• u = Electron Mobility
t( ) 0 1 t t0
What is an RTD made of?
• Platinum (pt)
• Nickel (Ni)
• Copper (Cu)
Metal
Resistivity
(Ohm/CMF)
Gold (Au) 13
Silver (Ag) 8.8
Copper (Cu) 9.26
Platinum (Pt) 59
Tungsten (W) 30
Nickel (Ni) 36
•Have relatively linear change in resistance over temp
•Have high resistivity allowing for smaller dimensions
•Either Thin-Film or Wire-Wound
*Images from RDF Corp
How Accurate is an RTD? • Absolute accuracy is “Class” dependant - defined by DIN-IEC 60751. Allows for easy
interchangeability of field sensors
• Repeatability usually very good, allows for individual sensor calibration
• Long-Term Drift usually <0.1C/year, can get as low as 0.0025C/year
*AAA (1/10DIN) is not included in the DIN-IEC-60751 spec but is an industry accepted tolerance class for high-performance
measurements
**Manufacturers may choose to guarantee operation over a wider temperature range than the DIN-IEC60751 provides
Tolerance Class
(DIN-IEC 60751)
**Temperature Range of
Validity
Tolerance Values (C)
Resistance at
0C (Ohms)
Error
at
100C
(C)
Error over
Wire-
Wound
Range (C)
Wire-
Wound Thin-Film
*AAA (1/10 DIN) 0 - +100 0 - +100 +/-(0.03 + 0.0005*t) 100 +/- 0.012 0.08 0.08
AA (1/3DIN) -50 - +250 0 - +150 +/-(0.1 + 0.0017*t) 100 +/- 0.04 0.27 0.525
A -100 - +450 -30 - +300 +/-(0.15 + 0.002*t) 100 +/- 0.06 0.35 1.05
B -196 - +600 -50 - +500 +/-(0.3 + 0.005*t) 100 +/- 0.12 0.8 3.3
C -196 - +600 -50 - +600 +/-(0.6 + 0.01*t) 100 +/- 0.24 1.6 6.6
Why use an RTD?
Table Comparing Advantages and Disadvantages of Temp Sensors
How to Measure an RTD Resistance?
• Use a…….
Wheatstone Bridge or Current Source
Vmeas Vsource
RRTD
RA RRTD
1
2
MEASV
+-
RTDR
AR
AR
AR
+Vsource
MEASV+
-SOURCEIRTDR
Vmeas Isource RRTD
RRTD
Vmeas
Isource
Vmeas Isource RRTD
RRT D
2 RA Vmeas RA Vsource
Vsource 2 Vmeas
Note on Non-Linear Output of Bridge
Vmeas Vsource
RRTD
RA RRTD
1
2
Denominator causes a non-linear
output even for a linear sensor
MEASV
+-
RTD
100
100
100
+Vsource
ΔRTD = 50Ohms
Input resistance (ohms)
100.00 112.50 125.00 137.50 150.00
Voltage (
V)
0.00
125.00m
250.00m
375.00m
500.00m
Simple Current Source / Sink Circuits
+5V
+5V
1u
1u 10u
Vin
Temp
GND
Vout
Trim
U8 REF5025
Rset 25k
RTD 100
I_Out-
++
U9 OPA340
100.05uA
+5V
+5V
Q1
Rset 10k
RTD 100R3 40k
R4 10k
I_Out
+
-
+
U1 OPA333
100uA
+5V
+5VR8 40k
R9 10k
R12 10k
RTD 100
AM
5
Q2+
-
+
U2 OPA333
100uA
REF200
V2 2.5
V3 2.5
R1 1
0k
R2 200k
+
Vdiff -49.85m
+Vcm 2.5 R
3 4
9.9
C1 1
00n
+
+
-R1
R1
R2
INA326T1 INA326T
I_Out
R4 1
00
100uA
RTD Types and Their Parasitic Lead Resistances
RTDR
LR
LR
Red
White
RTDR
LR
LR
LR
Red
Red
White
RTDR
LR
LR
LR
LR
Red
Red
White
WhiteRTDR
LR
LR
LR
LR
Red
White
Blue
Blue
2-Wire 3-Wire
4-Wire 2-Wire with
Compensating
Loop
2-Wire Measurements
SOURCEMEASV+
-IRTDR
LR
LR
Vmeas Isource RRTD Isource 2 RL
Error Isource 2 RL
MEASV+-
RTDR
LR
LR
AR
A
R
A
R
+Vsource
Vmeas Vsource
RRTD 2RL
RA RRTD 2.RL
1
2
Error Vsource
2 RA RL
RA RRTD RA 2 RL RRTD
3-Wire Measurements
MEASV+
-
SOURCE1I
RTDR
LR
LR
SOURCE2I
LR
MEASV
+-
RTDR
LR
LR
AR
AR
ARLR
+Vsource
Vmeas Vsource
RRTD RL
RA RRTD 2 RL
1
2
Error Vsource
RL RA RRTD
RA RRTD RA 2 RL RRTD
+
-
+ -
Isource1 Isource2 I
Vmeas I RL I RRTD 2 I( ) RL I RRTD 3 I RL
Vmeas I RL 2 I( ) RL 3 I RL
Vmeas Vmeas I RRTD 3 I RL 3 I RL I RRTD
Error = 0 as long as Isource1 = Isource2 and RL are equal
4-Wire Measurements
MEASV+
-IRTDR
LR
LRLR
LR
Vmeas Isource RRTD
System Errors reduced to
measurement circuit accuracy Error Vsource
RL 2.0 RA 2.0 RRTD
RA RRTD RA 4.0 RL RRTD
MEASV
+-
RTDRLR
LR
AR
AR
AR
LR
+Vsource
LR
VmeasRA Vsource RA RRT D
2 RA2
6 RA RL 2 RRT D RA 4 RL2
2 RRT D RL
Self-Heating Errors of RTD
• Typically 2.5mW/C – 60mW/C
• Set excitation level so self-heating error is <10% of the total error
budget
1 105
1 104
1 103
0.01
1 107
1 106
1 105
1 104
1 103
0.01
0.1
1
10
Self-Heating Error of an RTD vs. Exciation Current
Current (A)
Tem
per
atu
re (
C)
Errorselfheat200nI( )
Errorselfheat0 I( )
Errorselfheat850 I( )
I
RTD Resistance vs Temperature Callendar-Van Dusen Equations
IEC 60751 PT-100 RTD (α = 0.00385)
Equation Constants for
R0 100
A 3.9083103
B 5.775 107
C 4.183 1012
For (T > 0) : RTD T( ) R0 1 A T B T2
For (T < 0) : RTD T( ) R0 1 A T B T2 C T
3 T 100( )
200 100 0 100 200 300 400 500 600 700 8000
40
80
120
160
200
240
280
320
360
400
RTD Resistance vs. Temperature
Temperature (C)
Res
ista
nce
(O
hm
s)
RTD (T)
RTD Nonlinearity
200 95 10 115 220 325 430 535 640 745 8500
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0
10
20
30
40
50
Nonlinearity and Temperature Error vs. Temperature
Temperature (C)
Tem
per
atu
re N
on
lin
eari
ty (
%F
SR
)
Tem
per
atu
re E
rro
r (C
)
200 95 10 115 220 325 430 535 640 745 8500
40
80
120
160
200
240
280
320
360
400
RTD Resistance vs. Temperature
Temperature (C)
Res
ista
nce
(O
hm
s)
RTD Temp( )
R LINFIT Temp( )
Linear fit between the two end-points
shows the Full-Scale nonlinearity
Nonlinearity = 4.5%
Temperature Error > 45C
RTD Nonlinearity
200 95 10 115 220 325 430 535 640 745 8500
45
90
135
180
225
270
315
360
405
450
RTD Resistance vs. Temperature
Temperature (C)
Res
ista
nce
(O
hm
s)
RTD Temp( )
RTDlinear(Temp)
For (T > 0) : RTD T( ) R0 1 A T B T2
For (T < 0) : RTD T( ) R0 1 A T B T2 C T
3 T 100( )
R0 100
A 3.9083103
B 5.775 107
C 4.183 1012
RTDlinear T( ) R0 1 A T( )
B and C terms are negative so
2nd and 3rd order effects
decrease the sensor output
over the sensor span.
Measurement Nonlinearity
MEASV+
-SOURCEIRTDR
Vmeas Isource RRTD
0 80 160 240 320 400 480 560 640 720 8000.01
0.0135
0.017
0.0205
0.024
0.0275
0.031
0.0345
0.038
0.0415
0.045
RTD Sensor Output vs. Temperature (Isource = 100uA)
Temperature (C)
Vo
ltag
e (V
)
VRTD (Temp)
V RTD_linear (Temp)
Correcting for Non-Linearity
MEASV+
-SOURCEIRTDR
Vmeas Isource RRTD
Sensor output decreases over span? Compensate by increasing excitation over span!
MEASV+
-SOURCEI RTDR
Vmeas (Isource RRTD
CORRECTIONI
+ Icorrection
Icorrection = gain*Vmeas+Offset
0 80 160 240 320 400 480 560 640 720 8000.01
0.0135
0.017
0.0205
0.024
0.0275
0.031
0.0345
0.038
0.0415
0.045
RTD Sensor Output vs. Temperature (Isource = 100uA)
Temperature (C)
Volt
age
(V)
VRTD (Temp)
V RTD_linear (Temp)
Increasing excitation source over measurement
span produces linear sensor output
Correcting for Non-linearity Isource 0.0005
VRTD T( ) RTD T( ) Isource
VRTD_linear T( ) RTDlinear T( ) Isource
Isource_correction T( ) Isource
VRTD_linear T( ) VRTD T( ) RTD T( )
VRTD_correction T( ) RTDlinear T( ) Isource_correction T( )
VRTD_linearized T( ) Isource_correction T( ) RTD T( )
200 100 0 100 200 300 400 500 600 700 8000
0.025
0.05
0.075
0.1
0.125
0.15
0.175
0.2
0.225
0.25
RTD Resistance vs. Temperature
Temperature (C)
Volt
age
(V) VRTD Temp( )
VRTD_correction Temp( )
VRTD_linearized Temp( )
Temp
Isource 0.0005
VRTD T( ) RTD T( ) Isource
VRTD_linear T( ) RTDlinear T( ) Isource
Isource_correction T( ) Isource
VRTD_linear T( ) VRTD T( ) RTD T( )
VRTD_correction T( ) RTDlinear T( ) Isource_correction T( )
VRTD_linearized T( ) Isource_correction T( ) RTD T( )
Analog Linearization Circuits
Analog Linearization Circuits Two-Wire Single Op-Amp
This circuit is designed for a 0-5V output for a 0-200C temperature span. Components R2, R3,
R4, and R5 are adjusted to change the desired measurement temperature span and output.
A voltage-controlled current
source is formed from the op-amp
output through R4 into the RTD
R2 49.13kR
1 4
.99k
R3 60.43k
R5 105.83k
R4 1
kV1 5
-
+
Vout
I_Correction
I_RTD
RT
D 1
00
Example
Amplifiers:
Low-Voltage:
OPA333
OPA376
High Voltage:
OPA188
OPA277
Analog Linearization Circuits Two-Wire Single Op-Amp
Temperature (C)
0.00 50.00 100.00 150.00 200.00
I_Correction (A)
0.00
12.50u
25.00u
37.50u
50.00u
I_RTD (A)
980.00u
988.00u
996.00u
1.00m
1.01m
Non-linear increase in excitation current over temperature
span will help correct non-linearity of RTD measurement
R2 49.13k
R1 4
.99k
R3 60.43k
R5 105.83k
R4 1
k
V1 5
-
+
Vout
I_Correction
I_RTD
RT
D 1
00
Analog Linearization Circuits Two-Wire Single Op-Amp
With
Co
rre
ctio
n
With
out
Lin
ear
izat
ion
Te
mp
era
ture
(C
)
0.0
02
5.0
05
0.0
07
5.0
01
00
.00
12
5.0
01
50
.00
17
5.0
02
00
.00
Vo
ltag
e (
V)
0.0
0
62
5.0
0m
1.2
5
1.8
8
2.5
0
3.1
3
3.7
5
4.3
8
5.0
0
With
out
Lin
ear
izat
ion
With
Co
rre
ctio
n
With Correction
Without Correction
Temperature (C)
0.00 25.00 50.00 75.00 100.00 125.00 150.00 175.00 200.00
Voltage (V)
0.00
625.00m
1.25
1.88
2.50
3.13
3.75
4.38
5.00
Without Correction
With Correction
This type of linearization typically provides a 20X - 40X
improvement in linearity
R2 49.13k
R1 4
.99k
R3 60.43k
R5 105.83k
R4 1
k
V1 5
-
+
Vout
I_Correction
I_RTD
RT
D 1
00
Analog Linearization Circuits Three-Wire Single INA A voltage-controlled current
source is formed from the INA
output through Rlin into the RTD
+15V
+15V
-15V
-15V
Vout
Rg 8
01
R1 4
.99k
V2 5
R2 4
.99k
RL3 1
RL1 1
RL2 1
Rz 1
00
V1 15
V3 15
++
-
Rg
Rg
Ref
U2 INA826
Rlin 105.83kI_Correction
RTD 100
I_RTD
I_Bias
Remote RTD
This circuit is designed for a 0-5V output
for a 0-200C temperature span.
Components Rz, Rg, and Rlin are adjusted
to change the desired measurement
temperature span and output.
Example
Amplifiers:
Low-Voltage:
INA333
INA114
High Voltage
INA826
INA114
Analog Linearization Circuits Three-Wire Single INA
With Correction
Without Correction
Temperature (C)
0.00 25.00 50.00 75.00 100.00 125.00 150.00 175.00 200.00
Voltage (V)
0.00
622.27m
1.25
1.87
2.50
3.12
3.75
4.37
5.00
Without Correction
With Correction
+15V
+15V
-15V
-15V
Vout
R6 8
01
R7 4
.99k
V2 5
R9 4
.99k
RL3 1
RL1 1
RL2 1
R14 1
00
V1 15
V3 15
R1 1
0k
++
-
Rg
Rg
Ref
U2 INA826
R2 105.83kI_Correction
RTD 175.8
I_RTD
I_Bias
Remote RTD
This type of linearization typically provides a 20X - 40X
improvement in linearity and some lead resistance cancellation
Analog Linearization Circuits XTR105 4-20mA Current Loop Output
R1 975
R2 25
-+O
A3
RL 250
i_Q1
Q1_INT
R4 1
kR
5 1
kR
_C
L 0
Iref1 800u
Iref2 800u
Rz 100
Rlin1 16.099k
V_PS 24
Rcm 1.5k
Rg 162.644Rlin 1k
-
+OA1
-
+OA2
i_jfet
VIN-
VCM
Q1
i_afe
I_Out
i_lin
VIN+
Q1_EXT
i_rtd
V_420
RTD 100
XTR105
With Correction
Without Correction
Temperature (C)
0.00 25.00 50.00 75.00 100.00 125.00 150.00 175.00 200.00
I_Out (A)
4.00m
6.00m
8.00m
10.00m
12.00m
14.00m
16.00m
18.00m
20.00m
Without Correction
With Correction
Analog Linearization Circuits XTR105 4-20mA Current Loop Output
Analog + Digital Linearization Circuits XTR108 4-20mA Current Loop Output
Digital Acquisition Circuits and Linearization Methods
Digital Acquisition Circuits ADS1118 16-bit Delta-Sigma 2-Wire Measurement with Half-Bridge
RTD
+Vsource
R
LR
LR
AR
RTDR
LR
LR
AR
AIN0
AIN1
AIN2
AIN3
Digital Acquisition Circuits ADS1220 24-bit Delta-Sigma Two 3-wire RTDs
RTDR
LR
LR
LR
RTDR
LR
LR
LR
REFR
+Vdig+Vsource
COMPR
3-wire + Rcomp shown for AIN2/AIN3
Digital Acquisition Circuits ADS1220 24-bit Delta-Sigma One 4-Wire RTD
RTDR
LR
LR
LR
LR
REFR
+Vdig+Vsource
Digital Acquisition Circuits ADS1247 24-bit Delta-Sigma Three-Wire + Rcomp
Digital Acquisition Circuits ADS1247 24-bit Delta-Sigma Four-Wire
Digital Linearization Methods • Three main options
– Linear-Fit
– Piece-wise Linear Approximations
– Direct Computations
0 80 160 240 320 400 480 560 640 720 8000.01
0.013
0.016
0.019
0.022
0.025
0.028
0.031
0.034
0.037
0.04
RTD Sensor Output vs. Temperature (Isource = 100uA)
Temperature (C)
Vo
ltag
e (V
)
VRTD(Temp)
Digital Linearization Methods Linear Fit
Pro’s:
•Easiest to implement
•Very Fast Processing Time
•Fairly accurate over small temp span
Con’s:
Least Accurate
0 80 160 240 320 400 480 560 640 720 8000.01
0.013
0.016
0.019
0.022
0.025
0.028
0.031
0.034
0.037
0.04
RTD Sensor Output vs. Temperature (Isource = 100uA)
Temperature (C)
Vo
ltag
e (
V)
VRTD Temp( )
VLin_Fit Temp( )
Temp
0 80 160 240 320 400 480 560 640 720 8000.01
0.013
0.016
0.019
0.022
0.025
0.028
0.031
0.034
0.037
0.04
RTD Sensor Output vs. Temperature (Isource = 100uA)
Temperature (C)
Volt
age (
V)
VRTD Temp( )
VLin_Fit(Temp)
Temp
End-point Fit Best-Fit
TLinear t( ) A RTD t( ) B
Digital Linearization Methods Piece-wise Linear Fit
Pro’s:
•Easy to implement
•Fast Processing Time
•Programmable accuracy
Con’s:
•Code size required for coefficients
0 80 160 240 320 400 480 560 640 720 8000.01
0.013
0.016
0.019
0.022
0.025
0.028
0.031
0.034
0.037
0.04
RTD Sensor Output vs. Temperature (Isource = 100uA)
Temperature (C)
Vo
ltag
e (V
)
VRTD(Temp)
VLin_Fit(Temp)
TPeicewise T n 1( ) T n( ) T n 1( )( )RT D RT Dn 1( )
RT Dn( ) RT Dn 1( )
Digital Linearization Methods Direct Computation
Pro’s:
•Almost Exact Answer, Least Error
•With 32-Bit Math Accuracy to +/-0.0001C
Con’s:
•Processor intensive
•Requires Math Libraries
•Negative Calculation Requires
simplification or bi-sectional solving
0 80 160 240 320 400 480 560 640 720 8000.01
0.013
0.016
0.019
0.022
0.025
0.028
0.031
0.034
0.037
0.04
RTD Sensor Output vs. Temperature (Isource = 100uA)
Temperature (C)V
olt
age
(V)
VRTD(Temp)TDirect t( )
A A2
4B 1RTD t( )
R0
2B+
Positive Temperature Direct Calculation
Negative Temperature Simplified Approximation
TDirect t( ) 241.96 2.2163RTD t( ) 2.8541103
RTD t( )2
9.9121 106
RTD t( )3
1.7052108
RTD t( )4
-TDirect t( ) 241.96 2.2163RTD t( ) 2.854110
3 RTD t( )
2 9.912110
6 RTD t( )
3 1.705210
8 RTD t( )
4
Digital Linearization Methods Direct Computation
-
-
RTDError 100 Res 60.256 Tlow 250 Thigh 50
TBisection RTDTemp 0
TmidTlow Thigh( )
2
Rcal 100 1 A Tmid BTmid2
Tmid 100( ) C Tmid3
Tmid 0if
Rcal 100 1 A Tmid B Tmid2
Tmid 0if
Rcal 0 Rcal 0if
RTDError Res Rcal
Tlow Tmid RTDError 0if
Thigh Tmid RTDError 0if
RTDError 0.0001( )while
RTDTemp Tmid
RTDTempreturn
99.999
TBisection 99.999
Bi-Section Method for Negative Temperatures
Questions/Comments?
Thank you!! Special Thanks to:
Art Kay
Bruce Trump
PA Apps Team
Mike Beckman
Omega Sensors
RDF Corp
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