Signal Conditioning and
Linearization of RTD
Sensors
9/24/11
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
RTD Resistance vs. Temperature
400
360
320
R RTD
RTD (Temp)
Resistance (Ohms)
280
240
PT100
200
α = 0.00385
160
120
80
40
0
 200
 100
0
100
200
300
400
Temperature (C)
500
600
700
800
How does an RTD work?
• L = Wire Length
 L
Resi stan ce R
Resi sti v it y p
• A = Wire Area
A
• e = Electron Charge
(1.6e-19 Coulombs)
1
• n = Electron Density
e n  
• u = Electron Mobility
• The product n*u decreases over temperature, therefore resistance
increases over temperature (PTC)
• Linear Model of Conductor Resistivity Change vs. Temperature
( t)



0 1   t  t0
What is an RTD made of?
• Platinum (pt)
Metal
• Nickel (Ni)
• Copper (Cu)
•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
Resistivity
(Ohm/CMF)
Gold (Au)
13
Silver (Ag)
8.8
Copper (Cu)
9.26
Platinum (Pt)
59
Tungsten (W)
30
Nickel (Ni)
36
How Accurate is an RTD?
• Absolute accuracy is “Class” dependant - defined by DIN-IEC 60751. Allows for easy
interchangeability of field sensors
**Temperature Range of
Validity
Error
at
100C
(C)
Error over
WireWound
Range (C)
Tolerance Class
(DIN-IEC 60751)
WireWound
Thin-Film
Tolerance Values (C)
Resistance at
0C (Ohms)
*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
*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
• Repeatability usually very good, allows for individual sensor calibration
• Long-Term Drift usually <0.1C/year, can get as low as 0.0025C/year
Why use an RTD?
Table Comparing Advantages and Disadvantages of Temp Sensors
How to Measure an RTD Resistance?
• Use a…….
Current Source
or
Wheatstone Bridge
+Vsource
RA
RA
+
-
ISOURCE
-
VMEAS
RA
Vmeas
Vmeas
RRTD
Isource  RRTD
Isource RRTD
Vmeas
Isource
VMEAS
+
RRTD
RRTD
 RRTD  1
Vmeas Vsource 
 

 RA  RRTD  2
RRTD
2 RA Vmeas  RA Vsource
Vsource  2 Vmeas
Note on Non-Linear Output of Bridge
 RRTD 
Vmeas Vsource  

RA  RRTD


1

2

+Vsource
100
100
-
100
+
Denominator causes a non-linear
output even for a linear sensor
ΔRTD = 50Ohms
VMEAS
RTD
500.00m
Voltage (V)
375.00m
250.00m
125.00m
0.00
100.00
112.50
125.00
Input resistance (ohms)
137.50
150.00
Simple Current Source / Sink Circuits
+5V
+5V
REF200
R9 10k
RTD 100
+5V
R12 10k
U1 OPA333
+
-
Q1
R4 10k
+
+
Q2
U2 OPA333
-
I_Out 100uA
R8 40k
+5V
Rset 10k
V3 2.5
U8 REF5025
R2 200k
-
Vout
R1
INA326T1 INA326T
+
10u
Vdiff -49.85m
GND Trim
R1 +
+
1u
Rset 25k
Vcm 2.5
+5V
+
V2 2.5
I_Out 100.05uA
C1 100n
-
R2
R3 49.9
Tem p
+
U9 OPA340
RTD 100
R4 100
Vin
1u
RTD 100
+
+5V
100uA
R1 10k
+
AM5
R3 40k
I_Out 100uA
RTD Types and Their Parasitic Lead Resistances
RL
2-Wire
RL
White
3-Wire
RRTD
White
RRTD
Red
Red
RL
RL
Red
RL
RL
RL
4-Wire
White
White
RRTD
Red
RL
RRTD
2-Wire with
Compensating
Loop
Red
RL
RL
RL
Blue
Blue
Red
RL
White
RL
2-Wire Measurements
+Vsource
A
RL
+
-
I SOURCE
Isource  RRTD  Isource  2 RL
Error Isource  2RL
VMEAS
RRTD
RA
RL
-
VMEAS
+
RRTD
Vmeas
RA
R
RL
RL
 RRTD  2RL 
Vmeas Vsource  


 RA  RRTD  2.RL 
1


2
2 RA  RL


Error Vsource 

RA  RRTD   RA  2 RL  RRTD



3-Wire Measurements
+Vsource
ISOURCE1
RL
RA
VMEAS
ISOURCE2
VMEAS
RL
+
-
-
RRTD
RL
RA
+
RL
RA
RL
RRTD
RL
Isource1
Isource2
Vmeas I RL  I RRTD  ( 2 I)  RL
+
Vmeas I RL  ( 2 I)  RL
Vmeas  Vmeas
+
RRTD  RL


Vmeas Vsource 

RA  RRTD  2 RL


I
I RRTD  3 I RL
3 I RL
I RRTD  3 I RL  3 I RL
1


2
RL  RA  RRTD


Error Vsource  

RA  RRTD   RA  2 RL  RRTD



I RRTD
Error = 0 as long as Isource1 = Isource2 and RL are equal
4-Wire Measurements
+Vsource
RL
RL
RA
-
I
RL
VMEAS
+
VMEAS
-
RL
RL
+
RRTD
RA
RL
RRTD
RA
RL
Vmeas
RL
Isource  RRTD
Vmeas


RA  Vso urce RA  RRTD

2
2
2 RA  6 RA  RL  2 RRTD RA  4 RL  2 RRTD RL
System Errors reduced to
measurement circuit accuracy
RL  2.0 RA  2.0 RRTD


Error Vsource 

RA  RRTD   RA  4.0 RL  RRTD



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
Self-Heating Error of an RTD vs. Exciation Current
10
1
Temperature (C)
0.1
Errorselfheat200n( I)
Errorselfheat0( I)
Errorselfheat850( I)
0.01
110
110
110
110
3
4
5
6
7
110
5
110
110
4
110
I
Current (A)
3
0.01
RTD Resistance vs Temperature
Callendar-Van Dusen Equations
Equation Constants for
 2
2
3
RTD( T)  R0 1  A  T  B  T   C  T   ( T  100)
For (T > 0) : RTD( T)  R0 1  A  T  B T
For (T < 0) :
IEC 60751 PT-100 RTD (α = 0.00385)
R0   1 00
3
A   3 .90 83
1 0
RTD Resistance vs. Temperature
7
400
B   5 .77 5 1 0
360
 12
C   4 .18 3 1 0
320
RTD (T)
Resistance (Ohms)
280
240
200
160
120
80
40
0
 200
 100
0
100
200
300
400
Temperature (C)
500
600
700
800
RTD Nonlinearity
RTD Resistance vs. Temperature
400
Linear fit between the two end-points
shows the Full-Scale nonlinearity
360
320
RTD( Temp)
R LINFIT( Temp)
Nonlinearity and Temperature Error vs. Temperature
Resistance (Ohms)
280
240
200
160
120
5
50
80
4.5
40
0
 200
3.5
3
30
2.5
2
20
1.5
1
10
0.5
0
 200
 95
10
115
220
325
430
Temperature (C)
535
640
745
0
850
Temperature Error (C)
Temperature Nonlinearity (%FSR)
40
4
 95
10
115
220
325
430
Temperature (C)
Nonlinearity = 4.5%
Temperature Error > 45C
535
640
745
850
RTD Nonlinearity
 2
2
3
RTD( T)  R0 1  A  T  B  T   C  T   ( T  100)
For (T > 0) : RTD( T)  R0 1  A  T  B T
For (T < 0) :
R0   1 00
RTDlinear ( T)  R0 ( 1  A  T)
RTD Resistance vs. Temperature
450
3
A   3 .90 83
1 0
405
7
B   5 .77 5 1 0
360
 12
C   4 .18 3 1 0
RTD( Temp)
RTD linear (Temp)
B and C terms are negative so
2nd and 3rd order effects
decrease the sensor output
over the sensor span.
Resistance (Ohms)
315
270
225
180
135
90
45
0
 200
 95
10
115
220
325
430
Temperature (C)
535
640
745
850
Measurement Nonlinearity
+
RRTD
VMEAS
ISOURCE
-
Vmeas
Isource  RRTD
RTD Sensor Output vs. Temperature (Isource = 100uA)
0.045
0.0415
0.038
V RTD (Temp)
V RTD_linear (Temp)
Voltage (V)
0.0345
0.031
0.0275
0.024
0.0205
0.017
0.0135
0.01
0
80
160
240
320
400
480
Temperature (C)
560
640
720
800
Correcting for Non-Linearity
Sensor output decreases over span? Compensate by increasing excitation over span!
RRTD
+
VMEAS

ISOURCE
-
+
I SOURCE
RRTD
VMEAS
-
I CORRECTION
Icorrection = gain*Vmeas+Offset
Vmeas
Vmeas (Isource + I correction   R RTD
Isource  RRTD
RTD Sensor Output vs. Temperature (Isource = 100uA)
0.045
0.0415
Increasing excitation source over measurement
span produces linear sensor output
0.038
V RTD (Temp)
V RTD_linear (Temp)
Voltage (V)
0.0345
0.031
0.0275
0.024
0.0205
0.017
0.0135
0.01
0
80
160
240
320
400
480
Temperature (C)
560
640
720
800
VRTD_linear ( T)  RTDlinear ( T)  Isource
Correcting for Non-linearity
Isource  0.0005
Isource_correction ( T)  Isource 
VRTD( T)  RTD( T)  Isource
VRTD_linear (T)  VRTD( T) 
RTD( T)
VRTD_correction ( T)  RTDlinear ( T)  Isource_correction ( T)
VRTD_linear ( T)  RTDlinear ( T)  Isource
Isource_correction ( T)  Isource 
0.25
VRTD_linearized ( T)  Isource_correction ( T)  RTD( T)
Resistance vs. Temperature
VRTD_linear (T)  VRTD
RTD( T) 
RTD( T)
0.225
VRTD_correction ( T)  RTDlinear
( T)  Isource_correction ( T)
0.2
0.175
Voltage (V)
VRTD_linearized ( T)  Isource_correction ( T)  RTD( T)
VRTD ( Temp )
0.15
VRTD_correction ( Temp )
0.125
VRTD_linearized ( Temp )
0.1
0.075
0.05
0.025
0
 200
 100
0
100
200
300
Temp
Temperature (C)
400
500
600
700
800
Analog Linearization
Circuits
Analog Linearization Circuits
Two-Wire Single Op-Amp
R2 49.13k
Example
Amplifiers:
R3 60.43k
Low-Voltage:
R4 1k
V1 5
R1 4.99k
Vout
OPA333
OPA376
+
High Voltage:
OPA188
OPA277
R5 105.83k
RTD 100
I_Correction
A voltage-controlled current
source is formed from the op-amp
I_RTD
output through R4 into the RTD
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.
R2 49.13k
Analog Linearization Circuits
R4 1k
R1 4.99k
Vout
V1 5
Two-Wire Single Op-Amp
R3 60.43k
+
R5 105.83k
I_Correction
RTD 100
Non-linear increase in excitation current over temperature
span will help correct non-linearity of RTD measurement
I_RTD
50.00u
37.50u
I_Correction (A)25.00u
12.50u
0.00
1.01m
1.00m
I_RTD (A)
996.00u
988.00u
980.00u
0.00
50.00
100.00
Temperature (C)
150.00
200.00
75.00
R2 49.13k
V1 5
Two-Wire Single Op-Amp
R4 1k
Vout
R1 4.99k
50.00
Analog Linearization Circuits
R3 60.43k
+
R5 105.83k
I_Correction
25.00
RTD 100
This type of linearization typically provides a 20X - 40X
improvement in linearity
I_RTD
0.00
5.00
(V)
3.13
0.00
1.25
1.88
3.75
625.00m
Voltage (V)
2.50
4.38
Without Correction
2.50
With Correction
1.88
1.25
625.00m
0.00
0.00
25.00
50.00
75.00
100.00
125.00
Temperature (C)
150.00
175.00
200.00
Analog Linearization Circuits
Three-Wire Single INA
V1 15
I_Bias
R2 4.99k
R1 4.99k
+15V
A voltage-controlled current
source is formed from the INA
output through Rlin into the RTD
Example
Amplifiers:
Low-Voltage:
I_Correction
INA333
INA114
Rlin 105.83k
V2 5
-15V
-15V
Rg
Rg 801
Rz 100
V3 15
Ref
Rg
+
+
U2 INA826
High Voltage
INA826
INA114
+15V
RTD 100
Remote RTD
RL3 1
RL2 1
I_RTD
RL1 1
Vout
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.
V1 15
Analog Linearization Circuits
I_Correction
R2 105.83k
V2 5
-15V
V3 15
Rg
RL3 1
RL2 1
RL1 1
5.00
U2 INA826
+15V
I_RTD
This type of linearization typically provides a 20X - 40X
improvement in linearity and some lead resistance cancellation
Vout
Ref
Rg
+
+
RTD 175.8
Remote RTD
4.37
3.75
3.12
Voltage (V)
Without Correction
2.50
With Correction
1.87
1.25
622.27m
0.00
0.00
25.00
50.00
75.00
100.00 125.00
Temperature (C)
150.00
175.00
200.00
R1 10k
-15V
R6 801
R14 100
Three-Wire Single INA
I_Bias
R9 4.99k
R7 4.99k
+15V
Analog Linearization Circuits
XTR105 4-20mA Current Loop Output
XTR105
Iref1 800u
i_lin
OA1
+
i_rtd
Q1_EXT
Q1_INT
R5 1k
VIN+
i_jfet
Iref2 800u
R4 1k
Rlin1 16.099k
Rlin 1k
OA3
R_CL 0
Rg 162.644
VIN-
V_PS 24
+
-
+
Q1
OA2
Rz 100
RTD 100
VCM
i_afe
Rcm 1.5k
R2 25
R1 975
V_420
I_Out
i_Q1
RL 250
Analog Linearization Circuits
XTR105 4-20mA Current Loop Output
20.00m
18.00m
16.00m
14.00m
Without Correction
I_Out (A) 12.00m
10.00m
With Correction
8.00m
6.00m
4.00m
0.00
25.00
50.00
75.00
100.00
Temperature (C)
125.00
150.00
175.00
200.00
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
+V source
RA
RL
RRTD
RL
RL
RRTD
RA
AIN0
AIN1
AIN2
AIN3
RL
Digital Acquisition Circuits
ADS1220 24-bit Delta-Sigma Two 3-wire RTDs
R REF
+V source
RL
RL
R RTD
RL
RL
RL
R COMP
R RTD
RL
3-wire + Rcomp shown for AIN2/AIN3
+Vdig
Digital Acquisition Circuits
ADS1220 24-bit Delta-Sigma One 4-Wire RTD
R REF
+V source
RL
RL
R RTD
RL
RL
+Vdig
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
RTD Sensor Output vs. Temperature (Isource = 100uA)
0.04
0.037
0.034
V RTD (Temp)
Voltage (V)
0.031
0.028
0.025
0.022
0.019
0.016
0.013
0.01
0
80
160
240
320
400
480
Temperature (C)
560
640
720
800
Digital Linearization Methods
Linear Fit
Pro’s:
Con’s:
•Easiest to implement
Least Accurate
•Very Fast Processing Time
•Fairly accurate over small temp span
TLinear ( t)
A  RTD( t)  B
End-point Fit
Best-Fit
V Lin_Fit ( Temp)
RTD Sensor Output vs. Temperature (Isource = 100uA)
0.04
0.04
0.037
0.037
0.034
0.034
0.031
0.031
0.028
V RTD( Temp)
0.025
V Lin_Fit (Temp)
Voltage (V)
V RTD( Temp )
Voltage (V)
RTD Sensor Output vs. Temperature (Isource = 100uA)
0.028
0.025
0.022
0.022
0.019
0.019
0.016
0.016
0.013
0.013
0.01
0
80
160
240
320
400
480
Temp
Temperature (C)
560
640
720
800
0.01
0
80
160
240
320
400
480
Temp
Temperature (C)
560
640
720
800
Digital Linearization Methods
Piece-wise Linear Fit
Pro’s:
Con’s:
•Easy to implement
•Code size required for coefficients
•Fast Processing Time
•Programmable accuracy
RTD  RTD( n  1) 
TP ei cewi se T( n  1)  ( T( n)  T( n  1) ) 

RTD( n)  RTD( n  1)


RTD Sensor Output vs. Temperature (Isource = 100uA)
0.04
0.037
0.034
V RTD (Temp)
V Lin_Fit (Temp)
Voltage (V)
0.031
0.028
0.025
0.022
0.019
0.016
0.013
0.01
0
80
160
240
320
400
480
Temperature (C)
560
640
720
800
Digital Linearization Methods
Direct Computation
Pro’s:
Con’s:
•Almost Exact Answer, Least Error
•Processor intensive
•With 32-Bit Math Accuracy to +/-0.0001C
•Requires Math Libraries
•Negative Calculation Requires
simplification or bi-sectional solving
RTD Sensor Output vs. Temperature (Isource = 100uA)
0.04
Positive Temperature Direct Calculation
RTD( t) 
A  A  4B  1 
R0 


0.037
0.034
2
V RTD (Temp)
2B
Voltage (V)
TDirect( t)
+
0.031
0.028
0.025
0.022
0.019
0.016
Negative Temperature Simplified Approximation
3
0.013
2
0.01
0
80
160
6
TDirect ( t) 241.96  2.2163 RTD ( t)  2.8541 10  RTD ( t)  9.9121 10
3
2
6
3
8
4
0  RTD( t)  9.9121 10  RTD( t )  1.705210

 RTD( t )
240
320
3
400
480
560
640
8
 RTD ( t)  1.7052 10
Temperature (C)
720
800
 RTD ( t
Digital Linearization Methods
Direct Computation
Bi-Section Method for Negative Temperatures
RTDError  100
TBisection 
-
Res  60.256
Tlow  250
Thigh  50
RTDTemp  0
 99.999
while ( RTDError  0.0001)
Tmid 
( Tlow  Thigh )
2
Rcal  100 1  A  Tmid  B Tmid  ( Tmid  100)  C Tmid
2

Rcal  100 1  A  Tmid  B Tmid
Rcal  0 if Rcal  0
RTDError  Res  Rcal
Tlow  Tmid if RTDError  0
Thigh  Tmid if RTDError  0
RTDTemp  Tmid
return RTDTemp
TBisection  99.999
-

2
if Tmid  0
3
 if Tmid  0
Questions/Comments?
Thank you!!
Special Thanks to:
Omega Sensors
RDF Corp