Signal Conditioning and Linearization of RTD

SensorsCollin Wells

Texas Instruments

HPA Linear Applications

9/24/11

Contents

•RTD Overview

•RTD Linearization

•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

(Ohm

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)

MetalResistivity (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 BridgeorCurrent Source

Vmeas Vsource

RRTD

RA RRTD

1

2

MEASV

+-

RTDR

AR

AR

AR

+Vsource

RRTD

Vmeas

Isource

Vmeas Isource RRTD

RRTD

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

T

Input resistance (ohms)

100.00 112.50 125.00 137.50 150.00

Vol

tage

(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

10k

R2 200k

+

Vdiff -49.85m

+Vcm 2.5 R

3 49

.9

C1

100n

++

-R1

R1

R2

INA326T1 INA326T

I_Out

R4

100

100uA

2-Wire Measurements

SOURCEMEASV+

-IRTDR

LR

LRVmeas Isource RRTD Isource 2 RL

Error Isource 2 RL

MEASV+-

RTDR

LR

LR

AR

AR

AR

+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

+

-

+ -

Isource1 Isource2 I

Vmeas I RL I RRTD 2 I( ) RL IRTD 3 I

Vmeas I RL 2 I( ) RL 3 RL

Vmeas Vmeas IRTD 3 I 3 I( ) IRTD

MEASV+-

RTDRLR

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

4-Wire Measurements

MEASV+

-IRTDR

LR

LRLR

LR

Vmeas Isource RRTD

System Errors reduced to measurement circuit accuracy

Vmeas Vsource

RRTD 2RL

RA RRTD 4 RL

1

2

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

Self-Heating Errors of RTD• Typically 2.5mW/C – 60mW/C

• DIN/IEC 60751 requires self-heating to account for <25% of tolerance value when excited with max current (1mA /100Ω, 0.7mA/500 Ω, 0.3mA/1000 Ω)

RTD Resistance vs TemperatureCallendar-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

(Ohm

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

pera

ture

Non

line

arit

y (%

FS

R)

Tem

pera

ture

Err

or (

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

(Ohm

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

(Ohm

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.

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)

Vol

tage

(V

)

VRTD (Temp)

V RTD_linear (Temp)

Increasing excitation source over measurement span produces linear sensor output

Correcting for Non-linearity

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)

Vol

tag

e (V

) VRTD Temp( )

VRTD_correction Temp( )

VRTD_linearized Temp( )

Temp

Analog Linearization Circuits

Analog Linearization CircuitsTwo-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 49.13k

R1

4.99

k

R3 60.43k

R5 105.83k

R4

1k

V1 5

-

+

Vout

I_Correction

I_RTD

RT

D 1

00

Analog Linearization CircuitsTwo-Wire Single Op-Amp

T

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

4.99

k

R3 60.43k

R5 105.83k

R4

1k

V1 5

-

+

Vout

I_Correction

I_RTD

RT

D 1

00

Analog Linearization CircuitsTwo-Wire Single Op-Amp

T

With

Cor

rect

ion

With

out L

inea

rizat

ion

Tem

pera

ture

(C)

0.00

25.00

50.00

75.00

100.00

125.00

150.00

175.00

200.00

Vol

tage

(V)

0.00

625.00m

1.25

1.88

2.50

3.13

3.75

4.38

5.00

With

out L

inea

rizat

ion

With

Cor

rect

ion

T

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

4.99

k

R3 60.43k

R5 105.83k

R4

1k

V1 5

-

+

Vout

I_Correction

I_RTD

RT

D 1

00

Analog Linearization CircuitsThree-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

801

R1

4.99

k

V2 5

R2

4.99

k

RL3

1

RL1

1

RL2

1R

z 10

0

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.

Analog Linearization CircuitsThree-Wire Single INA

T

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

This type of linearization typically provides a 20X - 40X improvement in linearity and some lead resistance cancellation

Analog Linearization CircuitsXTR105 4-20mA Current Loop Output

R1 975

R2 25

-+O

A3

RL 250

i_Q1

Q1_INT

R4

1kR

5 1k

R_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

T

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 CircuitsXTR105 4-20mA Current Loop Output

Analog + Digital Linearization CircuitsXTR108 4-20mA Current Loop Output

Digital Acquisition Circuits and Linearization Methods

Digital Acquisition CircuitsADS1118 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 CircuitsADS1220 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 CircuitsADS1220 24-bit Delta-Sigma One 4-Wire RTD

RTDR

LR

LR

LR

LR

REFR

+Vdig+Vsource

Digital Acquisition CircuitsADS1247 24-bit Delta-Sigma Three-Wire + Rcomp

Digital Acquisition CircuitsADS1247 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)

Vol

tage

(V

)

VRTD(Temp)

Digital Linearization MethodsLinear 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)

Vol

tage

(V

)

VRTD Temp( )

VLin_Fit Temp( )

Temp0 80 160 240 320 400 480 560 640 720 800

0.01

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)

Vol

tage

(V

)

VRTD Temp( )

VLin_Fit(Temp)

Temp

End-point Fit Best-Fit

TLinear t( ) A RTD t( ) B

Digital Linearization MethodsPiece-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)

Vol

tage

(V

)

VRTD(Temp)

VLin_Fit(Temp)

TPeicewise T n 1( ) T n( ) T n 1( )( )RTD RTD n 1( )

RTD n( ) RTD n 1( )

Digital Linearization MethodsDirect 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

olta

ge (

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( ) 2.8541103 RTD t( )

2 9.9121106 RTD t( )

3 1.7052108 RTD t( )

4

Digital Linearization MethodsDirect 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 Tmid

3 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

PA Apps Team

Mike Beckman

Omega Sensors

RDF Corp