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INA Noise Analysis

Created By:

Arthur Kay, Texas Instruments Senior Applications Engineer

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Introductions

• Art Kay, Applications Engineering Texas Instruments• Mixed Signal “System-on-a-Chip”• Bridge Sensor Signal Conditioning• Evaluation Modules (hardware / software)• Noise• Northrop Grumman, Burr-Brown (Test Engineering)• Cleveland State, Georgia Tech Grad.

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Summary

• Short Review of INA’s

• Noise model for INA’s

• Hand analysis of INA’s

• Simulation

• Application Example – Averaging– Calculation, simulation, measurement

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We will terminate the noise sources.

5

6

Three OPA INA

150k

Vout

-

+

A1

-

+ A2

Vin-

Vin+

Rg

1k -

+

A3

5V

Vin_dif = 2mV

Vin+ = 2.501V

Vin- = 2.499V

150k 150k

50k

50k

150k

Differential Input Voltage

Reference Input

Gain Set Resistor

Output Voltage

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Real World Input to Mathematical Model Vcc

+

+

+

Vdif

2

Vdif

-Vdif

2Vinn

Vinp

Vinp + Vinn

2Vcm =

8

Analyze the Input and Output Separately

50k

50k

150k

150k

150k

150k

Vout

Va1

Va2

-

+

A1

-

+ A2

Vin-

Vin+

Rg

1k

-

+

A3

Output StageDif Amp

Input StageDifferential Gain Stage

++

+

VCM

-Vdif

2

Vdif

2

9

Split Input Stage in Half

50k

50k

Va1

Va2

-

+

A1

-

+ A2

Vin-

Vin+

Rg

1k

Input StageDifferential Gain Stage

Va1

-

+

A1

Vin-

Va2

-

+ A2

VCM

+

+

+

+

+

+

-Vdif

2

+

VCM

Vdif

2

VCM

-Vdif

2

Vdif

2

1 + 2 Rf

Rg

Vdif

2VCM -

Rf

Rf

Rg

2

Rg

2

Split Input Stage

Vin+

1 + 2 Rf

Rg

Vdif

2VCM +

10

Use Superposition on Output Amp

R3 150k

R4 150k

R5 150k

R6 150k

Vout

Va1

Va2

-

+

A3

Output StageDif Amp

R3 150k R5 150k

Vout

Va1

-

+

A3

R3 150k

R4 150k

R5 150k

R6 150k

Vout

Va2

-

+

A3

Va1

Va2

Va2 + Vref

Find Vout Through Superposition Vout = Va2 – Va1 + Vref

Inverting AmpGain = -1

Non-inverting Amp Gain = 2

Voltage DividerGain = 1/2

Va1

Vin_dif

Va2

-Va1

Vref

Va2

2 +

Vref

2

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Gain For Three Amp IA[1] Input Stage Top Half

[2] Input Stage Bottom Half

[3] Output Stage

Substitute[1] and [2] into [3]

[4] Simplify

Va1 Vcm

Vdif

21 2

Rf

Rg

Va2 Vcm

Vdif

21 2

Rf

Rg

Vout Va2 Va1 Vref

Vout Vcm

Vdif

21 2

Rf

Rg

Vcm

Vdif

21 2

Rf

Rg

Vref

Vout Vdif 1 2Rf

Rg

Vref

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Review of Key Noise Concepts

• Noise From 2 Independent Sources is Called UNCORRELATED noise

• Uncorrelated Noise Sources Add By RSS (Root Sum of Squares)

• Good Approximations Greatly Simplify Noise Analysis• Noise Given in Typical Values and can vary 10-20%

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Key Noise Equations

enf efnorm lnfH

fL

efnorm enlf flf

entot enBB2

enf2

enBB eBB kn f

ina in kn f

Broadband 1/f Or “Flicker” Noise

Total Voltage Noise

Current Noise

Thermal Noise in Resistor

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16

Complex Noise Model

50k

50k

150k

150k

Vout

Va1

Va2

-

+

A1

-

+ A2

Vin-

Vin+

Rg

1k -

+

A3

+

+

+

VCM

-Vdif

2

Vdif

2

150k

150k

Noise Sources are Voltage Noise, Current Noise, and Thermal Noise From Resistors

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The Complex Model is Simplified

Vout

Vn_in

Vn_out

in_outOutput

gain = 1Input

gain = G

Input Stage Output Stage

Vout

Vn_RTI

in_outTotal

gain = G

Input Stage Noise Modeled as Current and Voltage noise; Output stage lumps all noise sources into 1 Vn_out Source

Vn_INAout Vn_out 2 Vn_in G 2

Vn_RTI

Vn_out

G

2

Vn_in 2

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The Input amplifier dominates at High Gain

G Total Input-Referred Noise (nV/rtHz)

Total Output Noise (nV/rtHz)

1 206.2 206.2

2 111.8 223.6

5 64 320

10 53.9 539

100 50 5000

1000 50 50,000

From INA333 Data Sheet

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G Input-Referred Noise (nV/rtHz)

1 206.2

10 53.9

100 50

1000 50

G Input-Referred Noise (nV/rtHz)

1 110

10 12

100 8

1000 8

Taken directly from the graph

Calculated using graphs and formula

Two Ways to represent INA Spectral Density

From INA128 Data Sheet From INA333 Data Sheet

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21

Vss

150k

Vout

-

+A1

-

+A2

Rg

1k -

+A3

5V

Vin_dif = 2mV

Vin+ = 2.501V

Vin- = 2.499V

150k

150k 150k

50k

50k

5V

-

+

Vss

100k

100k

5k 5k

5k5k

INA333

+V= 5V

-V= GND

Find the total RMS Noise Voltage at the Output

Application example with bridge sensor and ½ supply reference buffer

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Vss

150k

Vout

-

+A1

-

+A2

Rg

1k

-

+A3

5V

Vin_dif = 2mV

Vin+ = 2.501V

Vin- = 2.499V

150k

150k 150k

50k

50k

5V

-

+

Vss

100k

100k

5k 5k

5k5k

INA333

+V= 5V

-V= GND

Look at Noise Sources: Bridge, INA333, Reference Buffer

Each Piece of the Application Contributes Noise to the Output Voltage

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Noise Equivalent Model for Reference Pin Buffer

5V

-

+

5V

100k

100k

5V

-

+

OPA333

OPA33355nV/rtHz

50k

100

k || 100k

30nV/rtHz

100fA/rtHzVref_pin

Vref_pin

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Reference buffer

kn 1.381023 Boltzmann’s constant

Tk 273 25 Temperature in Kelvin

Input resistance (parallel combination of voltage divider)Req 50k

en_r 4kn Tn Req 28.7nV

HzThermal Noise from input resistor

in 100fA

HzCurrent noise from OPA333

en_i in Req 5nV

HzVoltage Noise from current noise

en_opa 55nV

HzVoltage noise from OPA333

Total rms noise from reference driver circuiten_ref en_opa

2en_r

2 en_i2 62.2

nV

Hz

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en_ref 62.2109 Vn_out 20010

9

Output_Stage_Noise en_ref2

Vn_out2 209.449 10

9

Vn_in

Vn_out

in_outInput

gain = G

Input Stage Output Stage

ΣVoutOutput

gain = 1

en_ref

The reference voltage directly adds to the output noise

Reference buffer noise adds directly to diff amp noise stage

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Vcc

inn

inp

+

-

R R

R R

inn

+

-R/2en_r

inp

+

-

R/2en_r

Use superposition to combine noise sources on the negative and positive input.

The bridge generates: thermal noise, in x R_bridge

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Vcc

inn

inp

+

-

5k 5k

5k5kINA333

Noise From Bridge / Current Sourcesinn

R

2 Voltage noise from current noise

en_rb 4kn TnR

2 Resistor Noise

Use superposition to add the noise from the input resistance and both current noise sources

ein_i innR

2

2

en_rb 2 inpR

2

2

en_rb 2

Assume inn inpNote that these sources are uncorrelated

Total Noise from input resistors and current sourceein_i 2 in

R

2

2

2 en_rb 2

For this example (R=5kO, in = 100fA/rtHz)

en_rb 6.4nV

HzResistor noise

innR

2 0.25

nV

HzVoltage noise from current noise

Total Noise from input resistors and current sourceein_i 2 0.5( )

22 9.1( )

2 9.1nV

Hz

RSS noise contributions from the resistor bridge and the effect of INA333 current noise on the resistor values

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Combine all the noise sources

150k

-

+A1

-

+A2

Rg

1k -

+A3

5V

150k

150k 150k

50k

50k

5V

-

+

Vss

100k

100k

5k5k

5k5k

INA333

+V= 5V

-V= GND

OPA333

Vout

Vin-

Vin+

Sensor Noise9nV/rtHz

Input Stage Noise50nV/rtHz

Reference Buffer Noise

62nV/rtHz

Output Stage Noise200nV/rtHz

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3 Vn 2 Vn2 9 Vn

2 Vn2 3.16Vn

3.16Vn

3Vn

Vn

Dominant Neglect

When adding two uncorrelated noise terms, the larger term will dominate if it is 3 times larger then the smaller term. You can neglect the smaller term with a relatively small error (i.e. 6%).

Rule of 3x in Noise Analysis

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For this example compute noise spectral density refered to the input

Noise_Spec_Den_RTI Vn_in_stage2

Vn_bridge2

Vn_out_stage

G

2

Vn_ref_buf

G

2

Noise_Spec_Den_RTI 50( )2

9( )2

200

100

2

62

100

2

50.847nV

Hz

Dominant Neglect Approximately equal to the dominant term

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For G = 100

20dB/decade

1st order

Kn = 1.57

Bandwidth from Data Sheet

“Noise Bandwidth” (BWn) approximates the bandwidth over which the noise spectral density contributes to the total noise

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Calculate RMS Output Noise for INA333 From Voltage Noise

G 100

Vin_RTI 50.85nV/rtHz From "Input referred noise" equation

fH 3.5kHz From data sheet table for gain = 100

For first order function See Gain vs Frequency in the data sheetKn 1.57

BWn fH Kn 5.495kHz Noise Bandwidth

en_out G Vin_RTI BWn 376.9Vrms RMS Output Noise

en_outPP 6.en_out 2.26mVpp Peak-to-Peak Output

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To recap…In high gains we can Terminate the noise

contribution of the sensor, reference buffer, and output stage with little effect on the

total output noise

150k

-

+A1

-

+A2

Rg

1k -

+A3

5V

150k

150k 150k

50k

50k

5V

-

+

Vss

100k

100k

5k5k

5k5k

INA333

+V= 5V

-V= GND

OPA333

Vout

Vin-

Vin+

Sensor Noise9nV/rtHz

Input Stage Noise50nV/rtHz

Reference Buffer Noise

62nV/rtHz

Output Stage Noise200nV/rtHz

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35

Vcc

VccVcc

Vcc

Vcc+

VG1 0

RG

+

-V-

RefOut

V+RG

U1 INA333

Vout

R2

5k

R3

5k

R4

5k

R5

5k

Vjunk

VIN_N

VIN_P

R1

100

+

-

+

U2 OPA333

R6

100k

R7

100k

V4 5

Vref 2.5V2.5V

2.5V

0V

2.5V

Simulate the Circuit

Noise Analysis in TINA can only be performed if AC source is present

DC operation first ensures a good result

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Using Tina SpiceOutput Noise = Noise Spectral Density

Total Noise = RMS output Noise

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T

Frequency (Hz)1 10 100 1k 10k 100k 1M

Vou

t (V

/rtH

z)

10.00n

10.00u

5.2uV/rtHz Vout

Voltage Spectral Density Out vs. Frequency

-3db @ 3.91kHz

Noise Spectral Density at the Output

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Total RMS Noise at the OutputT

Frequency (Hz)1 10 100 1k 10k 100k 1M

0

125u

250u

375u

500uV

n ou

tput

Tot

al R

MS

Noi

se (

Vrm

s) Simulation = 422uVrmsHand Calc = 377uVrms

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T

Frequency (Hz)1 10 100 1k 10k 100k 1M

Vou

t (V

/rtH

z)

10.00n

10.00u

5.2uV/rtHz Vout

Voltage Spectral Density Out vs. Frequency

-3db @ 3.91kHz

Bandwidth from Data Sheet and simulated bandwidth is different.

The roll-off was approximated as first order in the calculations. Simulation shows that it is not first order.

Why doesn’t calculation match simulation exactly?

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Say “Hasta la vista, baby” to nano-volts of noise with averaging!

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Averaging Circuit

Vss

Vcc

Vref

+

-

OPA335

R1

Vout

V1

V2

V3

R2

R3

RNVN

Rf

Vout Vref Rf

V1

R1

V2

R2

V3

R3 ...

VN

RN

For an averaging circuit choose R1 = R2 = R3 = ... R N = R

Rf = R / N

Vout Vref

V1 V2 V3 ... VN N

[15]

[16]

•Inputs V1-Vn assumed are noise sources

•R1-Rn assumed to be of EQUAL value

•Feedback Resistor Rf scaled based on the # of equal-valued input resistors

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vnoise_output

vnoise1

N

2vnoise2

N

2

vnoise3

N

2

...vnoiseN

N

2

Where vnoise1 , vnoise2 , vnoise3 , ... vnoiseN are noise sources

If you assume that v noise1 , vnoise2 , vnoise3 , ... vnoiseN are equal

uncorrelated noise sources, then

vnoise_output Nvnoise

N

2vnoise

2

N

vnoise

N[17]

Noise in Averaging Circuit

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Vcc

Vss

Vcc

Vss

Vref

Vref

Vss

Vcc

Vref

Vcc

Vss

Vref

R1

100

+

RG

RG V+

V-

Ref

_

Out

2

1

8

3

6

75

4U1

R2

100

+

RG

RG V+

V-

Ref

_

Out

2

1

8

3

6

7

5

4

+

Vdif2.4mV

V2 2.5

+

-

+

U4 OPA335

R4 100k

R5 100k

R7 33.3k

Vout

R3

100

+

RG

RG V+

V-

Ref

_

Out

2

1

8

3

6

7

5

4

R6 100k

U2

U2

INA333

INA333

INA333

24uA

24uA

24uA

72uA

2.5V

2.4V

Vref

2.4V

Vref

Averaging Circuit with INA333

•Acts as a Single INA333

•R4-6 selected to limit output current to design-specific value

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OPA333 Averaging Circuit

20 INA333 amps in parallel (jumper selectable)

Socketed Gain Set Resistors

Experiment with 20 Parallel INA333

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Linear Power Source

Steel Paint Can for Shielding

Standard Noise Measurement Precautions

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Noise vs Number of Amplifiers

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 5 10 15 20

Number of Amplifiers in Average Circuit

To

tal O

utp

ut

No

ise

(V

rm

s) measured

ideal (from tina)

Total Output Noise vs Number of Amplifiers Being Averaged

48

Measured Noise Spectral Density vs Number of Averages

1.E-07

1.E-06

1.E-05

1.E-04

1 10 100 1000 10000Frequency (Hz)

Ou

tpu

t N

ois

e (

V/r

tHz)

Avg = 1

Avg = 2

Avg = 5

Avg = 15

Avg = 20

Frequency (Hz)1 10 100 1k 10k

Ou

tpu

t n

ois

e (V

/rtH

z)

1E-7

1E-6

1E-5

1E-4

Avg = 1Avg = 2Avg = 5Avg = 15Avg = 20

Simulated Noise Spectral Density vs Number of Averages

Measured vs simulated spectral density

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1. [1] Hann, Gina. "Selecting the right op amp - Electronic Products." Electronic Products Magazine – Component and Technology News. 21 Nov. 2008. Web. 09 Dec. 2009. <http://www2.electronicproducts.com/Selecting_the_right_op_amp-article-facntexas_nov2008-html.aspx>.

2. Henry W. Ott, Noise Reduction Techniques in Electronics Systems, John Wiley and Sons

References

Noise Article Series (www.en-genius.net)

http://www.en-genius.net/site/zones/audiovideoZONE/technical_notes/avt_022508

Acknowledgments:1. R. Burt, Technique for Computing Noise based on Data Sheet Curves, General Noise Information

2. T. Green, General Information

3. B. Trump, General Information

8. Matt Hann, General INA information and review

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I’ll be back.Next year with more

exciting noise …Or something else…

Noise = 1 trick pony.

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Thank You

for

Your Interest

in

INA Noise – Calculation and Measurement

Comments, Questions, Technical Discussions Welcome:Art Kay 520-746-6072 kay_art@ti.com

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PSRR EquationLike CMRR

INA2322: INA2321:

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