1

Instrumentation Amplifier Noise Analysis

2

3

Three Stage IA

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

4

Real World Input to Mathematical Model Vcc

+

+

+

Vdif

2

Vdif

-Vdif

2Vinn

Vinp

Vinp + Vinn

2Vcm =

5

Analyze the Input and Output Separately

Vss

Vcc

Vcc

Vcc

Vss

Vss

Vss

Vcc

VCC1 12 VEE1 12

R1 25k

R2 25k

R3 40k

R4 40k

R5 40k

R6 40k

Vout

Va1

Va2

-

+

A1

-

+ A2

Vin-

Vin+

R7

49.9

-

+

A3

Output StageDif Amp

Input StageDifferential Gain Stage

+

++

VCM

-Vdif

2

Vdif

2

6

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 +

7

Use Superposition on Output Amp

R3 40k

R4 40k

R5 40k

R6 40k

Vout

Va1

Va2

-

+

A3

Output StageDif Amp

R3 40k R5 40k

Vout

Va1

-

+

A3

R3 40k

R4 40k

R5 40k

R6 40k

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

8

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

9

10

Vcc

Vcc

Vss

Vss

Vss

Vcc

R1 25k

R2 25k

R5 40k

R6 40k

Vout

Va1

Va2

-

+

A1

-

+ A2

Vin-

Vin+

R7

49.9

-

+

A3

+

+

+

VCM

-Vdif

2

Vdif

2

Complex Noise Model

11

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

Vn_out Vn_out 2 Vn_in G 2

Vn_RTI

Vn_out

G

2

Vn_in 2

12

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

13

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

14

15

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

16

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

17

Noise Equivalent Model for Reference Pin Buffer

5V

-

+

Vss

100k

100kOPA333

5V

-

+OPA33355nV

50k

100k || 100k

30nV

100fAVref_pin

18

5V

-

+OPA33355nV

50k

100k || 100k

30nV

100fAVref_pin

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 Current 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

Reference buffer

19

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

20

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

21

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

22

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

23

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

24

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

25

For G = 100

20dB/decade

1st order

Kn = 1.57

Bandwidth from Data Sheet

26

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

27

28

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

29

Using Tina Spice

30

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

31

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

32

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?

33

34

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]

35

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

36

Vcc

Vss

Vcc

Vss

Vref

Vref

Vss

Vcc

Vref

Vcc

Vss

Vref

R1

10

0

+

RG

RG V+

V-

Ref

_

Out

2

1

8

3

6

75

4U1

R2

10

0

+

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

10

0

+

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

37

OPA333 Averaging Circuit

20 INA333 amps in parallel (jumper selectable)

Socketed Gain Set Resistors

Experiment with 20 Parallel INA333

38

Linear Power Source

Steel Paint Can for Shielding

Standard Noise Measurement Precautions

39

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

40

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

41

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

42

Thank You

for

Your Interest

in

INA Noise – Calculation and Measurement