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INA Noise Analysis. Created By: Arthur Kay , Texas Instruments Senior Applications Engineer. Introductions. Art Kay, Applications Engineering Texas Instruments Mixed Signal “System-on-a-Chip” Bridge Sensor Signal Conditioning Evaluation Modules (hardware / software) Noise - PowerPoint PPT Presentation
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1
INA Noise Analysis
Created By:
Arthur Kay, Texas Instruments Senior Applications Engineer
2
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.
3
Summary
• Short Review of INA’s
• Noise model for INA’s
• Hand analysis of INA’s
• Simulation
• Application Example – Averaging– Calculation, simulation, measurement
4
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
7
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
11
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
12
13
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%
14
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
15
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
17
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
18
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
19
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
20
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
22
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
23
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
24
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
25
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
26
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
27
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
28
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
29
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
30
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
31
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
32
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
33
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
34
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
36
Using Tina SpiceOutput Noise = Noise Spectral Density
Total Noise = RMS output Noise
37
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
38
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
39
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?
40
41
Say “Hasta la vista, baby” to nano-volts of noise with averaging!
42
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
43
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
44
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
45
OPA333 Averaging Circuit
20 INA333 amps in parallel (jumper selectable)
Socketed Gain Set Resistors
Experiment with 20 Parallel INA333
46
Linear Power Source
Steel Paint Can for Shielding
Standard Noise Measurement Precautions
47
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
49
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
50
I’ll be back.Next year with more
exciting noise …Or something else…
Noise = 1 trick pony.
51
Thank You
for
Your Interest
in
INA Noise – Calculation and Measurement
Comments, Questions, Technical Discussions Welcome:Art Kay 520-746-6072 [email protected]
52
PSRR EquationLike CMRR
INA2322: INA2321:
53