Transcript Document

INA Noise Analysis
Created By:
Arthur Kay, Texas Instruments Senior Applications
Engineer
1
Introductions
•
•
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•
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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.
2
Summary
•
•
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Short Review of INA’s
Noise model for INA’s
Hand analysis of INA’s
Simulation
Application Example – Averaging
– Calculation, simulation, measurement
3
We will terminate the
noise sources.
4
5
Three OPA INA
Gain Set
Resistor
Vin-
5V
Rg 1k
Vin- = 2.499V
+
-
150k
150k
A1
-
50k
A3
+
50k
Output
Voltage
Vin_dif = 2mV
+
Vin+
Differential
Input Voltage
Vout
Vin+ = 2.501V
150k
150k
A2
Reference
Input
6
Real World Input to Mathematical Model
Vcc
Vdif
Vinp + Vinn
Vcm =
2
+
Vinn
-Vdif
2
+
+
Vinp
Vdif
2
7
Analyze the Input and Output Separately
-Vdif
2
VinVa1
+
150k
+
-
150k
A1
50k
-
Rg 1k
VCM
+
Vdif
2
Vout
+
50k
+
+
A3
150k
A2
150k
Va2
Vin+
Input Stage
Differential Gain Stage
Output Stage
Dif Amp
8
Split Input Stage in Half
-Vdif
2
Va1
Vin-
+
-Vdif
2
VCM Vin-
+
+
- A1
Rg 1k
A1
Split Input Stage
50k
Rg
2
+
VCM
+
Vdif
2
Va1
Rf
Rg
2
+
+
+
-
VCM
50k
VCM
R
Vdif
1+2 f
Rg
2
+
Vin+
Rf
-
A2
Va2
Input Stage
Differential Gain Stage
Vdif
2
+ Vin+
VCM +
+
A2
Va2
R
Vdif
1+2 f
Rg
2
9
Use Superposition on Output Amp
Va1
Va1
R3 150k
R3 150k
Va1
R5 150k
Va1
Inverting Amp
Gain = -1
-
Vin_dif
Va2
A3
R3 150k
R6 150k
Va2
Output Stage
Dif Amp
A3
-
Vout
+
-Va1
Vout
+
R4 150k
R5 150k
Non-inverting Amp
Gain = 2
Voltage Divider
Gain = 1/2
Va2
Va2
R5 150k
+
R4 150k
Va2
Vref
+
2
2
A3
Vout
Va2 + Vref
R6 150k
Vref
Find Vout Through Superposition
Vout = Va2 – Va1 + Vref
10
Gain For Three Amp IA
Rf 

Va1 Vcm 
 1  2

2
Rg


[1] Input Stage
Top Half
Rf 

Va2 Vcm 
 1  2

2
Rg


[2] Input Stage
Bottom Half
Vdif
Vdif
Vout
Va2  Va1  Vref
Vout
Vdif 
Rf  
Vdif 
Rf 

Vcm  2   1  2 R   Vcm  2   1  2 R   Vref
g  
g 



Vout
Rf 

Vdif  1  2
  Vref
Rg


[3] Output Stage
Substitute
[1] and [2]
into [3]
[4] Simplify
11
12
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%
13
Key Noise Equations
1/f Or “Flicker” Noise
Broadband
enBB   eBB kn  f
efnorm   enlf  flf
   fH 
en f   efn orm l n 
  fL 
   
Current Noise
ina   in  kn  f
Thermal Noise in
Resistor
Total Voltage Noise
2
2
entot  enBB  enf
14
15
Complex Noise Model
-Vdif
2
Vin-
+
+
-
Rg 1k
VCM
+
Noise Sources
are Voltage
Noise, Current
Noise, and
Thermal Noise
From Resistors
Va1
A1
150k
50k
150k
-
A3
Vout
+
50k
-
Vdif
2
+
+
150k
150k
A2
Va2
Vin+
16
The Complex Model is Simplified
Input Stage
in_out
Input
gain = G
Output Stage
Vn_out
Output
gain = 1
Vout
Input Stage Noise
Modeled as Current
and Voltage noise;
Output stage lumps all
noise sources into 1
Vn_out Source
Vn_in
in_out
Vn_RTI
Total
gain = G
Vout
Vn _o ut2  Vn _i n G2
Vn _INA ou t
Vn _RTI
 Vn _o ut 


G
2
  Vn _i n2

17
The Input amplifier dominates at High Gain
From INA333 Data Sheet
G
Total InputReferred
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
18
Two Ways to represent INA Spectral Density
From INA333 Data Sheet
From INA128 Data Sheet
G
Input-Referred
Noise (nV/rtHz)
G
Input-Referred
Noise (nV/rtHz)
1
110
1
206.2
10
12
10
53.9
100
8
100
50
1000
8
1000
50
Taken
directly
from the
graph
Calculated
using
graphs
and
formula
19
20
Find the total RMS Noise
Voltage at the Output
+V= 5V
5V
Vin- = 2.499V
+
A1
-
150k
150k
Rg 1k
5k
5k
Vss
50k
INA333
Vout
A3
+
5k
5k
50k
-
Vin_dif = 2mV
-
150k
150k
A2
+
Vss
Vin+ = 2.501V
5V
-V= GND
100k
+
100k
Application example with bridge sensor and
½ supply reference buffer
21
Look at Noise Sources:
Bridge, INA333, Reference Buffer
+V= 5V
5V
Vin- = 2.499V
150k
+
A1
-
150k
Rg 1k
5k
5k
Vss
50k
INA333
Vout
A3
+
5k
5k
50k
-
Vin_dif = 2mV
-
150k
150k
A2
+
Vss
Vin+ = 2.501V
5V
-V= GND
Each Piece of the Application Contributes
Noise to the Output Voltage
100k
+
100k
22
Noise Equivalent Model for
Reference Pin Buffer
5V
5V
5V
Vref_pin
OPA333
100k
+
100fA/rtHz
+
55nV/
rtHz
30nV/rtHz
100k
100k || 100k
OPA333
-
Vref_pin
50k
23
Reference buffer
 23
kn
1 .381
 0
Boltzmann’s c onst ant
Tk
2 73  2 5
Temperat ure in Kelv in
Req
5 0k
4kn  Tn  Req
en _r
in
1 00
en _i
fA
2 8.7
nV
Thermal N oise f rom input res ist or
Hz
C urrent noise f rom OPA333
Hz
in  Req
en _o pa
en _ref
I nput res is tanc e
(parallel c ombination of v oltage div ider)
55
5
nV
Voltage N oise f rom c urrent noise
Hz
nV
Voltage noise f rom OPA333
Hz
2
2
2
en _o pa  en _r  en _i
6 2.2
nV
Hz
Tot al rms noise f rom
ref erenc e driv er circ ui
24
The reference voltage directly
adds to the output noise
Output Stage
Input Stage
in_out
Input
gain = G
Vn_in
Vn_out
Σ
en_ref
9
en _ref   6 2.21
 0
9
Vn _o ut   2 001
 0
2
Vout
Output
gain = 1
2
Reference buffer
noise adds
directly to diff
amp noise stage
9
O ut pu t_ St ag e_N oi se
  en _ref  Vn _o ut  2 09 .44 9 1 0
25
The bridge generates:
thermal noise, in x R_bridge
en_r R/2
inn
-
Vcc
R
R
+
inn
R
R
Use superposition to
combine noise sources
on the negative and
positive input.
+
inp
en_r R/2
+
inp
26
Noise From Bridge / Current Sources
Vcc
5k
5k
R
in n
2
Voltage noise f rom current nois e
en _rb
R
4kn  Tn 
2
U se s uperpos ition to add the nois e f rom
t he input res ist ance and both c urrent noise sources
inn
5k
INA333
5k
R es ist or N oise
2
ei n_ i
+
inp
2
i  R   e
 n n   n _rb 
2

As sume in n
in p
N ot e that t hes e sourc es are unc orrelated
2
ei n_ i
RSS noise contributions
from the resistor bridge
and the effect of INA333
current noise on the
resistor values
2
2
i  R   e
 n p   n _rb
2

R
2
2  in    2  en _rb
 2
Tot al Noise f rom input
res ist ors and c urrent source
For this ex ample (R=5kO, in = 100f A/rtH z)
nV
R es ist or noise
en _rb
6 .4
R
in n
2
0 .25
ei n_ i
2 ( 0 .5)  2 ( 9 .1)
Hz
nV
Voltage noise f rom current nois e
Hz
2
2
9 .1
nV
Hz
Tot al Noise f rom input
27
res ist ors and c urrent source
Combine all the noise sources
Sensor Noise
9nV/rtHz
Input Stage Noise Output Stage Noise
50nV/rtHz
200nV/rtHz
+V= 5V
Vin-
5V
+
-
150k
150k
A1
Rg 1k
5k
5k
50k
INA333
5k
5k
50k
Vin+
150k
A2
-
Vout
A3
+
150k
+
Reference
Buffer Noise
62nV/rtHz
Vss
5V
-V= GND
100k
OPA333
+
100k
28
Rule of 3x in Noise Analysis
Vn
6
1
.
3
Vn
3Vn
3 Vn
2
 Vn
2
2
9 Vn  Vn
2
3.16Vn
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%).
29
For this example compute noise spectral density refered to the input
2
Noise_Spec_Den_RTI
 Vn_ref_buf 
2
2  Vn_out_stage 
Vn_in_stage  Vn_bridge  
 

G
G

 

Noise_Spec_Den_RTI
200 
 62 
( 50)  ( 9)  

  
 100   100 
2
Dominant
2
2
Neglect
2
50.847
2
nV
Hz
Approximately equal
to the dominant term
30
Bandwidth
from Data
Sheet
For G = 100
20dB/decade
1st order
Kn = 1.57
“Noise Bandwidth” (BWn)
approximates the bandwidth
over which the noise
spectral density contributes
to the total noise
31
Calculate RMS Output Noise for INA333
From Voltage Noise
G
1 00
Vi n_ RTI 5 0.8 5n V/rtH z From "I nput ref erred nois e" equat ion
fH
3 .5k Hz
From data s heet table f or gain = 100
Kn
1 .57
For f irs t order f unc tion
See Gain v s Frequenc y in the dat a s heet
BWn
en _o ut
fH Kn
5 .49 5k Hz
G Vi n_ RTI BWn
en _o ut P P 6 .en _o ut
N ois e Bandwidt h
3 76 .9Vrms
2 .26mVp p
R MS Output Noise
Peak -t o-Peak Out put
32
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
Sensor Noise
9nV/rtHz
Input Stage Noise Output Stage Noise
50nV/rtHz
200nV/rtHz
+V= 5V
Vin-
5V
-
150k
150k
A1
50k
Rg 1k
5k
5k
+
INA333
5k
50k
5k
Vin+
150k
A2
-
Vout
A3
+
150k
+
Reference
Buffer Noise
62nV/rtHz
Vss
5V
-V= GND
100k
OPA333
+
100k
33
34
Simulate the Circuit
DC operation
first ensures a
good result
VIN_N 2.5V
R3 5k
RG
U1 INA333
VVout 2.5V
Out
RG
R5 5k
Ref
V+
+
VIN_P 2.5V
Vref 2.5V
Vcc
Vcc
+
Vjunk 0V
VG1 0
Vcc
V4 5
Noise Analysis
in TINA can only
be performed if
AC source is
present
+
U2 OPA333
+
R6 100k
R4 5k
R1 100
-
R7 100k
R2 5k
Vcc
Vcc
35
Using Tina Spice
Output Noise =
Noise Spectral
Density
Total Noise = RMS
output Noise
36
Noise Spectral Density at the Output
Voltage Spectral Density Out vs. Frequency
10.00u
5.2uV/rtHz
Vout
Vout (V/rtHz)
T
-3db @
3.91kHz
10.00n
1
10
100
1k
10k
100k
1M
Frequency (Hz)
37
Total RMS Noise at the Output
T
Vn output Total RMS Noise (Vrms)
500u
Simulation = 422uVrms
Hand Calc = 377uVrms
375u
250u
125u
0
1
10
100
1k
10k
100k
1M
Frequency (Hz)
38
Why doesn’t calculation match simulation
exactly?
Bandwidth from Data
Sheet and simulated
bandwidth is different.
Voltage Spectral Density Out vs. Frequency
10.00u
5.2uV/rtHz
Vout
Vout (V/rtHz)
T
The roll-off was
approximated as first
order in the calculations.
Simulation shows that it
is not first order.
-3db @
3.91kHz
10.00n
1
10
100
1k
10k
Frequency (Hz)
100k
1M
39
40
Say “Hasta la vista,
baby” to nano-volts of
noise with averaging!
41
Averaging
Circuit
Rf
R1
V1
Vcc
-
Vout
R2
+
V2
OPA335
Vss
R3
•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
Vref
V3
RN
VN
Vout
 V1 V2 V3
Vref  Rf 


 ... 
R1 R2 R3

VN 

RN

[15]
For an averaging circuit choose
R1 = R 2 = R 3 = ... R N = R
Rf = R / N
Vout
Vref 
V1  V2  V3  ...  VN
[16]
N
42
Noise in Averaging Circuit
v noise_output
 vnoise1


N
2
 vnoise2

 
 
N
2
 vnoise3

 
 
N
2
 vnoiseN

  ...  


N



2
Where v noise1 , vnoise2 , vnoise3 , ... vnoiseN are noise sources
If you assume that v noise1 , vnoise2 , vnoise3 , ... vnoiseN are equal
uncorrelated noise sources, then
v noise_output
 vnoise
N

N



2
v noise
N
2
v noise
N
[17]
43
Averaging Circuit with INA333
Vss
+
Vdif
2.4mV
R1 100
2
1
4
U1
RG V-
R4 100k
INA333
8
Out
Ref
6
RG V+
3
2.5V
_
72uA
24uA
5
+
R7 33.3k
7
V2 2.5
Vcc
Vref
Vss
Vss
R2 100
2
•Acts as a Single
INA333
-
4
U2
RG V-
8
Vout
+
U4
OPA335
Out
Ref
6
RG V+
Vcc
24uA
Vref
5
+
+
R5 100k
INA333
3
7
2.4V
Vref
Vcc Vref
Vss
2
R3 100
•R4-6 selected to
limit output current
to design-specific
value
1
_
1
_
4
U2
RG V-
R6 100k
INA333
8
Out
Ref
RG V+
3
6
24uA
5
+
2.4V
7
Vcc
Vref
Vref
44
Experiment with 20 Parallel INA333
Socketed Gain
Set Resistors
20 INA333 amps in parallel
(jumper selectable)
OPA333
Averaging
Circuit
45
Standard Noise Measurement
Precautions
Linear Power
Source
Steel Paint Can
for Shielding
46
Total Output Noise vs Number of
Amplifiers Being Averaged
Noise vs Number of Amplifiers
0.0016
Total Output Noise (V rms)
0.0014
measured
0.0012
ideal (from tina)
0.001
0.0008
0.0006
0.0004
0.0002
0
0
5
10
15
20
Number of Amplifiers in Average Circuit
47
Measured Noise Spectral Density vs Number of Averages
1.E-05
Avg = 1
Avg = 2
Avg = 5
1.E-06
Avg = 15
Avg = 20
1.E-07
1
10
100
Frequency (Hz)
1000
10000
Simulated Noise Spectral Density vs Number of Averages
1E-4
Output noise (V/rtHz)
Measured vs
simulated spectral
density
Output Noise (V/rtHz)
1.E-04
1E-5
Avg = 1
Avg = 2
Avg = 5
Avg = 15
Avg = 20
1E-6
1E-7
1
10
100
Frequency (Hz)
1k
10k
48
References
1.
2.
[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-articlefacntexas_nov2008-html.aspx>.
Henry W. Ott, Noise Reduction Techniques in Electronics Systems, John Wiley and Sons
Acknowledgments:
1.
2.
3.
8.
R. Burt, Technique for Computing Noise based on Data Sheet Curves, General Noise Information
T. Green, General Information
B. Trump, General Information
Matt Hann, General INA information and review
Noise Article Series (www.en-genius.net)
http://www.en-genius.net/site/zones/audiovideoZONE/technical_notes/avt_022508
49
I’ll be back.
Next year with more
exciting noise …
Or something else…
Noise = 1 trick
pony.
50
Thank You
for
Your Interest
in
INA Noise – Calculation and Measurement
Comments, Questions, Technical Discussions Welcome:
Art Kay
520-746-6072
[email protected]
51
PSRR
Equation
Like CMRR
INA2322:
INA2321:
52
53