Download Instrumentation Amplifier Noise Analysis

Instrumentation Amplifier
Noise Analysis
1
2
Three Stage IA
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
3
Real World Input to Mathematical Model
Vcc
Vdif
Vinp + Vinn
Vcm =
2
+
Vinn
-Vdif
2
+
+
Vinp
Vdif
2
4
Analyze the Input and Output Separately
Vss
VEE1 12
Vcc
VCC1 12
-Vdif
2
Vin-
Vcc
Va1
+
+
-
R3 40k
R5 40k
A1
Vss
R1 25k
R7 49.9
Vss
VCM
+
-
A3
Vout
+
R2 25k
Vcc
Vss
-
Vdif
2
R4 40k
+
+
A2
R6 40k
Va2
Vcc
Vin+
Input Stage
Differential Gain Stage
Output Stage
Dif Amp
5
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
6
Use Superposition on Output Amp
Va1
Va1
R3 40k
R3 40k
R5 40k
Va1
R5 40k
Va1
Inverting Amp
Gain = -1
-
Vin_dif
Va2
A3
R3 40k
R6 40k
Va2
Output Stage
Dif Amp
Vout
+
-Va1
Vout
+
R4 40k
A3
-
Non-inverting Amp
Gain = 2
Voltage Divider
Gain = 1/2
Va2
Va2
R5 40k
+
R4 40k
Va2
Vref
+
2
2
A3
Vout
Va2 + Vref
R6 40k
Vref
Find Vout Through Superposition
Vout = Va2 – Va1 + Vref
7
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
8
9
Complex Noise Model
-Vdif
2
Vin-
Vcc
Va1
+
+
-
R5 40k
A1
Vss
R1 25k
R7 49.9
Vss
VCM
+
-
A3
Vout
+
R2 25k
Vcc
Vss
-
Vdif
2
+
R6 40k
+
A2
Va2
Vcc
Vin+
10
The Complex Model is Simplified
Input Stage
in_out
Input
gain = G
Output Stage
Vn_out
Output
gain = 1
Vout
Vn_in
in_out
Vn_RTI
Total
gain = G
Vn_out

Vn_RTI



Vn_out

2


 Vn_in  G
2
Vout
Vn_out
G
2

2
   Vn_in 

11
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
12
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
13
14
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
15
Look at Noise Sources:
Bridge, INA333, Reference Buffer
+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
16
Noise Equivalent Model for
Reference Pin Buffer
Vss
5V
5V
100k
OPA333
+
-
Vref_pin
OPA333
100k
100fA
+
55nV
30nV
100k || 100k
50k
17
Reference buffer
5V
-
Vref_pin
OPA333
 23
kn
1.38 10
Boltzmann’s constant
Tk
273  25
Temperature in Kelvin
Req
50k
100fA
+
Input resistance
(parallel combination of voltage divider)
55nV
30nV
100k || 100k
4kn  Tn  Req
en_r
nV
28.7
Thermal Noise from input resistor
Hz
50k
in
Current noise from OPA333
100fA
en_i
in  Req
en_opa
en_ref
55
5
nV
Voltage Noise from current noise
Hz
nV
Voltage noise from OPA333
Hz
2
2
2
en_opa  en_r  en_i
62.2
nV
Hz
Total rms noise from
reference driver circuit
18
The reference voltage directly
adds to the output noise
Output Stage
Input Stage
in_out
Input
gain = G
Vn_in
Vn_out
Vout
Output
gain = 1
Σ
en_ref
9
en_ref  62.2 10
9
Vn_out  200 10
2
2
9
Output_Stage_Noise  en_ref  Vn_out  209.449  10
19
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
20
Noise From Bridge / Current Sources
Vcc
5k
5k
R
inn 
2
Voltage noise from current noise
en_rb
R
4kn  Tn 
2
Use superposition to add the noise from
the input resistance and both current noise sources
inn
5k
INA333
5k
2
ein_i
+
inp
Resistor Noise
2
i  R   e
 nn   n_rb  
2

2
2
i  R   e
 np   n_rb 
2

Assume inn
inp
Note that these sources are uncorrelated
2
ein_i
R
2
2  in    2  en_rb 
 2
Total Noise from input
resistors and current source
For this example (R=5kO, in = 100fA/rtHz)
nV
Resistor noise
en_rb
6.4
R
inn 
2
0.25
ein_i
2 ( 0.5)  2 ( 9.1)
Hz
nV
Voltage noise from current noise
Hz
2
2
9.1
nV
Hz
Total Noise from input
21
resistors and current 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
22
Rule of 3x
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%).
23
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
24
Bandwidth
from Data
Sheet
For G = 100
20dB/decade
1st order
Kn = 1.57
25
Calculate RMS Output Noise for INA333
From Voltage Noise
G
100
Vin_RTI
fH
Kn
From "Input referred noise" equation
50.85nV/rtHz
3.5kHz
From data sheet table for gain = 100
1.57
For first order function
See Gain vs Frequency in the data sheet
BW n
fH Kn
en_out
en_outPP
5.495kHz
G Vin_RTI BW n
6.en_out
Noise Bandwidth
376.9Vrms
2.26mVpp
RMS Output Noise
Peak-to-Peak Output
26
27
Simulate the Circuit
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
Vcc
+
+
U2 OPA333
VG1 0
V4 5
+
R6 100k
R4 5k
R1 100
-
R7 100k
R2 5k
Vcc
Vcc
28
Using Tina Spice
29
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)
30
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)
31
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
32
33
Averaging
Circuit
Rf
R1
V1
Vcc
-
Vout
R2
+
V2
OPA335
Vss
R3
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
34
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]
35
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
72uA
24uA
5
+
R7 33.3k
7
V2 2.5
Vcc
Vref
Vss
Vss
R2 100
2
1
_
-
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
2.5V
_
1
_
4
U2
RG V-
R6 100k
INA333
8
Out
Ref
RG V+
3
6
24uA
5
+
2.4V
7
Vcc
Vref
36
Vref
Experiment with 20 Parallel INA333
Socketed Gain
Set Resistors
20 INA333 amps in parallel
(jumper selectable)
OPA333
Averaging
Circuit
37
Standard Noise Measurement
Precautions
Linear Power
Source
Steel Paint Can
for Shielding
38
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
39
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
40
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
41
Thank You
for
Your Interest
in
INA Noise – Calculation and Measurement
42