BEN-GURION UNIVERSITY OF THE NEGEV
Department of Electrical and Computer Engineering
Optimization of Low-Frequency
Search Coil Magnetometers
Asaf Grosz
High Sensitivity Magnetometers - Sensors & Applications - School 2012
Outline
1.
2.
3.
4.
5.
6.
Ideal and optimal magnetometers
Operation principle
Optimization of single-axis search coils
Three-axial search coils
Experimental results
Conclusion
2
Ideal magnetometer: best for any application
Sensitivity
threshold
Size
Power
consumption
Price
Weight
Space magnetometry
Perimeter security (MAD)
Importance
Unattended ground sensors (MAD)
Low
Medium
High
Geophysical prospecting
Smart dust
Bio-magnetic applications
Ideal magnetometer
10fT/√Hz
0.1cc
0.1mW
1$
10g
Maybe in the future…
3
Optimal magnetometer: best for an application
Flux Gate
Atomic
Magnetoresistive
GMI
Magnetoelectric
Search Coil
Space magnetometry
Perimeter security (MAD)
Unattended ground sensors (MAD)
Geophysical prospecting
Smart dust
Bio-magnetic applications
S $
T
Utilized:
Today
Near future
Far future or not at all
S Size too large
$ Too expensive
W Power too high
T Not sensitive enough
4
Optimal magnetometer: best for an application
Flux Gate
Atomic
Magnetoresistive
GMI
Magnetoelectric
Search Coil
Space magnetometry
Perimeter security (MAD)
$
Unattended ground sensors (MAD)
W
Geophysical prospecting
Smart dust
Bio-magnetic applications
S $
$
T
Utilized:
Today
Near future
Far future or not at all
S Size too large
$ Too expensive
W Power too high
T Not sensitive enough
5
Optimal magnetometer: best for an application
Flux Gate
Atomic
Magnetoresistive
GMI
$
T
T
T
T
T
T
S
S
T
T
Magnetoelectric
Search Coil
Space magnetometry
Perimeter security (MAD)
Unattended ground sensors (MAD)
W
Geophysical prospecting
Smart dust
Bio-magnetic applications
S $
T
Utilized:
Today
Near future
Far future or not at all
$
S Size too large
$ Too expensive
W Power too high
T Not sensitive enough
6
Optimal magnetometer: best for an application
Flux Gate
Atomic
Magnetoresistive
GMI
$
T
T
T
T
T
T
S
S
S $
T
T
S T
Magnetoelectric
Search Coil
Space magnetometry
Perimeter security (MAD)
Unattended ground sensors (MAD)
W
Geophysical prospecting
Smart dust
Bio-magnetic applications
$
S $
T
Utilized:
Today
Near future
Far future or not at all
$
S Size too large
$ Too expensive
W Power too high
T Not sensitive enough
7
Operation principle
 Faraday law of induction
L
Lw
Lw / L
L / D
d
dB
V  N
  NSeff
dt
dt
d
D
 Core effective permeability
 eff 
r
1  r  H D  d / D
2
2
dw
dwins
dwins / dw
8
Noise at low frequencies
Coil thermal noise:
eR  4k BTRS
Total noise referred to the coil input:
nV
Hz
eT  eR2  en2  RS2in2
Amplifier voltage noise:
en
nV
Hz
L
Amplifier current noise:
in
fA
Hz
en
R
A
v(f)
vo
C
in
9
Sensitivity threshold
Input signal:
V ( f ) MAX  2fNSeff B0
Core apparent permeability:
 eff
r

1  r  H D  d 2 / D2
Input referred noise:
e e  R i
2
R
2
n
2 2
S n
Sensitivity threshold: Bmin ( f ) 
e R2  en2  RS2 in2
2fNS eff
10
Optimization of a search coil
Objectives
Constraints
Variables
Sensitivity threshold
Weight
Size
Price
Power consumption
Complexity
Wire diameter
Core diameter
Flux concentrators diameter
Flux concentrators thickness
Number of turns
11
Global analytical optimization
Allows finding the best possible sensitivity threshold for a given volume, aspect
ratio, amplifier noise, and core permeability, regardless of any constraints.
 Bmin ( f )
0

 d

 B ( f )
 min
0
 d w
The only real
and positive
solutions are:
1
d opt 
3 r H D
 D 2 (4  3 r H D ) 3

 A  2 D

3
A


A  D 3 [9  r H D (1  3 r H D )  8]
 27 D 6 (  r H D ) 2 [  r H D (19  27  r H D )  17]
d wopt  4
2
 L ( D 2  d opt
) in 
 2 en
12
Global analytical optimization
Approximate solution relates the best possible sensitivity threshold to a given
volume, aspect ratio, amplifier noise, and core permeability.
amplifier noise
aspect ratio
volume
core permeability
Bst min ( f )  3.65 104 8.28 1021  enin  (Vol ) 0.833(7.64 102  r0.449) f 1
13
Global analytical optimization
Approximate solution relates the best possible sensitivity threshold to a given
volume, aspect ratio, amplifier noise, and core permeability.
amplifier noise
aspect ratio
volume
core permeability
Bst min ( f )  3.65 104 8.28 1021  enin  (Vol ) 0.833(7.64 102  r0.449) f 1
en
(DC – 1kHz)
(nV/√Hz)
in
(DC – 1kHz)
(fA/√Hz)
Power consumption
at 3V (mW)
Resolution
reduction (%)
AD8628
22
5
2.55
0.5
OPA333
55
100
0.051
30
14
Global analytical optimization
Approximate solution relates the best possible sensitivity threshold to a given
volume, aspect ratio, amplifier noise, and core permeability.
amplifier noise
aspect ratio
volume
core permeability
Bst min ( f )  3.65 104 8.28 1021  enin  (Vol ) 0.833(7.64 102  r0.449) f 1
Relative permeability
Resolution
reduction (%)
Pros
Cons
Ferrite
2000
30
Cheap
Fragile
μMetal
50000
5.7
Strong
Expensive,
Difficult to integrate
15
Global numerical optimization
Allows finding the best possible sensitivity threshold for a given set of
constraints (numbers of turns, weight, size, wire diameter, etc.) defined
by the user.
 sensor structure
 wire diameter
 core and concentrators



size
electronics
noise matching
power consumption
Bmin ( f ) 
e R2  en2  RS2 in2
2fNS eff
16
Optimization methods comparison
 Analytical
+ Allows an immediate analysis of the theoretical limits of the magnetometer
sensitivity threshold as a function of the optimization parameters.
- Reduces the control over the requirements and limitations.
 Numerical
+ Absolute control over the requirements and limitations of the design.
- There is no direct, analytical relationship between the magnetometer parameters
and its optimal configuration.
The two methods complete one another
17
Improvements due to optimization
Sensitivity threshold (pT/√Hz)
Sensitivity threshold at 1Hz vs. volume
Volume (cc)
18
Hollow-core search coil
19
Minimization of three-axial search coils’ volume
20
The drawback of three-axial search coils miniaturization
Crosstalk
Crosstalk increases with decreasing the distances between the cores and
increasing the secondary flux at resonance
For optimizing three axial search coil:
One must have a model for crosstalk
21
Crosstalk
zp azp
azp
bzs
Total primary fluxes
 xp   ' xp  a  ' yp  ' zp   b ys   zs 



 yp   ' yp  a  ' xp  ' zp   b xs   zs 


 zp   ' zp  a  ' xp  ' yp   b xs   ys 
Iz
Z
Z
Y
X
Y
X
Applied flux a
Ix=0, Iy=0, Iz=0
(a)
No applied flux
Ix=0, Iy=0
(b)
’xp, ’yp, ’zp – applied, crosstalk-free primary fluxes
xs, ys, zs – total secondary fluxes
Crosstalk due to (a) applied and (b) secondary fluxes
22
Crosstalk
Crosstalk Reduction by magnetic feedback
The total crosstalk as a function of frequency
Crosstalk (%)
Without feedback
10
Rf=20k
5
Rf=70k
1
Rf=200k
0.5
10
50
100
500
1000
5000
10000
Frequency (Hz)
23
Analog and digital signal conditioning
Ultra-low power filters
Flat frequency response
No magnetic feedback
16-bit integrated ADC
Miniature electronic board
Power consumption:
200μW
24
Example of an optimized three-axial search coil
25
Search coil parameters
Sensitivity threshold
Frequency response
Crosstalk
Directivity: <2.5 deg
Crosstalk: <5%
26
Comparison against world leading magnetometers
Sensitivity threshold (pT/√Hz)
Sensitivity threshold at 1Hz vs. power consumption
Power consumption (mW)
27
Conclusion
New approaches to the design and optimization of low-frequency
search coils have allowed their advance to the level, where they
become an optimal solutions in a wide area of applications
28
Acknowledgments




Prof. Eugene Paperno
Mr. Shai Amrusi
Mr. Igor Faivinov
Mr. Boris Zadov
29
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