Scanning the Magnetic Field Distribution of
Loudspeaker Systems
Wolfgang Klippel,
Institute of Acoustics and Speech Communication
Dresden University of Technology
presented at the ALMA Symposium 2012, Las Vegas
Klippel: Scanning the Magnetic Field Distribution, 2012, 1
Abstract
The magnetic flux density in the magnetic gap and the geometry of the
moving coil determine the force factor Bl which is an important parameter
of the electro-dynamical transducer. The paper presents a new
measurement technique for scanning the flux density B(z, φ) on a
cylindrical surface within and outside the magnetic gap using a Hall sensor
and robotics changing the position of the sensor versus vertical position z
and angle φ. The results derived from the scanning process reveal the real
B field in the gap considering the fringe field and irregularities in the
magnetization which may initiate a rocking mode and rubbing of the voice
coil at higher amplitudes. Using the geometry of the coil the static force
factor Bl(x, i=0) can be calculated as a function of voice coil displacement
x and compared with the dynamic force factor B(x,i) measured by a
dynamic system identification techniques. Discrepancies between dynamic
and static force factor characteristics are discussed and conclusions for
loudspeaker design and manufacturing are derived.
Klippel: Scanning the Magnetic Field Distribution, 2012, 2
Questions addressed in the paper
• How to measure the magnetic flux density seen by the
voice coil directly ?
• What can not be predicted by magnetic FEM ?
• What are the consequences of a non-axial symmetrical
B field ?
• Are there any discrepancies between static and
dynamic measurement of the force factor ?
Klippel: Scanning the Magnetic Field Distribution, 2012, 3
Force Factor Bl(x)
magnet
back plate
pole plate
Φdc
B-field
coil
F
Force factor Bl vs. displacement X
Bl(X)
5,0
pole piece
4,5
displacement
0 mm
4,0
x
3,5
3,0
Bl [N/A]
F  Bl ( x)i
2,5
2,0
Electro-dynamical driving force
Voice coil current
1,5
1,0
0,5
U  Bl ( x)v
Back EMF
0,0
-10,0
Voice coil velocity
-7,5
-5,0
-2,5
0,0
2,5
Displacement X [mm]
5,0
Klippel: Scanning the Magnetic Field Distribution, 2012, 4
7,5
10,0
How to assess the Force Factor Nonlinearity ?
agreement ?
Klippel: Scanning the Magnetic Field Distribution, 2012, 5
Example: Static Measurement
of B-field in the gap and force factor characteristic Bl(x)
Hall principle
b
z-axis
UH
d
B field
Hall voltage
I
hall sensor
Neubert, Lars
Master thesis 2010
Turntable with r-axis and φ-axis
Klippel: Scanning the Magnetic Field Distribution, 2012, 6
Scanning Process
Angle 
Vertical
position
z
Cylindrical Coordinates
Klippel: Scanning the Magnetic Field Distribution, 2012, 7
Magnetic Flux Density
on the scanned surface
Vertical
position z
Magnetic
flux
density
B( zi ,  k , r0 )
 i  1,..., N z

k  1,..., N 
maximum
B
Angle 
minimum
(Tesla)
30
20
10
Vertical position z (mm)
Angle  (degree)
Klippel: Scanning the Magnetic Field Distribution, 2012, 8
Flux Density Variation
Vertical
position z
1.2
11.4 mm
T
1.1
1
10.2 mm
0.9
13.4 mm
0.8
9.5 mm
0.7
Angle 
0
50
100
150
200
Angle 
300
350
30
1.2
130o
mm
1
1.12
25
0.8
T
250
degree
0.98
0.84
310o
20
0.7
z
0.6
0.56
15
0.42
0.4
0.28
10
0.14
0.2
-0.2
0
0
5
0
-0.14
5
10
15
Height z
20
mm
25
30
0
0
50
100
150
200
250
Angle
300

Klippel: Scanning the Magnetic Field Distribution, 2012, 9
350
Tesla
Force Factor Nonlinearity Bl(x)
Integration of the B field versus coil length l
Bl  ez   B ( rl )  drl
z
Voice coil
displacement
x
l
Bl ( x )  m
N w

B( x 
 N w
Nw

D  z r ,  )  rd
2

iD
 m 2r  B ( x 
 zr )
2
i N w
Angle 
Height
zr
Gap width
W
Voice coil
Rest
Position
2nd
layer
Radius
r0
Angle

Klippel: Scanning the Magnetic Field Distribution, 2012, 10
Asymmetrical Field Distribution
Flux Density Variation
VB ( ) 
B z ( )  B 
B

z
Variation of Force Factor Distribution
z
VBl ( x, ) 
100%
2Bl ' ( x, )  Bl ( x )
100%
Bl ( x )
2
Bl ( x ) 
 Bl ' ( x,  )  d
0
10
VBl(x=0,)
%
5
0°
VB()
0
maximum
90°
minimum
180
°
-5
-10
0
45
90
135
180
Angle
225
270
315
270
°
360
f
Klippel: Scanning the Magnetic Field Distribution, 2012, 11
Asymmetries of the Magnetic Field
Causes:
• Geometry is not axially symmetrical
• Position of the magnet
• Position of the pole piece
• Magnetization process
Additional magnet
Consequences:
 Tilding of the voice coil former
 Rocking modes
 Rubbing coil
 Higher-order distortion
 damage
Klippel: Scanning the Magnetic Field Distribution, 2012, 12
Dynamic Measurement
of Motor and Suspension Nonlinearities
Stimulus
Noise,
Audio signals
(music, noise)
Multi-tone
complex
Voltage & current
Nonlinear
System
Identification
State Variables
• peak displacement during measurement
• voice coil temperature
• eletrical input power,
Linear Parameters
Nonlinear Parameters
Thermal Parameters
• T/S parameters at x=0
• Box parameters fb,Qb
• Impedance at x=0
• nonlinearities Bl(x), Kms(x), Cms(x),
• Thermal resistances Rtv, Rtm
• Thermal capacity Ctv, Ctm
• Air convection cooling
Rms(v), L(x), L(i)
• Voice coil offset
• Suspension asymmetry
• Maximal peak displacement (Xmax)
Klippel: Scanning the Magnetic Field Distribution, 2012, 13
Full Dynamic Measurement
Noise or
music
current
voltage
described in IEC Standard PAS 62458:2008
Klippel: Scanning the Magnetic Field Distribution, 2012, 14
Identification of Woofer Nonlinearities
Transducer operated in free air or vacuum
L2(x,i)
Re (Tv)
Le(x,i)
Fm (x,i)
Mms
Rms
Cms(x)
v
i
R2(x,i)
u
Bl(x)v
Bl(x)
Bl(x)i
Model used in LSI Woofer
Assumptions:
• Electro-dynamical transducer with fs < 400 Hz
• Mechanical resonator (2nd-order system for free air, vacuum, in
sealed box), creep is not considered
• Four nonlinearities: Bl(x), Le(x), Kms(x), Le(i)
• Bl(x) also reflects influence of magnetic ac-flux
• Linear damping Rms(x,v) = const. (sufficient if Qes < Qms)
Klippel: Scanning the Magnetic Field Distribution, 2012, 15
Comparing Static and Dynamic Measurement
3
2.5
Force Factor Bl in N/A
The Dynamic Measurement
consideres
• Magnetic ac field generated
by current in the coil
• Phase between current and
displacement x
Dynamic
measurement
2
1.5
1
0.5
0
-10
Static
measurement
-5
0
5
10
15
20
Therefore,
Results of static and dynamic
measurements are only
identical if the inductance is
negligible !
Example: 4 inch woofer with L=0.2 mH
Klippel: Scanning the Magnetic Field Distribution, 2012, 16
Force Factor Bl(i,x)
the ac flux generated by the coil is not negligible anymore
permanent flux 0
Force factor Bl(x,i)
magnet
i=0
i= - 10 A
i = 10 A
5,0
4,5
4,0
Bl [N/A]
alternating flux A(i)
3,5
Voice coil
3,0
not measured
2,5
Pole piece
-10,0
-7,5
-5,0
-2,5
0,0
2,5
Displacement X [mm]
Current i
Superposition of A(i) and 0
Klippel: Scanning the Magnetic Field Distribution, 2012, 17
5,0
7,5
10,0
Loudspeaker with high Inductance
Effective
force factor
Bl(x) 9
[Tm]
Dynamic Technique
8
Static Technique
(Voice coil current is zero)
•LSI uses noise as
electrical stimulus
Static
Technique
7
6
•Peak current is high
5
•Effective Bl curve
considering the
impact of the current
4
3
2
1
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
excursion x [mm], coil out =>>
The input current generates a magnetic ac-flux which modulates the Bl-factor
Klippel: Scanning the Magnetic Field Distribution, 2012, 18
Force factor Bl(x,i)
I<0
x
VC=2L_CW_20.47mm (SC)
force factor Bl(x) [Tm]
9
F<0
-10 A
Bdc
8
7
Bac
+10 A
6
5
4
3
F >0
I>0
2
1
0
*
-10 -8
-6 -4 -2 0 2 4
6 8
excursion x [mm], coil out =>>
10
Bdc
Bac
Klippel: Scanning the Magnetic Field Distribution, 2012, 19
Effective Bl(x) Versus Frequency
measured on a loudspeaker with Bl(x,i)
VC=2L_CW_20.47mm (SC)
VC=2L_CW_20.47mm (SC)
force factor Bl(x) [Tm]
force factor Bl(x) [Tm]
9
9
-10 A
8
-10 A
8
7
7
+10 A
6
6
5
5
4
+10 A
4
f < fs
3
3
2
2
1
1
0
f > fs
0
-10
-8
-6
-4
-2
0
2
excursion x [mm], coil out =>>
4
6
8
10
-10
-8
-6
-4
-2
0
2
4
excursion x [mm], coil out =>>
Klippel: Scanning the Magnetic Field Distribution, 2012, 20
6
8
10
Conclusions
Direct measurement of flux density B(r,,z,i=0)
• shows irregularities in the magnetic field due to
geometry, material and magnetization process
• reveals asymmetries causing rocking modes, voice
coil rubbing, impulsive distortion
• verifies result of static magnetic FEM
• basis for calculating nonlinear force factor Bl(x,i=0)
• cannot explain the force factor Bl(x,i>0) if the
magnetic ac field is not negligible (caused by high
voice coil inductance)
Klippel: Scanning the Magnetic Field Distribution, 2012, 21