ELEC-E5650 Electroacoustics, Lecture 2
Part 2: Electrodynamic loudspeaker driver
Ilkka Huhtakallio
Department of Signal Processing and Acoustics
Aalto University School of Electrical Engineering
March 03 2016
Electrodynamic (moving coil) loudspeaker driver
Flexible edge suspension
Flexible
wiring
Diaphragm
Flexible center suspension
Dust cap
Basket
Electric terminals
Soft iron structure
Voice coil
Airgaps
Vent hole
Magnet
“Shorting” ring or cap
Soft iron structure
Acoustic resistance
and dust protection
Figure adapted from [1]
ELEC-E5650 Electroacoustics, Lecture 2
Ilkka Huhtakallio
Aalto SPA
2/15
2016/03/03
ELEC-E5650
Electrodynamic (moving coil) loudspeaker driver
Mechanical system
Diaphragm
mass MMD
Electrodynamic
force F
Vibration
velocity u
F
u
Compliance
suspension CMS
MMD
CMS
rMS
Compliance
losses rMS
Basket (ground)
(a)
(b)
Figure: Single degree of freedom mechanical system. a) mechanical
elements, b) mechanical mobility analogy
Figure adapted from [1]
ELEC-E5650 Electroacoustics, Lecture 2
Ilkka Huhtakallio
Aalto SPA
3/15
2016/03/03
ELEC-E5650
Electrodynamic (moving coil) loudspeaker driver
i
R EG
R EC
L EC
eG
Bl :1
e
M MD C MS
r MS
1:SD
1:SD
Y ARb
uD
Bli
eG
F
Y
ARf
F
REG + REC
LEC
(Bl)2
(Bl)2
Bl
uD
MMD
CMS
rMS
Y MRf
Y
MRb
Figure: TOP: Electro-mechano-acoustic analogy for the moving coil
transducer showing all three domains. Acoustical domain in impedance
analogy and mechanical and acoustical domain in mobility (admittance)
analogy. BOTTOM: Mechanical equivalent circuit in mobility analogy
Figure adapted from [1]
ELEC-E5650 Electroacoustics, Lecture 2
Ilkka Huhtakallio
Aalto SPA
4/15
2016/03/03
ELEC-E5650
Electrodynamic (moving coil) loudspeaker driver
Using Norton-Thevenin transition to present the electrical circuit as
current source with parallel impedance, and then using "dot method" to
convert from parallel (mobility) circuit to series (impedance) circuit [1, p.
312-313]
LEC
(Bl)2
uD
e Bl
G
REG + REC + j ωLEC
(Bl)2
MMD
CMS
RMS
F
Z MRf
Z
MRb
REG + REC
Figure: Mechanical impedance equivalent circuit of moving coil
transducer.
Figure adapted from [1]
ELEC-E5650 Electroacoustics, Lecture 2
Ilkka Huhtakallio
Aalto SPA
5/15
2016/03/03
ELEC-E5650
Electrodynamic (moving coil) loudspeaker driver
Small signal parameters [2]
The suspension resonance frequency fs is given by
fs =
1
2π MMS CMS
√
Where MMS = MMD + 2MM1 and MM1 = 2.67a2 ρ0 is a mass air
load on one side of the piston when ka < 0.5 and a is the radius of
the piston.
The total Q value of the suspension resonance is given by
QTS =
(Bl )2
+ RMS
RE + RG
−1 s
MMS
CMS
ELEC-E5650 Electroacoustics, Lecture 2
Ilkka Huhtakallio
Aalto SPA
6/15
2016/03/03
ELEC-E5650
Electrodynamic (moving coil) loudspeaker driver
The total Q can be separated in two parts
QTS =
1
1
QES
+
1
QMS
QES QMS
QES + QMS
=
namely the electical Q
QES
RG + RE
=
(Bl )2
s
MMS
CMS
and the mechanical Q
QMS
1
=
RMS
s
MMS
CMS
ELEC-E5650 Electroacoustics, Lecture 2
Ilkka Huhtakallio
Aalto SPA
7/15
2016/03/03
ELEC-E5650
Electrodynamic (moving coil) loudspeaker driver
Thiele-Small parameters [2]
The low frequency model of loudspeaker driver can be defined by
just six parameters known as Thiele-Small parameters.
RE , QES , QMS , fs , SD and VAS .
VAS is the equivalent suspension volume, a volume of air having
the same acoustical compliance as the suspension:
VAS = CAS ρ0 c 2 = CMS SD2 ρ0 c 2
These parameters are usually found from the specification sheets
of (low frequency) loudspeaker drivers.
ELEC-E5650 Electroacoustics, Lecture 2
Ilkka Huhtakallio
Aalto SPA
8/15
2016/03/03
ELEC-E5650
Measuring voice coil impedance
Using known series resistor and voltage division the voice coil
impedance can be measured
MATLAB demo
ELEC-E5650 Electroacoustics, Lecture 2
Ilkka Huhtakallio
Aalto SPA
9/15
2016/03/03
ELEC-E5650
Moving coil high frequency drivers
Diaphragm
Sound
absorptive
plug
Diaphragm
Flexible edge
suspension
Flexible edge
suspension
Voice coil
Magnet
Airgaps
(a)
Soft iron structure
Airgaps
(b)
Figure: a) Convex and b) Concave dome diaphragm
Figure adapted from [1]
ELEC-E5650 Electroacoustics, Lecture 2
Ilkka Huhtakallio
Aalto SPA
10/15
2016/03/03
ELEC-E5650
Diaphragms
Material: Thickness, density, Young’s modulus
Profile: Flat, straight cone, hyperbolic cone, etc
Reinforcement, protective finishing
Straight cone
Hyperbolic cone
Corrugated cone
Some possible sections
ELEC-E5650 Electroacoustics, Lecture 2
Ilkka Huhtakallio
Aalto SPA
11/15
2016/03/03
ELEC-E5650
6.18 Nonlinearity
283
Suspension
However, from Fig. 6.21a we see that for large excursions, the suspension becomes stiffer as it
stretches and so the compliance becomes nonlinear, typically in an asymmetrical manner, as shown in
Fig. 6.21b. It is also common for hysteresis losses to prevent the coil from returning to the same
position as before. In order to combat this, a “regressive” spider design [15] has been proposed in
Should
the diminish
moving
system
stableradius.
and in control in high
which the hold
corrugations
in height
with increasing
Force factor. If the coil length hc is equal to the gap length hg (see Fig. 6.22a), the force factor
excursions.
decreases as soon as the coil starts to move in the x direction because the part of the coil which is
rubbersmaller
roll surround
Anechoic produces the dashed curve
then outside the gap experiences Nitrile
a much
force. This typically
termination for
shown in Fig. 6.22b. In order to improve linearity and to extend
the waves
maximum excursion, the length
bending
of the coil is often extended Basket
beyond the length of the gap and this is known as overhang. This
typically produces the solid curve shown in Fig. 6.22b. Alternatively, it can be shorter, which is
known as underhang. One disadvantage of overhang is that the ratio of force factor Bl to moving
Diaphragm
mass MMS is decreased, which tends to reduce efficiency somewhat (see Eq. (6.47)). Although
f
(a)
(b)
x
FIG. 6.21 (a) Sketch of suspension at center and extreme end positions and (b) non-linear force vs. displacement
curve (solid
curve) withfrom
ideal linear
curve[2]
(dashed line).
Figures
adapted
[1] and
ELEC-E5650 Electroacoustics, Lecture 2
(a)
12/15
2016/03/03
ELEC-E5650
Ilkka Huhtakallio
5
(b)
Aalto SPA
Overhang (hc
hg)
Voice coil and air cap
FIG. 6.21 (a) Sketch of suspension at center and extreme end positions and (b) non-linear force vs. displacement
curve (solid curve) with ideal linear curve (dashed line).
(a)
(b)
5
Overhang (hc
hg)
Equal-length (hc
= hg)
Force factor Bl (T.m)
4
hc
hg
3
2
1
0
x
-8
-6
-4
-2
0
2
Displacement x (mm)
4
6
8
FIG. 6.22 (a) Sketch of a coil of lengh hc in a magnetic gap of length hg and (b) force factor vs. displacement curves
with hc [ hg (dashed line) and hc > hg (solid line).
Voice coil inductance varies also as a function of position.
Voice coil resistance increases as a function of temperature,
that increases due to increase power dissipation. This leads
to power comprsession
Figure adapted from [2]
ELEC-E5650 Electroacoustics, Lecture 2
Ilkka Huhtakallio
Aalto SPA
13/15
2016/03/03
ELEC-E5650
Bibliography
[1] Kleiner, Mendel. Electroacoustics. CRC Press, 2013.
[2] Beranek, Leo L., and Tim Mellow. Acoustics: sound fields and
transducers. Academic Press, 2012.
ELEC-E5650 Electroacoustics, Lecture 2
Ilkka Huhtakallio
Aalto SPA
14/15
2016/03/03
ELEC-E5650