PAPERS
Moving-Coil LoudspeakerTopologyas an
Indicator of Linear Excursion Capability ·
MARK R. GANDER
James B. Lansing Sound, Inc., Northridge, CA 91329, USA
The knowledge of a loudspeaker structure's physical dimensions and features can
directly predict both the maximum excursion before damage and the linear excursion limit
as defined by psychoacoustic or performance criteria. Various voice-coil, magnetic-gap,
and suspension configurations are discussed in terms of'their potentials for linear motion.
Measurements which substantiate the predicted linearity are presented, and specific
structures and mechanisms which extend or degrade the predicted linearity are also
discussed.
0 INTRODUCTION
To make sound, you must move air. The most cornmon and popular electroacoustical
method of sound
production involves exciting the air with the motion of a
diaphragm, which is driven by an ac modulated electrical signal controlling a moving-coil permanent magnet
motor structure. The motion of this diaphragm-motor
assembly must be linear if the resulting sound output is
to be linear, that is, distortion free. The reproduction of
sound at low frequencies and high levels requires the
generation of considerable volume velocities, and the
finite dimensions of the diaphragm and motor components limit first the ultimate excursion capability before
damage, and further the excursion for some chosen
acceptable or allowable level of nonlinearity. By examining the topology (the basic layout and physical features) of various types of loudspeakers, inferences can
be made as to their individual performance and characteristics, and predictions made as to their relative and
absolute linearity,
1 EXCURSION
LINEARITY
CRITERIA
It is important to know the excursion capability of a
given transducer in order to determine its suitability for
the intended application. Knowing both the maximum
'* Presented at the64th Convention of the Audio Engineerlng Society, New York, 1979 November 2-5.
10
© 1981 Audio Engineering Society, Inc.
excursion and the thermal power input rating, the maximum sound output can be determined. The regions of
thermal and excursion limitation can be determined for
various enclosure
and system alignments.
From these
predictions the suitability of the transducer for various
applications and systems can be determined.
Before we can judge an individual transducer for excursion capability, we must determine what criteria we
will use to make this judgment. The absolute maximum
excursion is the physical limit of diaphragm motion as
defined by the mechanical structure of the device in
question. This defines the maximum excursion limits
before damage, or the "maximum throw" of a driver,
which is occasionally quoted by manufacturers
if any
mention of excursion capability is made at all. This
information is not without use, for the obvious reason of
preventing driver damage and also in applications where
only sound output and not sound quality is desired. In
most cases, however, we are interested in the extent of
motion that the device can undergo within some linearity constraint.
Most authors discuss the motional linearity of loudspeakers only in the general terms of requiring larger
magnet and coil structures [1, pp. 195, 252-253; 2, p,
262]. Thiele defines Xm_xas a peak displacement limit,
but assigns no criteria for its determination although he
derives various formulas using peak displacement values
[3, pp. 472-473]. Small has done the most extensive
work on displacement-limited
power ratings for frans-
0004-7554/81/010010-17500.75
J. Audio Eng. Soc., Vol. 29, No. 1/2, 1981Jan./Feb.
PAPERS
MOVING-COIL
LOUDSISEAKER
TOPOLOGY
ducers [4,'pp. 39_1-393] and suggests that the amount of
and gap. Here they are sketched with symmetrical
voice-coil
linearity
magnetic
coil, and
magnetic
geometries, but this is not always the case. Often there is
only a single slug center pole, as in Fig. 2, instead of a
separate protruding pole piece resting on a pole support
with a smaller outside diameter. The top plate support,
be it a magnet or fi metal magnetic circuit return casing,
may have its inside diameter only slightly larger than
that of the top plate. The exact configuration of the
magnetic gap becomes important because the magnetic
flux is never confined strictly to the gap, but spreads out
overhang be used as a rough estimate of driver
[5, p. 806]. This does not address voice-coil/
gap topologies other than the overhanging
neglects the effects of fringe flux outside the
gap, which are significant,
2 NONLINEARITY
COMPONENTS
GENERATING
HARMONIC
Olson has analyzed the effects of nonlinear elements
in producing harmonic distortion components [6]. He
has shown that for a force as a function of displacement
of the form
F(x) = ax + bx3
(1)
Fourier analysis will yield solutions of the form
x = A cos rot + B cos 3tot.
yields
x = A cos tot + B cos 2rot
forming fringe lines above and below the gap. If the
permeance of the region below the gap is higher than
that above due to the presence of magnetic structure
elementstoo near the gap, morelinesof fringefluxwill
existbelowthegapthanabove.
move in a nonsymmetrical
(2)
sides of the gap (Fig. 3). Various other symmetrical gap
geometries which attempt to equalize fringe flux, such as
extended center poles and chamfered gap tips, have also
been utilized [7, pp. 239-241].
32R
(4)
.
which shows the presence of second-harmonic distortion. In this case we are dealing with single-ended nonTypical loudspeakers can be seen to have a force
function with both square and cubic terms. The cubic
terms are manifested as the coil is driven out of the
magnetic field to an equal extent on both sides of the
linearities.
gap,
a symmetric nonlinearity yielding third-harmonic
distortion. Thus we would expect our linear excursion
limitto manifest itselfpurely in terms of third-harmonic
distortion. The square terms can come about if the gap
tion is not centered in the magnetic gap, or if rectification or other effects impart a dc offset to the coil travel
midpoint fringeare
under drive.
Any of these effects
produce
a
fluxand
nonsymmetrical,
if thewill
coilrest
posisingle-ended nonlinearity, giving second-harmonic distortion. It should be noted that the driver should be
inherently free of second-harmonic
distortion, only exhibiting third-harmonic
distortion due to finite coil and
gap heights. In both cases, higher order terms have been
left out of the analysis due to their much lower amplitudes compared to the second- and third-harmonic
components.
CONFIGURATIONS
Thiswillcausethecoilto
flux field and hence cause
distortion. Even in a symmetrical magnetic gap, fringe
lines are inevitable and can at best be made even on both
This is the form taken by balanced, or symmetric, nonlinearity, where the distortion manifests itself as a thirdharmonic term. For a force-displacement
function of
the form
the solution
gap
1
_-J
(a)
[I.
_tl
_,
_
i
_'"
(b)
l
_
1[
_[
[
]
fff
(c)
Fig. 1. Thethreebasicvoice-coil/magnetic-gapconfigurations.
(a) Overhanging coil. (b) Underhung coil. (c) Equal-length coil
and gap.
_//,;.z},.,
t t m/.=._',a _ _
AND FLUX DISTRIBUTIONS
'
__
///._-_,.
x
t / ,,;;z&q_',_ I
-'
Fig. 1 shows views of the three types of voice-coil/
magnetic-gapconfigurationsin cross section.Theyare
_
the long coil-short gap or overhung coil; the long gapshort coil or underhung coil; and the equal-length coil
Fig. 2. Flux distribution in nonsymmetrical gap showing uneven fringe field.
d. Audio
Eng. Soc., Vol. 29, No. 1/2, 1981 Jan./Feb.
f
_
11
GANDER
PAPERS
The presence of fringe flux is an important key to the
understanding
of loudspeaker linearity. Fig. 4 shows
typical flux distributions for various gap configurations.
Fig. 4(a) is the theoretical ideal, where all the lines are
concentrated evenly within the gap and no flux is present
outside. Fig. 4(b) represents the best that is practically
attainable, with even distribution across most of the
gap, which begins to reduce as the gap edges are approached and gradually approaches zero as the fringe
flux weakens away from the gap. If the gap is at all
nonsymmetrical,
the flux distribution will take a form
similar to Fig. 4(c). Here the fringe flux is significantly
greater in the inward direction. For wide gaps the flux
within the gap can also be affected,
For a coil moving in a flux field, the Bl product is
proportional
to the total flux passing through the surface ara of the coil. Bl will change if the total number of
lines of flux through the coil area changes. For underhung and equal-length topologies this occurs as one end
of the coil begins to leave the gap. For overhung coils,
where the fringe flux is a significant portion of the total
flux at rest position, this will begin to occur as soon as
there is any coil motion, The degree of change depends
on the specific spatial distribution of the fringe flux field,
but definitely becomes dominant as the end of the coil
approachesand entersthe gap.
4 MOTOR
FORGE
For the diaphragm to be capable of linear excursions,
the loudspeaker must provide linear diaphragm motion
relative to the electrical input signal. The force provided
by the motor is the product of current I, which is the
input signal, and the Bl product,
the motor strength:
F = (Bl)I.
(5)
The input signal is here a current, but in almost all
applications we drive loudspeakers from constant voltage source amplifiers. For an input voltage E, the current I is given by
In the region of resonance
F =
Zcm _
Zec, so that
EZm,
(9)
Bl
and the force is -inversely proportional
to Bl. Here we
have the surprising result that as the Bl decreases, the
motor force actually increases. The increased force will
continue until the decrease in BI causes the motional
impedance to no longer be dominant over the blocked
electrical impedance. The force will then decrease from
its maximum value to zero, passing through a point of
full linearity along the way. Under most operating conditions, loudspeakers are required to undergo maximum
excursion in the region of resonance and are subject to
this effect. It will also vary with the acoustic loading of
the driver, since the motional impedance will change
frequency and shape in sealed, vented, and horn-loaded
enclosures.
Another distortion mechanism is an offset in the coil
rest position. Any difference in the coil rest position
from the position of maximum Bl will cause secondharmonic distortion. This can come about due to improper physical construction, gravit.y bias depending on
the axial orientation of the unit, dc present in the drive
signal, or a nonsymmetrical
flux field, as already discussed.
A solenoidal force is generated between the voice coil
and the center pole, produced by the change in voice-coil
inductance both with coil position and with change in
saturation level of the center pole [8], [9]. This causes a
force creating a dc offset causing second-harmonic
distortion.
An offset in the coil rest position can also be imparted
due to dynamic instability, the electromechanical
rectification effect first described by McLachlan [7, pp.
245-251].
This is another
artifact
of the variation
of
//,i."-._.xxx
I
1
Zec
+
Zeta
(6)
where Z_cis the blocked electrical impedance consisting
of the dc resistance and voice-coil inductance, and Zem is
the electrical motional impedance generated by the back
EMF of the coil motion. This electrical motional impedance is givenby
x_,¢.-__-.
;,/ /
x_%_-5' / / I
_
/_"_'_
Fig. 3. Flux distribution with symmetrical field geometry
showingequalfringefieldon bothsidesof gap.
(B/) 2
Zero
Zmt
(7)
where gm, is the total mechanical impedance, including
the radiation impedance due to the air load on the
moving
diaphragm.
Combining
Eqs. (6) and (7) into Eq. (5),
F =
(BI)E
Zec
12
+
(Bl)2/Zmt
(8)
Cop
Gap
He;ght
]
Height
J
}
+
Cop
Height
X\
_
0,.,
.......
(a)
(b)
(c)
Fig. 4. Flux distribution with displacement along axial length
of magnet structure. (a) Ideal field. (b) Symmetrical field
geometry. (c) Nonsymmetrical gap geometry.
J. Audio
Eng. Soc., Vol. 29, No. 1/2, 1981 Jan./Feb.
PAPERS
motor
MOVING-COIL LOUDSPEAKER TOPOLOGY
force with displacement
caused by the fringe
field, where the coil rest position will actually jump in or
out to the suspension limit. In the mass-controlled region above resonance the coil acceleration is 180 ° out of
phase with the displacement. If the input level is large
enough to exceed the expansion region, where BI decreases cause motor force increases, both the acceleration and the current will be minimum at the extremes of
coil travel. The coil will tend to jump toward this weaker
field [10]. This will cause a distinct rise in distortion due
to the offset in the region from resonance up to 150 Hz or
so, where the amplitude is no longer sufficient to cause
jump-out. This effect is prevalent in long coil-short gap
loudspeakers,
and usually will not occur in underhung
coil structures since their coil motion is within a linear
fluxfield,
5 SUSPENSION
FORCE
The use of nonlinear or progressive suspensions can
prevent or reduce these distortion mechanisms. Harwood noted the fact of increasing motor force from the
linear level before the decrease, and showed how a loudspeaker could be fitted with a suspension which increased its stiffness force at the correct rate to compensate for the increased motor force, thus increasing the
linearity of the system l11 ]. This is so because the other
dominant force in the system is that provided by the
stiffness of the suspension elements at the instantaneous
excursion. Olson has shown that nonlinear suspensions
can
approximated order
by theas addition
cubicnonlineariterm, the
samebemathematical
the motororaforce
ty [ 12]. The stiffness, the BI product, and the suspension
losses all vary with displacement. For displacements
where the motor force factors remain approximately
constant and much greater than the suspension force
nonlinearities,
the total driving force will be relatively
will determine the force function, and if the nonlinear
components are in balance, the net force linearity can
actually be extended. The nonlinearity of the suspension
force
strong to in
overcome
the dc
linear. can
In be
all made
other sufficiently
cases the variations
these elements
6 OTHER FEATURES AFFECTING
Voice-coil/magnetic-gap
dimensions primarily determine linearity in the stiffness andresistance
controlled
regions, below approximately
150 Hz for most low-frequency loudspeakers. In the mass-controlled
region of
operation venting effects in the motor structure and
magnetic field nonlinearities tend to dominate the distortion characteristics
up to and slightly beyond the
piston-band
limit, where cone breakup distortions are
the major source of nonlinearities.
Venting of the loudspeaker structure
of the air from causing distortion. Methods employed to
eliminatethis problem includea porous or perforated
center dome, voice-coil former perforations, or a vent
hole through the center of the magnet structure [14, pp.
297-298]. A vent in the rear of the magnet structure
must have sufficient area to prevent turbulent nonlinearity, and must be partially blocked with open-cell foam or
screen to prevent foreign particles from entering the
magnetic gap.
The magnetic field itself can undergo modulation due
to the ac field generated by the current in the voice coil.
This effect was first identified by Cunningham [8] and
more fully investigated by Gilliom [15], and creates
second-harmonic
distortion proportional to coil current.
This effect manifests itself most when the center pole
within the coil is constructed to high-permeance
material, so that motors with center poles operated at a
saturated flux level, or centrally placed Alnico magnets,
are relatively immune. Fig. 5 illustrates some of the
various methods which can be employed to eliminate
this source of distortion, all involving the use ora shorted turn or Faraday loop within the magnet structure
_
] l_
d. Audio Eng. Soc., Vol. 29, No. 1/2, 1981 Jan./Feb.
;
I
_
(a)
Typical
progressive
suspension
e'ements
arethose l_
termined by the shape of the corrugations, the thickness
of the material, and the degree of treat. Half-roll surrounds
of foam or rubber
are usually of very beingdelow stiffplianceandlinearity,
the exactcharacteristics
ness,butevenloudspeakersfittedwiththesecanexhibit
progressive stiffness at long excursion if their limits are
reached. Conversely, if the suspension force increases at
too great a rate, it may exceed the motor force and limit
linearity,
is usually asso-
ciated with heat dissipation and power-handling considerations, but it is also necessary to prevent nonlinearity
components of the motor force, but insignificantcornpared to the ac motor force, preventing dc offset [13].
with high nominal stiffness, such as treated one-piece
cone edges and cloth rolls impregnated with phenolic
resin or other damping chemicals. Centering spiders
also contribute to the stiffness characteristics. These are
usually made oftreated cloth in a flat disk or cup shape
with corrugations to provide increased nominal com-
LINEARITY
[ ,!
!
_-_'"_'
J
(b)
r
_
_
_
_
_
[
i
]
f
(c)
Fig. 5. Methods of providing a shorted turn within the magnetic
field toplating
preventonmodulation
by Conductive
the voice-coil
(a)
Conductive
pole tips. (b)
capcurrent.
over pole
piece. (c) Conductive ring.
13
GANDER
PAPERS
which acts to generate a field equal and opposite to any
changing field induced by the voice coil. A conductive
ring can be placed around the center pole, a conductive
cap can be placed over the pole piece, or a ring of
conductive platingmay be applied to the pole tips. If the
conductive ring is placed in the gap, the effective gap size
and hence gap reluctance is increased, increasing the
fringe field and requiring a larger magnet for the same
gap flux. The pole piece cap also precludes symmetric
gap geometry, making the flux field unsymmetrical as
well. If conductive rings are used anywhere within the
coil, they will tend to reduce the voice coil inductance
rise at high frequencies and hence increase acoustic output. This effect may or may not be desirable, although in
some cases it is the only motivation for using the ring,
not for its distortion-reducing
characteristics [16]. If the
conductive ring is located around the center pole, care
must be taken in the placement and size of the ring to
prevent large changes of voice-coil inductance with the
position. In addition to causing second-harmonic
distortion from the solenoidal force, this effect can cause
modulation of high-frequency tones by large low-frequency excursions, a serious performance detriment and
a linearity criterion in itself [17].
The presence of conductive rings directly within the
gap may also tend to reduce third-harmonic
distortion
generated due to the magnetization of the magnetic gap
pole surfaces by the voice-coil flux. This particular problem can be attacked directly by constructing the pole
surfaces from material with a very linear magnetization
characteristic. This method has no effect on flux modulation of the permanent field, however, and hence does
not reduce second-harmonic distortion,
7 APPROXIMATE
LINEARITY
PREDICTION
From this analysis we can formulate predictions for
the linearity of the three basic types of loudspeaker
motors. If the height of the coil and the magnetic gap are
known, the peak displacement of the unit should be
approximately given by half the magnitude Of the difference of these two dimensions plus a correction factor for
fringe effects. For overhung coils the coil may move past
the fringe field on one side and just begin to enter the gap
before gross nonlinearity occurs. The correction factor
is therefore zero for this topology, and the formula is the
sam_ as that suggested by Small [5, p. 806]:
Xmax----
voice-coil height 2
gap height
(10)
Equal and underhung units may have their coils leave
the gap by some percentage approximating
the fringe
field on each side of the gap before gross distortion
occurs, effectively lengthening the gap and increasing
linearity. Ifa 15% factor is adopted as an approximation
for the fringe field extension on each side of the gap, then
the formula becomes for underhung and equal coil and
gap topologies:
Xm_x=
14
gap height - voice-coil height
2
+ 15% (voice-coil height).
(1 l)
While only direct measurement of the B/product and the
suspension stiffness values with displacement can accurately predict the exact linearity for a given unit, these
formulas should provide a good approximation
in the
absence of further data. A given unit will have to be
inspected for clues as to whether its linearity may be
increased due to the balancing of motor and suspension
nonlinearities, or decreased due to dc offset effects or
excessively stiff suspension
8 CHOICE
elements.
OF LINEARITY
LIMIT
The assignment ofa linearity limit presents a problem
because a definition of acceptable linearity must be
chosen. The desired or required linearity will depend on
the quality requirements of the particular application.
For most sound production and reproduction uses, the
question of assigning a number moves from the realm of
engineering acoustics to psychoacoustics.
When we talk
of the linearity of reproduced sound we are talking
about distortion. Noticeable, acceptable, and tolerable
levels of distortion vary with both frequency and the
level of the sound being produced, the content of the
sound, whether the signals are transient or steady state
in nature, as well as the quality of the listener.
Probably the most common method of assessing the
linearity of a given transducer is an "eyeball-earball"
test, driving the device near resonance and increasing
the input until it begins to "sound bad," and measuring
the displacement at this level, an arbitrary process at
best. Small suggests the criterion of driving the loudspeaker at resonance in free air and measuring the displacement at 10% total harmonic distortion [5, p. 806].
These methods assume no variation of excursion linearity with frequency and drive level, which can be substantial for certain topologies.
A 3% distortion level seems a more appropriate choice
for the linearity limit. Measurements on various types of
transducers indicate a good correlation of the peak piston displacement for this distortion level with the predieted maximum linear displacement. A 3% (-30 dB)
distortion component relative to the fundamental contributes less than Y4dB to the total acoustic output, so
that maximum sound pressure level calculations will not
be seriously affected [4, p. 393]. The peak-to-average ratio
in most program material is quite high, and the signal
material is usually transient in nature. These and other
factors indicate that under program conditions with a
system designed with this level of peak displacement in
mind, the 3% distortion level will only be reached occasionally, and then psychoacoustic factors should tend to
mask the full negative effects of such distortion. We
would like to think that distortions below 1% are possible as the chosen criterion, but these types of figures will
in general lead to unusually conservative linearity figures. At an input level approaching the thermal input
capabilities of the loudspeaker, other distortions assoelated with but not directly related to the motional
linearity will also be increasing, such as cone breakup
J. Audio
Eng. Soc., Vol. 29, No. 1/2, 1981 Jan./Feb.
PAPERS
MOVING-COIL
and electrical, thermal and magnetic field effects. The
choice of a 3% distortion limit on any and all distortion
products seems to be an appropriate compromise between the maximum excursion before damage and some
arbitrarily low distortion level. Adequate headroom will
normally be built in, as with any intelligent design, so
that this level will not often be reached. For those applications and
involving
sustained
high-output
low-frequency
tones,
for ultimate
quality
requirements,
both the
maximum excursion and the maximum input power
should be scaled down accordingly.
9 EXCURSION
MEASUREMENT
METHODS
themovingassembly,inwarduntilthebottomofthecoil
form hits the back of the structure and outward until the
coil form leaves the gap, or until the suspension elements
allow no more motion. The assignment of a linear limit
poses a more difficult problem in that the excursion must
be measured under sinusoidal excitation varying with
frequency and amplitude. Direct visual measurement,
displacement probe, laser [18], and accelerometer
[19]
techniques have all been utilized. Data can be taken at
constant amplitude input with varying frequency, and at
constant frequency with increasing input. The results
can be plotted directly and analyzed for linearity, or
acoustic measurements may be taken simultaneously
on
the sound output, analyzed for distortion components,
and compared with the excursion data. All these methods involve direct measurement of the displacement, but
computed from the
10 PEAK PISTON DISPLACEMENT
The axial sound intensity output from a piston source
operating into one side of an infinite baffle is given by [2,
p.175]
The intensity is related to the pressure by
p2
I =
I = 2PoCU2sin2 [ _-(¥/r
k
2 + a2 - r) ]
L
(12)
where
=
=
=
=
=
=
a
piston
= piston radius
intensity magnitude
density of air, 1.21 kg/m at 20°C
velocity of sound in air, 343 m/s
peak piston velocity
wave number, 2n-/X = ro/c
distance from measuring point to center of
For distances
radius, r >>
Combining Eqs. (13) and (14) and taking the square
root, the pressure is given by
P = pocka2u
2r
from the piston large compared
pock2a4u2
Eng. Soc., Vol. 29, No. 1/2, 1981 Jan./Feb.
excitation,
as
the piston displacement
x0 = xsin tot.
u -
dxo
-- dt
Therefore
is
cox cos tot.
the maximum
peak diaphragm
u
Xpeak= -_'
Substituting
can
(17)
The piston velocity u is the derivative
time of the piston displacement:
with respect to
(18)
displacement
(19)
Eq. (16) into Eq. (19),
rp
Xpeak =
(20)
2Pozr2f2a2
Eq. (20) can be modified for the case ofa 4rr sr radiating
field for measurement in anechoic environments by substituting a factor of 2 to account for the increase in the
integrating area:
rp
Poir2f2a
(21)
2
The stipulations are that r >> a, that the measurement
is performed in the far field of the transducer; and that
,k > 2rra, that we are radiating omnidirectionally.
This
stipulates that we are in the piston band of the transducer.
Keele's work on near-field measurement also applies
directly. His relationship between the near- and far-field
pressures [20, Eq. (5), p. 155]
2r
PN-
to its
(16)
For sinusoidal
be represented
a
(22)
PF
can be substituted
a, Eq. (12) can be shown to converge to
8r2
d. Audio
(15)
2rp
u = _
Pocka2
into Eq. (20), yielding
PN
Xpeak
I =
(14)
2poc
Xpeak-_
I
Po
c
u
k
r
TOPOLOGY
Solving for the velocity u,
Various methods have been employed to measure diaphragm displacements.
The destructive excursion limit
can be algebraically computed from structural dimensions or directly measured by physical displacement of
the displacement may be accurately
acoustic measurements
themselves.
LOUDSPEAKER
=
4p0 7r2f2a
(23)
(13)
The near-field
pressure
can then indicate directly the
15
GANDER
PAPERS
piston excursion, with all the appropriate
caveats
applied.
Instead of making a separate measurement,
we can
now make our normal acoustic sound pressure measurements and simultaneously know the excursion which
the driver is undergoing. In particular we can make
acoustic distortion measurements and correlate the levels of distortion and individual component contributions with the excursion,
11 EXPERIMENTAL
MEASUREMENTS
Swept sine wave sound
pressure
amplitude
versus
frequency curves were taken on an outdoor ground
platform with the measurement microphone directly
above the test loudspeaker at a distance of 1 m on axis.
The platform has no substantial obstructions for a distance of at least 15 m in all directions along the ground
surface so as to effectively provide a half-space 2rr sr
measurement envfronment. The rear of the loudspeaker
units were surrounded
by a 280-liter well-braced enclosure extensively lined with damping material. The
effective volume of the rear chamber was sufficient to
have only minimal effect on even the most highly cumpliant of the units tested. Gravity bias is a potential
problem in measurement environments such as this. The
most highly compliant loudspeakers have stiffnesses on
the order of 1.5 × 10 3 N/m, and for moving masses as
large as 0.15 kg under a gravity acceleration of 9.8 m/s 2
the moving assembly displacement
will be approximutely I mm. Stiffsuspension units show displacements
of less than 0.2 mm. This bias is a single-ended nonlinearity affecting only second-harmonic
distortion, and
the third-harmonic displacement linearity should not be
affected. A tracking filter was used to isolate the secondand third-harmonic components, which in all cases are
raised 20 dB each for convenience,
For pressure in terms of dB sound pressure level,
p
SPL = 20log
Prms
(24)
_-_/t'2prms
(Pfm-'----'L-_)
Pref
---_ l0 SPL/20 Pref
(25)
7.2 - 7.2
+ 0.15 (7.2) = 1.1 mm.
2
(28)
If we choose the point where the third-harmonic
distortion reaches 3.16% (-30 dB), here where the fundamental and third-harmonic
curves are 10 dB apart since the
distortion curves are raised 20 dB, the excursion that the
loudspeaker is undergoing at this distortion level is
Xp_ak=
(1.18 X 10 3) 10103/2°
= 0.9mm
(105) 2 (128) 2
(29)
which agrees very closely with the prediction. Fig. 7
shows another driver of the same type, but assembled
with the coil not centered but riding approximately
1
mm high. As predicted, the second harmonic is greatly
increased but the third harmonic remains at the same
level:
×peak=
(1.18 X 103) 10,0,/20
(88) 2 (128)2
-----1.0 mm.
(30)
Fig. 8 shows the response ufa 380-mm (167-mm effective
pistonradius)driverwithan underhung7.2-mmcoilin
P_r = 20_ N/m 2.
an 8.9-mm gap being driven by 13 V rms (16 1_ nominal
impedance). The predicted linearity is
Since all measurements are at 1 m, we can combine this
and the other constants of Eq. (20), reducing it to the
convenient form
(1.18 × 103) l0 svL/2°
_-
(27)
×max=
8.9 - 7.2 + 0.15 (7.2) = 1.9mm.
2
The -30 dB third-harmonic
distortion
(31)
point yields
f2a2
where xp_akand a are in millimeters.
Data were taken at different voltages to show the
effects of variations in drive levels, but as the formula
indicates, neither the actual input power level nor the
power transfer efficiency of the measured unit is of
16
Xma_--
(26)
where
Xpeak
concern in determining the excursion.
Other than measurementaccuracyin determiningthe
sound pressure level at a given frequency, the only variable in question is the effective piston _radius for the
loudspeaker diaphragm,
usually consisting of a rigid
truncated cone and flexible outer surround. Strictly geometrical considerations show that this can be accurately
given by the radius of the rigid part of the diaphragm
plus one-half the width of the flexible surround.
An initial test can be performed to indicate the unit's
susceptibility to dc shift and jumpout. The transducer
can be driven at a frequency above resonance where the
excursion will be significant and the input voltage increased to approach the thermal limit. A reference point
on the moving assembly can be viewed relative to a
stationary point on the frame, and any deviations from
equal positive and negative increase noted.
Fig. 6 shows the response of a 300-mm (128-mm effectire piston radius) loudspeaker with an equal coil and
gap height of 7.2 mm being driven by 9 V rms (8 11
nominal impedance). The suggested formula forlinearity predicts
Xpeak=
(1.18 × 103) 10102/2°=
(58)2 (167)2
1.6 mm.
(32)
showing good agreement with prediction. When dealing
with highly damped (low Q) drivers it is sometimes
difficult to accurately determine distortion data due to
d. Audio
Eng. Soc., Vol. 29, No. 1/2, 1981 Jan./Feb.
PAPERS
MOVING-COIL
LOUDSPEAKER
TOPOLOGY
_°r· · -,
L-..F
' ' "_
.....
- ....
,
} .....
........
J't:j-_
I_-_' i_'i_i
.....
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? '"
I I
"'i ; ....
I it ; ' ,
i
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.
i ,i
i
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J
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;
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_',
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'
_-30dB
i'-_
d8 k
:__
_
'
i
-
7-;-:-[ :
! ....
.
.'_....'L-.'._t
._:!. i -'.',t
_ .
....
(
.
_ i ..: ....
>
"h:
_°--__>_-_._
-/- ',.4._5:j:?-_.\::_:
L.-:_:5::!'z_':r
:-_'
4':_:i-'_:s:[_k
:L--_:-t:-:h--_::-I;:
-I.'i'_L_:-_-:-:_
2
' +-_:
3_-"/v4
5
_6
_ ;- '"'" _
78910
'"'""zl.5
_
'
4.
,-5 6-- ? _._F
, 1.5.... _ E-'..
_.'......
_'i"910 ........
891_
J
4'""'%_6--_'--_
u'u/3-'r""'--'_
100
1000
Fig. 6. Half-space
on-axis amplitude
response
height of 7.2 mm, 9 V rms input, 8 11 nominal
__i___
iii!i!'''
of a 300-mm (128-mm
impedance.
Distortion
10000
effective piston radius) loudspeaker
products raised 20 dB.
i''iiilli_iL-'::_1:_' 1'"
i_K_-%:?_,
, ',
'tO
I :
i,;
;
]
i
; ' :
ii
I%1
I_OdeH_:'_Hi+t)_il
2
3
4
Fig.
5
6
7
._11
[ I i
_-<:,,<_-::_:_-_
-
I _l I II II 11_[I ;_J
-:::i:
'
i '
'
_+_.-._/I;II',_III
li,"llllllillili?:-I
e 9 10
100
1.5
7. Same conditions
2
_
4
_
6
I
8 9 10
1000
as Fig. 6, but loudspeaker
1,5
assembled
_!_
_
·
'....
_ ........
....
.....
,
t
- _
_.
;-----,----?-_- ,.
.
k .....
_---t- -_....
-
?'-')'
_r '!-f-_-'_.!._-lr'---"_/_t
: f _ ........
! I
--t---:y."--',
- --?---fi
'.,'-(-; : !-_
__L_:
! ....
....
_....
: _--::
'.
_+"-,.: .,- -_ "___--_
' '_--"'-
:.!
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5
6
:"2
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L"
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!.
&.'
:.
.*
) -
;..;.
. _,
-_...L::-:L_
,_' '!'_: ,
8 9 10 '
10000
,
;
·
!
! i
_ ! i
_--._.__,_l_
7-..... _-----_- ...................
i _-! .... _-.:
.....
.-
?
_'_ 5_
Z
with voice coil 1 mm off center.
::---:::_:::1-:-:
::::::::::::::::::::::
: !:I:-:! _ ::I::
I ..... _,.......
with equal coil and gap
_
,
t
._,
1
:
__......
: : !
i
: ':
i-'
.. _ _ I
'
[
:
i ',
._,
t ....
_
'
I
I
',_---:'"7_,-:-_-_Od,_
_--:..... _......... r'-,_--:+'
'!-"t......_---!.... ,.... _l-.-!--.,
...., ....
F_-Z:..r::.._.:,E':_','I: .....-:--:::-;":_:'.:;F:',:/!i_'_'-__q--:--i--,-h:4½--l'?:_L,
': ':
; I_--_T
, ''
-
_,::ff
_'_-_--_-_.+-'
-- -
Ct ....
t":
,-Fi':
·-_-l"_
_='_-,,
I,
_:_"-,_-_
'
I r
iq
1
O0
Fig.
gap,
8. Half-space
on-axis response of a 380-mm (167-mm
13 V rms input, 16 11 nominal impedance.
Distortion
J. Audio Eng. Soc,, Vol. 29, No. 1/2, 1981 Jan./Feb,
d. %
......
·
_.:q_"T
:'_:
-;-:--F
..........
.... _' ' --_''
1000
effective
products
piston radius) loudspeaker
raised 20 dB.
111 T _
r:--'
-.............
t '
''
":-
10000
with a 7.2-mm
coil in an 8.9-mm
17
GANDER
PAPERS
the skewed shape of the curves. If the driver is ultimately
to be utilized in some flat response alignment, the distortion curves should be viewed in the perspective of fiat
acoustical output. A compressor or equalizer can be
used to adjust the acoustic output of the driver to some
constant sound pressure level with varying frequency
Fig. 10 shows the response of another 380-mm driver
with a progressive suspension and a heavier, stiffer cone
than the previous unit, driven with 10 V rms (8 fl nominal impedance). It is fitted with a ll.2-mm coil in a
7.2-mm gap, so that the predicted linearity is
down to the thermal or physical excursion limit of the
unit. Fig. 9 shows the same driver of Fig. 8 adjusted for a
11.2 - 7.2
xm,_x=
- 2.0 mm.
(34)
2
constant 104.5-dB sound pressure level. If we compute
the peak excursion for 3% distortion at this drive level,
The 3% distortion
point gives
(1.18 × 103) 10r°1.5/2°
Xpeak
(1.18 × 10 3) 10104/20
= 1.9mm
(60)2 (167) 2
_---
XPoak =
(33)
,,
_;l
''.l'
,.L '---r-_,.l[[
,
:
i ;
i
fll
'_
_
,_
.!;;t;;'i!
,
I-)
il
I,,
(1.18
Xp,,,k=
I I I
;
I
iJ
Ii!
IJll 'l_'llll
P,l_llIliilll]tlillllll[lltl_l_ll!"l
Ii,Ii
5
6
7
8
9
_0
illtlltllllllllll_
LJ
1.5
_
_'
'_
_
4'
_
1
hd/l_,
'
I
1_I t!i_=l_i
J-LLIL_ _'l_J LI
",iFi_l.lil
_i
'
i
' !
'
; Ill;INI rlnillU
II_
,,,i,i,,_[-_t_l-_,u,J,,,,,.,,.,[l+H-i+dSlil,htlh:,
4
(36)
,
·
I,:lUdl
Iq I Iliallr._l,l
Id'r
I id
* i
! [ J;f rii:i;:l
IIIilit'IlIilIUIII_LI
_tYrTq---':---V=
ri I_] lift.hi
'f
× 10 3) 10r°5/2°
(57) 2 (167)2
= 2.3 mm
_._L
i i _i-_q---I
; i P,J:i,;,i
, -:lilnlil/,lrll,,[/l,l,.;
! ;
·
_]
, I I I
I I I I
ilrli[
-t+,,i,
3
i
_
::,,:,_.d
[ IilL_i
I,
I [ I [ I !liill _ '_tff_ll_'/_l
! f I I]lilillilliJllllll.i,!.ltl
[,ll',','l
d_
'Jill
2
:
r
,
_!! F ] 'liT'
L!
: '_I
''
o[ 70
i
,
i
'_I
(35)
Fig. 11 shows the same unit equalized for 104.5-dB
constant output. The third harmonic gives
showing better agreement with the prediction. It is important to note that this method will not change the
frequency or shape of the resonance, so that possible
changes in linearity may not be noticed.
,I
= 1.9 mm.
(52)
2(167)
2
_6
7
8
9
wu
I
J II
I ;
I0
_.5
I
[
{ k'
'
"_"
I'-
i
'
'I
'
_
4
5
6
I
s
9
_0
lOOO
_.5
2
mooo
Fig. 9. Loudspeaker of Fig. 8 equalized for constant sound pressure level output. 45 V rms input at 30 Hz decreasing to 5V rms at
400 Hz and above. Distortion products raised 20 dB.
'tO _'__'_
F
3C
____ '
'
'
*
'
"
[_
'_
"
W
-r .................
I..........
I ....
'"'."',
.........
'
' ;
_
'? -_ ._,
' 'I,
*
.... ....
'
i
, --
·
".
_
,
r,....
_..-.-m_.t
.;
·
.,:.
.* _
.......
i-r:.
4-
t
:
·
i...
s
Tr.
,
_
-30dBi_--
L
_ .....
#,x_
,
._,
__
.....
.....
....
i :'
--
i
_'
k---!-t-':-i
_ u
,
s
_
7 8 9 _o
1O0
_._-...._,..a
'
'
_.
iq
L
I!t
_-
,i
,,.:,.._:::_h.,,
4 -_,',_ _
_,._
:
_
-
r -
: .... .....,.... 'r--q
;-:'-Jr:: ,l-'-_-_t_-_-_Tt--
75 i:
c
! ?
'
_
f '
' /_-4
v
II
r
,:
3
I-
.- i : -, '_---
_: pI
_
t, '/
__LJ
-
F
_,
_
1000
,,
/._'
a'u_
'_
10000
Fig. 10. Half-space on-axis response of a 380-mm (167-mm effective piston radius) loudspeaker with 11.2-mm coil in a 7.2-mm
gap, 10 V rms input, 8 1! nominal impedance. Distortion products raised 20 dB.
18
J. Audio
Eng. Soc., Vol. 29, No. 1/2, 1981 Jan./Feb.
PAPERS
MOVING-COIL
showing at this drive level some linearity increase due to
the action of the progressive
suspension.
The second
harmonic
shows a large increase
in the region from
resonance, 38 Hz, on up to 200 Hz. The fact that the
second harmonic drops at resonance indicates that this
rise is probably the result of a dc shift in the coil rest
and the third-harmonic
position
a constant
due to the magnetic
out effect.
rectification
In this case the progressive
(1.18
=
3% distortion
X 103) 10 m3/2°
(72)2 (167)2
-----
In Fig. 13, at the higher voltages
or coil jumpsuspension
sufficient to slightly increase linearity,
enough to prevent the dc offset.
Xpeak
LOUDSPEAKER
104-dB
was
(1.18
but not strong
Xpeak =
TOPOLOGY
point indicates
1.2 mm.
(38)
necessary
to produce
output,
×
103) 10 m4/2°
(72) 2 (167)2
= 1.3 mm.
Fig. 12 shows the response of a 380-mm unit with the
same 7.2-mm equal coil and gap motor of the unit in Fig.
The linearity
suspension.
6 fitted to the cone and progressive
suspension of the
unit in Figs. 8 and 9. The predicted linearity is again
Fig. 14 .shows a long-excursion
380-mm unit fitted
with a highly compliant foam surround,
a fairly linear
centering
spider, and an underhung
7.2-mm coil in a
15.2-mm
at 20 V drive (8 13,nominal impedance).
gap, linearityis
Thepredicted
7.2 - 7.2
2
+ 0.15 (7.2)
Xmax
' --
.....
= 1.1 mm
'_'--"--,
(37)
/
_'_[ilX4--L'
{
I''!';h_-_{
ii!il
i I_lil,l_il{I
=
I
dB
,
,:'
...........
! { ,
. }i!tli..I
iii*
i I i I ! I I I
[il
_
t
,,'_'"-!A.; I
I!/ ', iii
i i'_'
: i J i I t il]l
[ I {lll
I ! kill
,
,j_j
iq[ I _l_l_l,
Ih_h"B, li;\UJi[/
lr_
I ' J:l{J
i I'i lhll_
170,_ _q-FC-½d !I',_',t I ',',',Tiiill I ',,%
CH- ._
'x
,
_,
!
':l
is slightly increased
(39)
. ._.._:_,
4_1_.
: '
,
-
, :1:!i!
_,_
___._
i '
i_i ,.. {ir ?,i.ll
i
! i
[ _l; I i_!
i
[ :
i:l
due to the progressive
7'r_-
'{_V¢t :_
100
10000
1000
Fig. 11. Loudspeaker of Fig. 10 equalized for constant sound pressure level output. 30 V rms input at 20 Hz decreasing to 6 V rms
at 400 Hz and above. Distortion products raised 20 dB. The action of the progressive suspension has increased linearity at higher
drive, but is insufficient to prevent dc shift duc to rectification, causing high second-harmonic distortion.
_0--__.__..:__:__
_4----{.-_---:"!--{'-:-'--_-.-'-"-..._--[_.-':,-_{
4
--I ....
:i :7 71_L-i E:'[Z__£,_-_ ...........
_o
' ara
'
'i
:3'_'%TE:_77_
._o-,_--,
_"-L.."____
I_
:.......
· {.
_ ', ;-I ..........
,
r'-' "'_
__z-_
--_':z_:'_:'-.:iv__'.
:x._.__: ,,.! . _:__..
, , ,-t ,,!:.5
_"L'
__'
,_
_ ..............
i__2
I
:
L
I
i
--f
......
!.
-: I-'
:
----TF-_
:- -"-_ :,*.........: _--r_-'.....
:' ; C-U./-:
_'_''':
;. _.......
5'1 ....
- __:
)
{J'4L-_l--4;--_q-::-_--_+--¢---t--F (J/Jlt F- ...._
0
4
5
_
7-_'_"_'Ot""-t
I00
q._
'7
:
13
5
7
_91(_'
1000
'1.5
'--:i
I
Fig. 12. Half-space on-axis response of a 380-mm (167-mm effective piston radius) loudspeaker
13 V rms input, 16 f! nominal impedance. Distortion products raised 20 dB.
d. Audio
Eng. Soc., Vol. 29, No. 1/2, 1981 Jan./Feb.
4
5-{'-7
8 9'10
10000
I_
:2
with 7.2-mm equal coil and gap,
19
GANDER
PAPERS
15.2-7.2
2
Xrrlax
+ 0.15 (7.2) = 5.1 mm
15.8 - 7.2
and the 3% third harmonic
Xpc_k=
linearity
is
(40)
gives
xm_, =
(1.18 × 103) 101°7'5/2°
(43) 2 (167)2
With the response equalized
15),
5.4 mm.
=
(41)
2
= 4.3mm
and the 3% third-harmonic
for 104.5-dB output (Fig.
(43)
distortion
point indicates
(1.18 X 103) I0 m5.5/2°
= 4.3 mm.
(43) 2 (167)2
Xpe_k=
In.Fig. 17 at 104.5-dB constant
(44)
output,
(1.18 × 103) 101°4.5/2°
Xpe_k =
(37) 2 (167)2
5.2 mm.
=
(42)
(1.18
Xpeak=
Fig. 16 shows a different long-excurs'ion 380-mm unit
with the same high-cOmpliance surround and spider, but
with an overhung coil 15.8 mm long in a 7.2-mm gap at
20 V rms drive (8.11 nominal impedance). The predicted
4o
_ i
"
,,
-
t,
_ [ ; I i',I_; I ! I ! } ;
v!
II_FIM__!
r_ '
' ;
:
ill
}
02
_ ;./_/N_!!_I
' ltl"
:
'
3
4
_
I
5 6 ? 8 9_o
I
_oo
_!
i '
_.5'_2
it.
103) 101°4'5/2°
= 4.2 mm.
(45)
If we look at this same driver at a constant 30-V rms,
the offset rectification problem has manifested itself at
this drive level from resonance, 36 Hz, up to 125 Hz,
.....................
....
×
(41) 2 (167)2
, ,11 Iii' III[
i,l
,.f;l
i',-Crt
.
_ ; ';
1il _[ i _ ' _
' '
I;
!fill 11 Ilil_llll
lilllll
; ; i II;;i;l
'lFlll'r
hi!! I1 d ' _]l J
1_]!_
' : '
3
4
5=_
?"-{t'_{_ _'''_ _.5 u_
_ooo
_oooo
Fig. 13. Loudspeaker of Fig. 12 equalized for constant sound pressure level output. 46 V rms input at 30 Hz decreasing to 6 V rms
at 400 Hz and above. Distortion products raised 20 dB. At increased input, the linearity is increased due to the action of the
progressive suspension.
_-_ M
_1---._I
t
.... _--- '-,_i _ _-'
:
_
't ........
I
t
:Lzl-:
f 1--_t-4-__r----
_
4 .... !\--/¥x
!.........
0 2
3
:
-....
4
5
7
8 9 10
100
1.§
2
3
4
5
6
7 8 g 101000
1,§
:2
,
t
il-!-'t! !:ir-}i ........:"-'
i ....
, , !'; r F':-'.'!--7-
,: _
,
'
10000
Fig. 14. Half-space on-axis response ufa 380-mm (167-mm effective piston radius) loudspeaker with a 7.2-mm coil in a 15.2-mm
gap, 20 V rms input, 8 11 nominal impedance. Distortion products raised 20 dB.
20
J. Audio Eng. Soc., Vol. 29, No. 1/2, 1981 Jan./Feb.
PAPERS
MOVING-COIL LOUDSPEAKER TOPOLOGY
t
!
/
-.J-.M!_
J] J)I '
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'
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i
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3
4
5 _
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8 9 10
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f_,_,:
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1.5
I
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_
_ _'[I,J
i_
2
i i _ : ri:l,,,
i, ::.li_l
i, F--_Z].,EZE_ __7--E[
LL-._i , _]. ] ' i I ! . , _.M_.J_LJ___L:2_::2.J ,__:_:J2' :._
'
I _ I_,l_f
,1,i!;1
lIT
I
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3 _
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4
i
I:lll
lil:l
5
6
7
8
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:
fu
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_.
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9 10
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J_l
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il
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7
8
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9 10
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I_
1.5
2
_o0oo
Fig. 15. Loudspeaker of Fig. 14 equalized for constant sound pressure level output. 28 V rms at 20 Hz decreasing to 8 V rms at 400
Hz and above. Distortion products raised 20 dB.
'tO
_n
'_=.'__'_-
:
__
%..?_
IL:_..
_....
r......
_'_
i
'
_' l-_--
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4
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7
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4
§
6
7
8
910
1.5
100
'
""_"'_J4
,
_
mT
,I
:;,,
i_.11%i
-
:1
'
'
t....... _....
[
I
i
I
I
i
i.;
/
. .
/
--| _ I ..........
_-_ 'I'
_....... _--'
_--II---
, -F' : : [ --.'
_
b ' '!
+_'_
W-9_I'0
_ ¥._
2
]I
_II
,
:;:
:
I
with a 15.8-mm coil in a 7.2-mm
]
_
:
·
;
.
_
·
·
___
,
,'
.
:
,i
:
:_
: I]l_llll
1'
I I
] I
_ I
i I!IIHI
I I [II
; I,-,,AI
lil_
iil}l
_--:6'
·_.
,ooo0
'_'lWlli
Li_!!',l
3
_____
_o0o
so
02
p.
' ' --
Fig. 16. Half-space on-axis response of a 380-mm (167-mm effective piston radius) loudspeaker
gap, 20 V rms input, 8 fl nominal impedance. Distortion products raised 20 dB.
II ,
'.'
'
r ......
-
,
'
i
:
'
t .........
'i._
;"
_-t-
.....
_--
_ _iu
_?
_-
..... ti
-
'_8
I
L....... _.'
' :: i ', i i i _ _
J_'J
..?.
_
,
-_----_l-_'"'
'_
.........
_---4-'_-'=--I'---+
' _ '
fi-'
2
"-_
!
L '"I 'T- ?' - '-i'-'_t _......
'
i 'T-.T? ,- '
0 _
·_
I
'
_ ...........................
_o :_-_--¥-
=!.
! ...... ff-'
f
'
,_
,_
III
:1:1 il
I
I ,il
Ilil;lll
?
IL,ill
· Ii' Iii
_11, I ,
] 1,1'11
8
910
1000
_ul,;"'_
"_
'ur3
_4
5
6
?
8
910
1:5'"
10O00
Fig. l 7. Loudspeaker of Fig, 16equalized for constant sound pressure level output. 25 V rms at 30 Hz decreasing to 10V rms at
400 Hz and above. Distortion products raised 20 dB.
J. Audio Eng. Soc., Vol, 29, No. 1/2. 1981 Jan./Feb.
21
GANDER
PAPERS
giving high second-harmonic
distortion over much of
this region (Fig. 18).
Fig. 19 shows the same driver fitted with a progressive
suspension. 3% third harmonic gives
Xpeak_-_
(1.18 × 103) 10109'5/20
(54) 2(167) 2
= 4.3 mm.
and the curve shows 3% third-harmonic
Xp_ = (1.18 × 103) 1098.5/20= 4.0 mm.
(48) 2 (104) 2
14.0 2
.....
__
2:
iZT';.
:ZL
'::
;.
-zn_-
..,'71-/i2'"_
......
_- ......
/
r'-:'
_ ; ....
_/.V../I
\L:.',,'z_
Z '
_
'_,../i _./.\_:-'-.;_r
_.....
C 2'*
3
4
5
' '
'
I ....
_ ' .-_..
6 ? 8 9 10
r
_
F,---t
1.5
,"1
.....
__-}v ..........
'i '-'1
'i-,
, .......
i
44-4_._
-; r .....
r.....
2
'.[
i
-!-
,
,
I-'.
'_
?i
,.
4"'-J5 _ oJ'a_'/_8 I_b '_
' ]._
· _ -
:
i
' [ ........
!
i'_
i
..
t
.:.:
_....
.s
v -
-
P---
! _ _'_ i
_
:z-' _
' ......
_-,L' _F---4--4
i
;
....
:_i:4-. _';_.....
_
1 O0
}
i '_
(50)
L ......
'--"_
t -I
I
t--.r
.:-t-._c::z"_-'_
.... t r-'_
3
,
[ ......
,-.
--
. _ -
_ '?_A__L'_, r LA'"" i
_
"t/ ..... t'--_---'_I. -q-X,-i-t
'_,.,....... ,
7'-']'
Al!
_b '
!
, .... : .......
'_x.2X_L_L'_:_LLL'
' _iL' I:
:.........I
(1.18 × 10 3) 1095/20
(28) 2 (103)2
= 8 mm
Xpeak=
t · j ............
_ --_._ .
(49)
inspection of the unit reveals that the suspension limits
are reached at approximately
this excursion. The 3%
third-harmonic distortion point indicates
(47)
_, [ ,,,..L_}-
_ ' _ _
.....
_
fL
x,_= -
L-t .......................
_8 {=--=__ _. ',_
(48)
15.8 - 8.1
2
= 3.9 mm
5.7
= 4.2 mm
at
In this case a slight off-center placement of the rest
position of the coil is responsible for the second harmonic reaching the same level as the third.
Fig. 21 shows a lower efficiency 250-mm unit with a
15.8-mm coil in an 8.1-mm gap. While the formula predicts
(46)
As predicted, the second harmonic remains low throughout. The offset has been prevented at no loss in total
excursion
linearity,
All of the previous examples have used 100-mm-diameter single-layer ribbon-wire coils in 1.5 mm wide
symmetrical field geometry gaps. Fig. 20 shows a 250mm (104-mm effective piston radius) driver with a twolayer roundwire 50-mm-diameter coil, 14.0 mm high, in
a5.7-mmgap,
1.2mm wide, drivenat 10 V (81l nominal
impedance). The prediction gives
Xn_×--
distortion
,
i
1
;
.
:1
_ _ ; .....
, , I_t: ....
q.
_
_
,; --
/ 8-gWO
1000
"]'.,_
:z
10000
Fig. 18. Loudspeaker of Fig. 16 at 30 V rms input. Disidrtion products raised 20 dB. Rectification effects causing large dc offset
and increased distortion from resonance, 36 Hz, up to 125 Hz.
40
_,-_
II[___,_J.m
I
qll
i¥
i
i1_ _
_[Ir_
'
L
_s _-_-L_3Od_:__nL_'_-_FH
----7-r
......
=- ;-_:
' fl_v-
Xt2n d
=.-.---r
-
' --
-30dBti-i
-,-_tz
1':_
,L
:
,
''
_ i
:
,=
,
' '
[
J
,
i :',Ii
1O0
.
i
_
j, ii
IW"=_w-I_-'
,
d2
I
i
'
'____' ____z_
--
I Im_m,_L,
:
_4_
i1'11
i
I
_llll
;,1
i
iIIllllll[;i
i
t
i .,._.4..--_-'-;.+
',r; ; : [
_
t
{
}
_r ,---71_,
,
--_-
,
.
, , ; _ : :
'-_
il
i
_
: .:
ltl
51rL ,
'
,:I
:
I
I
_
,
A
!liP,,
:!
_
!
I
!
i
II1,,
[!
:
, . i
; ii;
1:
i,
,
, ,
i
iii1'11[
'
I I
,
[T_',':L
·
,
_
jill
'
I_-
I!1
1!
1000
=_=
L
-
i
i
---'
=_'--,
==--_..
_3 __- 1'_
_ , :I
I ._
r-+--'-'-%-_t-.'-.- _
, , -"_ '
r
,
i '
l!il:
,
Il
,
_'
,-_
,
10000
Fig. 19. Same type of loudspeaker as in Fig. lB fitted with progressive suspension, 30 V rms input. Distortion products raised 20
dB. Suspension has prevented dc offset and allowed linearity to reach the full potential of the motor topology.
22
. J. Audio Eng. Soc.,
Vol. 29, No. 1/2, 1981 Jan./Feb.
PAPERS
MOVING-COIL LOUDSPEAKER TOPOLOGY
which means that one end ofthe coil has moved halfway
through the gap before the distortion rises significantly,
Here we have a case where at the extremes of coil and
ize the flux, preventing modulation.
The second-harmonic components in the midband have been reduced
more than 20 dB.
cone motion, the nonlinearities of the motor are balanced by those of the suspension, yielding increased
total linearity (resonance was at 30 Hz). Unfortunately
this unit has a severe flux modulation problem, as evidenced by the relatively constant high level of secondharmonic distortion from resonance all the way out to
600 Hz. The unit is also constructed with nonsymmetricai field geometry, which together with miscentering is
responsible for the second harmonic also being higher
than-the third below resonance.
Fig. 24 shows a 460-mm unit (184-mm effective piston
radius) with a 19.1-mm-long coil in an 8.9-mm gap. This
unit is fitted with a one-piece paper cone with a treated
edge compliance, and while we would predict
k
l
'
--
I I
-'
_'
--
I
_-7-
t
',
j
· . -
----_---_
I
t
:
,
0l
,'' '. _
'--.----;-
i
_ ,
3
''4
5
6
7
,
I
-;
:.
._
"I'CS-'--'P
_
'
L
'--'J
!
.__''....
.
--
_
--7--_
5
8
7
, .....
·
.....
'1_5
'2
,
_
t
r- _T_-_ -_-
-
: -
,
'
[
4
i
_ I i
3
4
-----_---_
I ......
8'910
1000
,_, .... FT---I
t-- I
' _
'r
_
i---_,.-*-r-!_< ....... ,--!
_-'u'4
, .
,
.....
_' ; I ....
....
-......
t
-:----' .,1-'_----_ q_-----q------f-
_
I i\.
.
,
i..... v--- ---_-_-, --_-_ ,
_._ .__.:_._7
8'_10
100
/__,z ]_L_
i._ I
'f
_
_-- - + ......
(52)
In this case the surround is too stiff, too progressive, and
limits the linearity potential of the motor. A new cone
.............
--.-_---4-._-----,--
i
,_ '!_/._:_
T
'i'! _-'r -'
__.- --ii-.
·
-
_
'
I
-_-T- .4- ....
'f
"_'_,
__'__
'_-[ _
_ '
___
' ..... _L__
2_ 1---
--
(1.18.X 10 3) 10116/20
= 2.9 mm.
(87)2 (184)2
xp_k =
-v-_-,-_z,--- . '_ - }__:_-_T:1 }5 I
_¢7]_w--,-l-----r--._'--r
'
(51)
the curve shows
Fig. 22shows a 300-mmunit with symmetricalfield
geometry, but with a Similar flux modulation problem.
Fig. 23 shows the same type of structure, but assembled with an aluminum ring around the bottom of
the center pole support acting as a shorted turn to stabil-
a_
19.1 - 8.9
= 5.1mm
2
xm_.,-
_'_ .....
-- r
:
_ ,: ......
_
t:i
7
!'
_----_
i....
8'9¥_
10000
'
:--.
1.5 t"'_
Fig. 20. Half-space on-axis response of a 250-mm (104-mm effective piston radius) loudspeaker with a 14.0-mm coil in a 5.7-mm
gap, 10 V rms input, 8 fi nominal impedance. Distortion products raised 20 dB.
,oF,l_%._:_.
'_
I
;" ; I :_ I/lit,_L-r_%l_l!il
! ] ! [ Ililll
I i ' i Ik__
,
i I ',1i1111
l--_'"'t-_
I,
Illl
i
,:1
il!!
t '],/_l'l',f
.,_
L.-,-_2,,d
,_,-'_:_l
_
'1
11
i_
I_
! flt'il3J2fft
._
_ I/ : !___[.
'i I;'.,._.L--L-_%+T-I;
i'; IL,_LI
i I I III--Ltl
' ' , ' lill
_'__
'
_ '
:
,
,
_/11_,l
: II!l_l_l
iii
Ii _1
1!!'4'i:11
[il'!ill
:il _ i i
'l:
ij _
:
,_:
i
I_1 _ ll;l
,t"'"'
!
U_:_I'!'"I
rll;_5
Ii q
I'1'1
,_
il
_
_,]
,,,
i
!l:;[ilii
-oulJBtlr_-i .,_'_T-_-_l_T_[_J:llI
20
i,ii
' I Iff!F.,I ii,ii½,__,,,,,,,,,
F/llll,
301,_,
i i ; i
-
,il
_
,
u2
3
4
5
8
illl_lll'l!l_:
,1:
.I
_
I
I
I
[ I I I II
_
, : '
I:
, _
'
'
I I i I
'
[
2
:
I
_._2
a''/
ltmff
21-1-
] '
%
I
I
4
5 u8
?
8_JlouUUi._-_
1000
I
:'1
_i
,
:_;v
[
:
[;;
/
l,ili;,iiilr,i:_J__+llSt_z__
I I t ,%ki Ill 1/11 i
3
4
L---I
_-
'_i,_
I ;111111111 _! ', I ' ' i;
I lil;I-;I,VllMliil;I
t
I I:
: _
'
I I !1!1,111111;,
:!ill
!A
,
ill
;I
iiiillliil
I ; I _
t't
i; t_il'
';: :1' '______&4-___4;ill IiI'IiI
]i_ilL.'Ill;i'_
! ;:',
:x--L ] I I I
_
_t
;_11!!
'.', !'i t'I','I, I',I',I ;ll , i ' :-'
:,', i i I[I'_
7 6 910
100
i:,
, , j '/__"-_---2c::t-tdWf--_-h-.
il[I,l!llll`
t-',i i: li!J,I _I I I i, ,,;,'.:,ll
lilh',.
Li., ,i['21dllltli_i-_t[iiii'LiZ,
,
, i _.
!
_wm,m___,_i;,
I
,ill
I ii
a
'
L
_
'
_
I.
b
: ;
;
: ,
U '_[0'
v
10006
: .
_'
._/jn.-.,_
Fig. 21. Half-space on-axis response of a 250~mm (103-mm effective piston radius) loudspeaker with a 15.8-mm in an 8.l-mm gap,
10 V rms input, 8 11nominal impedance. Distortion products raised 20 dB. Unit has nonsymmetrical gap geometry and exhibits
flux modulation distortion, causing high second-harmonic distortion.
d. Audio Eng. Soc., Vol. 29, No. 1/2, 1981 Jan./Feb.
23
GANDER
PAPERS
3_!Y- t;.,
-
'
'
_'
'
'-_
'
_........ l' '"'_____ _ ......_-
,
."
-- ''T':_
_'
]
,T--_F......
,
.....
t'_
'_,_
.
., ._ _
.......
-'.---' I
__-___
,- - ',3_
'
'_
F ..
....
'
·
l-.
I '
- _......
......
'
_--
'
'
'
I ......... _
-7-
:
---E_-_,
-_'_____
i' '," _
I
;
"
_"
_o ..... L..=L-.-}-..... _LL_-:.L...... :_i-
_,
oi-2
ulj
3
'{
4
, r:::
,
,_
J
Ti
;',,
5
l,li/
7
8 9
6
10
1.5
' ......
'"-r
I _-'
V¥
·
_
,"-.'
.....
-:............
--
_--_---
!
5
I
6
8
9 10
1._
illL_'a
;
: .....
i--
....
· ';
_"
,"
-4--'
,
*
J
"
' _'
:- ---
_"--_
,
......
_-. t-
:_
' -- '_-'1'
,
1oo
....
- '
_,-_:-:.........
_......
_---'
:. _
r - I....
r--'
_-_-_--:i_:== : _:_
, _ rm'j
3
4
2
_--r
--i-'
'
' I_r
.......
_
.
IlL
I
_ff___j.
-._--q_'
_':_:4&.:'_-_i :¥_-F-'_"+_F_'_
'_q'_-_'I-_.
E..... r .... ' -:)':::_L' .i: .... ' .............
i .....
F ..... , .....
'
' : 1. _
? ---_i .........
_
........
__L_,_;:.':'
'-f ......
.......
t _._£_:__S__ ,.:':-:7
.," i'I
.....
! '-'_-[_--,'._-L_f
',- .......
r
-:__
,
=
?
6
gl-_l'O
1o0o
1.5
:
1oooo
Fig. 22. 300-mm loudspeaker at 9 V input, 8 11 nominal impedance. Distortion products raised 20 dB. Unit exhibits flux
modulation distortion.
' , :_VS__''
.
I.I
'_,',."__
_
Fl':ll!!il
Tililil)41
,',
-
'?.h
,o
'
Tim/!1&;
!;I
'::"=
I
{
"
I
_:I.,_!_:,L,'L__I
_
'
?
-4 :'_:
"
-
"_l:)i;i:i
l!,l/t[
3
Ii
,:LF' '
-Ld_:i_'.
02
."',_:,t_"{'{'{,
:,
_.
'[/..,
_
[]ilil!l
4
[
i
'_[.lll
6 '7 8 9 lo
_ l_',',ff7;_l_}:,_' i)i'i ,:I _:: I'_:__=-L!F_
':{I
_oo
_'J
II_L.z_{
1.5 _
"3
f
I.lnllii,!Nlid',_:
'/_.'_'J 6
II'i.:[
7 a _lo
_
! ;I;i:
',._ _.
3'
_ooo
__--d
{
I__,!:{.{[{
._!{;'_
.
5. o 7 _ _,,3
4
ml_'J---"z'
_oooo
Fig. 23. Same type of loudspeaker as in Fig. 22, but with conductive ring within magnet structure eliminating flux modulation.
9 V input, 8 11nominal impedance. Distortion products raised 20 dB. Midband second-harmonic distortion has been reduced 20
dB through the action of the ring.
,-.....!............
, .... T....:................
'--3:
-F
':-
{-'
'
' }
'
i...
t
Jl-'r
. t
'
-' ' {.......
I-' .......
r---- f -- -+---+- _-\-_-3o
,.: . '
f
,....
J S'-
tS::
Fig.
stiffness
24
3
4
5
6 7 8 9 _0
100
24. 460-mm
loudspeaker
limits
potential
motor
't .....
_.:_.:
"15
at 30 V input,
linearity.
__
2
:.':.
....
-'
8 _
:.-; S -
nominal
_""!
i ..........
L
'-:
+
..... _L"-
'.
-i /'t'l:
'-/-_- _--- _,,'-_----?
.... :.....
:jj_ .:_ ::
3 -:j
1...........
l .................
'
: ...._::'
...... _...........
_-_V__
_-__;.,,....
....
02
{..........
- _
-I. '-:-
: .:Pr _dS_
6
'_-.-S::,_S....
_
_
....
8 g-'rd'
--'/7_-'_ '
t000
impedance.
Distortion
-r-t-
L. _- ,_ h-
i....
i.....
products
4
_
L....
t
_-_' :*_- _--r--:l
_
J
-
t ....
t .....
--.L ..........
_t'_'""'910
1.5
10000
raised
20 dB.
Excessive
surround
J. Audio Eng. Soc., Vol. 29, No. 1/2, 1981 Jan./Feb.
PAPERS
MOVING-COIL
LOUDSPEAKER
TOPOLOGY
14 REFERENCES
and surround were fitted and the results (Fig. 25) show
that a better balance of forces has been achieved:
[1] L. L. Beranek,
(1.18 × 103) 10116/2°
Xpeak=
(67) 2 (184)2
12 SUMMARY
= 4.9 mm.
(53)
AND CONCLUSIONS
The peak displacement limit of a moving-coil loudspeaker can be approximately
predicted by the amount
of voice-coil overhang for long coil-short gap structures, and by the amount of voice-coil underhang plus a
15% increase due to the fringe field for underhung and
equal coil and gap units. This will predict the excursion
for 3% third-harmonic
distortion. This can be extended
in cases where the suspension force compensates for
nonlinear motor force, or degraded where the suspension force increases at too fast a rate. Second-harmonic
distortion can arise from a number of sources, all of
which place the rest position of the coil away from the
position of maximum Bl. These factors all apply to
motor geometry, which is the dominant distortion mechanism below approximately
150 Hz for low-frequency
drivers. In the region up to the piston band limit, motor
structure nonlinearities such as air venting, magnetization, and flux modulation are the dominant distortion
mechanisms. Above the piston band limit, cone breakup
is the dominant nonlinearity. The peak displacement for
a moving-coil direct-radiator
loudspeaker operating in
the piston band can be derived directly from acoustic
pressure measurements.
13 ACKNOWLEDGMENT
The author would like to thank in particular Terry
Sorensen whose theoretical background contributed
greatly to the analytical insights presented in this paper,
and the Transducer Engineering staff of James B. Lansing Sound, Inc., for providing an environment condusive to creative contributions to loudspeaker technology.
2
3
5
6 7 8 9
Acoustics
(McGraw-I_ill,
New
York, 1954).
_'1.5
_o0
2
3
4
5a6
[2] L. E. Kinsler and A. R. Frey, Fundamentals of
Acoustics, 2nd ed. (Wiley, New York, 1962).
[3] A. N. Thiele, "Loudspeakers
In Vented Boxes:
Part II," J. Audio Eng. Soc., vol. 20, pp. 471-483 (1971
June).
[4] R. H. Small, "Direct-Radiator
Loudspeaker Systern Analysis," J. Audio Eng. Soc., vol. 20, pp. 383-395
(1972 June).
[5] R. H. Small, "Closed-Box Loudspeaker Systems;
Part I: Analysis,"J. AudioEng. Soc., vol. 20, pp. 798-808
(1972 Dec.).
[6] H.F. Olson, "Analysis of the Effects of Nonlinear
Elements upon the Performance of a Back-Enclosed,
Direct Radiator Loudspeaker
Mechanism," J. Audio
Eng. Soc., vol. 10, pp. 156-162 (1962 Apr.).
[7] N. W. McLachlan, Loudspeakers: Theory, Performances Testing and Design, corrected ed. (Dover,
New York, 1960).
[8] W. J. Cunningham, "Non-Linear
Distortion in
Dynamic Loudspeakers
Due to Magnetic Effects," J.
Acoust. Soc. Am., vol. 21, pp. 202-207 (1949 May).
[9] D. Hermans, "Low Frequency Distortion in
Loudspeakers,"
presented at the 56th Convention of the
Audio Engineering Society, Paris, 1977 Mar. 1-4.
[10] D. A. Barlow,"Instability
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[14] J. R. Gilliom, "Distortion in Dynamic Loud-
7 8 _ _6
_ ']o
moo
-g
_
4
'5"--6
7 8 9 10
t,5
m0oo
2
Fig. 25. Loudspeakerof Fig. 24fitted with more linear sound.30V input, 8 Il nominal impedance.Distortion productsraised20
dB.
J. Audio
Eng. Soc., Vol. 29, No. 1/2, 1981 Jam/Feb.
25
GANDER
speakers
Due to Modulation
PAPERS
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IREE, Australia,
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of
THE
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AUTHOR
Mark R. Gander was born in New Brunswick, New
Jersey in 1952. Prior to college he received an extensive
musical education. He later earned a B.S. degree from
Syracuse University in 1974, and worked as a sound
engineer and audio systems designer in broadcasting,
studio recording, and concert reinforcement.
In 1976 he received an.M.S.E.E, from The Georgia
Institute of Technology, specializing in audio electronics and instrumentation,
including the multidisciplinary
program in acoustical engineering. That same year he
joined James B. Lansing Sound, Inc. as a transducer
26
1979 Sept.
engineer where he had design responsibility for various
consumer and professional loudspeaker products, including the Cabaret Series and E Series musical instrument loudspeakers. Since 1980 he has been an applications engineer for the JBL Professional Division.
Mr. Gander's articles have been published in the
Journal oftheAudio Engineering Society, dB Magazine,
Sound Arts, and Modern Recording. He holds an FCC
First Class Radiotelephone
Operator License, and is a
member of the AES, The Acoustical Society of America,
and the IEEE.
J. Audio
Eng. Soc., Vol. 29, No. 1/2, 1981 Jan./Feb.