Development of a Diaphragm for a Planar Acoustic Transducer
by Takeshi Nishimura * , Kenji Iizuka *2 , Hideharu Yonehara *Katsutoshi Sakai *3 and Motohiro Yamane *3

A diaphragm has been developed to meet the need for ultra-thin acoustic transducers (less than 1 cm thick) for use in liquid-crystal TV sets and in slimline lightweight equipment for automobiles. The diaphragms, which have a voice coil formed over thewhole of both surfaces of the base resin film, achieve a high level of sound quality by means ofcircuit design techniques using magnetostatic analysis. From the physical properties and configuration of the materials (base resin, copper coil and edges) making up the diaphragm, bass reproduction characteristics of better than 65 dB at 100 Hz were achieved through the development ofband design techniques using eigen-value simulation to predict the reproduction band in the bass
range. In planar acoustic transducers incorporating these diaphragms, driving force is generated
over the whole surface of the flat diaphragm, which acts as a planar wave radiator, providing flat
phase characteristics and sharp directionality. Other outstanding advantages are that, unlike conventional cone speakers, these acoustic transducers use no paper, resulting in superior resistance to heat and moisture and making underwater operation feasible, and that the individual
sound cells are smaller, reducing howling.

ABSTRACT1.

INTRODUCTION

With the growth in multimedia services information isprocessed at high speed leading to dramatic increases inthe volumes of data transmitted, but at the point at which
the information is imparted to a human it must be converted either into images or into sound. And with greater
demand for mobile information terminals there is a relentless pressure for equipment that is smaller, slimmer andlighter in weight. As for imaging devices, more and more
use is being made of liquid-crystal and plasma display
panels to achieve a slimmer profile, whereas acoustic
conversion devices still rely primarily on conventional
cone speakers, and have not effectively come to grips
with the growing need in automotive and home electronics
for equipment that is slimmer and lighter in weight.
This paper reports on the development of a diaphragm
optimized for a planar acoustic transducer (so-called
speaker) measuring less than 1 cm in thickness designed
for mounting in liquid-crystal TV sets and other ultra-slimline information terminals, and on its success in practicalapplications.

* Components & Mounting Technology Development Dept.,
Ecology & Energy Lab.
*2 Organic Analysis Sec., Ecology & Energy Lab.
*3 Engineering Sec., Electronic Components Dept., Electronic
Components Div.

2.

DEVELOPMENTAL CONCEPTThe acoustic transducer in which the diaphragm developed in this work was intended for use is an ultrathin planar acoustic transducer, classified as a conductive typewith multipoint drive, and known as a Gamuzon speaker 1).
Unlike conventional cone speakers, this acoustic transducer is less than 1 cm in thickness, is lighter in weight,
and is of extremely simple structure with a reduced parts
count. Because of its innovative structure, however, it presented problems with respect to diaphragm materials andreliability that made it difficult to apply conventional design
techniques, thus requiring the development of techniques
intended specifically for the evaluation of planar acoustic
transducers. In addition, restrictions imposed by the slim
profile required that maximum advantage be taken of theproperties of the resin material and copper used in thediaphragm, and that the 2-dimensional copper circuit
structure be optimized virtually to the limit value.
2.1

Structure and Operating Principle of Planar
Acoustic Transducer
Figure 1 shows the structure and operating principle of aplanar acoustic transducer 2). A planar acoustic transducer
consists of a flat yoke which doubles as the outer frame,and on which are disposed permanent magnets of alternate N and S polarity. The diaphragm and voice coil,
formed integrally on a flexible printed circuit (FPC) is supported flexibly by the edges at a fixed distance from thepole faces of the magnets 3).

62Printed coil
Permanent magnet

Diaphragm

thickness
Yoke

Figure 2

Rubber edge

Representation of a diaphragm voice coil.

Direction of action of force
Force

Magnetic field

Direction ofmagnetic field
Direction of current(Fleming's left-hand rule)Figure 1

Structure and operating principle of a planar acoustic
transducer.

The operating principle is as follows (see Equation (1)):
In a voice coil of length l passed through a magnetic fieldof density B, an electrical signal (acoustic current I) flows,
and, in accordance with the principles of electromagnetic
action, a driving force F is generated in a direction determined by Fleming's left-hand rule.
F = lIB(1)

The voice coil is formed over the whole surface of thediaphragm, which begins a reciprocating action proportional to the changes in current flowing in the circuit, causing the air to vibrate and generating acoustic pressure.
Following are the specifications of the planar acoustic
transducer in which the diaphragm under development is
to be mounted, and of the diaphragm itself.
Transducer type:
FFS-0212 (2 x 12-cell array)
Outline dimensions: 40 x 160 x 8 (thick) mm
Lowest resonating frequency:
160 Hz ± 20%
Effective frequency band:f0 - 20 kHz ± 20%
Output acoustic pressure level:
82 ± 3 dB/W/m
Rated input:
7.5 W,
Input withstand:
15 W (A)Mass:
87 g
Diaphragm under development
Nominal impedance: 6 Ω ± 10% or better
Continuous load tests: JIS 96 hr, 15-25°C(8 W white noise)
Humidity tests:
40°C 90-95% RH for 96 hr
Operating ambient temperature (I)50°C for 96 hr (8 W white noise)
Operating ambient temperature (II)-10°C for 96 hr (8 W white noise)
Appearance of FPC
Slackness within coil
not more than 0.1 mm
Additional items conform to JPCA DG02-1997/IPC6202.

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2.2 Materials Design
The diaphragm targeted for development, represented in
Figure 2, is a flexible printed circuit board with 24 spiralcoils formed on both surfaces of the base resin film in a 2
x 12-cell array, and is bonded to the acoustic transducer
unit by means of flexible edges.
Among the characteristics required of the acoustic
transducer diaphragm may be mentioned:
1) A broad reproduction frequency band and flat
acoustic characteristics;
2) Flat phase characteristics and low distortion;3) No abnormal noise or eigen-tones;4) Superior environmental resistance, including heatand cold; and
5) No variation over time, superior durability, andfreedom from open circuit faults.
Judging from conventional wisdom, an upright, slimline
planar acoustic transducer measuring 40 x 160 x 8 mmmight be expected to give relatively good reproduction in
the mid- and high-frequency ranges but to be limited withrespect to lower frequencies. If the acoustic transducer
can reproduce tones as low as 100 Hz, the whole range
could be covered by a one type of acoustic transducer
without needing a separate woofer just for the bass. For
this reason the bass reproduction capability of planar
acoustic transducers will have a major significance indesigning slimmer liquid-crystal TV sets. One of the targets of this development effort, therefore, was to achievea power of 65 dB or better at 100 Hz.
Generally speaking, low-frequency characteristics areclosely related to the value of bass resonance frequency
f0, which may be obtained using Equation (2)--------1
s
f0 =
[Hz]
(2)
2π M

√

where: s is the stiffness of the supporting portion of thevibrational system; and M is the equivalent mass of thesystem.
From Equation (2) we see that to reduce f0, designs
could be modified in the direction of increasing equivalentmass M and reducing support stiffness. However increasing mass M means using a thicker material for thediaphragm and increasing the weight of the copper coil,and if in fact mass is increased, rise-time characteristics
will be degraded and operating efficiency will decline. The
copper coil, on the other hand is subject to limitations interms of impedance settings and methods for fabricating
the printed circuits, making it difficult to change its weightat will. In general, adjustments to f0 are effected by modifying the configuration of the support structure, or edge,
and by using materials with different physical properties,
primarily Young's modulus.

Furukawa Review, No. 21

2002

Table 1

Material characteristics and coordinate system.
Copper coil Film resin Edge (hard) Edge (soft)

Young's modulus (Pa) 1.35x1011

MagnetMagnet4.35x109

2.00x1082.00x108

Poisson's ratio

0.33

0.47

0.40

0.40

Density (kg/m3)

6.10x103

1.40x103

9.60x102

4.80x102

Thickness (m)5.6x10-5

8.5x10-5

5.0x10-4

5.0x10-4

Yoke

Figure 3

Results of magnetostatic analysis.

In addition, the characteristics in the bass range also
depend on the sharpness Q0, which is in turn determinedprimarily by the physical properties of the diaphragm
material. On the other hand, since the Joule heat produced by the copper coil is transmitted directly to the baseresin film of the diaphragm it is desirable that this material
have good resistance to heat and humidity, as well as,
from the standpoint of diaphragm characteristics, high values of specific elastic modulus (E/ρ) and internal loss(tanδ).

3.

SIMULATED MATERIALS DESIGN AND
VIBRATIONAL ANALYSIS

3.1 Magnetostatic Analysis
Evaluating the acoustic performance of the diaphragm
requires that an actual flat planar acoustic transducer be
assembled. Thus to increase the efficiency of prototype
construction and evaluation a design review was conducted by means of simulation.
In the first stage, circuit design was determined by magnetostatic analysis. The procedure adopted was to find theregion of maximum magnetic flux from the arrangement ofmagnets on the yoke and then find a 2-dimensional spaceon the diaphragm such that the copper coils would be
optimally disposed. Also the impedance between terminals had to be set at 6 Ω, and this dictated the length andcross-sectional area of the copper coils. Finally the optimum plating thickness and coil-to-coil distance on theedging was decided. Figure 3 is a typical result of magnetostatic analysis which was a precondition for circuitdesign.
As shown in Figure 1, the diaphragm developed here
makes use of magnetic flux lines that parallel the polefaces of the permanent magnet, and so the coils werearranged so as to be longest in the region of highest horizontal magnetic flux density.
3.2

Vibrational Mode Analysis and Eigen-value
Analysis3.2.1 Analytical Method
In the second stage, in an effort to predict the diaphragmcharacteristics and acoustic characteristics from the properties of the materials and the configurations of components, a diaphragm analysis was carried out by means ofa finite-element technique using Japan Marc Co.'s MARC

Figure 4

Vibrational mode analysis of a planar acoustic transducer diaphragm by the finite element method.

program. The fundamental equation may be stated as(K - ω 2M)φ = 0
where:
K is a rigid matrix,
M is a mass matrix,
ω is an eigen-value (frequency), andφ is an eigen-vector(3)With respect to the coordinate system of the 2 x 12-cell
diaphragm, approximations were generated using thephysical properties and coordinate system shown in Table
1 for three components--the copper coils, the base resinof the film and the edges. For the Young's modulus of thebase resin, which was not available from the literature, weused measured values obtained from tension tests.
3.2.2 Vibrational Mode Analysis
The eigen-vectors obtained by solving Equation (3) represent displacement vectors and in physical terms signify
the vibrational modes of the 2 x 12-cell diaphragm. Figure64

4 shows the results of vibrational mode analysis from theeigen-vectors. In vibration mode 1, the center of thediaphragm is the loop of vibration where the amplitude is
the greatest. In vibration mode 2, the center of thediaphragm is the node of vibration where the amplitude iszero. In vibration mode 3, the diaphragm is divided lengthwise into three sections and there is a vibration node in
two places and a vibration loop in three places. As thenumber of vibration modes increases the diaphragm isdivided into smaller sections and the degrees of freedomof vibration increase.
3.2.3

Examination of the Reproduction Band by Eigenvalue Analysis
In eigen-value analysis simulations were carried out using
the physical properties of the materials of which thediaphragm is composed and the configuration of the components as variables. Eigen-frequencies were derived
from the eigen-values calculated by Equation (3) for avariety of prerequisite conditions. The proper-vibration
having the lowest frequency is equivalent to the primary
vibration mode, and corresponds to f0, which has a close
relationship to the reproduction band in the bass region.
Figure 5 shows the relationship between the Young's
modulus of the edge by which the diaphragm is mounted
to the acoustic transducer and the eigen-frequency. It was
found that the eigen-frequency increased with a rise in the
Young's modulus of the edge in all vibration modes,
agreeing with the prediction, based on Equation (2), that

Eigen-frequency (Hz)

500

400

300

200
mode1
mode2
mode3
mode4
mode5

100

0
1.0E+07

1.0E+08

1.0E+09

1.0E+10Young's modulus of edge (Pa)

Figure 5as the stiffness of the diaphragm support structure s
increased f0 would rise. This suggested that the best way
of widening the reproduction band in the bass range
would be to change to a material with a smaller Young's
modulus--that is to say a more flexible material such as
rubber or foam--for the edge.
As a means of investigating the relationship between
the mass of the diaphragm and its eigen-frequency, we
may examine the relationship shown in Figure 6 between
apparent diaphragm density (average of values for coils
and film) and the eigen-frequency. In Figure 6 the change
in the weight of the diaphragm, made up of copper coils
and base resin film, was approximated to a change indensity and analyzed. It was found that as the weight ofthe diaphragm increased the eigen-frequency tended toshift to a lower frequency, a result that could be anticipated from Equation (2). This agrees with the predicted resultthat as equivalent mass of a vibrational system increases
f0 will decrease. This in turn suggests that to broaden the
reproduction band in the bass range (i.e., to decrease f0),
the design should be modified to increase diaphragmweight by, for example, increasing the amount of copperor using thicker base resin for the film.
We then examined the relationship between the outerconfiguration of the diaphragm and the eigen-frequency.
Figure 7 shows the relationship with eigen-frequency
when the length dimension differs in proportion to thenumber of magnets disposed (2 x n), using identical edge
material and diaphragm material. As the number of magnets disposed in the length dimension increased from 2 to4, 8, 12 and 20, it was found that the eigen-frequency
showed a tendency to shift downward. This result meansthat the greater the length the wider the reproduction bandin the bass range, and is in agreement with the accepted
rule of thumb for acoustic transducer design.
The simulation techniques that have thus been established for predicting the reproduction frequency band (animportant characteristic of acoustic transducer
diaphragms) make it possible to reduce the number ofprototypes built, and promises to shorten the time that will
be required to develop 2 x 2-, 3 x 4-, 4 x 4- and 4 x 12-cell
diaphragms.

Effect of Young's modulus of edge on eigen-frequency.
800
1400

mode1

600

mode2

500

mode3
mode4

400

mode5
300
200
100

0

mode3
800

mode4
mode5

600
400

2

4

6

8

10

12

0
2x2

Apparent diaphragm density (g/cm3)

65

mode2

1000

200

0

Figure 6

mode1

1200

Eigen-frequency (Hz)Eigen-frequency (Hz)700

Effect of apparent diaphragm density on eigen-frequency.

2x4

2x8

2x12

2x20

Diaphragm length (no. of coils: L x W)

Figure 7

Effect of diaphragm length on eigen-frequency.

Furukawa Review, No. 21

2002

4.

RESULTS AND DISCUSSION

4.1 Frequency Characteristics
Prototypes of the 2 x 12-cell diaphragm here under development were fabricated by the subtractive method using alaminated sheet that was copper-clad on both sides, witha base material of heat-resistant plastic film. The acoustic
characteristics--sound pressure, impedance, etc.--vs. frequency were measured using an ASA-2 system manufactured by Etani Electric Co., Ltd., with the acoustic transducer attached to a standard baffle as specified in JIS C
5532.
Figure 8 shows the sound pressure level as a functionof frequency for diaphragms having a base film 50 µm
thick and three types of edge material. The sound pressure characteristics of the prototypes were substantiallyflat over a wide range of frequencies (200 Hz to 20 kHz),irrespective of the edge material used. However, as indicated by the arrow, in the bass range below 200 Hz there
were marked differences depending on the edge material.
Figure 9 is analogous to Figure 8, showing the results ofimpedance measured for the diaphragms. For planar
acoustic transducers using a urethane edge, the f0 was
163 Hz, while the values for planar acoustic transducers
using edges of compressed foam rubber 5 mm and 4 mm
thick were 135 Hz and 113 Hz respectively. Other than the

100
90

SPL (dB)

80
70
60
50
40
10

100

1000

10000

100000Frequency (Hz)4-mm rubber edge,
f0113

Figure 85-mm rubber edge,
f0135

Urethane edge

Sound pressure level as a function of frequency. (0.5
W, 50 cm)edges, these three types of diaphragms were identical interms of base film and copper coils, so that it may be concluded that the differences in f0 are attributable to thephysical properties of the edge materials. Thus it was confirmed that, as was predicted by the simulation shown in
Figure 5, the reproduction band in the bass range can be
designed by controlling the stiffness of the edge material.
In an effort to improve the sound characteristics, theinvestigation was pursued by fabricating prototype
diaphragms of varying materials and configurations, as
described above, and in parallel, by recreating these characteristics by simulation. This resulted in improvements inthe circuit configuration and edge materials of the 2 x 12cell diaphragm (the details of which are omitted here)
such that a sound pressure of 65 dB or better wasachieved. Further, through the development of band
design techniques whereby trends in f0 and reproduction
band can be predicted by eigen-frequency simulation, it
has become possible to predict the characteristics ofdiaphragms of differing configurations.
4.2 Vibration Characteristics
4.2.1 Vibration Measurement System
In the diaphragm developed here, the voice coils formedon the printed circuit vibrate integrally as the diaphragm,
with the result that it was necessary to establish the reliability of the diaphragm against open circuit faults--a problem that did not arise with conventional cone speakers. A
PSV-100 laser scanning Doppler vibrometer system madeby Polytech of Germany was therefore used to gain anunderstanding of the vibrational characteristics of thediaphragm. Figure 10 shows a schematic representationof the system.
The frequency response function was measured bydirecting a laser beam against the center of the vibrating
diaphragm of a planar acoustic transducer, converting the
speed information obtained from the Doppler effect of thereflected laser light, and performing frequency analysis. In
laser scanning vibrometry the beam was directed to anarray of 8 x 32 points distributed over the entire surface ofthe diaphragm and time synchronized to yield phase information, and frequency analysis was carried out.

10

Impedance (Ω)

98Planar acoustic
transducer

7

Video system

6

Power
amplifier

5
4
10

100

1000

10000

100000Frequency (Hz)Urethane edge

Figure 95-mm rubber edge,
f0135

4-mm rubber edge,
f0113

Impedance as a function of frequency. (0.5 W, 50 cm)

Laser scanningvibrometer (PSV-100)

FFT analyzer(Ono Sokki,
CF-6400)

Figure 10 Schematic diagram of vibration measurement system.

66

Figure 11 Frequency response function.

4.2.2 Frequency Response Function
Figure 11 shows typical measurements of the frequency
response function in a 2 x 12-cell diaphragm. The maximum or peak value of the function was measured in thevicinity of f0, and it was found that the peak frequency
depended on terminal voltage. This is attributed to theoccurrence, in a diaphragm gently constrained by theedge, of non-linear phenomena such as distortion andsplit vibration that were dependent on terminal voltage.
4.2.3 Vibrational Mode Measurement
Figure 12 shows measurement of the vibration mode at aphase angle of 90°C when inputting a frequency in thevicinity of f0. In the vibration mode shown in Figure 12,phase is coincident over the entire surface of thediaphragm, and it will be seen that this corresponds toMode 1 in the simulation in Figure 4.
When the frequency of laser light reflected from thediaphragm was analyzed, a frequency distribution equivalent to the second and third harmonics of the input frequency was measured, signifying that when frequency f0
was input vibration in Mode 2 and Mode 3 resulting fromdistortion etc. were co-present with Mode 1.
Figure 13 also shows a case in which more than one
vibration mode is thought to be present, where the primary
component of vibration is thought to be Mode 3 4).
Features of the Planar Acoustic Transducer
Diaphragm
The vibration behavior of the planar acoustic transducer
diaphragm was measured directly by laser Doppler
vibrometry, and it was concluded that reciprocating motion
occurred over the entire flat surface of the diaphragm, as
exemplified in Figure 12. This is attributed to the fact thatsince the voice coils were formed over the entire
diaphragm surface, the planar acoustic transducer acts as
an area sound source. Thus it is to be expected that theplanar acoustic transducer will be characterized by flat
phase and sharp directionality. When actual acoustic
transducer performance was checked it was discovered
that, in addition to the predicted advantages, howling did
not occur readily due to the small size of the cells, andthat underwater operation was possible thanks to the highlevel of water resistance.

Figure 12 Measurement of vibration. (Case I)

Figure 13 Measurement of vibration. (Case II)

4.3 Results of Reliability Tests
The reliability tests listed in Section 2.1 as required forordinary acoustic transducers were carried out, and it was
confirmed that no problems occurred under any conditions.

4.2.4

67

5.

CONCLUSION

A 2 x 12-cell diaphragm was developed for use in a planar
acoustic transducer having a thickness of 1 cm or less.
(1) Sophisticated circuit design techniques for the soundcharacteristics were established through the use of magnetostatic analysis, determining areas of high magnetic
field density from the arrangement of magnets on the yoke
and allocating the two-dimensional wiring space on thediaphragm.
(2) By modeling the diaphragm, simulation of eigen-frequencies was carried out and it was confirmed that there
was a correlation between the measured frequency characteristics and the eigen-frequencies. In this way band
design techniques were developed for predicting the
reproduction band in the bass range from the physicalproperties of materials and the outline dimensions.

Furukawa Review, No. 21

2002

(3) Vibrational mode analysis was carried out by laser
Doppler vibrometry, confirming the full-surface driving
capability (area sound source) that is characteristic of planar acoustic transducers, and phase flatness.
It has thus been possible to develop and bring to commercial viability a diaphragm that provides a satisfactory
reproduction band in the bass range and satisfies all reliability tests established for planar acoustic transducers.
In closing the authors would like to express their heartfelt thanks to Toshiiku Miyazaki and Masashi Hori of FPS
Co., Ltd. for their cooperation in designing circuitry andproviding components.

REFERENCES
1) Tamon Saeki: Encyclopedia of speakers and enclosures,
Seibundo-Shinkosha, (1999), 52. (in Japanese)
2) International patent disclosure, WO99/03304
3) Shoji Hori; What is a multi-cell flat speaker?, JAS journal, No. 3,
Vol. 40, (2000), 13-16. (in Japanese)
4) Nobuo Tanaka: Plate vibration and sound radiation, NoiseControl, No. 5, Vol. 11 (1998), 243-247. (in Japanese)

Manuscript received on July 2, 2001.

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