Note: Descriptions are shown in the official language in which they were submitted.
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PARAMETRIC LOUDSPEAKER WITH ELECTRO-ACOUSTICAL
DIAPHRAGM TRANSDUCER
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to electrostatic loudspeaker transducers. More
particularly, this invention relates to parametric loudspeaker transducers
that
include a stator element and are based on film type diaphragms. These
transducers involve a single stage, electro-mechanical conversion of
ultrasonic
voltage signals to ultrasonic compression waves whose difference in value
corresponds to new sonic or subsonic compression wave frequencies.
l0 2. Prior Art
A parametric loudspeaker is a sound emission device that directly emits
high frequency ultrasonic waves represented by a carrier frequency and
sideband
frequencies resulting from modulation of the carrier frequency with an audio
signal. These diverse ultrasonic frequencies are demodulated within a
nonlinear
medium such as air to regenerate the modulated audio signal into actual audio
output. In theory, parametric sound is developed by the interaction in air (as
a
nonlinear medium) of two ultrasonic frequencies whose difference in value
falls
within the audio range. Ideally, the resulting audio compression waves would
be
projected within the air and would be heard as pure sound. Despite the ideal
2 o theory; sound production by acoustic heterodyning for practical
applications has
eluded the industry for over 100 years.
Because the production of audio output extends along the length of the
ultrasonic propagation, increasing sound pressure levels (SPL) develop along
the
ultrasonic beam until the ultrasonic energy is dissipated. In this manner, the
2 5 output of the parametric speaker is similar to an end fired array of
conventional
speakers. Despite some similarities between parametric speakers and
conventional speaker systems, significant new properties arise because the
audio
output is indirectly generated from high energy ultrasonic emissions, rather
than
by cones or diaphragms moving at audio frequencies. Some of these unique
3 o properties are well known, such as a long range beaming effect and
localization
of sound to a projected area. Other properties have not previously been
recognized, and have prevented the realization of commercial parametric.
speaker
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systems. This disclosure, along with a concurrently filed application,
entitled
Modulator Processing for Parametric Speaker Systems, explores several of these
properties as part of a fully operational parametric speaker. The current
invention's parametric speaker has full range audio output with volume,
clarity
and fidelity which are competitive with high quality conventional sound
systems.
Prior art efforts in parametric speaker applications have generally been
limited to the theoretical investigation into certain limited properties and
applications of a transducer array of piezo bimorph transducers which are
collectively mounted on a support surface. Each bimorph emitter was separately
wired to the signal source. Based on this configuration, commercial
development
of parametric products have eluded the industry. This is primarily due to a
lack
of effective sound reproduction competitive with other conventional sound
systems such as dynamic and electrostatic speaker systems. Even where
parametric speakers offered a distinct advantage, such as enhanced
directionality,
commercial success has been nominal because of high cost, substantial power
requirements, and poor quality which have not satisfied discerning listeners.
Parametric speakers rely on the effective coupling of an ultrasonic sound
output of a unique nature with surrounding air. As mentioned above, previous
theoretical and commercial product research has focused primarily on emitter
2 0 devices that use piezoelectric bimorph structures, also known as
piezoelectric
benders. These devices use two layers of piezoelectric material that are
bonded
to each other and are driven out of phase. As one layer expands in length, the
other contracts, providing output movement in a plane 90 degrees to the
expansion/contraction direction. While the force of these devices is quite
high
2 5 the actual air displacement and coupling is rather poor. Therefore,
successful
performance of the bimorph relies on a second stage of conversion process in
which the localized movements of the bimorph are amplified within the
surrounding air. This is accomplished with various air matching means that
consist of plate and disc structures that are comparable in size to a
wavelength of
3 0 the frequency of interest.
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In order to develop meaningful SPL, many of these devices are spaced
along a support plate or other support structure. See, for example, Figure 6
taken
from Tanaka et al, U.S. patent 4,823,908, including clusters of 500 to over
1400
bimorph units. Because each of these devices represents a localized emitter,
the
present inventors have discovered that high drive intensity immediately in
front
of each device can readily drive the air into shock or saturation. This
phenomenon breaks down the effective demodulation of the audio signal, causing
loss of power output and severe distortion of the audio sound component, as
well
as other serious adverse effects upon the general process of parametric
l0 loudspeaker operation. In addition, bimorphs have poor frequency response
and
unwanted sub-harmonics.
To a large extent, prior art efforts for enhancement of SPL in bimorph
systems have focused on increasing the number of bimorph emitters. While it
has been perceived that increasing the number of bimorph emitters would
provide
high ultrasonic output, it merely exaggerates the problem of air saturation
and
serious power loss. Furthermore, the inventors have discovered a number of
accompanying limitations with phase matching errors due to variations from
device to device, distortion and bandwidth problems and the associated cost
and
complexity of using so many separate devices. Indeed, the phase relationships
of
2 0 these separate devices are such that the total output of many devices used
as a
cluster does not add up to the amount predicted by just summing all the
devices.
For example, it has been experimentally shown that an array of 10 bimorph
transducers, each individually capable of generating an SPL of 120 db,
produces
a collective SPL of only 125 to 127 db. Notably, this is surprisingly less
than the
2 5 130 db which theoretically represents the cumulation of ten devices having
individual outputs of 120 db. As indicated above, the present inventors
believe
that this power loss arises from the phase anomalies, and other deficiencies
identified in this disclosure.
3 0 Another factor which has perhaps channeled investigators to rely on
bimorph devices is a perception that the emitter should be structured with
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dimensions corresponding to wavelengths of the ultrasonic energy to be
emitted.
This is in accordance with other types of ultrasonic devices, such as
electrostatic
emitters, which are constructed at a size corresponding to the wavelength of
the
lowest frequency of interest. Even when using these devices, it is still
required to
use large device counts to achieve the required output. In fact, the
perception has
been that if higher SPL is desired, greater numbers of emitters must be
applied,
driven with higher voltage levels. Such logic arises from traditional design
perceptions from conventional audio systems. However, these conclusions do
not follow in parallel relationship with parametric speaker systems.
1 o The present inventors believe that, in addition to unsatisfactory results
in
parametric systems with bimorph transducers, other traditional perspectives
derived from conventional audio systems may have misguided early researchers
in the field of parametric speakers, leading to disappointing results which
have
deterred parametric speaker progress. This is represented by the fact that
early
research efforts were substantially limited to the use of bimorph transducers,
which are generally classified as high power devices. It seems that the
preferential use of bimorph transducers within parametric speakers may have
been a natural consequence of a parallel experience within the audio industry,
where dynamic speakers (also characterized as high power devices) were
strongly
2 o favored over electrostatic speakers. In other words, the popularity and
general
acceptance of magnetically driven cones (similar in nature to bimorph drivers
and
attached air coupling cones) appear to have channeled developmental thinking
within the parametric field in favor of bimorphs and away from low output-
emitter structures such as f lm emitters.
2 5 For example, approximately 99 percent of audio systems sold in the world
fall within the class of dynamic speakers, represented by a magnetic driving
unit
which is mechanically coupled to a cone or similar acoustic drivers. Dynamic
speakers operate based on two concepts. The first involves an electro-
mechanical
process of converting the voltage signal of the audio output to a mechanical
3 o movement. This is accomplished by the magnetic driving unit such as a
magnet
and coil combination. The second concept accompanies the first, wherein the
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mechanical movement is combined with an acoustical coupling device, such as
with movement of the cone for displacement of compression waves. This is
conceptually referred to as a two stage speaker.
Such dynamic speakers are referred to as high power devices because they
are able to generate high levels of volume, particularly at low frequencies,
based
on the strength of the drive system. They are also well suited for adaptation
within small spaces such as small rooms, automobiles, ete. The versatility of
dynamic speakers and their simplicity of operation (a moving cone) have
favored
a substantially uninterrupted lead position over electrostatic speakers and
other
ZO systems for audio reproduction. Furthermore, such development has occurred
despite the need for expensive and complex audio control systems for mixing,
cross-over, equalization, and related problems such as were enumerated in U.S.
parent application Serial No. 08/684,311, incorporated herein by reference.
Despite the market strength of dynamic speakers, the electrostatic speaker
industry has offered significant potential for commercial benefit. However,
because of low power output, large size requirements and construction
limitations, electrostatic speakers have failed to capture a significant
market
share--less than 1 %. In spite of the clear advantages offered by
electrostatic
speakers over dynamic speakers within the audio industry, commercial
2 0 development and research continues to focus on the higher power,
magnetically
driven dynamic systems.
It now appears likely that this trend within the acoustic world has affected
the direction of research within the parametric field of sound reproduction as
well. Specifically, virtually all parametric investigation prior to the
present
2 5 inventors has been with the use of bimorph transducers, similar in
construction to
the dynamic speaker with its high power operation. As noted above, bimorph
systems have not realized the necessary results for commercialization of
parametric speaker systems. Having failed to realize required levels of volume
and quality with the "high power" form (bimorph transducer) of a ultrasonic
3 0 emitter, there has been an apparent assumption by those skilled in the art
that
electrostatic or low power film-type emitters would be even less likely to
perform
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in the parametric sound field. So, the use of broad film diaphragms and
similar
single-stage electro-acoustical conversion systems have not been considered as
a
transducer suitable for parametric investigation.
The science of acoustics has long known of the utility of a movable
electrostatic membrane or film associated with and insulated from a stator or
driver member as a speaker and/or microphone device. Typical construction of
such devices includes a flexible Mylar(tm) or Kapton(tm) film having a
metalized
coating and an associated conductive, rigid plate which are separated by an
air
gap or insulative material. An applied voltage including a sonic or ultrasonic
signal is transmitted to this capacitive assembly and operates to displace the
flexible emitter film to propagate the desired ultrasonic or sonic compression
wave.
Two primary categories of electrostatic speakers exist. Single-ended
speakers comprise a single plate, typically having holes to allow the sound to
pass through. The film is suspended in front of or behind the plate, and may
be
displaced from contact with the plate by spacers. With ultrasonic emitters,
the
film has been biased in direct contact with an irregular face of the plate,
and the
film is allowed to vibrate in pockets or cavities. An insulation barner of
either
air, plastic film or similar nonconductive material is sandwiched between the
film
2 o and plate to prevent electrical contact and arcing. Typical ly, the plate
and
diaphragm are coupled to a DC power supply to establish opposing polarity at
the
respective conducting surfaces of the metalized coating and the plate.
The second primary category of electrostatic speakers is represented by
the push-pull configuration. In this case, the speaker has two rigid plates
which
2 5 are symmetrically displaced on each side of a conductive membrane. When
voltage is applied, one plate becomes negative with respect to the membrane
while the opposing plate assumes a positive charge. The transmission of a
variable voltage (e.g. AC) to the transducer reinforces the effect of push and
pull
on the membrane, thereby enhancing power output. Further details of theory and
3 o construction of common electrostatic emitter designs is found in
Electrostatic
Loudspeaker by Ronald Wagner, Audio Amateur Press, 1993.
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Many years of directed research have developed a variety of technical
improvements to this basic system, but the component definition has remained
substantially the same. Surprisingly, the present inventors have discovered
that a
single-stage conversion process using such low power transducers as
piezoelectric films, electrostatic films, and other similar film emitters
offer
significant advantages for parametric speakers. The following disclosure
provides further enhancements to these concepts and embodiments previously
recited in the referenced parent applications.
OBJECTS AND SUMMARY OF THE INVENTION
It is therefore an object of this invention to apply a film transducer to the
parametric field of sound reproduction.
Another object of this invention is to provide an improved speaker
diaphragm capable of generating high amplitude compression waves in response
to electrical stimulation, which does not require a rigid diaphragm structure
of a
conventional audio speaker or ultrasonic transducer.
It is the further object of the invention to have a substantially continuous
diaphragm that drives each portion of the air less for a given total amount of
2 0 system output.
It is a further object of the invention to have a transducer that can deliver
high output while minimizing distortion, phase shift, and harmonic resonances.
It is a still further object of the invention to have a transducer that may be
2 5 configured to provide control of the directivity pattern of the primary
frequencies
so that the beam width can be expanded to the diameter of the transducer
system
or even greater.
Yet another object of this invention to enable reduction in weight and
stiffness requirements by utilizing a foam material as the stator element of
the
3 o speaker system.
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Another object of the present invention is to provide a plate or support
member capable of operating in single or push-pull configuration.
It is another object to indirectly generate at least one new sonic or
subsonic wave having commercially acceptable volume levels by using a
magnetically driven thin film emitter, which provides interference between at
least two ultrasonic signals having different frequencies equal to the at
least one
new sonic or subsonic wave.
Another object of the present invention is to provide a film transducer
having an array of low power, common emitter sections which operate in phase.
A specific object of this invention is to provide a piezo-electric film
having arcuate emitter sections which are commonly powered through a single
contact by a parametric signal source.
It is a still further object of the invention to have a substantially
continuous diaphragm having an array of arcuate emitter sections which
generally
drive adjacent regions of surrounding air at levels short of saturation, yet
in a
controlled manner for maximizing total system output.
These and other objects are realized in a method for generating
parametric audio output based on interaction of multiple ultrasonic
frequencies
within air as a nonlinear medium, said method comprising the steps of:
2 0 a) generating an electronic signal comprising at least two ultrasonic
signals having a difference in value which falls within an audio frequency
range;
b) transferring the electronic signal to an electro acoustical film transducer
diaphragm which couples directly with the air as part of a single stage energy
conversion process;
2 5 c) converting the electronic signal at the diaphragm directly to
mechanical displacement as a driver member of a parametric speaker;
d) mechanically emitting the at least two ultrasonic signals from the
diaphragm into the air as ultrasonic compression waves; and
e) interacting the ultrasonic compression waves within the air to generate
3 0 the parametric audio output.
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Another embodiment of the invention is a speaker device having a rigid
emitter plate which includes an outer face having a plurality of apertures or
cavities; a thin piezoelectric film disposed across the apertures of the
emitter
plate with the film distended into the cavities to form an array of arcuate
emitter
configurations capable of constricting and extending in response to variations
in
an applied electrical input at the piezoelectric film to thereby create
compression
waves in a surrounding environment; and electrical contact means coupled to
the
piezoelectric film for providing the applied electrical input. The array of
arcuate
emitter configurations can be preformed, or extended to this position by
positive
or negative pressure.
An additional embodiment of this invention is characterized by a
method for enhancing parametric audio output comprising the steps of (a)
generating an electronic signal of at least two ultrasonic signals having a
difference in value which falls within an audio frequency range; (b)
transmitting
the electronic signal to an emitter film transducer diaphragm having an array
of
arcuate emitter sections formed within the film; (c) electro-mechanically
displacing the array of arcuate emitter sections in phase as a driver member
of a
parametric speaker; (d) emitting the at least two ultrasonic signals from the
diaphragm into the air as ultrasonic compression waves; and (e) interacting
the
2 o ultrasonic compression waves within the air to generate the parametric
audio
output.
The present invention is also represented by a method for enhancing
parametric audio output comprising the steps of (a) generating an electronic
signal comprising at least two ultrasonic signals having a difference in value
2 5 which falls within an audio frequency range; (b) concurrently transferring
the
electronic signal to an array of arcuate emitter sections formed within a
common
electro acoustical transducer diaphragm; (c) displacing the emitter sections
in a
controlled manner for minimizing saturation of surrounding air; (d} electro-
mechanically displacing the array of arcuate emitter sections in phase as a
driver
3 o member of a parametric speaker; (e) emitting the at least two ultrasonic
signals
from the diaphragm into the air as ultrasonic c~rnpression waves; and (f)
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interacting the ultrasonic compression waves within the air to generate the
parametric audio output.
A further embodiment of this invention is described as a method for
enhancing parametric audio output based on the steps of (a) generating an
5 electronic signal comprising at least two ultrasonic signals, including an
ultrasonic carrier signal and at least one additional ultrasonic signal,
having a
difference in value with respect to the earner signal which falls within an
audio
frequency range; (b) transmitting the electronic signal to an array of arcuate
emitter sections formed within a common electro acoustical film transducer
10 diaphragm which has a primary axis of propagation; (c) configuring the
array of
emitter sections in a generally concave form for providing convergence of
emitted ultrasonic beams from at least an outer perimeter of the array with a
predetermined angle of convergence with respect to the primary axis of
propagation; (d) electro-mechanically displacing the array of arcuate emitter
sections in phase as a driver member of a parametric speaker; (e) emitting the
at
least two ultrasonic signals from the diaphragm into the air as ultrasonic
compression waves; and (f) interacting the ultrasonic compression waves within
the air to generate the parametric audio output.
Another embodiment of the invention is realized through a method and
2 0 apparatus for an ultrasonic emitter device having broad frequency range
capacity
with relatively large diaphragm displacement compared to typical electrostatic
diaphragm movement. The device includes a core member able to establish a
first magnetic field. A movable diaphragm is stretched along the core member
and displaced a short separation distance from the core member to allow an
2 5 intended range of orthogonal displacement of the diaphragm with respect to
the
core member and within a strong portion of the magnetic field. At least one,
low
mass, planar, conductive coil is disposed on the movable diaphragm and
includes
first and second contacts for enabling current flow through the coil. A
variable
current flow is applied to the coil for developing a second magnetic field
which
3 o variably interacts with the first magnetic field to attract and repel the
diaphragm
at a desired frequency for development of a series of compression waves which
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may include an ultrasonic frequency range having an audio signal modulated
therewith.
In a different aspect of the invention, the emitter for a parametric speaker
includes a drum comprised of a single emitter membrane disposed over a
common emitter face comprised of a plurality of apertures therein, where the
apertures are aligned so as to emit all frequencies generated therefrom along
parallel axes, and where a near vacuum is created within the drum and behind
the
emitter membrane to thereby eliminate back-wave generation.
In another aspect of the invention, the emitter includes a drum comprised
of a single emitter membrane disposed over a common emitter face comprised of
a plurality of apertures therein, but where the drum is now pressurized.
In still another aspect of the invention, a drum having a piezoelectric film
as the emitter membrane, and being stretched across a sensor face having
apertures therein, is able to sense compression waves by detecting electrical
signals being generated from the impact of compression waves on the
piezoelectric film.
Other objects and features of the present invention will be apparent to
those skilled in the art based upon the following detailed description of
preferred
embodiments, taken in combination with the following drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
Fig. I a is a drawing representing prior art parametric loudspeakers using
multiple piezo bimorph transducers.
2 5 Fig. I b is drawing representing another embodiment of parametric
loudspeakers using multiple piezo bimorph transducers.
Fig. 1 c is a drawing of bimorph transducers driving the air at smal I points
in space and causing shock.
Fig. I d is a drawing of a film transducer of the invention driving the air in
3 0 a homogenous fashion that distributes the drive and reduces shock
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Fig. le is a drawing of a primary frequency waveform below shock level
and at shock level.
Fig. 2 is a representation of a circular V grooved back plate for a large
scale electrostatic film transducer.
Fig. 2a is a sectional view of the electrostatic back plate and diaphragm
film of Fig 2, taken along the lines of 2a -2a.
Fig. 2b is a drawing of an electrostatic transducer with a curved back plate
and diaphragm Fig. 3 is a drawing of a rectified sine form of piezo film.
Fig. 3a is a drawing of a rectified sine form of piezo film with a quarter
wave spaced back plate
Fig. 3b is a drawing of a shallow rectified sine form of piezo film.
Fig. 3c is a drawing of a shallow rectified sine form of piezo film with
back plate.
Fig. 4 is a drawing of a sinusoidal shaped piezo film
Fig. 4a is a drawing of a sinusoidal shaped piezo film with a backplate
Fig. 4b is a drawing of a sinusoidal shaped piezo film with a backplate
and a curvature to open up the directivity angle of the primary frequencies.
Fig. 4c is a drawing of a sinusoidal shaped piezo film used in dipolar
2 o primary frequency/bipolar secondary frequency mode.
Fig. 5 is a drawing of piezo film with a back plate used in a dimpled form
either concave or convex.
Fig. Sa is a drawing of piezo film used in a dimpled form convex.
Fig. Sb is a drawing of piezo film used in a dimpled form concave.
2 5 Fig. 6 is a drawing representing prior art parametric loudspeakers using
multiple piezo bimorph transducers as an ultrasonic emitting source.
Fig. 7 is drawing representing another prior art embodiment of parametric
loudspeakers using multiple piezo bimorph transducers and representing various
deficiencies in speaker performance.
3 0 Fig. 8 is an perspective view of an emitter drum transducer made in
accordance with the principles of the present invention
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Fig. 9 is a top view showing a plurality of apertures in an emitter face of
the emitter drum transducer.
Fig. 10 is a cut-away profile view of the emitter drum transducer and the
emitter face, showing the membrane which is disposed over the apertures in the
emitter face.
Figs. 1 lA-B are close-up profile views of membranes which are vibrating
while stretched over a plurality of the apertures in the emitter face.
Fig. 12 is a graph showing an example of membrane (piezoelectric film)
displacement versus frequency in the preferred embodiment. The graph shows
resonant frequency and typical bandwidth generated.
Fig. 13 is a cut-away profile view of the emitter drum transducer of an
alternative embodiment where the emitter drum transducer is pressurized.
Fig. 14 is a more specific implementation of the present invention which
transmits an ultrasonic base frequency and an ultrasonic intelligence carrying
frequency which acoustically heterodyne to generate a new sonic or subsonic
frequency.
Fig. 15 is an alternative embodiment showing a cut-away profile view of a
sensor drum transducer and the sensor face, showing the sensing membrane
which is disposed over the apertures in the sensor face.
2 0 Fig. 16 is a perspective view of a transducer with a diaphragm which has
preformed concave oval shapes.
Fig. 17 is a cross-section of Fig. 16 showing the transducer with
preformed membranes which vibrate to produce an ultrasonic wave.
Fig. 18 depicts a cross-sectional side view of a single-end electrostatic
2 5 speaker.
Fig. 19 shows an arcuate shape representing a curved configuration for the
present speaker device.
Fig. 20 shows a cylindrical shape representing a possible configuration for
the speaker device
3 0 Fig. 21 is a schematic of a basic form of a foam stator speaker
embodiment of the speaker device in push-pull configuration.
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Fig. 22 illustrates an embodiment of the speaker device where the film is
sandwiched between opposing foam stators.
Fig. 23 and 24 show multiple film embodiments of the speaker device.
Fig. 25 is a top perspective view showing a thin film diaphragm having a
plurality of magnetic coils disposed on the emitter diaphragm and suspended
over
a magnetic core element.
Fig. 26 is an exploded view of an alternate embodiment showing
oppasing magnetic coils on the emitter diaphragm and core.
Fig. 27 is a cut-away, top perspective view showing a thin film diaphragm
having a plurality of rings disposed on the emitter diaphragm and suspended
over
a core element. Fig. 28 is an elevated, perspective view of a
resonance tuned electrostatic emitter.
Fig. 29 is a cross section of the emitter of Fig. 28.
Fig. 30 is a cross-sectional side view of a hemispherical electrostatic
speaker.
Fig. 31 is a perspective view of a hemispherical electrostatic speaker.
Fig. 32 is a perspective side view of a spherical electrostatic speaker.
DISCLOSURE OF THE INVENTION
2 0 Reference will now be made to the drawings in which the various
elements of the present invention will be given numerical designations and in
which the invention will be discussed so as to enable one skilled in the art
to
make and use the invention. It is to be understood that the following
description
is only exemplary of the present invention, and should not be viewed as
2 5 narrowing the claims which follow.
Figs. I a and lb are drawings representing prior art parametric
loudspeakers 10 using multiple piezo bimorph transducers 11. These have been
used with clusters of S00 to over 1500 bimorph transducers. One of the
difficulties with parametric loudspeakers is that when driving the air at
ultrasonic
3 0 levels to provide reasonable conversion efficiency and loudness at the
secondary
resultant frequencies, the air can be driven into a shock limit where the
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fundamental frequency cannot get any louder and only the distortion component
levels increase. This shock limit is worse when driving individual, small
points
of air space. The more confined the intensity, the easier shock comes into
existence.
5 Fig. 1 c is a drawing of a group of bimorph transducers each driving the air
at small points in space 12 and causing shock. Fig. ld is a drawing of a film
transducer 13 of the invention driving the air in a homogenous fashion that
distributes the drive 14 and reduces shock. Fig. 1 a is a drawing of a primary
frequency waveform below shock level 15 and at shock level 16. One preferred
10 embodiment of a large scale film transducer is based on electrostatic drive
principles. The electrostatic type transducer uses a conductive backplate with
a
conductive film in close proximity to the backplate. A bias is applied to
either
the film or the backplate and both the film and the backplate are driven by
two
polarities of the drive signal. Fig.2 is a top view representation of a large
scale
15 electrostatic film transducer with a circular V-grooved back plate 21. The
back
plate design may alternatively be pitted (concave) or dimpled (convex) in
shape.
Fig. 2a is a sectional view of an electrostatic back plate 23 and diaphragm
film
22.
When high frequencies are projected from relatively large diaphragms, as
2 0 compared to the wavelength of the frequency of interest, the beam of sound
can
achieve such high directivity that the high frequencies will focus down to a
tight
beam. This can cause overly concentrated directivity and premature shock
formation of the sound waves due to high intensities being focused in a small
airspace. By curving the diaphragm, the radiation pattern can be opened up to
2 5 have a directivity window comparable in width to the size of the
transducer or
even a somewhat wider spreading of sound to minimize shock limited
waveforms.
Fig. 2b shows an electrostatic film transducer with a curved backplate 23
and complimentary shaped film diaphragm 22 that solves this problem.
3 0 Another embodiment of the invention utilizes piezo electric film (PVDF 1
This
film expands and contracts when electrically excited and must therefore be
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formed to achieve acoustic output. It should be realized that these large area
film
transducers include but are not limited to electrostatic film, electret film,
and
piezo film such as PVDF, electrothermal mechanical film, and planar magnetic
configurations. A preferred shape of the piezo film 30 as a rectified sine
shape is shown in Figure 3. Fig. 3a is a drawing of a rectified sine form of
piezo
film 30 with a quarter wave spaced back plate 31. By spacing the backplate at
a
quarter of a wave length from the film, the output of the emitter can increase
up
to 3 dB at the frequency whose wavelength is four times the distance from film
to
back plate. Fig. 3b is a drawing of a shallow rectified sine form of piezo
film 32.
Fig. 3c is a drawing of a shallow rectified sine form of piezo film 32 with
back
plate 31.
Fig. 4 is a drawing of a sinusoidal shaped piezo film. This form can be
efficient in utilizing all of the film. For sine shapes that are much greater
than or
much less than'/z wL in height, the peaks and troughs can be out of phase with
each other. In this case, a compensating means, such as electrically driving
the
peaks in opposite phase from the troughs may be required. Fig. 4a is a drawing
of a sinusoidal shaped piezo film 33 with spaced backplate 31. Fig. 4b is a
drawing of a sinusoidal shaped piezo film with a backplate and a curvature to
open up the directivity angle of the primary frequencies. This arrangement
2 o minimizes shock formation and opens up the window of dispersion as in the
above mentioned electrostatic example.
Most ultrasonic emitters and parametric loudspeakers are essentially
monopole in radiation pattern. A bipolar parametric loudspeaker can be
realized
with the invention by using a open film without backplate such as PVDF, Fig.
4c,
2 5 and radiate in a bipolar out-of phase radiation pattern in the primary
frequency
range while simultaneously operating in a bipolar in-phase manner for all
secondary parametrically derived signals. This could be used where one wanted
to project highly directive, in phase sounds in two opposite directions. This
is not
practical to do with any prior art devices. Fig. 4c is a drawing of a
sinusoidal
3 c shaped piezo film used in bipolar primary frequency/bipolar secondary
frequency
mode. Another diaphragm form for piezo film is either a concave or convex
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17
dimpled structure. This shape may be achieved by thermo-forming the film or
utilize foam support structure to push the film into this shape. Forming the
film
into curved emitter sections can also be achieved by pushing or pulling the
film
into cavities with positive or negative pressure. In addition, it is possible
to
utilize foam or plastic support structure to push the film into desired
shapes.
Fig. 5 is a drawing of piezo film 51 with a back plate 52 generating either
concave or convex forms. Fig. Sa is a drawing of piezo film 51 a used in a
dimpled form with a concave extension. Fig. Sb is a drawing of piezo film S l
b
used in a dimpled form of convex character. It will be apparent to those
skilled in
the art that many variations for developing the desired curvature in piezo
film can
be applied under the concepts of this invention. Furthermore, numerous support
mechanisms may be developed to provide these desired curvatures within the
piezo film, particularly as applied to the development of parametric output of
audio sound as a secondary emission from the primary ultrasonic emissions.
The adaptability of a flexible film diaphragm offers many advantages over
the conventional rigid bimorph devices. Some of these benefits are more
specifically illustrated in Figures 6 and 7. Fig. 6 is a drawing representing
a prior
art parametric loudspeaker 60 using multiple piezo bimorph transducers 62. As
mentioned, these have been used in clusters of between 500 to 1 S00 bimorph
2 0 transducers in an effort to generate effective parametric output. This
disclosure
has already identified one deficiency in the use of bimorph emitters which
arises
from the saturation of air at local emission regions immediately in front of
the
transducer face. Figure 7 graphically illustrates this cause of distortion, as
well as
other deficiencies that arise from the prior art parametric array 60 by reason
of
phase distortion and misalignment. These incongruities, such as the referenced
phase anomalies, are represented in items 70, 71 and 72 of Figure 7.
It is important to note that these bimorph emitters are separate structures
which typically have different physical and electrical properties. Indeed,
such
bimorph transducers may be manufactured from different batches of material,
3 0 with different construction environments. Typically, they are thrown into
a
common bin and distributed on a random selection basis as customers designate
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18
particular design specifications. As a consequence, mismatch of phase in
propagated ultrasonic waves 66 can result in phase cancellation and other
forms
of sound and directional distortion represented by phantom lines 76 and 78.
Item
78 shows the bending effect of adjacent ultrasonic beams where the respective
frequencies from each emitter are out of phase. For example, emitter 70 is
propagating waves 66a which are slightly out of phase with waves 66b from
emitter 71. Phantom line 78 illustrates a directional shift of the audio
output
from the parametric speaker which arises from the phase misalignment. Emitter
72 has been mounted askew, as illustrated by the acute angle 69 which is
slightly
divergent from a perpendicular axis 77 with respect to a mounting support
plate
64. Here again, the beams propagated from emitters which would not be
collimated and properly phase aligned would result in loss of energy and
possible
distortion. As these factors are multiplied by 500 to 1500 emitters which are
typically combined to make a conventional parametric array, the adverse
effects
can be significant. In addition, it appears that these devices tend to have
many
harmonic resonances and anti-resonances which are further distorted in the
demodulated audio component of the parametric loudspeaker.
In addition to the phase anomalies identified above, Figure 7 represents
the air saturation problem 63 previously introduced. Indeed, one of the
2 0 difficulties noted by the present inventors with parametric loudspeakers
is that
when driving the air at ultrasonic levels that provide reasonable conversion
efficiency and loudness, the air can be driven into a shock limit where the
fundamental frequency cannot get any louder and only distortion components are
increasing in level. This shock limit increases when driving small, individual
2 5 points of air space, as occurs with bimorph transducers 73 . The more
confined
the intensity, the easier shock comes into existence. This is particularly
true of
high intensity devices such as the conventional bimorphs.
The present inventors have discovered that by distributing high levels of
energy over broad surface areas of film, as opposed to the localized emitter
3 0 elements of bimorph array transducers, the management of shock is
controlled.
Where an array of small bimorph emitters would be expected icy generate a
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desired SPL when supplying 130 db to the emitters, the desired SPL falls
short,
and the distortion is greatly magnified. Under the principles of the present
invention, a broad emitter film is supplied with less than 120 db. However, by
dispersing the energy over many small emitter sections of the film, the air is
not
driven into saturation or shock at any local point in front of the transducer.
The
conversion efficiency for parametric output produced by film emitters is very
high, and distortion is substantially reduced. This process represents a
diversion
from prior art techniques of attempting to increase the volume by focusing
higher
db output from high intensity emitters, such as the bimorph family.
1 o In general, these various concepts represent a method for enhancing
parametric audio output based on interaction of multiple ultrasonic
frequencies
within air as a nonlinear medium, where the following basic steps are
implemented through one or more of the preceding types of structures. These
steps are listed below, and involve:
a) generating an electronic signal comprising at least two ultrasonic
signals having difference in value which falls within an audio frequency
range;
b) transmitting the electronic signal to an emitter film transducer
diaphragm having an array of arcuate emitter sections formed within the film;
c) electro-mechanically displacing the array of arcuate emitter sections in
2 0 phase as a driver member of a parametric speaker; and
d) mechanically emitting the at least two ultrasonic signals from the
diaphragm into the air as ultrasonic compression waves which interact within
the
air to generate the parametric audio output.
Where the prior art techniques sought to increase SPL output by
2 5 increasing db levels at the bimorph emitter surface, the present invention
spreads
out the energy over a larger surface area. Although this decreases the db
level of
compression waves propagated at any point in space, the overall effect is to
increase the SPL because of the large surface area. Furthermore, because
distortion is minimized, SPL can be raised to more effective levels. This
3 o represents a conceptual step of limiting the electronic signal with a
maximum
strength level which saturation of minimizes surrounding air at the respective
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arcuate emitter sections. The following geometries and correlated db levels
illustrate appropriate balances of broad geometry with db emission levels of
the
film emitter.
An additional step which is readily implemented under the concepts of the
5 present invention involves providing for improved collimating of the
respective
beams of ultrasonic energy propagated from each of the film emitter sections.
The orientation of the beams can be controlled by the support structure of the
backplate. Specifically, the single, common plate structure provides physical
positioning of the array of emitter sections with greater accuracy. Prior
10 positioning of bimorph devices required individual positioning of each
emitter,
leading to misalignment. With all the emitter sections properly aligned,
ultrasonic emissions are collimated. Interference losses from out-of phase
interaction resulting from uncollimated emissions is significantly reduced.
Tighter beaming of ultrasonic energy also provides more efficient conversion,
in
15 view of the virtual end-fired-array of demodulation of the audio signal
from the
ultrasonic emissions. Specifically, the tighter beam pattern provides more
concentration to the demodulation of energy, thereby increasing the audio SPL
along the length of the ultrasonic beam.
Another embodiment of this invention is FIG. 8 which shows a more
2 o efficient embodiment of an ultrasonic emitter. In the preferred embodiment
shown in this orthogonal view, the emitter drum transducer 100 is a generally
cylindrical object. The sidewall 106 of the emitter drum transducer 100 is
preferably a metal or metal alloy. However, an emitter face 102 which
generates
compression waves from the top surface of the emitter drum transducer 100 is
2 ~ comprised of at least two materials. The outer surface of the emitter face
102 is
comprised of a piezoelectric film 104. The piezoelectric film 104 is
stimulated
by electrical signals applied thereto, and thereby caused to vibrate at
desired
frequencies to generate compression waves. Above the piezoelectric film 104
and disposed about the perimeter of the emitter face 102 is a conductive ring
114.
3 ,'.'~ The conductive ring 114 is used to apply voltages to the piezoelectric
film 104.
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Underneath the piezoelectric film 104 is a preferably metallic cookie 108 (but
which will be referred to hereinafter as a disk, see FIG. 8) to be described
later.
The emitter drum transducer 100 is generally hollow inside, and is closed
at a bottom surface by a back cover 110. The emitter drum transducer 100 is
sealed so as to be generally airtight so that either a near-vacuum
(hereinafter
referred to as a vacuum) or a pressurized condition can exist within the
emitter
drum transducer 100. A positive pressure in the drum transducer 100 with a
diaphragm one quarter of a wave length of a selected frequency from the rear
plate can produce a useful back wave. Of course, a rear plate can also be used
to
absorb the back wave with fiberglass, foam or other sound wave absorbing
materials.
To better understand the structure of the emitter drum transducer 100,
FIG. 9 provides a top view of an outward facing side 126 of the disk 108
disposed underneath the piezoelectric film 104 (see FIG. 8}. In the preferred
embodiment, the disk 108 is metallic and perforated by a plurality of
apertures
112 of generally uniform dimensions. The apertures 112 extend completely
through the thickness of the disk 108 from an inward facing side 128 (see FIG.
10) to the outward facing side 126. To provide predictability and the greatest
efficiency in performance, the apertures 112 are formed in the shape of
cylinders
2 0 if bidirectional piezo film is used. Where unidirectional film is applied,
an
elongate shape as illustrated in Figure 16 is preferable.
The aperture pattern 112 shown on the disk 108 in FIG. 8 is chosen in this
case because it enables the greatest number of apertures 112 to be located
within
a given area. The pattern is typically described as a "honeycomb" pattern. The
2 5 honeycomb pattern is selected because it is desirable to have a large
number of
apertures 112 having parallel axes because of the characteristics of
acoustical
heterodyning. Specifically in the case of generating ultrasonic frequencies,
it is
desirable to cause heterodyning interference between a base frequency and a
frequency which carries intelligence to thereby generate a new sonic or
subsonic
3 0 frequency containing the intelligence. Consequently, a greater number of
base
and intelligence carrying signals which are caused to interfere in close
proximity
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22
to each other has the effect of generating a new sonic or subsonic frequency
of
greater volume than if a single pair of base and intelligence carrying
frequencies
are interfering. In other words, the present invention provides the
significant
advantage of generating a volume which is loud enough to be commercially
viable. Parallel axes of frequency emission provides greater predictability
for
determining where the new sonic or subsonic frequency will be generated.
FIG. 10 provides a helpful profile and cut-away perspective of the
preferred embodiment of the present invention, including more detail regarding
electrical connections to the emitter drum transducer 100. The sidewall 106 of
1 o the emitter drum transducer 100 provides an enclosure for the disk 108,
with its
plurality of apertures 112 extending through the disk 108. The piezoelectric
film
104 is shown as being in contact with the disk 108. Experimentation was used
to
determine that it is preferable not to glue the piezoelectric film 104 to the
entire
exposed surface of the disk 108 with which the piezoelectric film 104 is in
contact. The varying size of glue fillets between the piezoelectric film 104
and
the apertures 112 causes the otherwise uniform apertures 112 to generate
resonant
frequencies which were not uniform. Therefore, the preferred embodiment
teaches only gluing an outer edge of the piezoelectric film 104 to the disk
108.
The back cover 110 is provided so that in the preferred embodiment, a
2 0 vacuum or near-vacuum can be created within the emitter drum transducer
100
The near-vacuum will be defined as a pressure which is small enough to require
measurement in millitorrs. There are several reasons for having a vacuum
inside
the emitter drum transducer 100. First, the vacuum causes the piezoelectric
film
104 to be pulled against the disk 108 generally uniformly across the apertures
112. Uniformity of tension of the piezoelectric film 104 suspended over the
apertures 112 is important to ensure uniformity of the resonant frequencies
produced by the piezoelectric film 104 over each of the apertures 112. In
effect,
each of the piezoelectric film 104 and aperture 112 combinations forms a
miniature emitter element or cell 124. By controlling the tension of the
3 o piezoelectric film 104 across the disk 108, the cells 124 advantageously
respond
generally uniformly.
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23
A second reason for the vacuum is that it advantageously eliminates any
possibility of unintentionally generating "back-wave" distortion. In other
words,
by definition, a compression wave requires that there be a compressible medium
through which it can travel. If the piezoelectric film 104 can be caused to
generate ultrasonic compression waves "outward" in the direction indicated by
arrow 130 from the emitter drum transducer 100, it is only logical that
ultrasonic
compression waves are also being generated from the piezoelectric film 104
which will travel in an opposite direction, backwards into the emitter drum
transducer 100 in the direction indicated by arrow 132. Consequently, these
backwards traveling or back-wave distortion waves can interfere with the
ability
of the piezoelectric film 104 to generate desired frequencies. This
interference
occurs when the back-waves reflect off surfaces within the emitter drum
transducer 100 until they again travel up through an aperture 112 and reflect
off
of the piezoelectric film 104, thus altering its vibrations. Therefore, by
eliminating a medium for travel of compression waves within the emitter drum
transducer 100, vibrations of the piezoelectric film 104 are not interfered
with.
FIG. 10 also shows that there are electrical leads 120 which are
electrically coupled to the piezoelectric film 104 and which carry an
electrical
representation of the frequencies to be transmitted from each cell 124 of the
2 0 emitter drum transducer 100. These electrical leads 120 are thus
necessarily
electrically coupled to some signal source 122 as shown.
FIG. 1 lA is a close-up profile view of two cells 128 in FIG. 10(comprised
of the piezoelectric film 104 over two apertures 112). The piezoelectric film
104
is shown distended inward toward the interior of the emitter drum transducer
100
2 5 in an exaggerated vibration for illustration purposes only. It should be
apparent
from a comparison with FIG. 11B that the distention inward of the
piezoelectric
film 104 will be followed by a distention outward and away from the interior
of
the emitter drum transducer 100. The amount of distention of the piezoelectric
film 104 is again shown exaggerated for illustration purposes only. The actual
3 0 amount of distention will be discussed later.
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FIG. 12 is a graph showing frequency response of the emitter drum
transducer 100 produced in accordance with the principles of the preferred
embodiment as compared to displacement of the piezoelectric film 104 (as a
function of applied voltage RMS). The emitter drum transducer 100 which
provided the graph of FIG. 11 which is exemplary of typical results had a near
vacuum in the interior of the emitter drum transducer 100. The membrane
(piezoelectric film 104) used in this embodiment is a polyvinylidiene di-
fluoride
(PVDF) film of approximately 28 mm in thickness. Experimentally, the resonant
frequency of this particular emitter drum transducer 100 is shown to be
approximately 37.23 kHz when using a drive voltage of 73.6 Vpp, with a
bandwidth of approximately 11.66 percent, where the upper and lower 6dB
frequencies are 35.55 kHz and 39.89 kHz respectively. The maximum amplitude
of displacement of the piezoelectric film 104 was also found to be
approximately
just in excess of 1 micrometer peak to peak. This displacement corresponds to
a
sound pressure level (SPL hereinafter) of 125.4 dB.
What is surprising is that this large SPL was generated from an emitter
drum transducer 100 using a PVDF which is theoretically supposed to withstand
a drive voltage of 1680 VPP, or 22.8 times more than what was applied.
Consequently, the theoretical limit of these particular materials used in the
2 0 emitter drum transducer 100 result in a surprisingly large SPL of 152.6.
It is important to remember that the resonant frequency of the preferred
embodiment shown herein is a function of various characteristics of the
emitter
drum transducer 100. These characteristics include, among other things, the
thickness of the piezoelectric film 104 stretched across the emitter face 102,
and
2 5 the diameter of the apertures I 12 in the emitter disk 108. For example,
using a
thinner piezoelectric film 104 will result in more rapid vibrations of the
piezoelectric film 104 for a given applied voltage. Consequently, the resonant
frequency of the emitter drum transducer 100 will be higher.
The advantage of a higher resonant frequency is that if the percentage of
3 0 bandwidth remains at approximately 10 percent or increases as shown by
experimental results, the desired range of frequencies can be easily
generated. In
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other words, the range of human hearing is approximately 20 to 20,000 Hz.
Therefore, if the bandwidth is wide enough to encompass at least 20,000 Hz,
the
entire range of human hearing can easily be generated as a new sonic wave as a
result of acoustical heterodyning. Consequently, a signal with sonic
intelligence
5 modulated thereon, and which interferes with an appropriate carrier wave,
will
result in a new sonic signal which can generate audible sounds across the
entire
audible spectrum of human hearing.
In addition to using a thinner piezoelectric film 104 to increase the
resonant frequency, there are other ways this can be accomplished. For
example,
1 o in an alternative embodiment, the present invention uses a cell 124 having
a
smaller diameter aperture 112. A smaller aperture will also result in a higher
resonant frequency for an applied driving voltage.
FIG. 13 shows an alternative embodiment which is at present less
advantageous than the preferred embodiment of the present invention, but which
15 also generates frequencies from an emitter drum transducer 116 which is
constructed almost identically to the preferred embodiment. The essential
difference is that instead of creating a vacuum within the interior of the
emitter
drum transducer 116, the interior is now pressurized.
The pressure introduced within the emitter drum transducer 116 can be
2 0 varied to alter the resonant frequency. However, the thickness of the
piezoelectric film 104 is a key factor in determining how much pressure can be
applied. This can be attributed in part to those piezoelectric films made from
some copolymers having considerable anisotropy, instead of a bidirectional
film
such as PVDF used in the preferred embodiment. The undesirable side affect of
25 an anisotropic piezoelectric film is that it may in fact prevent vibration
of the film
in all directions, resulting in asymmetries which will cause unwanted
distortion
of the signal being generated therefrom. Consequently, PVDF is the preferred
material for the piezoelectric film not only because it has a considerably
higher
yield strength than copolymer, but because it is considerably less anisotropic
3 0 One drawback of a pressurized emitter drum transducer 116 is unwanted
frequency resonances or spurs. These frequency spurs can be attributed to hack-
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26
wave generation within the emitter drum transducer 116 because instead of a
vacuum, an elastic medium is present within the emitter drum transducer 116.
However, it was also determined that the back-wave could be eliminated by
placing a material within the emitter drum transducer 116 to absorb the back-
s waves. For example, a piece of foam rubber 134 or other acoustically
absorbent
or dampening material which is inserted into the emitter drum transducer 116
can
generally eliminate all frequency spurs.
Experimental results using the pressurized emitter drum transducer 116
showed that at typical selected pressures and drive voltages, the emitter drum
transducer I 16 operated in a substantially linear region. For example, it was
determined that an emitter drum transducer 116 using a 28 mm thick PVDF with
a pressure of 10 pounds per square inch (psi) inside the emitter drum
transducer
116 can generate a resonant frequency approximately 43 percent greater than an
emitter drum transducer 116 which has an internal pressure of 5 psi.
Alternatively, it was confirmed that a generally linear region of operation
was
discovered when it was determined that doubling the drive amplitude also
generally doubles the displacement of the PVDF.
It was also experimentally determined that the pressurized emitter drum
transducer 116 could generally obtain bandwidths of approximately 20 percent.
Therefore, by constructing an emitter drum transducer 116 having a resonant
frequency of only 100 KHz results in a bandwidth of approximately 20 KHz,
more than adequate to generate the entire range of human hearing. By
acoustically damping the interior of the emitter drum transducer 116 to
prevent
introducing back-wave distortions or low frequency resonances, the pressurized
2 5 embodiment is also able to achieve the impressive results of commercially
viably
volume levels of the preferred embodiment of the present invention.
Turning to a more specific implementation of the preferred embodiment
of the present invention, as a practical matter, the emitter drum transducer
100
can be included, for example, in the system shown in FIG. 14. The system
3 0 includes an oscillator or digital ultrasonic wave source 220 fir providing
a base
or carrier wave 221. This wave 221 is generally referred to as a first
ultrasonic
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27
wave or primary wave. An amplitude modulating component 222 is coupled to
the output of the ultrasonic generator 220 and receives the base frequency 221
for
mixing with a sonic or subsonic input signal 223. The sonic or subsonic signal
may be supplied in either analog or digital form, and could be music from any
convention signal source 224 or other form of sound. If the input signal 223
includes upper and lower sidebands, a filter component is included in the
modulator to yield a single sideband output on the modulated carrier
frequency.
The emitter drum transducer is shown as item 225, which is caused to
emit the ultrasonic frequencies f, and f2 as a new wave form propagated at the
face of the transducer 225x. This new wave form interacts within the nonlinear
medium of air to generate the difference frequency 226, as a new sonic or
subsonic wave.
The present invention is able to function as described because the
compression waves corresponding to f, and f2 interfere in air according to the
principles of acoustical heterodyning. Acoustical heterodyning is somewhat of
a
mechanical counterpart to the electrical heterodyning effect which takes place
in
a non-linear circuit. For example, amplitude modulation in an electrical
circuit is
a heterodyning process. The heterodyne process itself is simply the creation
of
two new waves. The new waves are the sum and the difference of two
2 o fundamental waves.
In acoustical heterodyning, the new waves equaling the sum and
difference of the fundamental waves are observed to occur when at least two
ultrasonic compression waves interact or interfere in air. The preferred
transmission medium of the present invention is air because it is a highly
2 5 compressible medium that responds non-linearly under different conditions.
This
non-linearity of air is possibly what enables the heterodyning process to take
place without using an electrical circuit. Of course, any compressible fluid
can
function as the transmission medium if desired.
As related above, the acoustical heterodyning effect results in the creation
3 0 of two new compression waves corresponding to the sum and the difference
of
ultrasonic waves f, and fz. The sum is an inaudible ultrasonic wave which is
of
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28
little interest and is therefore not shown. The difference, however, can be
sonic
or subsonic, and is shown as a compression wave 226 which is generated
generally omni-directionally from the region of interference.
Whereas successful generation of a difference wave in the prior art
appears to have had only nominal volume, the present configuration generates
full sound. While a single transducer carrying the base frequency and
modulated
single sideband frequency was able to project sound at considerable distances
and
impressive volume levels, the combination of a plurality of co-linear signals
significantly increases the volume. When directed at a wall or other
reflective
surface, the volume was so substantial that it reflected as if the wall were
the very
source of the sound generation.
An important feature of the present invention is that the base frequency
and single sideband are propagated from the same transducer face. Therefore,
the
component waves are perfectly collimated. Furthermore, phase alignment is at
maximum, providing the highest level of interference possible between two
different ultrasonic frequencies. With maximum interference insured between
these waves, one achieves the greatest energy transfer to the air molecules,
which
becomes the "speaker" radiating element in a parametric speaker. Accordingly,
the inventors believe this may have developed the surprising increase in
volume
2 0 to the audio output signal.
The embodiment of FIG. 14 using an array of emitter sections on a single
film diaphragm is preferred for many reasons. For example, the system does not
require individual mounting of bimorph devices and will therefore be less-
expensive to produce. Nevertheless, the single film transducer will actually
be
2 5 generating a plurality of collimated signals. The system will also be
lighter,
smaller and, most importantly, will have the greatest efficiency. In contrast
to
prior art devices, the present embodiment will always generate a new
compression wave which has the greatest efticiency. That is because no
orientation of two separate ultrasonic transducers will ever match or exceed
the
3 0 perfect coaxial relationship obtained when using the same ultrasonic
transducer
225 to emit the new ultrasonic wave form '_'?? embodying both ultrasonic
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29
compression waves. This coaxial propagation from a single aperture of the
emitter drum transducer 100 would therefore yield the maximum interference
pattern and most efficient compression wave generation.
The development of full volume capacity in a parametric speaker provides
significant advantage over conventional speaker systems. Most important is the
fact that sound is reproduced from a relatively massless radiating element. In
the
region of interference, and consequently at the location of new compression
wave
generation, there is no direct radiating element. This feature of sound
generation
by acoustical heterodyning can substantially eliminate distortion effects,
most of
which are caused by the radiating element of a conventional speaker. For
example, cone overshoot and cone undershoot can modify an otherwise pure
sound reproduction signal with harmonics and standing waves on a loudspeaker
cone.
This improvement will be most significant when compared with the prior
art limitations of conventional speaker diaphragms. A direct physical
radiating
element, for example, has. a frequency response which is not truly flat.
Instead, it
is a function of the type of frequency (bass, intermediate, or high) which it
is
inherently best suited for emitting. Whereas speaker shape, geometry, and
composition directly affect the inherent speaker character, acoustical
heterodyne
2 0 wave generation utilizes the natural response of air to avoid geometry and
composition issues and to achieve a truly flat frequency response for sound
generation. With the achievement of acceptable amplitude levels in sound, the
parametric system may now be commercially implemented in direct competition
with conventional speakers--a result heretofore unrealized by prior art
parametric
2 5 or beat mixing devices.
Distortion free sound implies that the present invention maintains phase
coherency relative to the originally recorded sound. Conventional speaker
systems do not have this capacity because the frequency spectrum is broken
apart
by a cross-over network for propagation by the most suitable speaker element
3 0 (woofer, midrange or tweeter). By eliminating the radiating element, the
present
invention makes obsolete the conventional cross-over network frequency and
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phase controls. This enables realization of a virtual or near point-source of
sound.
Other advantages arise directly from the unique nature of the ultrasonic
film transducers 225. Because of their small size and low mass, such
transducers
5 are generally not subject to the many limitations and drawbacks of
conventional
radiating elements used in loudspeakers. Furthermore, the use of ultrasonic
transducers at extremely high frequencies avoids the distortion, harmonics and
other undesirable features of a direct radiating element which must reproduce
sound directly in the low, mid and high frequency ranges. Consequently, the
10 many favorable acoustic properties of a relatively distortion free
ultrasonic
transducer system can now be transferred indirectly into sonic and subsonic by-
products.
Figures 15 and 16 disclose a further embodiment of the piezo film
diaphragm and support plate which does not require application of pressure or
use
15 . of a drum. The illustrated transducer 160 includes a base plate 161 and a
supported film diaphragm 162 made of piezo material. Electrical contacts on
the
film enable application of a voltage as previously discussed. The arcuate
emitter
sections 165 are molded or thermo-formed to a stable configuration.
Corresponding cavities or openings in a top face of the support plate 161 are
2 0 aligned to receive the curved portion of the film. These cavities have
sufficient
depth to allow the emitter sections to move freely, without incurring
interfering
contact with the cavity wall 167. The intermediate surfaces 168 of the support
plate contact the flat portion 162a of the film and stabilize the film and
emitter
sections for proper alignment as illustrated with collimated propagation axes
170.
2 5 In-phase operation occurs because the film is a monolithic structure which
responds uniformly to the applied voltage to generate compression waves 172
which are in phase and properly aligned.
The support plate 1 G 1 may be constructed from any rigid material which
provides the ability to stabilise the emitter film 162 for correct operation..
3 0 Conductive plates may be used in place of the contacts 163, to enable
application
of the signal voltage to the piero film. The illustrated piezo film comprises
a co-
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31
polymer film having unidirectional response oriented transverse the elongate
emitter sections, as illustrated by line 174. This is in contracts to
bidirection
filins such as PVDF. The unidirectional film has approximately 80% of its
shape
distension along the transverse direction 174, and therefore provides
excellent
response. With the larger size of arcuate emitters 165, increase surface area
is
provided with favorable SPL output.
Figure 17 illustrates one method for implementing the present invention
with an alternative method for forming the emitter sections 180. This relies
on
displacement of a monolithic, flat sheet of piezo material into arcuate shapes
by a
support plate 183 having bumps 184 configured with the desired emitter shape.
A force F is applied to deform the film over the bumps as shown. This force
may
be tension applied from the periphery of the film to draw the film against the
bumps, or other suitable methods. The bumps are desirably made of foam
material to enable the vibration of the piezo film in response to the applied
voltage.
An additional alternative embodiment of the present invention uses foam
stators with a electrostatic form of diaphragm to produce ultrasonic
parametric
compression waves. Figure 18 shows a single-end speaker device 310 with
ultrasonic output 31 I being propagated in a forward direction 312. This
speaker
2 o may be coupled to an ultrasonic driver 313 which provides the various
electronic
circuitry support elements for applying the desired signal as previously
discussed.
The device includes an electrostatic emitter film 315 which is responsive
to an applied variable voltage to emit ultrasonic output. The emitter film
comprises a plastic sheet and thin metallic coating or other conductive
surface.
2 5 Electrostatic emitter films are also well known, having been applied to
many
capacitive or stratified charge systems which will be generally referred to
hereafter as electrostatic devices. Typically, the plastic sheet is a
Mylar(tm),
Kapton(tm) or other nonconductive composition which can serve as an insulator
between the metal layer and a stator member 32(a. A surface or coating having
3 0 partial conductivity may be used to develop charge distribution uniformly
across
the diaphragm surface. A preferred range of resistivity is greater than l OK
ohms.
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32
This provides less charge migration and prevents static buildup leading to
arcing
A higher impedance such as 100M ohms is not uncommon in this application.
Obviously, this selection also affects the capacitance between two plates.
One of the primary features of this embodiment of invention involves the
use of a foam member as the stator 320. The stator serves as a base member or
rigid component which offers inertia with respect to the light, flexible
emitter
film 315. This stator is a conductive element which supplies one polarity to
the
capacitor combination. Resistivity of this component is selected to favor a
uniform charge migration to avoid arcing and other adverse effects inherent in
electrostatic systems. A preferred composition which has demonstrated
effective
properties is conventional static packing foam (generally known as "conductive
foam") used as packing material with computers and other charge sensitive
contents. This material operates to provide static discharge away from
sensitive
components. It not only protects the components from adverse electrical
discharge or exposure, but is very light weight and inexpensive. It is
typically
formed in a conventional foam molding device in virtually any shape, density,
or
dimension.
Prior art use of the material has generally been limited to a passive role
(packing material) whose purpose is merely to protect sensitive components.
2 o Like other packing material, utility was based on temporary placement for
filling
space within a carton or container. Often, this material is discarded with the
container as having no independent value. Its presence within the electronics
market has been taken for granted and is evidenced by massive quantities-in
landfill throughout the world.
2 5 The drawings illustrate a foam composition of random pockets or cavities.
Use of available technology also permits more uniform sizing of voids within
the
plastic matrix. Therefore, the stator component may be tuned or optimized for
specific frequency applications, resonances, and related properties. Stiffness
or
rigidity of the foam will be a function of material properties, as well as
pocket
3 o density and wall thickness defining the respective voids or pockets.
Accordingly,
further control of stator acoustic response can be controlled by variations in
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33
numerous physical parameters, in addition to control of random versus uniform
void sizing. The importance of rigidity within the stator element is well
known,
and can now be partially affected by new design factors associated with the
uniqueness of a foam composition.
Although the foam member illustrated comprises an open cell structure, a
combination of open and closed cell structure is also available. The advantage
of
open cell structure is bidirectional propagation of sound. This bidirectional
aspect has been dampened in the Figure 18 embodiment by attachment of a
nonporous membrane 335 on the rear face of the foam member. This membrane
may also be replaced by a stiffening member formed of plastic or some other
rigid material. The stiffening member may be attached to conform to a desired
speaker configuration.
For example, conventional electrostatic speakers are usually planar
because the diaphragm is not in contact with the stator, but is suspended in
front
of the stator. It is therefore difficult to bend the diaphragm in a curved
path
without distorting the gap between the stator and film. With the present
invention having direct contact of the emitter film on the face of the foam,
however, a curved configuration is as simple to form as a planar shape.
Indeed,
the curved surface offers a desirable resistance against the film which
performs
2 0 part of the biasing function for enhancing contact. The ability to mold
virtually
any form or shape with foam permits equal latitude in configuring various
shapes
for the speaker face.. For example, the speaker may be a curved surface as
shown
in Figure 19, providing improved dispersion of sound propagation; or it can be
circumferential as with a cylinder in Figure 20 and a sphere (not shown). Each
o f
2 5 these embodiments offers unique dispersion patterns which have been very
difficult to incorporate within electrostatic speaker systems, particularly
for audio
output.
An additional embodiment of this invention provides push-pull operation
and is illustrated in Figure 2I. In includes a first foam member 359, second
30 foam member 360 having a forward face 361, an intermediate core section 362
and a rear face 363. 'The forward face of the second foam member (referred to
as
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34
the second forward face) is positioned on an opposing side of the
electrostatic
emitter film 365 from the first foam member. The second forward face is
composed of a composition having sufficient stiffness to support the
electrostatic
film and including conductive properties which enable application of the
variable
voltage to the second forward face to supply the desired ultrasonic signal.
The
second forward face comprises a surface including small cavities as discussed
above, with surrounding wall structure defining each cavity, said surrounding
wall structure terminating at contacting edges approximately coincident with
the
forward face of the foam member. Film application means (not shown) for
applying the electrostatic film to the forward face of the second foam member
would follow the format as with the single-end embodiment above. As above,
biasing means are coupled to the second foam member for biasing the film in
direct contact with the contacting edges of the second forward face such that
the
film is directly supported by the second forward face. The signal source is
also
applied to the second forward face with the variable voltage.
The electrostatic emitter film 365 needs to include a conductive layer in
non-contacting relationship with the respective first and second foam members
for enabling the film to capacitively respond with the first and second
forward
faces to the variable voltage in a push-pull relationship. An insulating
member
2 0 may be required with respect to the second foam member.
Several configurations of the emitter film are possible. For example,
Figure 22 shows first and second foam members 370 and 371 which sandwich the
film member. In this case, the electrostatic emitter film comprises at least
two
sheets 372 and 373 of nonconductive emitter film which respectively included a
conductive surface 374 and 375. The nonconductive emitter film provides
insulation between the conductive layer and the respective first and second
forward faces. The respective conductive surfaces 374 and 375 are bonded
together to form an integral conductive layer.
Figures 23 and 24 illustrate the use of multiple emitter films 332 and 342,
3 0 sandwiched between foam or general support members 330, 331, 340, 341.
Each
additional emitter film will add approximately 3 db output to the emitted
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ultrasonic signal. It will be apparent that numerous configurations can be
adapted
within this multiple combination pattern.
Yet another embodiment of the present invention involves planar
magnetic film diaphragms which use magnetic forces to create a parametric
5 transducer. Figure 25 depicts one configuration of the present invention.
Specifically, it comprises an ultrasonic emitter having broad frequency range
capacity with relatively large diaphragm displacement compared to the nominal
movement of a typical electrostatic diaphragm. Indeed, orthogonal displacement
(peak to peak movement of the diaphragm from a full extended to a full
retracted
10 position) may be as great as 1-2 mm. This compares very favorably with a
movement range of .1 to 3 micrometers for a rigid transducer emitter face.
The benefits of extended motion for the magnetic diaphragm of the
present invention include a significant increase in amplitude in ultrasonic,
as well
as sonic output for a parametric array. The enhanced sonic output of the
present
15 invention is enabled by use of a magnetic field generated by a magnetic
core
member 426. This core may be a permanent magnet or a composition adapted for
electromagnetic use. Such materials may be either flexible or rigid, depending
upon the configuration of the speaker array. For example, a planar plate will
generate a column of sound which has surprising projection capacity over long
2 0 distances. A curved emitter diaphragm may be formed and supported by a
curved
support core made of flexible magnet material similar to removable magnets
attached to appliances, etc. This curved configuration provides a greater
dispersion pattern for projected sound, and also enables a sense of
directional
movement to emitted sound. This can be implemented by sequentially triggering
2 5 sound transmission along a linear sequence of emitter elements (or
conductive
coils) 430 disposed along the diaphragm 434. When these elements are radiated
outward in a diverging configuration, the audience perceives the source as
having
a physical element of motion along that direction.
Returning to the basic embodiment of Figure 25, it will be noted that a
3 0 permanent, rigid magnetic core or plate 426 has been used as a support for
the
flexible emitter diaphragm 434. This permanent magnet 426 operates as the
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36
primary means for establishing a first magnetic field adjacent the core
member, in
a manner similar to the permanent magnet of an acoustic speaker. In this case,
however, there is no telescopic core or recess which receives the stator
element.
Instead, the core 426 is a planar body which establishes a uniform magnetic
field
along its length, thereby providing necessary counter force for a variable
magnetic field to be established in the diaphragm 434.
The illustrated movable diaphragm 434 is stretched along the core
member 426 and displaced a short separation distance from the core member to
allow an intended range of orthogonal displacement of the diaphragm with
respect to the core member and within a strong portion of the magnetic field.
Typically, this diaphragm 434 comprises a thin film of Mylar or other strong,
lightweight polymer. Many such materials are already in use in the
electrostatic
speaker or ultrasonic emitter industry.
The enhanced displacement of the diaphragm 434 is enabled by at least
one, low mass, planar, conductive coil (or emitter element 430) disposed on
the
movable diaphragm. The thin conductive coil 430 creates a magnetic field when
current is conducted through the coil. The present inventor has discovered
that
the power of a magnetic field can be implemented in a voice coil disposed on
planar film, yielding the benefits of substantial diaphragm 434 displacement
far
2 0 beyond prior art electrostatic speaker systems. This current is supplied
to the coil
430 by first and second contacts 438 and 442 which are coupled to a power
source. The first contact 438 is coupled to one end of the coil 430, typically
at a
side common with the coil itself. The second contact 442 is disposed on the
opposing side of the coil 430, thereby providing electrical isolation from the
first
2 5 contact 438. The illustrated embodiment shows the second contact 442
penetrating the film (or diaphragm 434)and extending along the opposite face
of
the film to a pick up point for closing the circuit for current flow. Other
methods
of electrically isolating the respective first and second contacts will be
apparent to
those skilled in the art.
3 0 As shown in Figure 26, a further alternate embodiment of the core
member 426 could comprise a rigid plate 446 formed of nonmagnetic
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37
composition, one surface of which includes at least one opposing conductive
coil
450 similar in design to the conductive coil 430 described for the vibrating
diaphragm above. Such a coil would include first and second contacts 454 and
458 for enabling current flow through the opposing conductive coil 450 to
thereby establish the required second magnetic field. This at least one
opposing
conductive coil 450 would be positioned on the rigid plate in a location which
is
juxtaposed to the at least one conductive coil 430 on the vibrating or movable
diaphragm 434 to enable the at least one conductive coil 430 and the at least
one
opposing conductive coil 450 to cause respective magnetic fields from each
coil
to interact to develop the compression waves emitted from the diaphragm.
Again, the first contact 454 is positioned on one side of the diaphragm
and the second contact 458 is positioned on an opposing side of the diaphragm.
This may be in the form of a single coil as illustrated in Figure 26, or as a
plurality of conductive coils equally spaced along the diaphragm as depicted
in
Figure 25. Ideally, the conductive coils 430 and 450 are disposed in a
plurality of
rows in juxtaposed position to maximize uniformity of the magnetic field, as
well
as the quantity of coil applied.
Figure 27 depicts an alternative planar magnetic configuration of the a
parametric speaker. Specifically, it comprises a core member 460 for giving
rigid
2 0 support, at least one conductive coil 462 coupled to the core, and a
diaphragm
468 which includes a conductive ring 466 which responds to a magnetic field
developed by the conductive coil. The operative principles in this structure
are
founded on the nature of a conductive ring to develop current flow when passed
through a magnetic field. Specifically, when a conductive ring experiences a
2 5 magnetic field gradient, a current will flow through the ring in an
orientation
which establishes a magnetic moment counter to the magnetic force generated by
the coil. This phenomenon results in a repulsion between the coil and the
conductive ring. Many physics students have observed the power of this
repulsive force in classroom demonstrations which launch an aluminum ring
3 0 twenty to thirty feet into the air. The interaction between the coil 462
and the
ring 466 is partially described by two principles of physics commonly known as
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38
Faraday's Law of Induction and Lenz's Law. See Fundamentals ofPhysics,
Halliday and Resnick, Second Edition, Chapter 34.
The present inventors have applied these principles to generate a speaker
diaphragm which variably extends and retracts to create a desired series of
compression waves. By applying an array of conductive rings to a resilient,
flexible film such as Mylar,~ or Kapton,~, etc., and superimposing this film
over a
corresponding array of conductive coils, it is possible to repel the film to a
biased state of tension and, via modulation of the amplitude of current
through
the coils, to develop a controlled diaphragm oscillation. The resilience of
the
1 o film allows its retraction to the biased rest position in which the film
is in a
slightly stressed, extended state. This biased, rest position is developed by
a base
or earner signal of alternating current which maintains a minimum level of
repulsion between the coils and rings.
A continuous input of variable alternating current which is modulated
with intelligence enables translation of frequency and amplitude representing
the
intelligence into physical compression waves representing sound. Thus, a
conventional modulated earner such as a sinusoidal wave can be used to supply
a
desired audio output signal to the described magnetic film emitter to develop
an
effective speaker system.
2 0 This system also provides a unique capacity for use as an ultrasonic
emitter having broad frequency range capacity with relatively large diaphragm
displacement compared to the nominal movement of a typical electrostatic
diaphragm. It has long been recognized that the limited range of movement of
an
electrostatic diaphragm (within the micrometer range for ultrasound) is a
major
2 5 hurdle to development of high amplitude output. The magnetically repelled
film
of the present embodiment, however, provides an orthogonal displacement (peak
to peak movement of the diaphragm from a fully extended to a biased rest
position) which may be as great as several millimeters. Therefore, the
diaphragm
displacement of the present invention compares very favorably with a
3 0 substantially smaller movement range of a rigid transducer emitter face,
or even
the flexible diaphragm of a conventional electrostatic emitter.
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39
Such enhanced displacement is possible because the effective range of a
magnetic field extends greater distances than the short range forces
associated
with an electrostatic field. It will therefore be noted that whereas the
effective
force of the electrostatic emitter may extend only in the range of
micrometers, the
magnetic diaphragm of the present invention has a greater range by a factor of
more than one hundred. Therefore, the use of magnetic force is able to repel
or
attract an emitter diaphragm over a significantly greater path.
The benefits of extended motion for the large magnetic diaphragm of the
present invention include a significant increase in amplitude of sonic output
for a
parametric or acoustic heterodyne array, as compared to a comparable system of
bimorph transducers. Furthermore, near linear response is stronger with the
film
emitter, compared to the rigid transducers. These are significant factors that
enable the field of parametric speakers to have enhanced commercial utility,
whereas such utility has been somewhat limited to date.
Another embodiment of the invention is illustrated in Figure 28 showing
an electrostatic emitter 510. Specifically, the emitter comprises a rigid
substrate
511 capable of carrying a voltage, a thin film dielectric material S 12
suspended
over the substrate, and a conductive layer 513 positioned over the dielectric
film
512. Typically, the dielectric material 12 (such as Mylar) is coated with a
2 0 conductive film 513 directly on its top surface. Therefore, the basic
emitter 510
is operable with just the substrate and the metallic coated Mylar film.
As shown in Figure 29, the preferred embodiment also includes an air
chamber 514 disposed below the substrate, with small passageways 530 for air
flow between the chamber and small cavities 516 formed at a top surface of the
2 5 substrate.
Refernng to both Figure 28 and Figure 29, the rigid substrate S 11 may be
formed of materials which have been applied in electrostatic emitters
generally in
the prior art. These include molded plastics, wood, silicon wafers coated at a
top
side with a conductive surface, or simply conductive materials processed with
a
3 0 top side to include the required cavities. A cross-sectional view of this
structure
is provided in Figure 29. The rigid substrate 511 is shown with small conduits
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5 I S communicating from the air chamber 5 I 4 to each cavity 5 I 6 formed in
the
top surface of the substrate. This chamber 514 operates as a common pressure
chamber, providing a more uniform tension across the dielectric film S 12
because
of the common pressure associated with the chamber and each connected cavity
5 516. This chamber 514 can also be subjected to a negative pressure to
mechanically bias the thin film 512 into the recessed cup 520 as shown in
Figure
28. Use of biasing pressure avoids well known problems associated with the use
of a biasing voltage.
It is this recessed cup 520 which becomes the vibrating emitter element
10 which responds to a variable signal input 521 enabling propagation of the
ultrasonic earner signal with side bands which heterodyne to generate a column
of audio sound 525. The present invention provides a uniform recessed cup
referred to as an emitter element, which is substantially isolated from the
effects
of adjacent emitter elements to develop a carefully tuned, resonant frequency
of
15 uniform value. The cavities 516 formed in the substrate 51 I are preferably
precision molded in uniform size and configuration. This permits a more
precise
uniformity among the respective cavities 516 to yield a more finely tuned
resonant frequency.
The embodiment of the present invention just described provides
2 0 surprising results as a parametric speaker device. It provides an array of
cavities
which respectively, and indirectly generate audio output within an emitted
ultrasound column. The occurrence of ultrasonic heterodyning within each of
these columns emitted from tuned emitter elements actually reinforces the
sound
pressure level (SPL) at a distance from the emitters 510. As shown in Figure
29,
2 5 each emitter section 520 propagates a column of sound 525 which is highly
directional. By providing an array of many emitting sectors 520 uniformly
tuned
to a desired resonant frequency, a simulation of a uniform wave front is
accomplished with much greater amplitude than from an electrostatic diaphragm
comprising a single film operable on a single voltage source. The use of
uniform
3 0 cavities is also an advantage over the prior art in manufacturing which is
duplicatable and therefore predictable. Prior art techniilues required quality
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41
control that includes careful inspection of every emitter substrate to insure
that an
operable surface of pits or cavities was developed. This was necessary because
mechanical and chemical etching techniques produce varying results depending
on differences in the environment, the materials used, and the random nature
of
the process. In contrast, the present embodiment can be practiced with
conventional molding or machining procedures.
Another embodiment of an ultrasonic electrostatic transducer is shown in
Figure 30. A cross section view of a hemispherical electrostatic transducer
551 is
shown anchored to a base 552. Fig. 30 is a cross section of the Fig. 31 along
arrow 570. Two cylindrical corrugated stators 556 create a hemispherical shape
and a non-planar diaphragm 560 is arranged between the two opposing stators.
In
addition, a supporting structure 553 runs along the inside of the hemisphere
or
along a longitudinal axis of the hemisphere. It should be realized that the
stators
have holes or apertures, so they are acoustically transparent and allow
ultrasonic
waves to pass through. The diaphragm is biased by a bias voltage 550 and the
audio signal 554 is applied to produce an ultrasonic compression wave. A
cushioning or insulating layer 558 is contained within the stators so the
diaphragm will not directly contact the conductive layer on the stators and
avoids
other distorting contact with the stator.
2 0 Fig. 31 is a perspective view of a hemispherical electrostatic speaker.
Because of the hemispherical nature of this embodiment, the sound that
emanates
through the stators 556 radiates in 180 degrees in multiple axes. A full
sphere
embodiment of the present embodiment is shown in Fig. 32. This figure shows a
partially exploded view of the spherical embodiment 580 which is a combination
2 5 of two hemispheres as shown in Fig. 3 I . This spherical arrangement
allows the
ultrasonic sound waves 590 to be generated in all possible directions. An
electrical assembly 584 (shown cut away) can be the base for the two
hemispheres. The electrical assembly can also be sized small enough to be
contained within the hemispheres. A bias is applied to the diaphragms
contained
30 within the hemispheres through the input 588 and the audio signal is then
applied
through 586.
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It will be apparent that numerous variations and combinations may be
developed by those skilled in the art, based upon the aforementioned
embodiments of the present invention. Accordingly, it is to be understood that
the invention is to be defined in accordance with the following claims, and
not
limited by specific examples set forth above.