Patent Application
20110211722
1. Technical Field
The invention relates to acoustic devices, such as loudspeakers and microphones, more particularly bending wave devices.
2. Background Art
From first principles, a point force applied to a pistonic loudspeaker diaphragm will provide a naturally flat frequency response but a power response which falls at higher frequencies. This is due to the radiation coupling changing as the radiated wavelength becomes comparable with the length l of the diaphragm, or the half diameter or radius a for a circular diaphragm, i.e. where ka is greater than 2 or kl is greater than 4 (k is the wave number frequency). However for a theoretical, free mounted bending wave panel speaker, a pure force, i.e. mass-less point drive, will provide both flat sound pressure and flat sound power with frequency.
A practical bending wave panel will however be supported on a suspension, and have an exciter with a complex driving point impedance including a mass. Such an object will demonstrate an uneven frequency response compared with the theoretical expectation. This is due to the various masses and compliances now present unbalancing the panel's modal behaviour. Where the modal density is high enough, the system may be designed so that the modes are beneficially distributed over frequency for a more even acoustic response. But this distributed mode method may not be so effective at the lower bending frequencies where modes are sparse and generally insufficient to construct a satisfactory frequency response.
The objective of flat pressure and power response down to the lowest bending frequency, so bridging the gap to the pistonic or whole body range, requires that the theoretical condition of modal balance be re-established. If this can be achieved, the adjusted modal balance restores the acoustic action of the practical panel to the desired theoretical condition. This would provide a new class of loudspeaker radiator and where the radiated response, in terms of power or frequency, is independent of drive point mass.
The goal for the designer of transducers and loudspeakers employing practical diaphragms and drive methods is to obtain an operation essentially independent of frequency. Once that primary objective is realised, other desired characteristics may be engineered by the designer.
According to the invention, there is provided an acoustic device comprising a diaphragm having an area and having an operating frequency range and the diaphragm being such that it has resonant modes in the operating frequency range, an electro-mechanical transducer having a drive part coupled to the diaphragm and adapted to exchange energy with the diaphragm, and at least one mechanical impedance means coupled to or integral with the diaphragm, the positioning and mass of the drive part of the transducer and of the at least one mechanical impedance means being such that the net transverse modal velocity over the area tends to zero.
According to a second aspect of the invention, there is provided a method of making an acoustic device having a diaphragm having an area and having an operating frequency range, comprising choosing the diaphragm parameters such that it has resonant modes in the operating frequency range, coupling a drive part of an electro-mechanical transducer to the diaphragm to exchange energy with the diaphragm, adding at least one mechanical impedance means to the diaphragm, and selecting the positioning and mass of the drive part of the transducer and the positioning and parameters of the at least one mechanical impedance means so that the net transverse modal velocity over the area tends to zero.
The mechanical impedance Z(ω) of the at least one mechanical impedance means is defined by
Z(ω)=j·ω·M(ω)+k(ω)/(j·ω)+R(ω)
where ω is the frequency in radians per second,
M(ω) is the mass of the element,
k(ω) is the stiffness of the element, and
R(ω) is the damping of the element
The at least one mechanical impedance means may be a discrete element, e.g. mass or a suspension, which is coupled to the diaphragm. Alternatively, the diaphragm may have mass, stiffness and/or damping which varies with area to provide the at least one mechanical impedance means at the selected position. In this way the mechanical impedance means is integral with the diaphragm. For example, the diaphragm may be formed with varying thickness, including ridges or projections out of plane on one or both faces of the diaphragm, e.g. by a moulding process. The ridges or projections may act as the mechanical impedance means.
The net transverse modal velocity over the area may be quantified by calculating the rms (root mean square) transverse displacement which is not affected by phase cancellation. By way of example, for a circular diaphragm, rms transverse displacement may be calculated from
Where R is the radius of the diaphragm and
ψ(r) is the mode shape.
A measurement of the merit of a particular acoustic device may be calculated from
Relative mean displacement Ψrel=Ψmean/Ψrms.
Where, for the circular diaphragm
The mean transverse displacement should be low for best balancing. If the net transverse modal velocity over the area is zero, the relative mean displacement will also be zero. In the worst case, the relative mean displacement will equal one. To achieve net transverse modal velocity over the area tending to zero, the relative mean displacement may be less than 0.25 or less than 0.18. In other words, net transverse modal velocity over the area tending to zero may be achieved when the relative mean displacement is less than 25%, or preferably less than 18% of the rms transverse velocity.
For zero net transverse modal velocity, the modes of the diaphragm need to be inertially balanced to the extent, that except for the “whole body displacement” or “piston” mode, the modes have zero mean displacement (i.e. the area enclosed by the mode shape above the generator plane equals that below the plane). This means that the net acceleration, and hence the on-axis pressure response, is determined solely by the pistonic component of motion at any frequency.
There is a wide class of objects for which all the non-pistonic modes have zero mean displacement, e.g. plates of uniform mass-per-unit area with free edges driven by point sources. However, such objects represent theoretical acoustic devices because in practice point drive and free edges are not achievable.
Net transverse modal velocity tending to zero may be achieved by mathematically mapping the nodal contours and hence modes and velocity profile of the practical acoustic device above to those of the ideal theoretical device (e.g. freely vibrating diaphragm). In mathematics, mapping is a rule which relates each element x of one set X to a unique element y in another set Y. The mapping is expressed as a function, f, thus: y=f(x). There can only be said to be a mapping from X to Y if no elements are left unmapped from X, and if each value of x is assigned to only one value of y.
One method for achieving this is to calculate the locations where the drive point impedance Zm is at a maximum or the admittance Ym is at a minimum for the modes of an ideal theoretical acoustic device and mounting the drive part and/or at least one mechanical impedance means at these locations. The admittance is the inverse of the impedance (Zm=1/Ym).
For example, for the circular case, the locations may be calculated by varying the drive diameter of the diaphragm between its centre and its periphery, calculating the mean drive point admittance as the drive diameter is varied, and adding mechanical impedances at the positions given by the admittance minima.
The impedance Zm and the admittance Ym are calculated from a modal sum and thus their values depend on the number of modes included in the sum. If only the first mode is considered, the location lies on or quite near a nodal line of that mode. More generally, the locations will tend to be near the nodes of the highest mode considered, but the influence of the other modes means that the correspondence may not be exact. Nevertheless, the locations of the nodal lines of the highest mode chosen for a design solution may be acceptable. The solution from the first three modes is not an extension of the solution from the first two modes and so on. The positions may be considered to be average nodal locations and thus the drive part of the transducer and/or the at least one mechanical impedance means may be positioned at an average nodal position of modes in the operating frequency.
As an alternative to using the admittance, the locations for the mechanical impedance means may be calculated by defining a model in which the mechanical impedance means is an integral part of the system and optimising the model to provide net volume displacement tending to zero. For example for a circular diaphragm, the model may be defined as a disc comprising concentric rings of identical material, with circular line masses at the junction of the rings. The net volume displacement may be calculated from:
where R is the radius of the diaphragm and
ψ(r) is the mode shape.
Alternatively, the locations for the mechanical impedance means may be calculated by defining a model in which the mechanical impedance means is an integral part of the system and optimising the model to provide relative mean displacement tending to zero.
Combinations of the different methods may also be used, for example a mechanical impedance means may be mounted at a nodal line of the third mode and optimisation may be used to address the first two modes.
The transducer location is a position of average low velocity, i.e. admittance minimum. The standard teaching for a standard distributed mode loudspeaker is to mount the transducer(s) at the location(s) having the smoothest impedance so as to couple to as many modes as possible, as equally as possible. Accordingly, from one viewpoint, the above invention differs from that of distributed mode.
The diaphragm parameters include shape, size (aspect ratio), bending stiffness, surface area density, shear modulus, anisotropy and damping. The parameters may be selected to optimise performance for different applications. For example, for a small diaphragm, e.g. 5 to 8 cm in length or diameter, the diaphragm material may be chosen to provide a relatively stiff, light diaphragm which has only two modes in the desired upper frequency operating range. Since there are only two modes, good sound radiation may be achieved at relatively low cost by balancing these modes. Alternatively, for a large panel, e.g. 25 cm in length or diameter, which has good low frequency power in the pistonic range, the diaphragm material and thickness may be chosen to place the first mode in the mid band, e.g. above 1 kHz. A sequence of modes up the seventh or more may then be balanced to achieve a wide frequency response with good power uniformity, and well maintained off-axis response with frequency.
In design the relative effect of variations in parameters is relevant and the balance of modal radiation is more dependent on uniformity of surface area density than bending stiffness. For example, for a simple circular diaphragm, anisotropy of bending stiffness of up to 2:1 has only a moderate effect on performance and up to 4:1 is tolerated. High shear may be exploited to produce a reduction in efficiency at higher frequencies.
The transducer may be adapted to move the diaphragm in translation. The transducer may be a moving coil device having a voice coil which forms the drive part and a magnet system. A resilient suspension may couple the diaphragm to a chassis. The magnet system may be grounded to the chassis. The suspension may be located at an average nodal position of modes in the operating frequency range. The position at which the voice coil is coupled to the diaphragm may be a different position to that at which the said suspension is coupled to the diaphragm.
The operating frequency range may include the piston-to-modal transition. The diaphragm parameters may be such that there are two or more diaphragm modes in the operating frequency range above the pistonic range.
The diaphragm may have a circular periphery and a centre of mass. The parameters of the diaphragm may be such that the first diaphragm mode is below ka=2, where k is the wave number and a is the diaphragm radius measured in metres (m) and the unit for k is m−1. For example, this may be achieved by selecting panel material having an appropriate stiffness. The stiffness of the panel material may also be used to position the coincidence frequency to help control the directivity.
The diaphragm may be isotropic as to bending stiffness. Moderate diaphragm anisotropy of bending stiffness may be designed for by rms (root mean square) averaging the resultant mode locations. For an elliptical diaphragm of (by way of example), x=2y the pure circular equivalent modal result may be achieved with a corresponding stiffness ratio of 16:1. In this way, the diaphragm may be elliptical and may be anisotropic as to bending stiffness so that it behaves like a circular diaphragm of isotropic material.
Anisotropy, for example for the circular case, will alter the actual frequencies of the resonant modes but the circular modal behaviour is strong and asserts itself on the diaphragm. As set out above, moderate anisotropy of up to 4:1 is tolerated.
The at least one mechanical impedance means may be in the form of an annular mass which may be circular or elliptical. Several annular masses may be coupled to or integral with the diaphragm at average nodal positions of modes in the operating frequency range. The masses may reduce in weight towards the centre of the diaphragm. The or each annular mass may be formed by an array of discrete masses. More than three such masses may be enough and six such masses is sufficient to be equivalent to a continuous annular mass. The masses and/or the mass of the suspension may be scaled to the voice coil mass.
Damping means may be located on or integral with the diaphragm at a location of high panel velocity whereby a selected mode is damped. For the circular or elliptical panel, the damping means may be in the form of a pad located at an annulus of high panel velocity. In a bending wave device, regions of high panel velocity are regions of maximum curvature of the panel. Damping (whether constrained-layer or unconstrained-layer) is most effective when it is subject to maximum strain by bending to the maximum degree possible.
For all frequencies, there is maximum bending curvature at the centre and edge of the panel and thus it is known to use central and/or edge damping, although central damping is preferred. However, for different mode orders there are also regions of high panel velocity at different diameter ratios in between the central and edge areas. Accordingly, use of damping only at central and/or edge areas gives a correctly damped on-axis response but the off-axis contribution from the un-damped high velocity regions means that there is not adequate damping of the off-axis response. Placing the damping pad at an annulus of high panel velocity addresses this problem.
The mode may be selected because it causes an unwanted peak in the acoustic response and the effect of the damping pad is to reduce or eliminate this peak. Damping is not additive and different modes require the damping to be in different places. A damping pad may be mounted at more than one location, for example, if more damping accuracy is required. However, applying an overall damping layer covering the whole panel is to be avoided.
By damping only a selected mode or selected modes, the need to damp the whole panel is avoided and thus there is no loss in sensitivity. The whole of the selected mode may be damped, i.e. on-axis and off-axis are both damped. Furthermore lower frequency modes are not significantly damped and thus the behaviour of the loudspeaker below the damped mode is preserved.
The damping pad may be a continuous annular pad or may be segmented whereby small pieces of non-circular damping are used. Alternatively, only parts of the annulus may be damped, depending on the magnitude of the response peak which needs to be damped.
For circular and elliptical shapes, there are two types of modes, radial modes having nodal lines which are concentric with the diaphragm perimeter and axial modes having nodal lines on the diaphragm radii. The axial modes are secondary modes and are generally not acoustically important. Nevertheless, if required they may be attenuated, damped or even minimised by cooperative adjustment of the mechanical impedance means. For example, providing stiffness in the plane of the diaphragm will reinforce the diaphragm with respect to the axial modes, without affecting the balancing of the radial modes. Axial modes are also called ‘bell’ modes in some texts.
The diaphragm parameters may be selected so that there are two diaphragm radial modes in the operating frequency range. The annular masses may be disposed substantially at any or all of the diameter ratios 0.39 and 0.84, whereby these two modes are balanced. If a third radial mode is in the operating frequency range, damping pads may be disposed at any or all of the diameter ratios 0.43 and 0.74. Alternatively, the annular masses may be disposed substantially at any or all of the diameter ratios 0.26, 0.59 and 0.89, whereby the first three modes are balanced.
If a fourth radial mode is in the frequency range, the damping pads may be disposed at any or all of the diameter ratios 0.32, 0.52 and 0.77, whereby the fourth mode is damped. Alternatively, the annular masses may be disposed substantially at any or all of the diameter ratios 0.2, 0.44, 0.69 and 0.91 whereby the first four modes are balanced.
If a fifth radial mode is in the frequency range, the damping pads may be disposed at any or all of the diameter ratios 0.27, 0.48, 0.63 and 0.81 whereby the fifth mode is damped. Alternatively, the annular masses may be disposed substantially at any or all of the diameter ratios 0.17, 0.35, 0.54, 0.735 and 0.915. If there are additional modes in the frequency range, greater numbers of modes may be chosen for balancing following the basic strategy which has been outlined.
The diaphragm may be annular. The tables below show the possible annular locations of the masses and voice coil for hole sizes ranging from 0.05 to 0.35 of the radius of the panel. The innermost location is most affected by the hole size.
Locations if two radial modes are considered:
Locations if three radial modes are considered:
Locations if four radial modes are considered:
For example, the diaphragm may comprise a hole of diameter ratio 0.20 and annular masses may be disposed substantially at any or all of the diameter ratios 0.33, 0.62 and 0.91 whereby three modes are balanced. Alternatively, annular masses may be disposed substantially at any or all of the diameter ratios 0.23, 0.46, 0.7 and 0.92 whereby four modes are balanced.
The diaphragm may be generally rectangular and have a centre of mass. The parameters of the diaphragm may be such that the first diaphragm mode is below kl=4, where k is the mode number (unit is m−1) and 1 the panel length measured in metres (m).
The suspension, drive part of the transducer and/or the at least one mechanical impedance means may be located at opposed positions away from the centre of mass and periphery of the diaphragm. If the diaphragm is of uniform mass per unit area, these opposed positions may be equidistant from the centre of mass. The mechanical impedance means may be in the form of a pair of masses which are located at opposed positions spaced from the centre of mass of the diaphragm.
The diaphragm may be beam-like or beam-shaped, i.e. have an elongate rectangular surface area, and the modes may be along the long axis of the beam. The transducer, pairs of masses and/or suspension may be coupled to the diaphragm along the long axis of the beam.
If there are two modes in the operating frequency range, the pairs of masses may be disposed substantially at any or all of the ratios from the centre of mass 0.29 and 0.81. The pairs of masses may be disposed substantially at any or all of the ratios from the centre of mass 0.19, 0.55 and 0.88 where three modes are to be balanced. Alternatively, where four modes are to be balanced, the pairs of masses may be disposed substantially at any or all of the ratios from the centre of mass 0.15, 0.4, 0.68 and 0.91. Alternatively, where five modes are to be balanced, the pairs of masses may be disposed substantially at any or all of the ratios from the centre of mass are 0.11, 0.315, 0.53, 0.74 and 0.93. In design greater numbers of modes may be chosen for balancing following the basic strategy which has been outlined.
For beam-like diaphragms, there are two types of modes, modes having nodal lines which are parallel to the short axis of the beam and cross-modes having nodal lines which are parallel to the long axis of the beam. The cross-modes are secondary modes and are generally not acoustically important except at high frequencies. The ratio of transducer diameter to panel width may have a value of about 0.8 whereby the lowest cross-mode may be beneficially suppressed.
Where the beam is of variable thickness, the ratio concept described above can be replaced by distances related to the average nodal regions determined by the stiffness variation. For a symmetric distribution of stiffness, the use of the centre as a reference is relevant, in a sense equivalent to radii from the centre, but when the beam has an asymmetric distribution of stiffness, the locations for drive and masses are referred to one end of the beam.
In each of the above embodiments, the transducer voice coil may be coupled to the diaphragm at one of the said ratios. For a circular or annular diaphragm, the voice coil may be concentrically mounted on the diaphragm.
For a rectangular panel, a pair of transducers may be mounted at opposed positions each having the same ratio or at two opposed positions having different ratios. Alternatively, a single transducer may be mounted so that its drive part drives two opposed positions each having the same ratio. Alternatively, a transducer and a balancing mass may be mounted at opposed positions each having the same ratio, the mass dynamically compensates the diaphragm for the pistonic range. It will, however, be appreciated that if pistonic operation of the diaphragm is not required, then such mass compensation to avoid diaphragm rocking is not a constraint.
The loudspeaker may comprise a size adapter in the form of a lightweight rigid coupler, which adapts the size of a voice coil which has been chosen to fit a suitable convenient economic frame so that the drive is at an averagely nodal position. The coupler may be coupled to the transducer at a first diameter and is coupled to the diaphragm at a second diameter. The second diameter may be an annular location which is a first average nodal position of modes in the operating frequency range.
The coupler may be frusto-conical. The first diameter may be larger than the second diameter whereby a large coil assembly may be adapted to a smaller driving locus by an inverted coupler and a smaller coil assembly to a large locus by fixing the smaller end of a frusto-conical coupler to the voice coil assembly and the larger end to the diaphragm.
Additional benefits might be had with the possible use of oversize voice coil assemblies for high power capacity and efficiency while preserving the power response to the higher frequencies expected from a small coil drive. Conversely small voice coil assemblies, which are often of moderate cost, may now be adapted to a larger driving circle. In this case the first diameter may be smaller than the second diameter. For example for wider directivity to the highest frequencies for a circular diaphragm the designer would choose a smaller voice driving circle, whether directly driven or via a reducing coupler. Alternatively where higher efficiency and maximum sound level is required a larger voice coil adapted to a larger driving circle, for example a larger radius average nodal line on the diaphragm.
The suspension may be coupled to the diaphragm substantially at any of the outer ratios. Suitable materials for the suspension include moulded rubber or elastic polymer cellular foamed plastics. The effective mass of the suspension may move slightly with frequency and the mass itself may vary with frequency. This is because the composition and geometry of suspensions may result in a complex mechanical impedance where the behaviour changes with frequency.
In design, the physical position of the suspension on the panel may be adjusted to find the best overall match in the operating frequency range. Additionally or alternatively the behaviour of the suspension may be modelled, e.g. with FEA to ascertain the effective centre of mass, damping and stiffness and thus facilitate its location on the panel.
Tolerances of between +/−5% to +/−10% on the locations of the mechanical impedance means may be acceptable depending on diaphragm properties. Tolerances of between +/−5% to +/−10% on the mass of the mechanical impedance means may also be acceptable. In general, the tolerance for changing mass is greater than that for changes in location.
The diaphragm is preferably rigid in the sense of being self-supporting. The diaphragm may be monolithic, layered or a composite. A composite diaphragm may be made from materials having a core sandwiched between two skins, Suitable cores include paper cores, honeycomb cores or corrugated plastic cores, and the core may be longitudinally or radially fluted. Suitable skins include paper, aluminium and polymer plastics. One suitable composite material is Correx®. The materials used may be reinforced isotropically or anisotropically by woven or by uni-directional stiffening fibres.
The diaphragm may be planar or may be dished. The term “dished” is intended to cover all non-planar diaphragms whether dished, arched or domed, including cone sections and compound curves whether circular or elliptical. A dished form may have a planar section at the centre. The diaphragm may have a thickness or width which varies with length.
The loudspeaker may comprise an aperture. A second diaphragm may be mounted in the aperture. The second diaphragm may be similar in operation to the first diaphragm, for example may have a transducer coupled to a first average nodal position and at least one mass coupled at a second average nodal position. Alternatively, the second diaphragm may be operated pistonically or as a bending mode device.
A sealing member may be mounted in the aperture whereby the aperture is substantially acoustically sealed to prevent leakage of acoustic output. The ratio of the radius of the sealing to the outer radius of the diaphragm is an additional parameter which may be adjusted to achieve a desired acoustical response.
The acoustic device may be mounted in an enclosure and the acoustic properties of the enclosure may be selected to improve the performance of the acoustic device.
The acoustic device may be a loudspeaker wherein the transducer is adapted to apply bending wave energy to the diaphragm in response to an electrical signal applied to the transducer and the diaphragm is adapted to radiate acoustic sound over a radiating area. Alternatively, the acoustic device may be a microphone wherein the diaphragm is adapted to vibrate when acoustic sound is incident thereon and the transducer is adapted to convert the vibration into an electrical signal.
The method and acoustic device of the present invention thus concerns the exploitation of bending wave modes. By contrast the piston and cone related prior art has sought to discourage modal behaviour, for example by using damping or specific structural and drive coupling aspects. However, the acoustic device of the present invention concerns the lowest bending frequencies. It does not require these modes to be densely or evenly distributed. The modes that are addressed are encouraged to radiate but their on-axis contribution is radiation balanced by mounting the transducer, the suspension and/or masses at the average nodal positions of modes in the operating frequency range.
The invention utilizes the principle of sound radiated by a simple free plate, that is the diaphragm, driven into bending by a theoretical pure point force with no associated mass. This cannot be achieved in practice as the force has to be applied by a mechanism which will inevitably involve a mass, e.g. that due to a voice coil assembly of an electro-dynamic transducer or exciter. Also, a practical force will generally also be presented to the plate not at a single point, but along a line, as in a circular coil former.
The designer of the acoustic device has the freedom within the principle of the invention to tune the performance for varying situations and applications by adjusting the net transverse modal velocity, globally, or selectively with frequency. For example, a different frequency characteristic may be required at different frequencies or a different angle of radiation for certain applications, e.g. in a vehicle, the listener is off-axis.
The following aspects of the invention also utilize the same principle and have the same subsidiary features.
According to another aspect of the invention, there is provided an acoustic device having an operating frequency range comprising a diaphragm having a circular periphery and a centre of mass and the diaphragm being such that it has resonant modes in the operating frequency range, and a transducer coupled to the diaphragm and adapted to apply bending wave energy thereto in response to an electrical signal applied to the transducer, the transducer being coupled to the diaphragm at a first average nodal position of modes in the operating frequency range, and at least one mass coupled to or integral with the diaphragm at a second average nodal position of modes in the operating frequency range.
According to another aspect of the invention, there is provided a loudspeaker having an operative frequency range comprising a diaphragm having a centre of mass and the diaphragm being such that it has resonant modes in the operating frequency range, transducer means coupled to the diaphragm and adapted to apply bending wave energy thereto in response to an electrical signal applied to the transducer, the transducer means being coupled to the diaphragm at opposed positions spaced from the centre of mass of the diaphragm, and at a first average nodal position of modes in the operating frequency range, and at least one pair of masses integral with, or coupled to, the diaphragm at opposed positions spaced from the centre of mass of the diaphragm and located at a second average nodal position of modes in the operating frequency range.
From yet another aspect, the invention is a method of making a loudspeaker having an operating frequency range and having a planar diaphragm with a circular periphery and a centre of mass, comprising choosing the diaphragm parameters to be such that it has resonant modes in the operating frequency range, coupling a transducer to the diaphragm and concentrically with the centre of mass of the diaphragm, to apply bending wave energy thereto in response to an electrical signal applied to the transducer, and coupling a resilient suspension to the diaphragm concentrically with the centre of mass of the diaphragm and away from its periphery and located at an annulus at an average nodal position of modes in the operating frequency range.
From a further aspect, the invention is a method of making a loudspeaker having an operating frequency range and having a planar diaphragm with a circular periphery and a centre of mass, comprising choosing the diaphragm parameters to be such that it has resonant modes in the operating frequency range, coupling a transducer to the diaphragm to apply bending wave energy thereto in response to an electrical signal applied to the transducer at a first average nodal position of modes in the operating frequency range and adding at least one mass to the diaphragm at a second average nodal position of modes in the operating frequency range.
The invention is diagrammatically illustrated, by way of example, in the accompanying drawings, in which:—
a is a plan view of a first embodiment of the present invention;
b is a cross-sectional view along line AA of
a is a graph showing the variation of on-axis sound pressure with frequency for the device of
b is a graph showing the variation of the half space power (i.e. integrated acoustic power over the hemisphere in front of the embodiment) with frequency for the device of
a is a graph showing the variation of voltage sensitivity with frequency for the device of
b and 4c are cross-sectional views of the outer section of the devices measured in
a is cross-sectional view of the device of
b is a graph showing the variation of voltage sensitivity with frequency for the device of
a and 6b are graphs showing the variation of on-axis sound pressure and half space power with frequency, respectively for a second embodiment of the invention with and without masses;
a, 7b and 7c are graphs showing the variation of on-axis sound pressure and half space power with frequency for two theoretical loudspeakers and a practical loudspeaker respectively;
a to 9e show the variation of the mean value of the real part of the admittance Ym with panel diameter for the first mode to the first five modes respectively;
f shows the mode shapes for the first five modes and the annular locations;
g and 9h shows the variation of the mean value of the real part of the admittance Ym with panel diameter for the first eight mode modes with discrete and extended masses;
i and 9j show the sound pressure level and sound power level varying with frequency for a four mode solution using discrete and continuous masses respectively;
k shows the first three modes for a panel after the optimisation method;
a shows the frequency responses below the first mode, for the first mode to the second mode and for the second mode and above respectively, for a loudspeaker comprising a circular diaphragm;
b shows the piston displacement for the loudspeaker in the ranges of
c and 10d show the modal displacement for the loudspeaker in the ranges of
e shows the frequency responses below the first mode, for the first mode to the second mode and for the second mode and above respectively, for the loudspeaker of
f shows the piston displacement for the loudspeaker in the ranges of
g and 10h show the modal displacement for the loudspeaker in the ranges of
i shows the frequency responses below the first mode, for the first mode to the second mode and for the second mode and above respectively, for the loudspeaker of
j shows the piston directivity for the loudspeaker of
k and 10l show the modal directivities for the loudspeaker in the ranges of
a to 11d are simulations of the variations of sound pressure and power with frequency for a loudspeaker having a circular panel driven at four different annular positions;
e is a simulation of the variations of sound pressure and power with frequency for a loudspeaker having a circular panel driven at the annular position used in
a and 12b are cross-sectional views of other embodiments of the present invention;
c is a graph of power response against frequency for the embodiments of
a and 17b are graphs of the sound pressure against frequency showing the effect of 10% variations in mass and annular location, respectively for the middle annular location,
a and 18b are graphs of the sound pressure against frequency showing the effect of 10% variations in mass and annular location, respectively for the innermost annular location,
a is a plan view of a loudspeaker according to another aspect of the invention;
b shows the on-axis sound pressure level (SPL) and sound power level (SWL) curves (lower and upper curves respectively) for the loudspeaker of
a to 26d show sound pressure (db) against frequency (Hz) for variations of the drive unit of
a is a plan view of a second embodiment of the present invention;
b is a cross-sectional view along line AA of
a is a graph showing the variation of on-axis sound pressure and half-space power with frequency for the device of
b, 28c and 28d are graphs showing the variation of on-axis sound pressure and half-space power with frequency for the device of
a is a plan view of another embodiment of the present invention;
b is a cross-sectional view along line AA of
a is a plan view of another embodiment of the present invention;
b is a cross-sectional view along line AA of
a is a graph showing the variation of on-axis sound pressure and half-space power with frequency for the device of
b, 32c and 32d are graphs showing the variation of on-axis sound pressure and half-space power with frequency for the device of
a and 33b are cross-sectional views of alternative panels which may be incorporated in devices according to the present invention;
a is a plan view of another embodiment of the present invention;
b is a cross-sectional view along line AA of
a and 35b are graphs showing the variation of on-axis sound pressure and half-space power with frequency respectively for the device of
a, 36b and 36c are graphs showing the variation of on-axis sound pressure and half-space power with frequency for two theoretical loudspeakers and a practical loudspeaker respectively;
d to 36g are graphs of the logarithmic mean admittance of the first two to five modes of the panel of
h and 36i are graphs of the sound pressure level against frequency for a two mode and a five mode solution respectively;
a and 39b are graphs showing the variation of on-axis sound pressure and half-space power with frequency respective for the device of
a is a plan view of another embodiment of the present invention;
b is a cross-sectional view along line AA of
a is a graph of the first four mode shapes for the diaphragm of the embodiment of
b is a graph of the Fourier transforms of the mode shapes of
c is a graph showing the logarithmic mean of the response for both the first mode and the first two modes of the diaphragm of
d is a graph showing the logarithmic mean admittance for both the first three modes and the first four modes of the diaphragm of
a, 42b and 42c are graphs showing the variation of on-axis sound pressure and half-space power with frequency for two theoretical loudspeakers and a practical loudspeaker respectively;
a is a plan view of an alternative embodiment of the invention;
b is a graph of the first four mode shapes for the diaphragm of the embodiment of
c is a graph showing the logarithmic mean admittance for both the first mode and the first two modes of the diaphragm of
d is a graph showing the logarithmic admittance for both the first three modes and the first four modes of the diaphragm of
a is a plan view of an alternative embodiment of the invention;
b is a graph of the first four mode shapes for the diaphragm of the embodiment of
a and 48b are plan and side views of another embodiment of the present invention;
a and 51b are graphs showing the variation of on-axis sound pressure and half-space power with frequency for a variation on the embodiment of
a and 52b are cross-sectional and rear views of a loudspeaker comprising a coupler, and
a and 53b are cross-sectional and rear views of a loudspeaker comprising a second embodiment of a coupler;
a and 55b are plan views of a quarter of a circular and beam-like diaphragm, respectively;
c is a side view of the quarter diaphragms of
a and 56b shows the variation of on-axis sound pressure and sound pressure at 45° with frequency for a loudspeaker without and with suspension balancing masses respectively;
c shows the variation of half-space power with frequency for a loudspeaker without and with suspension balancing masses;
a is a plan view of another embodiment of the present invention;
b is a cross-sectional view along line AA of
a and 1b show a loudspeaker comprising a diaphragm in the form of a circular panel 10 and a transducer 12 having a voice coil 26 concentrically mounted to the panel 10. Three ring-shaped (or annular) masses 20,22,24 are concentrically mounted to the panel 10 using adhesive tape. The voice coil and masses are each located at annular positions which may be termed positions 1 to 4 with position 1 being the innermost location and position 4 the outermost.
The panel and transducer are supported in a circular chassis 14 which comprises a flange 16 to which the panel 10 is attached by a circular suspension 18. The flange 16 is spaced from and surrounds the periphery of panel 10 and the suspension 18 is attached at an annulus spaced from the periphery of the panel 10. In this way, the panel edge is free to move which is important since there is an anti-node at this location. Similarly, there are no masses located at the centre of the panel since there is also an anti-node at this location. The transducer 12 is grounded to the chassis 14.
The panel 10 is made from an isotropic material, namely 5 mm thick Rohacell™ (expanded poly methylimide) and has a diameter of 125 mm. The masses are brass strip and are 1 mm thick. The locations of the voice coil 26, each mass and the suspension are average nodal positions of the modes of the panel which appear in the operating frequency range and are calculated as described in
The values of the masses are scaled relative to their location and the mass of the voice coil as described in
a and 2b show the on-axis pressure and half space power for the loudspeaker with the three ring masses (solid line) and without the masses (dashed line). The loudspeaker with the masses has an extended off-axis frequency response and has improved sound quality and intelligibility over the listening region. Another advantage is that the device with masses is coherent with no significant delay with frequency. Accordingly, accurate stereo images may be formed.
The mass of the loudspeaker diaphragm assembly without masses is 11.8 g and the masses add an extra 10.8 g. As is shown in
a shows the effect of reducing the overall mass at position 4 by 1.25 g. The dashed line shows the response for the reduced mass and the solid line, the higher mass. There is an increase in sensitivity from 150 to 600 Hz as expected. However, there is a decrease in sensitivity in the mid-band which suggests that the mass at the outermost position affects the frequency response up to 4 kHz. The sensitivity below 150 Hz is unchanged. The mass contribution of the suspension may vary with frequency and the mass contribution was determined at 85 Hz which may be a source of error in respect of precisely balancing modes at higher frequencies.
b and 4c show how the reduction in mass at the outermost position is achieved. The suspension 18 used in the device of
a and 2b suggest there is diffraction from the panel edges.
In a second embodiment, the panel material was changed to 1 mm thick aluminium and the table below compares the material properties and mode values.
The aluminium panel has a significantly higher bending stiffness. This does not significantly change the on-axis pressure or sound power but does change the frequency of the modes. Thus in general the stiffness may be chosen or adjusted to ensure that the panel is modal soon enough relative to the panel diameter to provide good sound power with the benefit of high frequency extension and smoothness. Furthermore, although the frequency of the modes is different for each panel stiffness, the ratio of the frequency of each mode to the first mode is the same and is set out below. Thus the annular positions for the voice coil, masses and suspension remain the same. Furthermore, since the frequency of the fifth mode is 27 times that of the first mode, by addressing the first five modes, coverage of approximately 6 octaves of modal balancing may be achieved to be added to the piston range.
a and 6b show the on-axis sound pressure and 180 power for the device using an aluminium panel. The solid line shows the device with masses and the dashed line without masses. As shown, the device without masses is unusable while the addition of the three masses gives significant performance improvements. The greatest improvement is shown in the mid-band, particularly around the frequency of the second mode, namely 2.6 kHz. The improvement is not as marked as for the embodiment using a Rohacell™ panel since the aluminium panel is significantly heavier and has lower damping. Accordingly, the ratio of added masses to panel mass is reduced and the overall sensitivity loss is reduced. The large peak at 16 kHz appears to be unaffected by the addition of the masses shown, perhaps because it is due to the sixth mode.
a to 10 illustrate a method for choosing the annular positions of the masses and suspension and the drive location for the devices of
b shows the sound pressure and sound power levels for a theoretical loudspeaker comprising a free, resonant circular panel driven by a mass-less point force applied at the panel centre. The sound pressure is still substantially constant with frequency but now the fall-off in sound power has been significantly improved compared to that shown in
c shows the sound pressure and sound power levels for a practical loudspeaker similar to that of
Since the loudspeakers are axisymmetric, simple modelling may be used for the modes.
In contrast, the modes of the practical loudspeaker of
The dashed curved line in
The impedance Zm and real part of the admittance Ym are calculated from a modal sum and thus their values depend on the number of modes considered. The admittance Ym and its logarithmic mean μ(ρ) as it varies with radius ρ are calculated using the equations below:
N=Number of modes.
S=Scaling factor over the operative frequency range.
λi=eigenvalue≈(n−½)·π/(1−ρ0); ρ0=0.2
ω=frequency.
γ(i,ρ)=mode shape of ith mode.
a to 9e show the variation in Ym with panel diameter for one to five modes respectively. The minima are tabulated below:
In the case of a panel with little damping, the width of each minimum is quite narrow. This suggests that mounting at the annular locations may be quite critical and that the tolerance may be as low as 2%. This particularly true for the first mode taken alone. For a panel with typical damping, such as a polymer film skinned foam core panel, the tolerance may increase to as much as 10%, as can be seen in
It should be noted that as the average is taken over an operative frequency range, modes at frequencies outside this range will not affect the result. This, in part, explains why modes five and higher generally have less effect than their predecessors. Thus, the higher order modes may be satisfactorily mapped if the first four modes are mapped when the higher modes are out of the frequency band of interest, and the panel is reasonably stiff in shear. When this is not true, then higher orders of modal balancing are possible.
The method is flexible enough to allow a designer to map only particular modes. The annular locations calculated for the first four or five modes correspond to the positions of the masses and voice coil in the devices of
f compares the annular locations with the mode shapes of the theoretical loudspeaker. At the first mode there are two annular locations 50,52 inboard of the nodal line 54 and two outboard 56,58. As the mode order increases there are annular locations disposed on opposite sides of the nodal lines 54.
g shows that as the number of modes to be fixed increases (in this case to eight), there does seem to be, by observation, a pattern in the admittance curve which looks to be asymptotic. The ratios of inner and outer minima start to settle down to values of around 0.13 and 0.95 respectively. Also, with increasing mode order, the minima in the impedance become ever closer together which tends towards a continuum.
The masses to be mounted at the minina are still small and discrete and are shown as discrete circles. The location of the voice coil and the suspension are indicated by a C and S, respectively. In practice the masses may well be of extended size, and could be represented as shown in
i and 9j show the acoustic sound pressure and acoustic sound power for a loudspeaker using discrete masses M1 and M2 (solid line) and a loudspeaker using a continuous mass (dotted line). The solutions have a small amount of structural damping applied (5%).
Locations for masses in the discrete solution were:
Locations for the continuous mass solution were:
The continuous mass was modelled as a very flexible thin shell with suitable density but very low Young's Modulus, thus avoiding any stiffening of the diaphragm. Although
It may be possible to reduce in amplitude some of the unwanted peaks in the continuous mass solution, if the continuous mass had a small amount of intrinsic damping. This may be achieved by using a material such as flexible rubber sheet, or the like, which gives the correct mass and a small amount of additional damping.
As an alternative to using admittance, net transverse modal velocity tending to zero may be achieved by optimisation as follows. First a model is defined, e.g. for a circular diaphragm consider a disc comprising concentric rings of identical material, with circular line masses at the junctions of the rings, the modal frequencies and mode shapes are solved from:
N—mode fix; μl=mass per unit length of ring masses
ψ0=A0·J0(k·r)+C0·I0(k·r)
Section n=1 . . . N
ψn=An·J0(k·r)+Bn·Y0(k·r)+Cn·I0(k·r)+Dn·K0(k·r)
ψ(k·rn)n=ψ(k·rn)n-1
ψ′(k·rn)n=ψ(k·rn)n-1
MR(k·rn)n=MR(k·rn)n-1
MR(k·R)=0
ψn is the mode shape of the nth ring
k is the wave number
r is the radius
μl is the mass per unit length of the ring masses
N is the number of the highest mode to be addressed
J(0) is a Bessel function of the first kind, order 0
Y(0) is a Bessel function of the second kind, order 0
I(0) is a modified Bessel function of the first kind,
K(0) is a modified Bessel function of the second kind
An, Bn, Cn and Dn are constants
MR is the radial component of bending moment
QR is the radial component of shear force
α are the ratios of mass per length of the ring masses to a reference mass per length, typically that of the voice-coil, and α=1 for all rings except the outermost ring, typically.
The net volume displacement is calculated from:
Optimising the outermost αN for fixed values of r so that the net volume displacement tends to zero gives values of αN between about 0.75 and 0.80, depending on the exact values of rn. The average nodal positions calculated using the admittance method described above give optimal values of αN of about 0.79 to 0.80. If the actual nodal positions for the last mode are used, values of αN of about 0.74 to 0.76 appear optimal.
As an example, the optimisation method is used to design a 92 mm diameter panel driven by a transducer having a 32 mm voice coil. The two mode solution calculated using the admittance method gives radial locations of 0.4 and 0.84 for the voice coil. However, the ratio of coil diameter to panel is 0.348.
Assuming, B=7 Nm, μ=0.45 kg/m2, ν=1/3, R=0.046 m, Coil mass=1.5 gm, and by varying the position and mass of the outer ring in the optimisation method for two modes, i.e. N=2, by, we get;
Accordingly, by mounting a ring of diameter 75.14 mm (0.816764×2R=0.816764×92 mm) and of mass 3.224 gm (0.915268×75.14/32×1.5 gm) to the panel driven by the selected transducer, the modal residual volume displacements for the first two modes have all but vanished as shown in
As a second example, a mass is placed at each nodal line of the third mode, the values of the masses to balance the first two modes are then determined using optimisation. The results are:
Locations (ratio of radius): 0.257, 0.591 and 0.893
The optimised masses per unit length are also scaled as set out below in the following ratios 1, 0.982 and 0.744.
In the first two embodiments of the invention, the panel is driven at the innermost annular position (0.2). However, since the other annular positions are also average nodal lines, the panel may be driven at one or more of these positions with annular masses at the remaining locations to balance the mass of the transducer(s). The balancing action of the masses is related to the relative distance from the drive point and/or centre of the panel. For example, for a single 8 gram transducer mounted at the 0.91 drive point, the value of the masses to a good approximation at the other locations may be derived as follows:
a shows the frequency responses for three different ranges for a loudspeaker comprising a circular diaphragm.
b shows the piston displacement for the loudspeaker of
e show the frequency responses for the three different ranges for the loudspeaker in which the first and second mode are balanced.
f and 10g show the modal displacement for the first and second mode for each range. In the pistonic range, there is no modal displacement. Each mode is balanced, i.e. the sum of the mean transverse displacement for each tends to zero, and thus its net contribution is balanced. Accordingly, there is no level change in the response. A simple, sharp notch 360 remains but this is psychoacoustically benign.
i corresponds to
a shows the sound pressure and power variation with frequency for a circular panel driven by a transducer having a mass of 8 g at the 0.91 ratio with the balancing masses set out above.
a shows an alternate embodiment of the present invention which is similar to that of
b shows a variation on
c compares the variation in the power response for the devices of
The annular locations of the masses and voice coil are calculated in a similar manner to and using the equation for impedance outlined above.
The annular panel 72 is driven by a concentrically mounted transducer which has a voice coil 82 mounted at 0.62 of the radius of the panel. A ring mass 78 is mounted to the annular panel at an annular location of 0.91 of the radius. The annular panel 72 is mounted to a chassis as in
The circular panel 70 is driven by a concentrically mounted transducer which has a voice coil 84 mounted at 0.62 of the radius of the panel. A ring mass 86 is concentrically mounted to the circular panel at an annular location of 0.91 of the radius.
In general, the tolerance for changing mass is greater than that for changes in location. Furthermore, the effect on the frequency response of the location changes are most severe at frequencies above the last balanced mode. Overall, the greatest tolerance to change of is for locations closest to the centre of mass. Not only is this location tolerant to quite wide changes in either the diameter ratio or mass, but also it is observed that in the pass-band the changes are complementary. It may be possible to cope with a change of up to +/−30% on either mass or diameter ratio, providing the mass per unit length is unchanged. The outer locations are more sensitive to changes in ratio, but possibly less sensitive to changes in mass.
For an optimal solution, relative mean displacement Ψrel=0. For a two-mode optimum fix, varying the radius of the outer mass moves from optimal according to
where r2 is the radius of the mass divided by the plate radius
In other words, a 1% change in r2 results in a 1.75% change in Ψrel. The above work shows that tolerances of +/−5% to +/−10% on r2 are acceptable. This corresponds to a tolerance on Ψrel between 8% and 18%, respectively.
In
When shear flexibility is taken into account, the frequency of a mode may change substantially from what would be predicted by thin-plate theory. The shape of the mode, however, is largely unchanged. For example, with materials typically used, a reduction in the diameter ratios by about 0.01 to 0.02 results in a slightly better balancing of the modes. This improvement is largely academic, given the tolerances described in the previous paragraph. A simple equivalent compensation is to make the panel slightly larger—typically by 1 or 2 mm.
The size of the panel is limited by the size of the transducer voice coil. Given industry-standard coil sizes, the size of the panel is restricted. However, as described above, the frequency response of the device is quite tolerant to changes at the innermost ratio and this observation may be used to advantage, allowing changes in panel diameter of probably at least +/−10% from the tabulated values. For example, the method may be adapted by first finding the closest panel/transducer combination to that required (the voice coil of the transducer would be set to the inner-most diameter ratio) and then scaling all the diameter ratios and masses, except for that of the voice coil, to get the correct panel size.
Alternatively, work on annular shaped panels may be used to release a designer from constraints on the panel size. The argument is that if the hole is small, then its effect will also be small, so maybe it is not needed. The tables set out in relation to annular panels suggest that hole sizes having a diameter ratio of less than 0.1 have minimal effect on the annular locations. Thus the method may be adapted by designing an annular panel, but building a circular panel. For example, a panel diameter of 108 mm with a coil of 32 mm may be achieved by designing an annular panel with a hole ratio of 0.14. The nearest circular design would require a coil of 28 mm.
Either of the methods discussed above, namely using the tolerances or annular shape to relax the restrictions on panel size may also be used to “detune” the pass-band modal balance in favour of a more graceful departure from a flat response at higher frequencies. This is important where the number of modes addressed does not fully cover the intended bandwidth or shear in the panel material results in higher-order modes reducing in frequency to the point where they appear in-band. The frequency response often becomes irregular near these higher modes, especially when the voice-coil falls on or near an anti-node of one of these modes. Improvement for these higher order modes may be addressed by using the tolerances or by choosing an annular form.
The use of a central damping disc follows traditional teaching, since for a circular panel, this is always an antinode (likewise at the panel edge). However, this will mean that all the modes will have some damping applied, but unfortunately, not all of the velocity profile will be equally damped. Thus as shown in
In order to understand how this peak from the third mode can be effectively damped, we need to re-visit
There are also two other broad regions of high velocity which peak at panel diameters of 0.42 and 0.74. Selective damping may usefully be applied in these regions. Since the regions are broad admittance, the damping locations are not as critical as the balancing mass locations. For the loudspeaker shown in
a shows a loudspeaker comprising a circular panel 90 having a diameter of 85 mm which is driven by a 32 mm voice coil transducer 92. An annular balancing ring 94 of diameter 71 mm is mounted to the panel together with a damping ring 96 of diameter 63 mm and a central damping pad of diameter 9 mm. The damping rings 96, 98 are made from ethylene propylene diene rubber.
b shows the on-axis sound pressure level (SPL) and sound power level (SWL) curves (lower and upper curves respectively) for the loudspeaker of
The location of the damping rings is determined by the number of modes which are balanced. Using
For example, if the fourth mode is to be damped, damping pads should be mounted at diameter ratios 0.32, 0.52 and 0.77.
As shown in
a to 26d show sound pressure and sound power levels obtained by finite element analysis.
In
In
The coupler in the models was of thin paper but depending on the ratio of diameter matching, allowable coupler mass, and cost, stronger shell constructions for the coupler are possible such as carbon fibre reinforced resin, and crystal orientated moulded thermoplastic such as Vectra. While the coupler in the models was a single frusto-conical section, it would also be possible to arrange the coupler to be a flared device, resembling a typical curved loudspeaker cone.
a and 27b show a variation on the embodiment of
In both embodiments, the panel 110 is made from an isotropic material, namely 5 mm thick Rohacell™ (expanded poly methylimide) and has an outer periphery with a diameter of 100 mm and an inner periphery with a diameter of 20 mm. The balancing action of the masses is related to the relative distance from the drive point and/or centre of the panel. The value of the masses is balanced as follows:
a and 28b show the on-axis pressure and half-space power for the loudspeakers of
a and 29b shows a variation on the device of
a and 30b show a variation on the embodiment of
a and 32b show the on-axis pressure and half-space power for the loudspeakers of
c and 32d then show variations of the devices shown in
c shows the effect of reducing the mass of the transducer to 6 g and the value of the mass at the 0.7 location from 6.06 gm to 5.8 gm on the flat panel.
a and 33b show alternative diaphragms which may be incorporated in the preceding embodiments. In
In each of the above embodiments, the annular masses are discrete masses mounted to the panel. The width or a real extent of the masses does not appear to be critical provided the centre of mass is referred to the correct annular location. Furthermore, the masses do not need to be mounted on the opposed surface of the panel to the voice coil. The extra mass may be provided at the annular locations by increasing the panel density in these locations. The panel may be injection moulded with additional masses at the annular locations.
a and 34b show a loudspeaker comprising a diaphragm in the form of a beam-shaped panel 220 and two transducers mounted thereto. Two pairs of masses 228, 226 are mounted at locations at 0.19 and 0.88 of the distance from the symmetry line (or centre) to the edge of the panel (i.e. over the half-length of the panel). The voice coil 222, 224 of each transducer is mounted at a location which is 0.55 away from the centre of the panel. The panel 220 is mounted to a chassis 221 via a suspension 223 mounted at the 0.88 location.
The voice coils 222, 224 and masses 228 at 0.19 have equal mass. Since the beam is of constant width, the mass per unit length is proportional to mass but independent of position. However, due to edge effects, those masses nearest the edges of the panel may beneficially be smaller in value, typically by up to about 30%
a and 35b show the on-axis pressure and half-space power for the loudspeaker of
As shown in the
a to 36g illustrate a method for choosing the positions of the masses and the drive location for the device of
b shows the sound pressure and sound power levels for a theoretical loudspeaker comprising a free, resonant beam-shaped panel driven by a mass-less point force applied at the panel centre. The sound pressure is still substantially constant with frequency but now the fall-off in sound power has been significantly improved compared to that shown in
c shows the sound pressure and sound power levels for a practical loudspeaker similar to that of
Since the loudspeakers are quasi one-dimensional, simple modelling may be used for the modes. The results are similar to that shown in
As outlined above, the location(s) are at positions of average low velocity, i.e. admittance minima. For a beam-shaped panel, the admittance Ym and its logarithmic mean μ(ξ) as it varies with half-length ξ are calculated using the equations below:
N=Number of modes.
S=Scaling factor over the operative frequency range.
λi=eigenvalue≈(n−¼)·π
ω=frequency
γ(i,ξ)=mode shape of ith mode
d shows the logarithmic mean admittance of the first two modes (N=2) of the panel of
e shows the logarithmic mean admittance of the first three modes (N=3) of the panel of
f shows the logarithmic mean admittance of the first four modes (N=4) of the panel of
The higher order modes may be satisfactorily mapped if the first four modes are mapped when the higher modes are out of the frequency band of interest, and the panel is reasonably stiff in shear. When this is not true, then higher orders of modal balancing are possible; e.g. five or more modes.
g shows the logarithmic mean admittance of the first five modes (N=5) of the panel of
The various minima restrict the location of the transducer on the panel any thus the overall panel size may be determined by industry standard voice coil sizes. However, it is possible to have more than one transducer on the panel and thus the constraints on panel size are relaxed. The effect of the ratio of transducer diameter to panel width on the presentation of cross-modes is profound and a value of about 0.8 for this ratio may beneficially suppress the lowest cross-mode.
h compares the output from a diaphragm with a pair of transducers mounted thereon (dotted line) with the same diaphragm having the pair of transducers and a pair of masses mounted at an average nodal position of the two modes in the frequency range (solid line). The first mode is not seen in either case due to the location of the transducer. The second mode is balanced by the addition of the masses. The average nodal locations are 0.29 and 0.81 and are calculated using the same method above. The nodal locations translate to locations of 0.095, 0.355, 0.645 and 0.905 when expressed as fractions of the length of the diaphragm.
i compares the output from a diaphragm with only a transducer mounted thereon (dotted line) with the same diaphragm having the transducer and a pair of masses mounted at an average nodal position of the five modes in the frequency range (solid line). The average nodal radii are 0.11, 0.315, 0.53, 0.74 and 0.93 which translate to locations (as fractions of the length of the diaphragm) of 0.035, 0.13, 0.235, 0.3425, 0.445, 0.555, 0.6575, 0.765, 0.87 and 0.965.
a and 39b show the on-axis pressure and half-space power for the loudspeaker of
a and 40b show an alternate embodiment of the present invention in which the beam-shaped panel 250 has a thickness which varies with length. The overall length of the panel 250 is 306 mm and the thickness increases linearly from t1=2 mm at each edge to t2=5 mm in the centre. The voice coils 252, 254 of each transducer are mounted at a location which is 0.08 away from the centre of the beam. Pairs of masses 256, 258, 260 are mounted at locations at 0.28, 0.53 and 0.80 of the distance from the symmetry line to the edge of the panel. The masses mounted at 0.28 and 0.53 are equal in mass to the voice coils 252, 254 whereas the pairs of masses 260 at 0.80 have reduced mass. Thus for modelling purposes, the mounting locations are 12 mm, 45 mm, 85 mm and 128 mm. The voice-coils and inner two pairs masses are 550 mg each, and the outer masses are 400 mg.
Since the panel is symmetrical,
c and 41d shows the logarithmic mean of the response of the first four modes (N=1 . . . 4) of the panel of
As described above in relation to
The table below shows the frequencies for the first five free-symmetric modes of the wedge of
The approximate locations of nodal lines for the first four modes are set out below. Since the panel is symmetric, only the nodal lines in one half of the panel are shown: a line at “x” implies one at “200−x”.
Comparing the results with those from
a shows the sound pressure and sound power levels for a theoretical loudspeaker comprising a free symmetrical wedge-shaped, rigid panel driven by a mass-less point force applied at the panel centre. The panel is 200 mm long and 20 mm wide, tapering from 5 mm thick at the centre to 2 mm thick at either end. The sound pressure and sound power are generally constant with frequency up to about 10 kHz, although there is some break-through of modes at 4.8 kHz and 9.5 kHz. The far-field, on-axis pressure should be flat, however, the pressure is simulated at 200 mm so there is variation.
b shows the sound pressure and sound power levels for a practical loudspeaker comprising the free, wedge-shaped panel driven by a transducer with a voice coil having a 25 mm diameter and a finite mass which is dependent upon the design of the voice coil (materials, turns, etc.) The sound pressure and sound power has been significantly impaired compared to that shown in
c shows the sound pressure and sound power levels for a practical loudspeaker similar to that of
In each of
a shows an alternate embodiment of the present invention in which the beam-shaped panel 270 has a thickness which varies with length and is not symmetrical. The overall length of the panel 270 is 153 mm and the thickness increases with a square root dependency from 2 mm at one end to 5 mm at the opposite end. The voice coils 274, 272 of each transducer are mounted at locations which are 0.23 and 0.43 away from the thinner end of the panel. Pairs of masses 276, 278, 279 are mounted at locations at 0.06, 0.66 and 0.88 of the distance from the thinner end of the panel. The masses mounted at 0.66 and 0.88 are equal in mass to the voice coils 272, 274 whereas the pairs of masses 280 at 0.06 have reduced mass. Thus for modelling purposes, the mounting locations are 9 mm, 35 mm, 66 mm, 101 mm and 134 mm. The voice-coils and inner two pairs masses are 550 mg each, and the outer masses are 400 mg.
b shows the shape of the first four modes of the panel of the embodiment used in
As described above in relation to
The table below shows the frequencies for the first five free-symmetric modes of the wedge of
The approximate locations of nodal lines for the first four modes are set out below.
Comparing the results with those from
a shows a beam varying in thickness linearly with length x. If we consider a narrow slice of the beam, taken across the width at x, then we have another, conceptual beam of uniform properties. As shown in
The mode shapes of the varying width beam are shown in
The mean volume velocity Vn for each mode is set out below, where V0 is the mean volume velocity for the “piston” mode.
In both cases, the mean volume velocity of all the bending modes is zero (within the tolerance of the calculation), so both embodiments may be used as a theoretical ideal to which the unbalanced modes of a practical acoustic device may be mapped.
a and 48b show a loudspeaker comprising a diaphragm in the form of a rectangular panel 280 and two transducers 282 mounted thereto. The panel is made from skinned, cored lightweight composite material. Two pairs of masses 288, 286 are mounted at locations at 19% and 88% of the distance from the centre to one corner of the panel (i.e. over the half-diagonal of the panel). The voice coil of each transducer 282 is mounted at a location which is 55% away from the centre of the panel along the half-diagonal. The panel is mounted to a chassis 281 by a suspension 283 and sealed in a baffle (not shown).
The locations of the transducers and masses are calculated in a similar manner to the earlier embodiments. The mode shapes for the X-axis and Y-axis are considered separately and may be computed from the bending stiffness and the surface area mass of the panel. The average nodal positions are calculated from the minima in impedance. In the embodiment shown, the locations of the masses and transducers are average nodal positions for both axes when the first three modes for each are considered. There are additional effective locations along the diagonal if four modes are addressed. For a panel of 460 mm by 390 mm, the (x,y) locations of each of the masses and transducers are given as follows:
The voice coils each have a mass of 4 g and the value of the masses is scaled to that of the voice coil as follows:
The coil masses are not summed when obtaining the values for the balancing masses because each transducer relates only to the axis which it drives.
Where an outer suspension has significant mass there is an opportunity for the designer to distribute this mass by choice of surround material noting that it is distributed near the panel perimeter. The advantage is some additional control via damping and loading of higher order, e.g. 2 D coupled modes which are not susceptible to the single axis modal balancing technique
a and 51b show the sound pressure and sound power levels for a variation of the loudspeaker of
The table below shows the modes for the rectangular panel of
Moderate modal density appears above 250 Hz where the chosen panel parameters such as aspect ratio additionally confer distributed mode operation at these higher frequencies. If this type of embodiment is not required to be full range then the modal balancing alone is sufficient to provide an extended, piston equivalent performance in the lower frequency range from a resonant panel diaphragm.
If the diaphragm is also required to have useful modal behaviour at higher frequencies, e.g. Distributed Mode, then in a further improvement, the available options for the balancing drive positions may also be iterated with respect to the preferred drive points for good modal coupling at higher frequencies. The latter teaching indicates a preference for off-centre and also for off-cross-axis locations. Such combination locations may be found by inspecting an analysis of the modal distribution with frequency over the area of the panel.
If more output is required from the speaker four exciters could be used, exploiting the second diagonal, and now working with eight masses. Typically all the exciters would be wired for an in-phase connection to the signal source.
a and 52b show a coupler 300 disposed between a beam-like panel diaphragm 302 and a transducer voice coil 304. The magnet assembly of the transducer has been omitted for clarity. As shown in
a and 53b show a coupler 310 disposed between a beam-like panel diaphragm 302 and a transducer voice coil 304. The magnet assembly of the transducer has been omitted for clarity. As shown in
In both
where y(n,ξ) is the mode shape for the nth mode.
In order to avoid exciting a particular mode, the corresponding average net force should vanish. In other words, we want the zero-crossings of the functions F(n, ρ), i.e. effectively driving at a nodal line. The results are tabulated for up to four modes, together with the nodal line nearest the origin. From these results, it suggests that the actual diameter of the voice coil is about 1½ times the effective drive diameter of the voice coil.
Furthermore, it is noted that F(1) has a zero crossing at about 0.8. Mounting a voice coil having a diameter in the ratio of 0.8 to the width of the panel will thus suppress the lowest cross-mode.
The teaching above suggests mounting the suspension away from the periphery of the diaphragm.
c shows a cross-section of the quarter diaphragm in which M1 is the mass mounted near the nodal line, Ms is the mass of the glue-zone of the suspension, Md is the mass of the active part of the suspension, ξ0 and ξ1 are the distances from the centre of the diaphragm to the nodal line and mass near the nodal line, respectively and 1−ξ2 is the width of the glue-zone. There are three basic ways of ensuring that the suspension balancing mass and edge suspension are equivalent to the inboard suspension.
The simplest is when the mass of the glue zone is considered lumped with the mass of the suspension's active part. For the beam this means solving:
F(n,ξ1)=M1y(n,ξ1)+(Md+Ms)y(n,1)=0
Where y(n,ξ1) is the mode shape.
For example, starting from a transducer having a voice coil of diameter 32 mm and mass 1.5 g, the diaphragm has a width of 40 mm and 156.8 mm. The width is selected so the voice coil diameter is 80% thereof and the length so that the effective net force for the fourth mode is zero, i.e. F(4)=0.
The nodal lines of mode 4 are tabulated below, along with the corresponding locations and masses from the text-book.
The suspension has the following properties:
Ms+Md=1.8 g/m×40 mm=72 mg.
Ks (stiffness)=443.5 N/m/m
Rs (damping)=0.063 Ns/m/m
Width (1−ξ2)·L/2=4.0 mm, giving ξ2=0.949
Accordingly, M1=M−Md−Ms=528 mg. Using the lumped approximation above gives ξ1=0.897, i.e. the location of the suspension balancing mass is at 8.1 mm and 148.7 mm measured from one end of the diaphragm. Without the lumped simplification, the locations are calculated to be 7.9 mm and 148.9 mm (i.e. very similar). In both cases, the attachment points are at least 1 mm further from the edge of the diaphragm than the nodal line.
a and 56b shows the loudspeaker response without and with the suspension balancing masses, respectively.
The equation for a circular diaphragm is
This may be solved either by preserving the total mass or the total mass per unit length. If ξ0 (i.e. location of nodal line) is 0.919 for the fourth mode, preserving the total mass gives ξ1=0.8947 and M1=3.4. Preserving the total mass per unit length gives a similar result, namely ξ1=0.8946 and M1=3.387.
It is also possible to incorporate the suspension balancing mass as part of the suspension by ensuring that the suspension balancing mass butts up to the glue zone. The equations are now more complicated, for example for the beam diaphragm:
F(n,ξ1)=M1(ξ1)y(n,ξ1)+μl(yi(n,1)−yi(n,ξ1))+Mdy(n,1)=0
where μl is the mass-per-unit-length of the glue zone region, and M is the required total mass.
a and 57b show a microphone which is generally similar to the loudspeaker of
Incident acoustic energy 338 causes the panel to vibrate and the vibration is detected by the transducer and converted into an electrical signal. The signal is outputted via wires and a microphone output connection 340.
The voice coil has a mass of 1 g but driving at separate locations means that the effective mass at each location is halved. The masses 346 are strips of plain rubber having a mass which balances the effective mass of the voice coil at each location, i.e. 0.5 g.
The panel is supported in a moulded plastics frame 350 by a suspension 348 of low mechanical impedance whereby the panel is essentially free to resonate. Such a speaker is suitable for higher quality flat panel TV and monitor applications and has a nominal 100 Hz to 20 kHz bandwidth with uniform frequency and good power response.
The ratio of the radius r of the planar section 354 to the outer radius R of the cone 352 is an additional diaphragm parameter which may be adjusted to achieve a desired acoustical response. This adjustment may be done with a number of intermediate objectives. For example:
Additional parameters which may be varied are the height h, shape and angle of the dished portion, all of which are found to cooperatively relate to the planar section. For example, the latter may be found to balance a mode for which the drive is on the nodal line. A solution may then be found with just one additional balancer. The locations of the drive and the balancing mechanical impedance or impedances are not shown. The mechanical impedances may be added according to the other parameters and the intended operating range.
| Number | Date | Country | Kind |
|---|---|---|---|
| 0408464.6 | Apr 2004 | GB | national |
| 0408499.2 | Apr 2004 | GB | national |
| 0408519.7 | Apr 2004 | GB | national |
| 0415631.1 | Jul 2004 | GB | national |
| 0425921.4 | Nov 2004 | GB | national |
| 0425923.0 | Nov 2004 | GB | national |
| 0500161.5 | Jan 2005 | GB | national |
This application is a continuation of application Ser. No. 11/578,256, filed on Apr. 8, 2005 as PCT/GB2005/001352 and issued as U.S. Pat. No. 7,916,878 (incorporated by reference herein in its entirety), which claims the benefit of U.S. provisional application Nos. 60/563,472, 60/563,475 and 60/563,476, all filed on Apr. 20, 2004, and of U.S. provisional application No. 60/587,495, filed on Jul. 14, 2004.
| Number | Date | Country | |
|---|---|---|---|
| 60563472 | Apr 2004 | US | |
| 60563475 | Apr 2004 | US | |
| 60563476 | Apr 2004 | US | |
| 60587495 | Jul 2004 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 11578256 | Nov 2006 | US |
| Child | 12929980 | US |
