WO2017220816A1

WO2017220816A1 - Method for simulating total harmonic distortion of a loudspeaker

Info

Publication number: WO2017220816A1
Application number: PCT/EP2017/065686
Authority: WO
Inventors: Francois Malbos
Original assignee: Harman Becker Automotive Systems Gmbh
Priority date: 2016-06-24
Filing date: 2017-06-26
Publication date: 2017-12-28
Also published as: EP3476135A1

Abstract

A method for simulating the total harmonic distortion of a loudspeaker, the method comprises performing a linear simulation or measurement to determine a real speaker displacement, performing a linear or non-linear lumped element model prediction, wherein the resulting speaker displacement of the lumped element model is adapted to correspond to the real speaker displacement by tuning an input voltage of the lumped element model, and performing a non- linear lumped element model prediction using the tuned voltage as an input voltage, thereby simulating the total harmonic distortion.

Description

METHOD FOR SIMULATING THE TOTAL HARMONIC DISTORTION OF A

LOUDSPEAKER

TECHNICAL FIELD

[0001] The disclosure relates to a method for simulating the total harmonic distortion or the harmonics level of a loudspeaker, in particular for simulating the total harmonic distortion of a loudspeaker mounted in a closed or vented enclosure.

BACKGROUND

[0002] A loudspeaker is generally an electromechanical transducer that produces sound in response to an electronic input signal. A loudspeaker may include a front side and a back side that is opposite the front side. The front side of the loudspeaker may communicate with a first volume of air, and the backside may communicate with a second volume of air. The loudspeaker may be mounted to an infinite baffle such that soundwaves from the backside of the loudspeaker do not interfere with soundwaves from the front side of the loudspeaker. A loudspeaker may be housed within a closed box or a vented enclosure and may include a speaker cone and a voice coil centered therein. The vented enclosure may include a port. The port may communicate with the backside of the loudspeaker such that the port places the second volume of air in communication with a third volume of air, but not the first volume of air. In such a case, the vented enclosure may include an infinite baffle. Alternatively, the port may communicate with the backside of the loudspeaker such that the port places the second volume of air in communication with the first volume of air. In such a setup, soundwaves from the front side and soundwaves from the back side of the loudspeaker may radiate to the first volume of air. When an electrical voltage is applied across the ends of the voice coil, an electrical current may be produced which in turn may interact with the magnetic fields to create movement of the speaker cone. An electrical waveform may be applied to the voice coil causing the loudspeaker to produce sound waves corresponding to the electronic input signal. Harmonic distortion adds overtones that are whole number multiples of a sound wave's frequencies. Nonlinearities that give rise to amplitude distortion in audio systems are most often measured in terms of the harmonics (overtones) added to a pure sinewave fed to the system. Harmonic distortion may be expressed in terms of the relative strength of individual components, in decibels, or the root mean square of all harmonic components (total harmonic distortion), as a percentage. Total harmonic distortion may be determined in different ways.

[0003] The total harmonic distortion may be determined using a lumped parameter model (LPM), for example. Using a linear LPM, any enclosure configuration (closed box, vented pass band with passive radiators, etc.) may be simulated. For a vented box (linear) simulation, it may be assumed that the front side of the loudspeaker and the back side of the loudspeaker via the port radiate to the listener. Using a non-linear LPM generally only allows to simulate closed box configurations where the front side of the loudspeaker radiates to the listener. In a typical vented enclosure including an infinite baffle, the front side of the loudspeaker radiates to the listener, while the port does not radiate to the listener. This means that, as in the closed box configuration, only the front side of the loudspeaker is radiating to the listener. Loudspeaker displacements are usually not the same for a closed box or for a vented configuration.

SUMMARY

[0004] A method for simulating the total harmonic distortion of a loudspeaker comprises, performing a linear simulation or measurement to determine a real speaker displacement, performing a linear or non-linear lumped element model prediction, wherein the resulting speaker displacement of the lumped element model is adapted to correspond to the real speaker displacement by tuning an input voltage of the lumped element model, and performing a non- linear lumped element model prediction using the tuned voltage as an input voltage, thereby simulating the total harmonic distortion.

[0005] A software is configured to execute the method steps of, performing a linear simulation or measurement to determine a real speaker displacement, performing a linear or non-linear lumped element model prediction, wherein the resulting speaker displacement of the lumped element model is adapted to correspond to the real speaker displacement by tuning an input voltage of the lumped element model, and performing a non-linear lumped element model prediction.

[0006] Other systems, methods, features and advantages will be or will become apparent to one with skill in the art upon examination of the following detailed description and figures. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention and be protected by the following claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007] The method may be better understood with reference to the following description and drawings. The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. Moreover, in the figures, like referenced numerals designate corresponding parts throughout the different views.

[0008] Figure 1 is a diagram illustrating a fundamental and its harmonics.

[0009] Figure 2 is a schematic diagram of a loudspeaker. [0010] Figure 3 illustrates an equivalent circuit for the loudspeaker of Figure 2.

[0011] Figure 4 illustrates a method for determining the total harmonic distortion of a loudspeaker.

DETAILED DESCRIPTION

[0012] Generally, all transducers have limitations. In an ideal system, the fast Fourier transform (FFT) of a sinusoid would result in a single peak at a specific frequency. However, in real-world systems, non-linearity and noise result in imperfections. Distortion, for example, occurs whenever the input/output transfer function alters the waveform of a signal, discounting noise, interference, and amplification or attenuation. Harmonic distortion, for example, adds overtones that are whole number multiples of a sound wave's frequencies. This is exemplary illustrated in Figure 1. Figure 1 illustrates a plot of an example set of total harmonic distortion values for a range of frequencies up to 20kHz at one particular volume level. The plot shows the fundamental F at a fist frequency and the 2^nd, 3^rd and 4^th harmonics H2, H3, H4 at multiples of the first frequency. Harmonic distortion is a measure of the amount of power contained in the harmonics of a fundamental signal and can be divided into two main categories, namely linear distortion and non-linear distortion. Linear distortion is the time and frequency dependent characteristic of the amplitude and phase response of the transfer function. This occurs with no changes in the frequency content of the input signal such that one frequency at the input results in only one frequency at the output. Non-linear distortion, on the other hand, causes changes in the frequency content of the input signal such that energy is transferred from one frequency at the input to more than one frequency at the output. Non-linear distortion products usually have a fixed frequency relationship to the fundamental frequency. Total harmonic distortion (THD) may be expressed in terms of the relative strength of individual components, in decibel (see Figure 1), or as a percentage of the power sum of all the harmonics to the power sum of all the harmonics plus the fundamental:

[0013] o/o THD = ^»*™^#+→»«* _(1)>

F² +H2² +H3² + - - -+HN² '

[0014] wherein HN is the harmonic response of the Nth harmonic and F is the fundamental response.

[0015] The total harmonic distortion of a loudspeaker can be determined by performing measurements. However, it is generally difficult to perform loudspeaker measurements, because loudspeakers are transducer which have a higher distortion than other audio system components. The standard way to test a loudspeaker requires an anechoic chamber with an acoustically transparent floor-grid. The measuring microphone is normally mounted on an unobtrusive boom (to avoid reflections) and positioned at a certain distance in front of the drive units on axis with the high-frequency driver. While this will produce repeatable results, such a "free-space" measurement is not representative of the performance in a room, especially in a small room. For valid results at low frequencies, a very large anechoic chamber is needed, with large absorbent wedges on all sides. However, most anechoic chambers are not designed for accurate measurement down to 20Hz. Further possibilities are to perform measurements outdoor, to perform half-space measurements or to perform room measurements.

[0016] Figure 2 illustrates a cross-sectional view of a loudspeaker. The loudspeaker includes a magnet 210, a back plate 285, a top plate 290, a pole piece 225, and a voice coil 230. A magnetic gap may be defined between the top plate 290 and the pole piece 225. The voice coil 230 may be arranged in this magnetic gap. The top plate 290, back plate 285, and pole piece 225 may direct the magnetic field of the permanent magnet 210, thus generating a radial magnetic field in the magnetic gap. The voice coil 230 may include a wire such as an insulated copper wire wound on a coil former with the two ends of the wire forming the electrical leads of the voice coil 230. The voice coil 230 may be centered within the magnetic gap. The two ends of the voice coil wire may be configured to receive a signal from an amplifier (not illustrated). This signal may create an electrical current within the voice coil 230. The magnetic field in the magnetic gap may interact with the current carrying voice coil 230, thereby generating a force. The resulting force my cause the voice coil 230 to move back and forth and consequently displace the cone (or membrane) 250 from its rest position. The motion of the cone 250 moves the air in front of the loudspeaker, creating sound waves, thus acoustically reproducing the electrical signal.

[0017] The cone 250 extends radially outward from the voice coil 230, thereby creating a conical or dome-like shape. The cone 250 may be produced from a variety of materials, including but not limited to plastic, metal, paper, composite material, and any combination thereof. An opening may be defined at the center of the cone 250 and a dust cap 245 may create a dome-like cover at the opening. The outer edge of the cone 250 may be attached to the frame 255 by a surround 260. The center of the cone 250 near the voice coil 230 may be held in place by a spider 275. The spider 275 and surround 260 together generally allow only for axial movement of the cone 250. The frame 255 may be a conical casing that holds the cone 250 in a fixed position. The frame 255 may surround the cone 250 and may include a more rigid material to help maintain the shape and placement of the cone 250 during operation.

[0018] During operation, and while the electrical current is being driven through the voice coil 230, the voice coil 230 may move laterally along the pole piece 225. This movement of the voice coil 230 may in turn cause movement of the cone 250. This cone excursion or displacement, in general, is the distance that the cone 250 moves from a rest position. The distance from the rest position varies as the magnitude of the electric signal supplied to the voice coil 230 changes. For example, the voice coil 230, upon receiving an electronic signal with a large voltage, may cause the voice coil 230 to move out of or further into the magnetic gap. When the voice coil 230 moves in and out of the magnetic gap, the cone 250 may be displaced from its rest position. Thus, a large voltage may result in a large cone excursion which in turn causes the non-linearities inherent in the loudspeaker to become dominant.

[0019] One model for determining the total harmonic distortion is the so-called lumped element model. However, a distinction has to be made between linear and non-linear lumped element models. A linear lumped element model does not allow to predict the harmonics because the force factor, the suspension stiffness and the voice coil inductance are constant (versus the voice coil position). The use of a non- linear lumped-element model where the force factor, the suspension stiffness and the voice coil inductance are non-constant (versus the voice coil position) allows to predict the fundamental and the harmonics in different domains such as in sound pressure, in speaker membrane displacement or velocity, and in coil current. The lumped element model (linear or non-linear), also known as lumped parameter model (LPM) or lumped component model, simplifies the description of the behavior of spatially distributed physical systems into a topology consisting of discrete entities that approximate the behavior of the distributed system under certain assumptions.

[0020] To obtain a complete model of a loudspeaker, the loudspeaker can be split into three different domains, namely an electrical domain, a mechanical domain, and an acoustical domain. The electrical domain is characterized by the voice coil with a given DC resistance R_E and self-inductance L_e. As described above, the electrical signal is converted to a mechanical motion. The strength of this coupling from the electrical to the mechanical domain is related to the force factor Bl, which is the product of the magnetic field strength B of the static magnet in the voice coil gap, and the length 1 of the voice coil in the static magnetic field.

[0021] The mechanical domain is characterized by the mass MMD of the diaphragm, the compliance CMS of the suspension and a mechanical damping RMS. The mass, the compliance and the damper will introduce a resonant frequency fs with a given quality factor QMS (mechanical Q-factor). At the resonant frequency the driver will reach its maximum impedance. The electrical domain is also characterized by a Q-factor QES which is dependent on the force factor Bl, the DC resistance R_E, the mass MMD, and the compliance CMS. Combining the mechanical and electrical Q-factors results in a total Q-factor known as QTS. The mechanical motion is converted to acoustical sound through the cone and the strength of this coupling is related to the area of the cone SD. The acoustical domain is characterized by the acoustical impedance in front ZAF, and behind ZAB the cone. When the loudspeaker is mounted in an enclosure, the acoustical load on each side of the cone is unequal. The volume of the enclosure VAB functions as an acoustical compliance. These fundamental small-signal parameters described above are generally known as Thiele-Small parameters. Other small- signal parameters may be determined on basis of these fundamental small-signal parameters. [0022] Figure 3 illustrates an equivalent circuit for a closed box loudspeaker. The electrical part of the loudspeaker generally includes a driving amplifier and the voice coil. The amplifier can be approximated as a perfect voltage source VI in series with an amplifier resistance Rl . The voice coil can be approximated as a voice coil resistance R2 in series with a voice coil inductance LI . When the loudspeaker is fed an electrical signal, the voice coil and magnet convert current to force. Similarly, voltage is related to the velocity. The relationship between the electrical side and the mechanical side can be modeled by a first transformer Tl .

[0023] In a first approximation a moving coil loudspeaker may be thought of as a mass-spring system where the cone and the voice coil constitute the mass and the spider and surround constitute the spring element. Losses in the suspension can be modeled as a suspension resistance R3. The suspension compliance may be modeled as a suspension inductance L2 and the moving mass (voice coil and cone) can be modeled as a capacitance CI . In the equivalent circuit of Figure 3, the suspension resistance R3, the suspension inductance L2 and the capacitance CI are coupled in parallel. [0024] A loudspeaker's cone may be thought of as a piston that pushes and pulls on the air facing it, converting mechanical force and velocity into acoustic pressure and volume velocity. The relationship between the mechanical side and the acoustical side, therefore, can be modeled by a second transformer T2. The air load impedance at low frequencies is mass-like and can be modeled by a simple inductance L3. This results in the simplified low frequency model equivalent circuit that is illustrated in Figure 3.

[0025] The input voltage provided by the voltage source VI may be a pure sine wave or a more sophisticated signal such as the sum of two different sine waves, for example. A linear lumped element model, however, does not allow to predict the harmonics of a loudspeaker, because the force factor, the suspension stiffness and the voice coil inductance are constant (in relation to the voice coil position). Non- linear lumped element models are known, which combine the lumped element model with differential equations, and in which the force factor, the suspension stiffness and the voice coil inductance are non-constant (in relation to the voice coil position). Such non-linear lumped element models allow to predict the fundamental and the harmonics in the sound pressure. However, neither the linear lumped element model, nor the non-linear lumped element model take into account the geometry of the loudspeaker enclosure. Only the volume of the speaker enclosure is taken into account when using a lumped element model. This means that for small loudspeaker enclosures (i.e. simple square boxes), the lumped element approach delivers quite accurate results. For more complex enclosure geometries, however, the results are generally less accurate, because the acoustical resonance of the air in the enclosure influences the displacement of the speaker membrane. In some cases, the effect of the air resonances within the speaker enclosure may be negligible. However, in other cases the effects may significantly influence the speaker displacement such that the real speaker displacement considerably differs from the speaker displacement that can be predicted using a linear lumped element model. Speaker displacement means the displacement of the membrane or diaphragm from its rest position. Using a lumped element model with a constant input voltage, the amplitude of the harmonics cannot be predicted for a speaker that is mounted on an enclosure in which the resonances of the air within the enclosure considerably influence the speaker membrane displacement. Constant input voltage in this context means that the absolute value (the amplitude) of the input signal is constant (for each sine wave). [0026] There are two cases, namely a first case in which the air resonance of the enclosure does not correspond to the speaker frequency working range and a second case in which the air resonance of the enclosure corresponds to the speaker frequency working range. If the air resonance of the enclosure does not correspond to the speaker frequency working range, which means that the first eigenfrequency of the air volume is higher than the upper frequency limit of the speaker frequency working range, the amplitude of the fundamental and the harmonics of the sound pressure (real speaker displacement) can be predicted using a non-linear lumped element model and a constant input voltage at the speaker terminals.

[0027] If the air resonance of the enclosure corresponds to the speaker frequency working range, a non-linear lumped element model approach using a constant voltage (sine wave with constant amplitude) as an input voltage cannot be used to determine the real speaker displacement, as has already been described above. Therefore, according to one example of the present invention a measurement or a subsystem simulation is performed first to determine the real speaker displacement. Based on this real speaker displacement, the input voltage at the speaker terminals of a non-linear LPM (lumped parameter model) approach is then tuned (adapted) until the same speaker displacement is received as in the measurement or in the FEM/BEM prediction. In other words, the speaker displacement of the non-linear LPM approach is the same as the real speaker displacement. The transfer function between the tuned voltage (after adapting the voltage) and the non-tuned (constant) voltage (before adapting the voltage) is equal to the transfer function between the real speaker displacement and the displacement predicted by the LPM model using the constant voltage at the speaker terminals. This tuned voltage is then used for a simulation tool which combines a LPM model and differential equations to simulate the amplitude of the fundamental and the harmonics in the sound pressure.

[0028] As mentioned before, a linear LPM model does not allow to predict the harmonics because the force factor, the suspension stiffness and the voice coil inductance are constant (constant versus the voice coil position). The use of a non-linear LPM model where the force factor, the suspension stiffness and the voice coil inductance are non-constant (versus the voice coil position) allows to predict the fundamental and the harmonics in the sound pressure. In any case, no (neither linear nor non-linear) LPM approach considers the geometry of the speaker enclosure. In LPM approaches, the speaker enclosure usually is only defined by the volume of the air in the enclosure. This means that a non- linear LPM model using a constant voltage at the speaker terminals cannot be used to predict the amplitude of harmonics for a speaker mounted on an enclosure where the resonances of the air in the enclosure will influence the speaker membrane displacement. If the effects of the air resonances are not negligible, the real speaker displacement will be different from the predicted speaker displacement delivered by the linear LPM approach. Therefore, according to an example of the present invention, in oder to measure the harmonics level and then compute the total harmonics distortion, the voltage at the speaker terminals is a concatenation of pure sine waves at different frequency values (the same voltage amplitude for all frequency values). In order to get the same speaker displacement delivered by the measurement (or FEM/BEM simulation) and the linear LPM approach, the amplitude of each sine wave at the speaker terminals is tuned. This tuned voltage is used in the non-linear LPM model to predict the amplitude of the harmonics and the total harmonics distortion level. The same method could be used if the voltage at the speaker terminals was a multitoned signal (used to predict sound pressure intermodulation).

[0029] In other words, to simulate or predict the total harmonic distortion THD (or harmonics levels or harmonics combinations levels) of a speaker mounted on any enclosure geometry, a non-constant voltage is used in combination with a non-linear speaker lumped element model. For the non-linear LPM prediction method, this tuned voltage allows to control the fundamental of the speaker displacement. For each frequency, the amplitude of the tuned voltage is computed to reach the same speaker fundamental displacement as delivered by a measurement or simulation method, which both include the interaction between the speaker membrane and the air in the speaker enclosure. To improve the accuracy of the harmonics prediction or simulation, every harmonic amplitude delivered by the non-linear LPM simulation may be updated. The harmonic magnitude update is based on the use of the transfer function between the fundamental speaker displacement delivered by the non-linear LPM and the linear speaker displacement delivered by the simulation or measurement methods. The ratio used to increase or decrease the harmonic level is computed by checking the relative amplitude of the speaker displacement at the fundamental and the harmonic frequencies.

[0030] In the following, the principles of the present invention that already have been explained above are further described in other words. A measurement or a subsystem simulation may first be performed to determine the real speaker displacement. The real speaker displacement is also called first speaker displacement in the following. The simulation may include a finite element method (FEM) or a boundary element method (BEM), for example. If a first (constant) input voltage is used as an input voltage of a lumped element model prediction, this results in a second speaker displacement, which is usually different from the first speaker displacement. This means, that performing a non-linear LPM method with a first (constant) input voltage, this does not result in the real speaker displacement, but in a second speaker displacement which differs from the real speaker displacement. Based on the previously determined first speaker displacement, the input voltage of the lumped element model may then be adapted until the resulting (third) speaker displacement is the same as the real speaker displacement obtained from the measurement or in the simulation that has been performed in the previous step (third speaker displacement = first (real) speaker displacement). This means, that in order to obtain a (third) speaker displacement from the non-linear LPM which is the same as the first (real) speaker displacement, a second (tuned) input voltage needs to be used for the non-linear lumped element model. The transfer function between the tuned voltage (after adapting the voltage) and the non-tuned (constant) voltage (before adapting the voltage) is equal to the transfer function between the real speaker displacement and the displacement predicted by the LPM model using the constant voltage at the speaker terminals. This tuned voltage, which results in the real speaker displacement, is then used in a simulation tool combining a LPM model and differential equations to simulate the amplitude of the fundamental and the harmonics in the sound pressure.

[0031] Referring to Figure 4, a method is illustrated that allows to more accurately determine the total harmonic distortion for loudspeakers that are mounted in (complex) loudspeaker enclosures. In a first step, a first (real) speaker displacement is determined (step 401). To determine the first (real) speaker displacement, a measurement or simulation may be performed. A simulation may take into account speaker parameters and computer-aided design (CAD), for example. The simulation may be based on a finite element method (FEM) or a boundary element method (BEM), for example. Any other suitable method may be used. Such FEM or BEM methods are commonly known. Several simulation tools are available which use FEM or BEM. The real membrane displacement of the loudspeaker may be determined for a case in which the air resonance in the enclosure corresponds to the frequency working range of the loudspeaker.

[0032] In a next step, the membrane displacement may be determined by means of a (linear or non-linear) lumped element model of the loudspeaker (step 402). Using a first (constant) voltage as an input voltage for the lumped element model results in a (second) speaker displacement which may differ from the first (real) speaker displacement that has been determined by means of a measurement or simulation at the first voltage. This second membrane displacement may be determined for a case in which the air resonance in the enclosure does not correspond to the frequency working range of the loudspeaker, for example. Constant input voltage in this context means that the signal, i.e. a sine wave or a more complex signal, has a constant amplitude which does not change over time. The input voltage may have a certain frequency and a certain voltage (amplitude). The first (constant) input voltage may then be altered until the resulting (third) membrane displacement equals the first (real) speaker displacement (step 403). Generally, when the voltage/amplitude of the input voltage changes, the resulting membrane displacement and also the harmonics change as well. The resulting (third) speaker displacement and the first (real) speaker displacement are the same when a second (tuned) input voltage is used as an input for the lumped element model. Amending the input voltage allows to control the fundamental of the speaker displacement. The input voltage is adapted for each frequency separately. [0033] The second (tuned) input voltage may then be used to simulate the amplitude of the fundamental and the harmonics of the sound pressure (step 404). The simulation may be based on a non-linear lumped element model that allows to predict the amplitude of the fundamental, the harmonics of the sound pressure and the total harmonic distortion. The same method as has been described above, may be used if the input voltage at the speaker terminals is a multitoned signal which is generally used to predict sound pressure intermodulation.

[0034] Input parameters for the lumped element model in step 402 (linear or non-linear simulation) may include the force factor Bl, the self inductance of the voice coil L_e, and the suspension compliance CMS while the voice coil is in its rest position for the linear lumped element model and for all voice coil positions for the non- linear lumped element model. Input parameters for the lumped element model in step 403 (non-linear simulation) may include the force factor Bl, the self inductance of the voice coil L_e, and the suspension compliance CMS for all voice coil positions.

[0035] While various embodiments of the invention have been described, it will be apparent to those of ordinary skill in the art that many more embodiments and implementations are possible within the scope of the invention. Accordingly, the invention is not to be restricted except in light of the attached claims and their equivalents.

[0036] A method for determining total harmonic distortion of a loudspeaker may comprise determining a first speaker displacement at a first loudspeaker input voltage, using a measurement or a simulation. The method may further comprise determining a second speaker displacement at the first loudspeaker input voltage, using a lumped element model. Using a linear lumped element model, the first loudspeaker input voltage may be adapted resulting in a third speaker displacement. A second loudspeaker input voltage may be determined at which the third speaker displacement equals the first speaker displacement. Using a non-linear lumped element model, the total harmonic distortion of the loudspeaker at the second loudspeaker input voltage may be determined.

[0037] The method may further comprise determining of at least one of the amplitude of the fundamental, the harmonics of the sound pressure, and the sound pressure intermodulation. The speaker displacement may be the displacement of a membrane of the loudspeaker from its rest position.

[0038] A software may be configured to execute the steps of determining a first speaker displacement of a loudspeaker at a first loudspeaker input voltage, by using a measurement or a simulation, determining a second speaker displacement at the first loudspeaker input voltage, by using a lumped element model, adapting the first loudspeaker input voltage resulting in a third speaker displacement and determining a second loudspeaker input voltage at which the third speaker displacement equals the first speaker displacement, by using a linear lumped element model, and determining the total harmonic distortion of the

loudspeaker at the second loudspeaker input voltage, by using a non- linear lumped element model.

[0039] The descriptions of the various embodiments have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art. [0040] Aspects of the present embodiments may be embodied as a system, method or computer program product. Accordingly, aspects of the present disclosure may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a "circuit," "module" or "system." Furthermore, aspects of the present disclosure may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon.

[0041] Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable readonly memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a software or program for use by or in connection with an instruction execution system, apparatus, or device.

[0042] Aspects of the present disclosure are described above with reference to flowchart illustrations of methods, and computer program products according to embodiments of the disclosure. It will be understood that each block of the flowchart illustrations and combinations of blocks in the flowchart illustrations, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, enable the implementation of the functions/acts specified in the flowchart block or blocks. Such processors may be, without limitation, general purpose processors, special-purpose processors, application-specific processors, or field-programmable processors or gate arrays.

[0043] The flowcharts in the figures illustrate the functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the flowchart illustration, and combinations of blocks in the flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

Claims

1. Method for simulating the total harmonic distortion of a loudspeaker, the method comprises: performing a linear simulation or measurement to determine a real speaker displacement; performing a linear or non-linear lumped element model prediction, wherein the resulting speaker displacement of the lumped element model is adapted to correspond to the real speaker displacement by tuning an input voltage of the lumped element model; and performing a non-linear lumped element model prediction using the tuned voltage as an input voltage, thereby simulating the total harmonic distortion.

2. The method of claim 1, further comprising simulating at least one of:

the amplitude of the fundamental;

the harmonics of the sound pressure; and

the sound pressure intermodulation.

3. The method of claim 1 or 2, wherein the speaker displacement is the displacement of a membrane of the loudspeaker from its rest position.

4. The method of any of claims 1 to 3, wherein the linear simulation comprises a finite element method (FEM) or a boundary element method (BEM).

5. The method of any of the preceding claims, further comprising:

performing a lumped element model prediction using a constant input voltage, wherein the constant input voltage results in a speaker displacement which differs from the real speaker displacement.

6. The method of claim 6, wherein a transfer function between the tuned input voltage and the constant voltage equals the transfer function between the real speaker displacement and the displacement predicted by the LPM prediction at the constant voltage.

7. The method of any of the preceding claims, wherein the tuned input voltage is used in a simulation which combines a LPM model and differential equations to simulate the amplitude of the fundamental and the harmonics in the sound pressure.

8. The method of any of the preceding claims, wherein tuning the input voltage allows to control the fundamental of the speaker displacement.

9. The method of any of the preceding claims, wherein the input voltage is a sine wave or a concatenation of pure sine waves at different frequency values.

10. The method of claim 9, wherein the input voltage is tuned for each of the different frequency values separately.

11. A software configured to execute the method steps of:

performing a linear simulation or measurement to determine a real speaker displacement; performing a linear or non-linear lumped element model prediction, wherein the resulting speaker displacement of the lumped element model is adapted to correspond to the real speaker displacement by tuning an input voltage of the lumped element model; and performing a non-linear lumped element model prediction using the tuned voltage as an input voltage, thereby simulating the total harmonic distortion.