Proceedings of the Institute of Acoustics

PROFESSIONAL SPEAKER USING SMART

TRANSDUCERS W. Klippel KLIPPEL GmbH, Dresden, Germany 1 INTRODUCTION

Loudspeakers use an electro-acoustical transducer (drive unit) which converts an electrical input signal via mechanical vibrations into sound pressure output. Most applications prefer an electro- dynamical transducer that uses a moving coil in a static magnetic field, a cone, and a mechanic suspension system. Those hardware components determine the loudspeaker’s maximum output, audio quality, size, weight, and cost. The progress in electroacoustical modeling, amplification, and digital signal processing provide new opportunities for pushing the transducer to the physical limits. New software algorithms actively compensate for undesired loudspeaker properties, increase system reliability and endurance, and provide other intelligent features that simplify product design, manufacturing, and maintenance. This paper gives an overview of recent developments essential for professional applications. 2 LOUDSPEAKER MODELING

Physical modeling is the basis for numerical simulation of the predicted loudspeaker behavior in an early design stage and also provides valuable a priori information for loudspeaker control.

A loudspeaker model providing sufficient accuracy with a minimum number of free parameters is essential for self-learning capabilities, adaptive parameter identification, robust control, and low implementation effort and processing load. 2.1 Black Box Modeling of Signal Distortion

The reproduced audio signal p ( t , r ) at a point r in the sound field is not identical with the original stimulus u ( t ) at the loudspeaker input. Figure 1 shows a signal flow chart comprising five subsystems that describe the generation of particular signal distortions.

H V ( f|t )

H L ( f , r )

p ( r ) u

p ID ( r )

n ( r )

sound

field u I

Irregular Dynamics

Noise source

N I

Figure 1 Signal flow chart describing the generation of signal distortion in loudspeakers

This signal flow chart is the basis for acoustic output-based testing defined in IEC standard 60268- 21 [ 4 ], which assesses the parameters of the subsystems and meaningful characteristics of the signal distortion summarized in Table 1.

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Table 1 Classification of signal distortion

Signal Distortion

Black Box Modeling Test Methods (IEC 60268-21 [4] ) linear (time- invariant)

Linear system with spatial transfer function H L ( f , r ) at any point r in 3D space

Wave expansion based on near-field scanning or directivity far-field measurements (linear) time- variant

Time-variant, linear transfer function H V ( f | t ) describes heating, aging, fatigue, climate

Amplitude compression reveals the variation of the SPL frequency response

nonlinear (regular)

Dominant loudspeaker nonlinearities N i generate equivalent input distortion u i

Harmonic and intermodulation distortion measurement (e.g., multi-tone stimulus)

abnormal sound

Irregular, nonlinear dynamics with random properties (rub&buzz)

Time-domain analysis (peak value and crest factor of impulsive distortion), higher- order harmonics noise Modeling not possible Noise floor measurement without stimulus or using a second microphone for detecting ambient noise

The spatial transfer function H L ( f , r ) describes the SPL and phase information of the direct sound at point r generated by the loudspeaker under free-field conditions. This function H L ( f , r ) represents not only the loudspeaker directivity, which is the angular dependency of the SPL at a constant far- field distance r but considers the complex near field properties.

All linear properties that change over time by heating, aging, climate, and other influences can be merged into a time-variant, linear transfer function H V ( f | t ) of a prefilter at the loudspeaker input in Figure 1, generating the same changes at all points in the sound field. It is assumed that all changes occur with a slow integration time constant (> 50 ms), generating new spectral components at low frequencies far below the audio band.

The loudspeaker nonlinearities limit the maximum output, reduce the audio quality, and require a compromise with the loudspeaker’s size, weight, and cost. They generate instantaneous variations of the loudspeaker parameters, which causes harmonic and intermodulations in the audio band. A nonlinear feedback system N i modeling the dominant nonlinearities generate equivalent input distortion u I added to linear input u shown in Figure 1. The linear transfer functions H V ( f | t ) and H L ( f , r ) distribute the equivalent input distortion u I with the linear signal part to any point in the sound field.

The abnormal sound p ID is generated by irregular dynamics caused by material properties (e.g., paper), complex manufacturing process, and diversity of possible loudspeaker defects. Voice coil bottoming is almost a deterministic mechanism. Still, most causes have semi-random properties, such as coil rubbing and modulated noise generated by air turbulence in a port or box leak. A loose particle (dirt) in the gap can cause a random incidence. Time-domain analysis of the isolated signal components reveals the particularities of each cause but shows a common property: Abnormal sound has an impulsive fine structure generating a high crest factor and a spectrum covering a wide range of the audio band. The irregular dynamics can neither be modeled, predicted, or actively compensated, but the impulsive distortions are not acceptable if audible.

While the audio signal or the test stimulus activates the irregular vibration, including the modulated air noise in the loudspeaker port, the electronics noise primarily generated in the microphone or other sensors is typically independent of the stimulus. Stationary noise can be assessed by performing an additional noise floor measurement with a muted input signal. Ambient noise generated by external sources is non-stationary. It requires a second microphone placed in the far-field to identify the corruptions in the sound pressure signal of the test microphone placed in the near-field of the loudspeaker by correlating the captured signals. 2.2 Lumped Parameter Modeling

Lumped parameter modeling is helpful at lower frequencies where the wavelength is much larger than the size of the mechanic or acoustic structures.

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K

Bl [N/A]

6

3,0

N/mm

nonlinear suspension

5

2,5

4

2,0

3

1,5

2

1,0

1

0,5

0,0

-6 -4 -2 0 2 4 6

-10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0

Displacement X [mm]

displacement x mm

inductance force factor stiffness radiation area

port resistance

L E (ω,x,i,t) F=Bl(x,t)i

R E (t)

F A

q q p S D (ω,x)

F rel (x,i) R L (ω,x,i,t)

i

R AP (q p )

C AB (x,p box )

M MS K MS (ω,x,t) -1 R MS (ω,v,t) -1 Bl(x,t)

Bl(x,t)v u

R AB

v

p

p box

M AP

C AR (p rear )

acoustical domain mechanical domain electrical domain

Figure 2 Equivalent circuit of a vented-box loudspeaker based on lumped parameter modeling considering nonlinear, time-variant behavior and frequency-dependency

Figure 2 shows, for example, the lumped parameter model of a vented-box system using an electro-dynamical transducer. A transformer with force factor Bl ( x,t couples the electrical with the mechanical domain. The gyrator with the effective radiation area S D ( ω,x ) connects the mechanical with the acoustical network. The moving masses M MS and M AP of the mechanics and air plug in the port, respectively, and the acoustical resistance R AB representing the box filling and air leakage are constant parameters. In contrast, the other lumped parameters depend on time, frequency, displacement x , and other internal state variables. The frequency dependency in R L ( ω,x,i,t ) and L E ( ω,x,i,t ) show that the lossy inductance generated by eddy currents cannot be lumped together into two parameters. Visco-elastic behavior of the suspension related to the mechanical creep causes a frequency dependency in the mechanical stiffness K MS ( ω,x,t ) and resistance R MS ( ω,x,t ). The effective radiation area S D ( ω,x ) also depends on frequency after cone break-up.

Power dissipation and ambient temperature change the coil temperature of the electrical resistance R E ( t ) which is the dominant cause for time-variant speaker behavior followed by the mechanical stiffness K MS ( ω,x,t ) due to aging, fatigue, and reversible material processes. Gravity, static air pressure and other forces change the voice coil rest position causing variation in the force factor Bl ( x,t ) and lossy inductance L E ( ω x,i,t ) .

Finally, most of the parameters in Figure 2 are nonlinear and depend on the instantaneous state and vary with coil displacement x , velocity v , current i , sound pressure p Box , and volume velocity q p in the port. For example, a large voice coil displacement can easily reduce the instantaneous electro- dynamical force factor Bl ( x,t ) to a quarter of the value at the rest position. At the same time, the mechanical stiffness K MS ( ω,x,t ) becomes four times higher, as illustrated in the nonlinear parameters in Figure 2. The lossy inductance shows a multi-variant dependency on current i , displacement x , and frequency f , as shown in the contour plot on the left-hand side in Figure 2. 2.3 Distributed Parameter Modeling

The cone vibration and sound radiation at higher frequencies require models with distributed parameters, as illustrated in Figure 3. The modal expansion separates the total vibration into independent modes. Each mode behaves as an independent mechanical resonator with a natural frequency f n , a modal loss factor η n , and a characteristic vibration pattern (mode shape ψ n ) becoming more complex with rising order n . Each mode contributes to the total sound radiated with a characteristic directivity. The modal vibration becomes nonlinear if the mechanical structure’s geometrical deformation is high and causes the variation of the effective radiation area S D ( ω,x ) versus displacement x in the lumped parameter modeling.

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Expansion Mode Shape Modal Expansion Transducer

Sound Field Spherical Wave

q 0

L E R E

F S

i

q

R G

Bl

-1 v 0

M C R 0

Blv

Z AL

monopole

u G

v

z

dipoles

q 1

quadrupoles

S

speaker

near-field

-1 v 1

M C R 1

far-field

y

Neumann function

y

(kr)

Bessel function

j

(kr)

n

n

q M

S M

x

-1 v M

M M C M R M

Figure 3 Distributed parameter modeling using modal expansion of mechanical vibration and spherical wave modeling required at higher frequencies

A second acoustic model based on a spherical wave expansion explains the sound propagation from the near-field to any point in the 3D space, as illustrated on the right-hand side in Figure 3. This expansion uses basic functions (spherical harmonics, Bessel and Neumann) that are wave equation solutions and separate the angular and radial dependency. Laser vibrometry and acoustical near- field scanning provide the free parameters modal and spherical wave expansion. The nonlinearities in the sound propagation from direct-radiating loudspeakers can be neglected because the sound pressure is relatively small. On the contrary, the high SPL in the horn-loaded compression loudspeaker can cause wave steepening and significant distortion. 2.4 Thermal Modeling

magnet,

voice coil

frame iron path

dome

coil

R tv

P tv P g

R tg

P mag

v

P con

T g T v T m

R tc (v)

R tt (v)

P coil

air convection

input current eddy currents

 T v  T m

 T g

R tm

cooling

C tv C tm

C tg

P eg

enclosure,

C ta R ta (x)

ambience

T a

Figure 4 Equivalent circuit representing the heat sources, power flow, and local temperatures in loudspeakers

Since direct-radiating loudspeakers usually have low efficiency, most of the electrical input power heats the voice coil. The equivalent circuit in Figure 4 models the heating, cooling, and transfer into the ambiance. The thermal capacities C tv , C tg, and C tm and the thermal resistances R tv , R tg, and R tm of the coil, gap, and magnet, respectively, determine important time constants of the thermal dynamics. Air convection cooling is a bypass from the coil to the ambiance, which depends on the voice coil displacement and velocity nonlinearly.

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2.5 Consequences for Control

Loudspeaker modeling provides valuable information for selecting the optimum control scheme providing maximum benefit for the user with a minimum cost (DSP). Table 2 Impact on performance, cost, and active loudspeaker control rated in four stages (-, *,**,***) from negligible to high rated by the author.

Model Parameters and Other Characteristics

Max SPL

Audio Quality

Spatial Sound

Reli- ability

Cost Size, Weight

Active Control

Resistance R e ( t ) *** - - - - - *** Inductance L E ( ω,x,i ) * ** - * ** * *** Force factor Bl ( x,t ) *** ** - ** *** ** *** Stiffness K ms ( ω,x,t ) ** * - *** - * *** Moving mass M ms ** - - - - - * Mech. resistance R ms ( ω,v,t ) - * - - - * Front and rear air compliances C AB ( x, p Box ) and C AR ( x , p rear )

* * - - - ** *

Port resistance R P ( q p ) * * - * - ** * Modal compliances C n ( t,x ) and resistances R n ( t )

* * * - - - * 1

effective radiation area S D ( ω,x )

*** * * - * ** * 1

nth-order mode shape ψ n * * ** - - * * 1 directivity, spatial transfer function H L ( f , r )

* ** *** - - * ** 2

Thermal resistances R tv , R tc ( v ), R ta ( x ), R tg, , R tm

** - - ** * * **

Thermal compliances C tv , R tc (v), R ta (x), C tg, , C tm

** - - ** * * **

Impulsive distortion (rub&buzz)

** *** - *** * * *

1 requires active control of multiple electromechanical transducers (shakers), exciting the radiator 2 requires active control of multiple electro-acoustical transducers in one loudspeaker

Table 2 summarizes the impact of the model parameters and standard characteristics on essential dimensions of the loudspeaker performance, weight, size, and cost, and opportunities for virtually improving the loudspeaker by active loudspeaker control. The maximum sound output represented by max SPL as defined in IEC 60268-21 [ 4 ] is limited by the electro-acoustical efficiency of the loudspeaker, primarily determined by the motor efficiency factor Bl 2 /R e , the moving mass M MS and the effective radiation area S D .

The voltage sensitivity of the transducer matched to the maximum current and voltage capabilities of the amplifier also limits the short-term SPL generated by the loudspeaker system. Conductive shorting materials (e.g., copper rings) placed close to the coil reduce the voice coil inductance L E ( x, i ) to improve the linearity of the speaker and the voltage sensitivity. The nonlinear dependency of force factor Bl(x) and stiffness K MS ( x ) limits the maximum peak displacement X max and the bass performance. Voice coil heating changing the resistance R e ( t ) and abnormal sound measured as impulsive distortion according to IEC 60268-21 [4] are essential limits for max SPL.

Impulsive distortion has a disastrous impact on audio quality and impairs the reliability of the loudspeaker because it indicates an overload or defect of the speaker. Intermodulation distortion generated by Bl ( x ) and L e ( x, i ) spread over the entire audio band and cause an unnatural roughness in the reproduced sound, which is more critical than the common nonlinear distortion generated by K MS (x) limited to lower frequencies.

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The DC displacement caused by Bl ( x ), L e ( x, i ), K MS ( x ) , and other loudspeaker nonlinearities shifts the voice coil away from the optimum working point usually defined by the rest position. This DC displacement can generate an unstable behavior that reduces max SPL, causes unacceptable distortion, and damages the loudspeaker, reducing the product’s reliability in the target application.

The modal parameters C n ( t,x ), R n ( t ) and S D ( ω,x ), the mode shape of the mechanical vibration ψ n , and the spatial transfer function H L ( f , r ) represented by the coefficients of the spherical wave expansion is essential for the 3D sound applications.

The force factor characteristic Bl ( x ) is very sensitive for the application’s cost, size, and weight, depending on the magnet material used. The effective radiation area S D ( x,f ) and the acoustic parameters of the vented or sealed enclosure with and without passive radiators define the loudspeaker’s size and weight. A larger port diameter reduces the nonlinear distortion and modulated noise from air turbulence.

The last column in Table 2 shows that active transducer control provides new opportunities for virtually modifying all critical speaker parameters and detecting irregular distortion in the target application. The measurement or modeling of the instantaneous voice coil temperature T v allows active compensating for the amplitude compression caused by the time-varying resistance R E ( t ) while providing thermal loudspeaker protection.

Adaptive nonlinear control can reduce time-variant and nonlinear distortion generated by the transducer nonlinearities represented by the lumped parameter model in Figure 2. This linearization requires an active stabilization of the voice coil position and mechanical protection. Thus, the passive transducer can safely operate in the nonlinear region, giving more max SPL from smaller speakers while using less input power and resources.

The active corrections of the spatial transfer function H L ( f , r ) require multiple exciters to control modal vibration on a sound radiating surface (e.g., baffle) or use various speakers for beamforming and other spatial sound control techniques.

Active control can not cancel abnormal sound with random properties, but the protection system can operate the transducer in the intended working range to avoid irregular vibration generation. 3 ADAPTIVE NONLINEAR CONTROL

This section shows how the results of loudspeaker modeling can be used for adaptive nonlinear control of moving-coil transducers and complete loudspeaker system based on current sensing, as illustrated in Figure 5.

w ( t ) u l ( t )

Mirror

p ( t, r )

Filter Equalization Protection

audio stimulus

u off

transducer in

Stabilization x off

enclosure

P

current

i ( t ) DSP

Detector

sensor

Transducer Diagnostics

Figure 5 Block-diagram of an active loudspeaker system with adaptive, nonlinear loudspeaker control [1 ] based on KCS-technology.

The KCS technology [10] uses the mirror filter to compensate for time-variant and nonlinear distortion modeled by lumped parameters in Figure 2.

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Loudspeaker

Mirror Filter

(Model)

(DSP)

H V ( f|t ) -1

H V ( f|t )

H L ( f , r )

p ( r ) u

w

- w

sound

u I

field u I

N I

N I

Figure 6 Active compensation of the nonlinear and time-variant loudspeaker distortion by the mirror filter

The mirror filter [ 8 ] uses two subsystems in a feed-forward structure. The first subsystem H V ( f | t ) -1 is the inverse function of H V ( f | t ) in the loudspeaker model and compensates for the linear time-varying loudspeaker behavior. The nonlinear subsystem N I generates the same equivalent input distortion u I subtracted from the linear signal. The digital input signal w becomes identical with w’ at the input of the spatial transfer function H L ( f , r ), and the undesired nonlinear and time-variant distortions are reduced at all points in the sound field. Typically the distortion reduction is about 6 dB … 20 dB depending on the test stimulus, the loudspeaker, and other measurement conditions.

Total Harmonic Distortion

40

without linearization

35

30

THD in percent

25

-20dB

20

15

with linearization

10

5

0

40 60 80 100 200 Frequency in Hz

Figure 7 Total harmonic distortion in the sound pressure output of a woofer measured without and with linearization using the mirror filter [1]

For example, Figure 7 shows a total harmonic distortion (THD) measured on a woofer operated in a sealed enclosure. The plain loudspeaker without linearization generates about 40 % distortion at an excitation frequency of 80 Hz, where a high voice coil displacement activates the nonlinear parameters Bl ( x ), K ms( x ) , and L e ( x, i ) . The mirror filter cancels the dominant distortion leaving a residuum of 5 % caused by unmodelled dynamics.

Sound pressure spectrum p(f) of reproduced multi-tone signal

80

70

Fundamental

Fundamental (with linearization)

dB

60

50

without linearization

Distortion

40

-15 dB

30

20

With linearization

10

50 100 200 500 1k 2k

Frequency in Hz

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Figure 8 Fundamental components and nonlinear distortion in a multi-tone test stimulus without and with linearization using the mirror filter [1 ]

The conventional measurement of the total harmonic distortion with a single tone at a particular frequency reveals the most critical excitation frequency. Still, it does not assess intermodulation distortion generated only by multiple spectral components in music. Figure 8 shows the distortion reduction of the same woofer reproducing a multi-tone stimulus simulating typical program material. The active linearization can reduce all distortion by more than 10 dB over a wide frequency range.

The mirror filter generates no additional latency, is stable, and requires a low processing load. The control parameters P in the mirror filter correspond to the lumped parameters in Figure 2 and Figure 4. Production variances, aging, climate, and other influences require a permanent measurement of the model parameters while reproducing any audio signal in the target environment.

A detector shown in Figure 5 optimally estimates the loudspeaker parameters P and checks the parameter’s physical plausibility before they update the control parameters in the mirror filter. Such an adaptive control scheme needs a sensor for sensing the transducer’s electrical, mechanical or acoustical state. A mechanical sensor requires access to moving parts (e.g., diaphragm) and additional hardware, increasing costs. Sound pressure measurements, performed with inexpensive MEMS microphones in the near-field, are corrupted by ambient noise, disturbing the parameter measurement.

Therefore, monitoring the electrical voltage and current at the speaker terminals is a robust and cost-effective alternative. Suppose that the power amplifier supplies the terminal voltage with a linear and time-invariant transfer behavior. In this case, it is sufficient to measure only the current and use a predicted voltage, as shown in Figure 2. The transducer operated in the loudspeaker as an actuator also becomes a sensor for its mechanic and acoustic states. The back EMF generated as a voltage Bl ( x ) v on the electrical side reveals the velocity distorted by the nonlinear force factor modulation Bl ( x ) . Thus detector in Figure 2 has to compensate for those nonlinearities to accurately estimate the speaker parameters, voice coil displacement, velocity, and other acoustic variables in the equivalent circuit in Figure 2. This part of the KCS technology is widely used as a measurement instrument (LSI in KLIPPEL Analyzer System) to identify the nonlinear speaker parameters.

The detector measures the instantaneous voice coil offset X off from the initial rest position caused by production variance, fatigue, and external influences [ 1 ]. A stabilization system in Figure 5 generates an electrical DC voltage U off and shifts the coil back to the optimum working point. The active X off compensation ensures full peak-to-peak displacement giving maximum bass, high efficiency, and reduced peak voltage requirements.

The protection system uses the updated transducer parameters to automatically adjust the maximum peak displacement X max and other protection limits to ensure reliability during product life. A close link between online diagnostic and protection is essential to cope with the changes in the mechanical suspension, increasing the risk for rocking modes, voice coil rubbing, and other subsequent faults. The status of the natural aging process is a piece of essential diagnostic information to replace a transducer module in time.

Linearization, stabilization, protection, and diagnostics are required to cope with time-variant and nonlinear speaker properties. An equalizer shown in Figure 5 can be applied to the input signal to correct the SPL response at a particular point r in the sound field, the mean SPL in an acoustical zone, or the total sound power radiated from the loudspeaker.

An automatic system alignment provides a desired target system function (e.g., Butterworth with a specified cut-off frequency) for any transducer and enclosure type. A protection system copes with the bass boost and keeps the displacement, terminal voltage, and voice coil temperature in permissible limits for any input signal supplied to the loudspeaker. 4 ACTIVE TRANSDUCER MODULE

The new software opportunities provided by adaptive, nonlinear control accelerate changes in the hardware components. DSP, amplification, and transduction will eventually merge into one active module, as illustrated in Figure 9.

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enclosure

port

shielding

current sensing

output

filter

cone

audio

i ( t )

input

voice

DSP

w ( t )

amplifier

coil

x(t)

U =

supply voltage

C

gap

microphone

digital control interface

optional

Figure 9 Smart transducer module comprising digital signal processing, amplification, and electro- acoustical conversion [1 ]

The hardware changes are motivated by the Green Speaker Design paradigm [3], maximizing the electro-acoustical efficiency without increasing cost, size, or weight:

Placing the amplifier and voice coil closer together reduces electrical losses in the cables. The Class D amplifier uses a simplified output filter compliant with EMC because the iron path, magnet, and frame provide sufficient shielding. A reduced coil resistance ( R e < 2 Ohm) improves the voltage sensitivity of the transducer required to generate the maximum SPL for a limited peak voltage and peak current provided by the power amplifier. The amplifier tolerates a varying supply voltage caused by a relatively thin wire diameter.

A short voice coil overhang exploiting the fringe field outside the air gap increases the motor efficiency factor ( Bl ) 2 / R e and reduces the moving mass M MS . The iron path and inexpensive shorting material reduce the voice coil inductance and improve the voltage sensitivity at higher frequencies. The mechanical suspension has a reduced stiffness K MS ( x ) in the intended working range - X max ≤ x ≤ X max while keeping imbalances in mass and stiffness distribution and rocking modes small. This design sacrifices transducer linearity for efficiency and requires active nonlinear control to cope with the increased nonlinear distortion and endurance.

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Table 3 Important characteristics of the transducer module

Characteristics Condition Spatial transfer function H L ( f , r )

Transducer operated in free field in a half-space (2 π ) at small and high amplitudes (protection not active) Directivity index D I ( f ) free field, far-field, half-space (2 π ) max SPL Maximum SPL (IEC 60268-21 [ 4 ]), on-axis, 1 m distance, free-field measured in a short-time test with a pink noise stimulus in the rated frequency range, short-time measurement (1 min), endurance tested with the same stimulus for 100 h Effective radiation area S D

below cone break-up

Maximum displacement X max

with adaptive, nonlinear control (linearization, stabilization, and protection) Minimum box air volume V mBox

transducer mounted in a sealed enclosure with internal air volume V mBox generates X max for a low-frequency stimulus Voltage supply range u =min < u = < u =max

required for generating max SPL

Maximum supply current i =max

required for generating max SPL at minimum voltage supply u =min

Weight, size, cost without enclosure A few meaningful characteristics listed in Table 3 describe the acoustic performance of the active transducer module mounted in an infinite baffle giving perfect half-space condition. The spatial transfer function H L ( f , r ) represents the sound pressure output at any point r in the sound field over the product life for any signal amplitude as long as the transducer needs no active protection. The directivity index D I ( f ) is a far-field characteristic that compares the sound generated on-axis with the total sound radiated in all directions. The directivity index depends on the geometry of the radiating surface, is time and production invariant, and can not be changed by controlling one transducer module.

Max SPL, rated according to IEC 60268-21 [ 4 ], describes the maximum output generated with a broadband stimulus. The product of effective radiation area S D and maximum displacement X max limits the bass performance of direct radiating loudspeakers. The active transducer module operated in a sealed box can generate the peak displacement X max if the enclosed air volume is larger than V mBox .

The transducer module can only generate the max SPL if the power supply complies with the voltage and current requirements of the transducer module. The active protection system prevents an overload of the transducer and amplifier and limits the maximum output if the battery needs charging in portable applications. Finally, the weight, size, and cost must be considered to select a suitable active transducer module for a particular application.

5 LOUDSPEAKER SYSTEM DESIGN

The selected transducer module can be operated in any enclosure type, sealed, vented, or with or without an additional passive radiator (drone). An automatic measurement on a prototype identifies the acoustical load and generates the control parameters required to create the optimal system alignment in all manufactured units.

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Table 4 Additional characteristics of the transducer module required for system design

Characteristics Condition Displacement transfer function H w,u ( f , r r )

describes the relationship between control input w and displacement x at the point r r on the radiation surface at small amplitudes Linear and time-invariant lumped parameters

electric, mechanic, acoustic and thermal parameters of the active transducer with adaptive, nonlinear control Nonlinear lumped parameters loudspeaker nonlinearities Bl ( x ), L E ( x,i ), K ms ( x ), R ms (v), R AP ( q p ) Maximum amplifier output peak voltage U AMP

provided by the power amplifier under normal supply voltage and current Maximum voice coil temperature

rated by the transducer manufacturer in Celsius

However, a numerical simulation based on additional module characteristics in Table 4 can optimize directivity, max SPL, size, weight, energy consumption, and heat transfer in the loudspeaker system before finishing the prototype. For example, the displacement transfer function H w,u ( f , r r ) measured by laser vibrometry according to IEC 60268-22 [ 7 ] is required for boundary element analysis (BEA) to find the optimal geometry of the enclosure surface and horn shape. The lumped parameters of the transducer module are essential for designing port and passive radiator. The nonlinear transducer parameters and maximum values of the amplifier output and voice coil temperature are the basis for defining the limits of the active protection system. 6 SELF-TEST

The active, nonlinear control compares the measured and predicted electrical input current and generates an error signal from lumped parameter modeling to reveal any electrical, mechanical or acoustical problem in the loudspeaker. However, the electrical measurement is less sensitive for detecting irregular vibrations causing impulsive distortion in the sound pressure output. At least one microphone placed behind the cone, as illustrated in Figure 9, measures reliable symptoms of the loudspeaker defects with a good signal-to-noise ratio. The combination of electric and acoustic sensors is sufficient to perform a comprehensive quality assurance test in manufacturing the transducer module and the complete loudspeaker system and regular maintenance in the target application or at a service station. An artificial test stimulus (e.g., sinusoidal chirp) provides the most critical excitation and simplifies the detection of the impulsive distortion following IEC 60268-21 [ 4 ]. Online loudspeaker monitoring of abnormal sound while reproducing any audio signals in the target application requires adaptive modeling of the microphone signal, which requires additional processing load in the DSP. 7 CONCLUSION

Combining DSP, amplifier, transducer, and sensor in one active transducer module provides new software opportunities to improve the performance of the loudspeaker hardware:

• DSP algorithms reduce undesired signal distortion and generate a desired (linear) relationship between electrical input and acoustical output, • Sensors monitor voice coil displacement, temperature, and other internal transducer states and external influences, • The transducer protects itself against mechanical and thermal overload generated by the electrical input signal, • The monitored information adaptively corrects production spread and other time-variant properties over product life for any audio stimulus, • Online diagnostic detects hardware malfunction, • Self-testing simplifies end-of-line testing and maintenance. The active transducer module with the new intelligent features becomes a partially autonomous system that simplifies the design, manufacturing, and integration in more complex sound systems.

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Green Speaker Design [ 2 ] increases the acoustic output (max SPL) from smaller, lighter, and more cost-effective transducers by maximizing efficiency in the passive components and actively compensating for nonlinear signal distortion.

There is also more freedom for the design of the port, enclosure, and other acoustic loads by providing an automatic alignment of the overall transfer function. Beamforming, wave field synthesis, and other 3D sound applications using many loudspeakers can assume that the loudspeaker properties are identical and time-invariant.

The adaptive compensation of parameter variances allows less tight limits for fundamental resonance and voice coil rest position caused by the mechanical suspension. Thus, manufacturing can focus on irregular vibrations causing abnormal sound and impairing the product’s reliability.

Online diagnostics and self-testing provide valuable information over product life to replace a transducer module before a total failure occurs. This collected data is beneficial for suppliers and manufacturers to select, for example, better suspension materials reducing fatigue and improving endurance under harsh climate conditions.

The active transducer module is beneficial for professional equipment used on stage and fixed installations and for automotive, home, and other consumer applications. 8 REFERENCES

[1] W. Klippel “Novel Loudspeaker and Headphone Design Approaches Enabled by Adaptive Nonlinear Control” J. Audio Eng. Soc., vol. 68, no. 6, pp. 454–464, (2020 June.). DOI: https://doi.org/10.17743/jaes.2020.0037

[2] W. Klippel, “Green Speaker Design (Part 1: Optimal Use of System Resources),” presented at the 146th Convention of the Audio Eng. Soc. in Dublin (March 10, 2019), paper 10138.

[3] W. Klippel, “Green Speaker Design (Part 2: Optimal Use of Transducer Resources),” presented at the 146th Convention of the Audio Eng. Soc. in Dublin (March 10, 2019), paper 10139

[4] Sound System Equipment – Part 21: Acoustical (output-based) Measurements, IEC 60268- 21

[5] W. Klippel, “Loudspeaker Nonlinearities – Causes Parameters, Symptoms,” J. Audio Eng. Soc. vol. 54, no. 10, pp 907 – 939 (Oct. 2006).

[6] W. Klippel, “Nonlinear Modeling of the Heat Transfer in Loudspeakers,” J. Audio Eng. Soc. vol. 52, no. 1/2, pp. 3-25, (2004).

[7] Sound System Equipment – Part 22: Electrical and Mechanical Measurements on Transducers, IEC 60268-22

[8] W. Klippel, “The Mirror Filter - a New Basis for Reducing Nonlinear Distortion Reduction and Equalizing Response in Woofer Systems,” J. Audio Eng. Soc. vol. 32, no. 9, pp. 675-691, (1992).

[9] Sound System Equipment – Electro-acoustical Transducers – Measurement of Large Signal Parameters, IEC 62458

[10] KLIPPEL Controlled Sound (KCS), https://www.klippel.de/products/klippel-controlled- sound.html

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