Active Transducer Protection Part 1: Mechanical Overload
Wolfgang Klippel, KLIPPEL GmbH, Dresden, Germany
The generation of sufficient acoustical output by smaller audio systems requires maximum exploitation of the usable working range. Digital preprocessing of audio input signals can be used to prevent a mechanical or thermal overload generating excessive distortion and eventually damaging the transducer. The first part of two related papers focuses on the mechanical protection defining useful technical terms and the theoretical framework to compare existing algorithms and to develop meaningful specifications required for the adjustment of the protection system to the particular transducer. The new concept is illustrated with a micro-speaker and the data exchange and communication between transducer manufacturer, software provider and system integrator are discussed.
technical paper, which addresses the specification of transducer characteristics to simplify the 1. INTRODUCTION communication between transducer manufacturer, In many audio applications, the required acoustical software provider and system integrator. Test output has to be reproduced at sufficient quality by procedures and rating methods have been developed in using smaller, lighter and efficient transducers. The this paper to specify the maximal voice coil excursion maximum voltage provided by available power Xmax required for tuning the protection systems in smart amplifiers is usually large enough to move the voice amplifiers. Two related papers presented here follow coil to the maximum mechanical boundaries generating this approach and investigate this interesting topic in a mechanical overload and impulsive distortion, which greater detail to improve the definition of the technical have a high impact on the perceived sound quality. The terms and to develop a common framework for heating of the coil is a second mechanism, which may evaluating different protection schemes. damage the transducer. Micro-speakers as used in personal audio devices are a critical example because Attenuation element Transducer audio amplifier the suspension system provides no natural protection of signal Variable the coil as found in normal woofers with a progressive w(t) High-pass spider. Amplifiers used in mobile phones can provide v(t) significantly more power than the micro-speaker can handle safely. This discrepancy causes the need for Mechanical Tv,max Thermal Displacement xrel active protection, which is the most important feature of Attenuation Attenuation smart amplifiers. Control Control The basic requirements and most important goals of X protection systems are: p± voice coil temperature Tv(t) Protection Transducer Limits States • Reliable protection of the transducer against mechanical and thermal overload for any audio input. • Maximum of acoustical output • Minimum of additional signal distortion and other Figure 1 Input information required by an active artifacts degrading sound quality protection system • Minimum delay increasing the latency in the audio path The first paper presented here addresses the mechanical • Cost-efficient implementation protection while the following paper is dedicated to the thermal protection. The mechanical overload can be A variety of ideas and solutions for this important and prevented by activating a high-pass filter as depicted in challenging issue has been developed so far and is Figure 1 and attenuating only low frequencies which accessible as patent literature [1-16]. The paper contribute to the voice coil displacement xrel(t). The presented by Vignon and Scarlett [17] is the first thermal protection requires the attenuation of low and
high frequency components which increase the voice L xabs (t) L (2) coil temperature Tv. Mechanical and thermal control systems activating the corresponding attenuation The boundaries L+ and L- depend on the particular elements require the absolute voice coil position xabs(t) or relative voice coil displacement x (t) and design, but are considered as time invariant and rel independent of the particular device under test (DUT). temperature T (t), which are the critical state variables v The positive and negative clearances indicating the two overload conditions. The information can be provided by direct measurement of the X clear (t) L X 0 (t) transducer state or by transducer modeling. (3) X clear (t) L X 0 (t) The attenuation control also shown in Figure 1 represent the distance between the instantaneous rest compares the measured or modeled state variables with position X0(t) and the upper and lower boundaries L±, protection limits, which describe the limits of the and give the theoretical limits of the voice coil permissible working range. displacement xrel(t). However, the attenuation control system uses the maximum positive and negative 2. DEFINITIONS protection limits
X p (t) xrel (t) X p (t) The instantaneous position of the voice coil (4) X clear (t) M xrel (t) X clear (t) M x (t) X (t, DUT) x (t) (1) abs 0 rel which are the clearance values reduced by safety margins M+ and M- to cope with inaccurate state depends on the voice coil rest position X0(t,DUT) and information and the reaction time of the attenuation the voice coil displacement xrel(t) generated by the audio control system. signal w(t). The voice coil rest position X0(t,DUT) is a (slowly) varying transducer parameter depending on the particular device under test (DUT) due to production xabs spread. It also changes over time t due to aging, viscoelasticity, gravity, load and climate. L+ M+ xabs Xclear+(t) upper boundary x (t) L+ x (t) Xp+(t) AC rel 2X M safety AC + margin xDC (t) upper upper X 0 (t) Xclear+(t) X (t) clearance protection limit 0 xrel (t) X 0 Xp+(t) Xp-(t) X 0 (t) rest position Xclear-(t)
Xp-(t) M- lower X (t) clearance clear- L lower - protection limit
M safety - margin L- lower boundary Figure 3 DC-component xDC(t) and AC-component xAC(t) of the voice coil displacement and the influence of an offset ΔX0(t) in the voice coil rest position Figure 2 Limits and other characteristics describing the permissible displacement of the voice coil. The mechanical protection shall ensure that the While reliable protection under all circumstances is the instantaneous voice coil position stays in the primary goal, the protection system shall reduce the permissible working range: input signal only to prevent an overload situation. An overreaction of the protection system would reduce
acoustical output, which is related to the AC close to the geometrical center of the boundaries L+ and displacement : L- generating symmetrical clearances:
xAC (t) xrel (t) xDC (t) (5) X clear X clear L L / 2 (11)
The DC component xDC(t) shifts the voice coil away Furthermore, the transducer manufacturer spends from the instantaneous rest position X0(t) but generates significant effort to reduce the asymmetries in the no acoustical output. The DC component xDC(t) which nonlinear stiffness Kms(x) and force factor Bl(x) and to may be in the same dimension as the AC components keep the generated DC displacement xDC(t) small. xrel(t) is generated by transducer nonlinearities Unfortunately, production spread and the influence of rectifying the audio signal [21]. Contrary to the voice acoustical load in the audio system, aging of the coil rest position X0(t), the DC component xDC(t) is a suspension, gravity and climate may generate an offset fast varying signal component depending on the in the rest position: instantaneous properties of the audio signal. This is a critical problem in transducers with a soft suspension, X o (t) X 0 (t) X 0 (12) especially in micro-speakers, as investigated by Vignon This offset reduces the clearance on one side of the coil et. al. [17]. and generates asymmetries in the nonlinearities which A useful criterion for assessing the performance of the may additionally increase the DC component xDC(t). protection system is the nominal maximum amplitude XAC(t) which limits the desired AC-signal 3. OVERVIEW ON PROTECTION SCHEMES X AC xAC (t) X AC (6) 3.1. Attenuation Control while assuming that the audio signal w(t) has a symmetrical probability density function pdf(w(t)). The attenuation control element in Figure 1 activates the The end-of-line test completing the manufacturing high-pass filter which attenuates the low frequency process can provide valuable statistical information components in the audio signal w(t) to keep the which describe the initial properties (t=0) of devices following peak value of the displacement signal within under tests (DUTs) such as the mean initial voice coil the protection limits Xp+ and Xp+. The mechanical rest position attenuation control element receives the instantaneous displacement signal xrel(t) depending on the attenuated 1 ND audio signal v(t). This feedback structure can cope with X X (t 0,n ) (7) 0 N 0 DUT the time-variant and nonlinear transfer responses of the D nDUT attenuator and transducer and the properties of the and the mean initial positive and negative clearances instantaneous audio signal w(t).
N D x 1 rel X (t ) X X (t 0,n ) (8) peak 0 clear N clear DUT D nDUT Xe(t) Envelope averaged over a representative number ND of DUTs. Protection The Golden Reference DUT selected in end-of-line limit testing has properties close to those initial mean values. Xp+(t) The initial value of the maximum positive and negative protection limits of the displacement t X p (t 0) X clear M x (t) 0 t (9) rel X p (t 0) X clear M Xp-(t) are the initial clearances reduced by the safety margins Protection M+ and M-. limit dx ( t ) The transducer manufacturer is interested in maximizing rel dt Envelope the nominal maximum amplitude XAC by placing the voice coil at the optimum rest position
X L L / 2 (10) 0 Figure 4 Anticipation of the peak displacement at an overshoot case
The attenuation control system has to cope with the xrel(t) with the protection limits Xp± and attenuates the restoring force and inertia of the mass-spring system input signal w(t) and the delayed input signal w(t-τ) generating a low-pass characteristic between terminal simultaneously. If the time delay τ is large enough the voltage u(t) and voice coil displacement xrel(t). The modeled displacement xrel may temporally exceed the inertia of the moving mass causes a further increase of allowed protection limits but the voice coil of the the displacement xrel(t) even if the electrical input signal transducer will stay within the permissible limits. This is switched off. The displacement maximum xpeak= approach requires a transducer model and increases the xrel(t0) occurs at the instant of time t0 where the gradient latency in the audio path, which is undesired in many (velocity) becomes zero and all kinetic energy Wkin of applications. the coil is stored as potential energy Wpot in the suspension. Considering the total energy Wtot in the audio transducer mass-spring system without external excitation and signal Attenuator Latency dissipation w(t) Delay (high-pass) v(t-τ ) In DAC
Wtot Wkin Wpot const. Attenuator 2 (high-pass) (13) Parameter dxrel (t) M ms 2 Kms 2 Kms x (t) x Mechanical Measurement dt 2 rel 2 peak 2 Attenuation Control the maximum displacement v(t) xrel(t) displacement 2 1 dx (t) Non-adaptive transducer 2 rel Linear Model parameters X peak (t) xrel (t) (14) 2f s dt
can be anticipated based on the instantaneous Figure 5 Protection based on transducer states predicted displacement xrel(t) at an earlier time (t which describe the acceleration and deceleration of the (21) coil in transient excitation phases [11]. Xo (t) X0,meas (t) X 0,meas defined as the difference between instantaneous and 3.2. State Information initial rest position. The total safety margins for the state measurement The attenuation control element needs accurate technique information on the instantaneous voice coil position as M M M early as possible to activate the attenuator in time. This m act information can be provided either by direct state (22) M M m M act measurement or by indirect state modeling combined with a parameter measurement. only comprise a first component Mm coping with the measurement error 3.2.1. Measurement emeas (t) xabs(t) xmeas (t) (23) A displacement sensor depicted in Figure 6 provides the and the activation margin Mact required to cope with measured voice coil position xmeas(t) with minimum delay to the mechanical attenuation control system. inertia of the moving transducer parts and the delay in the audio path (DAC) and measurement path (ADC). The margin Mact for state measurement can only be audio amplifier mechanical reduced by anticipating the peak value in accordance signal Sensor Attenuator Latency w(t) with chapter 3.1.2. (high-pass) In DAC xabs transducer t=0 t>0 Attenuation L+ M+ Control Voice coil position xmeas(t) MDC++M0+ Xclear+(t) X Xp+(t) Figure 6 Protection based on measured transducer states clear x (t) Xp+(0) 2X rel X 0 (t) AC Averaging of the measured signal xmeas(t) over a large X0(t) time window (Tm >> 1/f) gives the instantaneous voice X 0 2XAC coil rest position X (0) Xp-(t) X (t) Tm p- clear- 1 X clear X (t) x (t )d 0,meas meas (17) MDC-+M0- Tm 0 , M L - and the voice coil displacement: - xrel (t) xmeas (t) X 0,meas (t) (18) Figure 7 Protection limits for state measurement (SM) and adaptive nonlinear modeling (ANM). The initial mean rest position defined by The maximum positive and negative protection limits of N D 1 the displacement X 0 X 0,meas X 0,meas (t 0,nDUT ) (19) N D n DUT X p (t) X p (0) X 0 (t) can be determined by measuring the Golden Reference X clear M X 0 (t) DUT representing the mean production yield. (24) X (t) X (0) X (t) The varying rest position detected by state measurement p p 0 gives the instantaneous clearances X clear M X 0 (t) X clear (t) X clear X o (t) are not constant but vary with the offset ΔX0(t) over time (20) as illustrated in Figure 7. The voice coil offset ΔX0(t) X clear (t) X clear X o (t) and a DC displacement xDC(t) requires no additional depending on the measured offset in the voice coil rest safety margins M0± and MDC±, respectively, because position they are directly monitored in the measured absolute voice coil position. However, both effects reduce the AC displacement and the acoustical output if the coil caused by modeling error eAC(t), offset in voice coil rest move to one of the boundaries. position ΔXo(t) and a DC displacement xDC(t) generated dynamically by transducer nonlinearities. The nominal maximum amplitude The AC margin (1Uact )X p (0) M DC M 0 X Min (25) AC M AC M AC,spread M AC,time (30) (1Uact )X p (0) M DC M 0 can be derived from the minimum of the negative and copes with the modeling error of the AC displacement positive protection limits Xp± reduced by the eAC (t) espread (t) etime(t) edist (t) eres (t) (31) undershoot factor Uact and margins MDC± and M0± describing the maximum shift of the voice coil rest considering the variation of the transducer properties position ΔX0(t) and maximum DC displacement. due to production spread and temporal changes of the transducer parameters over time. The nonlinear signal 3.3. Transducer Modeling edist(t) comprises harmonics and intermodulation distortion. The nonlinear distortion at frequencies above The attenuation control system in section 3.1.1 requires resonance frequency provide only a small contribution an accurate transducer model to provide the voice coil to the total displacement and can be neglected in the displacement xrel(t) earlier before this state variable is context of mechanical protection. However, the generated by the transducer. A linear model with fixed nonlinear distortion at excitation frequencies (f < fs) parameters is the simplest solution but neglects the time may cause a nonlinear compression C of the variance and transducer nonlinearities. Adaptive fundamental component (typically 2 dB < C < 6 dB). schemes provides updated estimates of the transducer This effect is not considered in the safety margin in Eq. parameters and simplify the initial identification. (30) because it reduces the acoustical output and Nonlinear modeling and active linearization provides relaxes the mechanical load. The residual error eres(t) the highest accuracy and copes with DC displacement represents the visco-elastic behavior, hysteresis and and offset of the rest position. other mechanisms which are not considered in current modeling. 3.3.1. Non-adaptive Linear Modeling The margins M M M 0 0,spread 0,time The voice coil displacement (32) M 0 M 0,spread M 0,time x (t) x (t)S (v(t), P ) rel lin LDE lin (26) correspond to the varying rest position X 0 (t) X 0 X 0,spread (DUT) X 0,time(t) (33) is a part of the solution SLDE of a set of linear differential equations (LDE) with time invariant depending on the particular device (DUT) and time t. parameters Plin(t)= Plin(t=0). This model can be realized as a digital IIR-filter receiving the attenuated audio signal v(t) as an input and generating a linear approximation xlin(t) of the displacement xrel. The protection limits X p (t) X p (0) X clear M (27) X p (t) X p (0) X clear M are time invariant and depend only on the initial clearances and the total safety margins: M M AC M 0 M DC M act (28) M M AC M 0 M DC M act The first three components of the total margin correspond to the positioning error x (t) (x (t) X ) abs lin 0 (29) eAC (t) X o (t) xDC (t) xabs (36) xrel (t) xlin(t)SLDE (v(t), Plin(t)) t=0 t>0 L+ as the solution of the linear differential equation using time varying linear parameters Plin(t) which are M+ permanently updated by measured voltage and current Xclear+(t) at the transducer terminals while reproducing an audio signal. xrel (t) X clear Xp+(0) Xp+(t) 2XAC X 0 (t) Like the LM scheme, the ALM protection scheme uses X0(t) constant protection limits Xp±(t)=const. defined in Eq. X 0 2XAC (27) and the safety margins Xp-(0) Xp-(t) M M 0,spread M 0,timeM DC M act M m Xclear-(t) (37) M M 0,spread M 0,time M DC M act M m X clear corresponding to the positioning error M- L- xabs (t) (xlin(t) X 0 ) (38) Figure 8 Protection limits for non-adaptive linear eAC (t) X o (t) xDC (t) em (t) modeling (LM) and adaptive linear modeling (ALM). comprising error components as discussed earlier related to Eq. (29) for the LM protection scheme. The The linear model used in LM protection scheme cannot margin Mm represents the adaptive modeling error em(t) model monitor the nonlinear compression and has the which may be increased as long as the model has not tendency to predict a larger displacement and to activate learned the varying transducer properties, climate the attenuator without an overload. The resulting conditions and sudden changes in the acoustical undershoot reduces the acoustical output and the environment. The margin Mm in Eq. (37) is much nominal maximum amplitude smaller than the margin MAC required in the LM scheme because variations of the linear parameters are identified (1Uact )Fcom X p (0), X Min after a short learning time. The AC error eAC(t) in Eq. AC (34) (38) describes the nonlinear compression of the AC (1Uact )Fcom X p (0) signals while the time variance of the linear parameters which is the minimum of the negative and positive is compensated by the adaptive scheme. The DC displacement xDC(t) and the offset ΔX0(t) provide the protection limits Xp± reduced by the reduction factor largest contribution to the safety margins. C / 20dB Fcom 10 (35) corresponding to the nonlinear compression C in dB and attenuator amplifier transducer Attenuator Latency the undershoot factor Uact of the attenuation control. w(t) DELAY (high-pass) v(t-τ ) DAC audio amplifier transducer signal voltage Attenuator Latency Attenuator Latency w(t) DELAY ADC (high-pass) DAC (high-pass) v(t-τ ) displacement Mechanical Latency audio Attenuation ADC voltage v(t) signal Control current Attenuator Latency xrel(t) ADC (high-pass) ΔX0(t) Nonlinear Mechanical Latency Nonlinear Adaptive Attenuation Pnlin(t) ADC Model Model v(t) Control current parameters displacement Linear Linear xrel(t) Adaptive Figure 10 Protection based on transducer states Plin(t) Model Model predicted by an adaptive nonlinear model (ANM) parameters Figure 9 Protection based on transducer states predicted Consequently, the ALM protection scheme usually by an adaptive linear model (ALM) provides a larger nominal maximum amplitude XAC in accordance with Eq. (34) compared to the LM scheme. 3.3.2. Adaptive Linear Modeling 3.3.3. Adaptive Nonlinear Modeling The protection system based on linear adaptive modeling (ALM) as shown in Figure 9 provides the The ANM protection scheme generates the most voice coil displacement accurate estimate of the voice coil displacement However, a large offset ΔX0(t) in the rest position and a xrel (t) xnlin(t)SNDE (v(t), Pnlin(t)) (39) dynamic DC displacement x (t) generated by DC rectification of the audio signal will increase the based on the solution SNDE of the nonlinear differential asymmetry of the protection limits (for t > 0) as equations (NDE). The nonlinear model in protection illustrated on the right hand side of Figure 11 and system is provided with the time varying parameters reduce the nominal maximum amplitude XAC in Pnlin(t) provided by a second adaptive model monitoring accordance with Eq. (25) and the acoustical output. voltage and current at the transducer terminals as Both state measurement (SM) and adaptive nonlinear depicted in Figure 10. modeling (ANM) provide a similar accuracy in the predicted and measurement displacement. However, the xabs ANM scheme only can cope with latency in the t=0 t>0 feedback of the transducer information because the L+ parameters vary much slower than the activation time of M+ the attenuation control. MDC++M0+ Xclear+(t) Xp+(t) X clear x (t) transducer rel Xp+(0) X (t) 2XAC Attenuator Nonlinear 0 w(t) DELAY (High-pass) Control X0(t) v(t-τ ) z(t) 2X audio X 0 AC signal Attenuator voltage (High-pass) Xp-(t) Xp-(0) Xclear-(t) current X clear displacement Mechanical v(t) Attenuation M +M DC- 0- xrel(t) Control Nonlinear Linear Pnlin(t) Adaptive M- Model L- parameters Model Figure 11 Protection limits for state modeling with Adaptive Nonlinear Modeling (ANM). Figure 12 Protection based on Adaptive Nonlinear Control (ANC) Based on the permanently updated parameters Pnlin the nonlinear model is capable of predicting the DC 3.3.4. Adaptive Nonlinear Control displacement, the nonlinear compression of the AC signals and time variant changes of the transducer The ANC scheme combines mechanical protection with properties. nonlinear transducer control to equalize, linearize and Thus the total safety margins stabilize the transducer for any audio input. The control is based on a feed-forward filter structure [22] having a M M act M m (40) mirror symmetry to the nonlinear transducer model. M M act M m This filter, performing an inverse preprocessing of the input signal v(t-τ), requires the parameters Pnlin(t) require only the activation margin Mact and the adaptive provided by the nonlinear adaptive model as illustrated modeling margin Mm corresponding to the positioning in Figure 12. Using a DC coupled amplifier, the control error: can also generate a small DC voltage based on the identified offset ΔX0(t) to keep the coil at the desired xabs(t) xnlin(t) X 0 em (t) (41) initial rest position X 0 as discussed in [23]. The adaptive modeling error em(t) comprises a transient component which will vanish after convergence of the By compensating all signal distortion caused by time parameter updating and a residual component which variant and nonlinear properties the series connection corresponds to limitations of the nonlinear modeling. nonlinear controller and transducer becomes a linear The attenuation control receives the instantaneous offset system with constant properties. Thus the voice coil displacement ΔX0(t) from the nonlinear adaptive model and determines the time variant clearances Xclear±(t) and xrel (t) xlin(t)SLDE (v(t), Pnlin(0)) (42) protection limits Xp±(t) according to Eqs. (20) and (24), respectively. can be modeled by a linear IIR-filter which is part of the xabs solution SLDE of the linear differential equation (LDE) t=0 t>0 using the initial parameters Pnlin(t=0). L+ The error in the voice coil position M+ x (t) x (t) X e (t) (43) abs lin 0 m X clear Xclear+(t) Xp+(0) requires only safety margins Mact and Mm for the xrel (t) Xp+(t) activation of the attenuator and the adaptive parameter X (t) 0 measurement in accordance with Eq. (40). Synthesizing 0 X 2XAC 2XAC a DC voltage which compensates the offset in rest 0 position Xp-(0) Xp-(t) X (t) X (t) X 0 (44) X Xclear-(t) 0 0 0 clear the clearances M- L- X clear (t) X clear (45) X (t) X clear clear Figure 13 Protection limits for Adaptive Nonlinear and the protection limits Control (ANC). X p (t) X p (0) X clear M (46) 4. SPECIFICATION OF PROTECTION PARAMETERS X p (t) X p0 (0) X clear M After presenting a general framework for the important correspond to the initial values corresponding to the protection schemes this section addresses the target performance of the transducer. communication between transducer manufacturer, If the designed prototype and the mean production yield software provider and system integrator as illustrated in (Golden DUT) exhibits symmetrical clearances, the . ANC protection scheme provides the maximum acoustical output corresponding to the nominal 4.1. Transducer Characteristics maximum amplitude The transducer manufacturer provides the clearances, (1U )X (0), margins and transducer parameters required by the act p X AC Min (47) system integrator to adjust the selected protection (1U )X (0) act p scheme to the particular transducer. The end-of-line test considering the undershoot factor Uact as illustrated in provides the “Golden Reference DUTs” that are the best Figure 13. representatives of the production yield. The mean clearance values X clear and X clear are determined for this Golden DUT by measuring the maximum displacement using a laser displacement sensor without generating impulsive distortion commonly known as “rub&buzz” in the sound pressure output signal. Starting at small amplitudes the test is repeated with increased amplitudes until both the crest factor of the high-pass filtered distortion exceeds 12 dB and the peak distortion value exceeds 1%. The crest factor of the impulsive distortion [21] plotted versus voice coil displacement indicates at which voice coil position the impulsive distortion is generated. This information is the basis for finding the root cause (bottoming, voice coil rubbing, limitations by the suspension, …) and a meaningful specification of the clearances. The minimum of the upper and lower clearance values corresponds to the mechanical peak displacement The long-term test also provides the safety margin M X Min X , X (48) 0,± mech clear clear which corresponds to the shift of the voice coil rest as defined by IEC standard [26]. position over time. The end-of-line test provides the safety margins The value Xmech or a value specified by the customer is M0,spread± and MAC,spread± representing the production used as the target displacement Xtarget for adjusting the stimulus [21] in other tests required to define the safety spread of the voice coil rest position and resonance margins. frequency fs. If those parameters are checked by a pass- fail decision, the margin M corresponds to the The positive and negative safety margins M of the 0,spread± DC± production limit of the permissible offset of voice coil maximum DC displacement can be measured by rest position and the margin exciting the Golden DUT with sinusoidal signals at 2 target displacement. f M X s,spread (50) A long-term test also known as “power test” is required AC,spread t arg et f s to measure the shift Δfs,spread of the resonance frequency over time and to specify the corresponding margin corresponding to the allowed spread Δfs,spread of the resonance frequency fs used in the pass-fail decision. 2 f M X s.time (49) The mean value of the lumped parameters measured in AC,time t arg et end-of-line testing or the measured parameters of the f s Golden DUT give the initial parameters P(t=0) provided which assesses the increase of the peak displacement to the system integrator. due to aging and fatigue increasing the suspension compliance. Transducer Manufacturer Software Provider End-of-Line test Long-term test Test with Audio Shift of Golden DUT Golden Modeling- resonance Selection DUT Measurement frequency Error Spread of Shift of resonance voice coil Undershoot frequeny rest position (over- reaction) Spread of voice coil rest Laser test Overshoot position Impulsive over the limit Distortion Mean (Rub&Buzz) transducer parameters Dynamic DC- displacement MAC,±spread M0±,time MDC± Oact Em P(t=0) M0±,spread MAC± ,time X clear Mean initial Mean initial Margin Margin Margin Margin Margin Parameters clearance Rest position Spread, Aging Distortion Activation Error M P(t=0) MAC± MDC± act M0± Total Margin Mm Initial M Protection ± X (0) Protection System p± Audio System Integrator Limits Figure 14 Work flow for the determination of the protection parameters 5. DISCUSSION 4.2. Software Provider The performance of the different protection schemes The developer of the protection algorithm specifies the presented in section 3 are illustrated on a data set given overshoot, undershoot as well as the adaptation and in Table 1 representing typical micro-speakers as used measurement error of the protection system by relative in smartphones. percentage values Oact, Uact and Em, respectively. Multiplying overshoot Oact and error Em with the target Table 1: Specification of the transducer peak displacement Xtarget in Eq. (48) gives the activation margin Mact and the error margin Mm in mm, Transducer Characteristics Symbol Value respectively. Initial clearances 500 µm X clear 4.3. System Integrator 450 µm X clear The initial protection parameters Xp+(t=0) and Xp-(t=0) used by the software algorithm can only be determined Rest position offset margins M0+ 20 µm by the system integrator who has access to hardware and software characteristics. M0- 50 µm The protection schemes and adjustment procedure have DC-displacement margin MDC+ 10 µm been discussed so far only to avoid damage and bottoming, voice coil rubbing and other impulsive MDC- 80 µm distortion, which are inacceptable by the end user. This Linear AC-Displacement margin MAC 150 µm approach satisfies the current needs in personal audio and communication systems where maximum loudness, Maximum nonlinear compression C 2 dB reliability, cost, weight, height and other geometrical constraints are more important than sound quality. The initial clearances found on the Golden DUT are almost symmetrical in the example showing that the However, transducers developed for home, automotive, coil’s initial rest position is well placed between the professional and other applications have a much larger boundaries. A high negative safety margin MDC is clearance and usually use a spider in the mechanical required to cope with negative DC component in the suspension, which improves the stability with respect to displacement generated by the rectification of the audio voice coil rubbing. Here the intermodulation distortion signal. The rectification may be caused by a distinct generated by the motor geometry (voice coil height and asymmetry in the force factor characteristics Bl(x) as gap depth limits) also limits the maximum output. The found in most micro-speakers which use no voice coil maximal peak displacement Xmax defined in accordance former to place the coil symmetrically in the magnet with IEC [26] and AES [25] is limited by a certain gap. The nonlinear stiffness characteristic Kms(x) may amount of nonlinear distortion acceptable for the also have a significant asymmetry corresponding to the particular application (typically 10 %). shape of a single corrugation role of the diaphragm used as suspension in micro-speakers. The DC displacement The protection schemes presented in the paper can also may also cause a permanent offset in the voice coil rest be used as a compressor of the low frequency signal position due to the viscoelastic memory effect in the components to keep the generated harmonic and material which is visible when the audio signal vanishes intermodulation distortion below permissible limits. The and no DC force is generated by the rectification system integrator determines the maximal peak process anymore. displacement Xmax based on the decay of the nonlinear force factor Bl(x) and compliance Cms(x) as proposed in Table 2: Specification of the protection algorithms [24] and replaces the initial clearances by the Xmax value if this value limits the maximum output. Characteristics Protection (Symbol) Scheme 5.1. SM LM ALM Protection Limits ANM The spreadsheet in Table 3 illustrates how the system integrator generates the initial protection limits X (0) ANC p+ and Xp-(0) and the nominal AC displacement Xac based Additional delay of the τ 0 3 3 on the information from transducer and software audio signal (in ms) supplier. Maximum measurement Em 2 0 10 The high margins M0- and MDC- representing the offset or adaptation error (in of the voice coil rest position and the maximum DC- percent) displacement, respectively, cause an asymmetry in the total margins and in the initial protection limits with Xp- Maximum overshoot (in O 30 5 5 act (0) Maximum undershoot (in Uact 50 10 10 The state measurement (SM) and nonlinear protection percent) schemes (ANM, ANC) do not require the margins M0- and MDC- because those schemes cope with a varying coil offset and a DC component in different ways: The software provider specifies an additional time delay and other relative performance characteristics for the The protection schemes without nonlinear control (SM protection algorithm. These characteristics are and ANM) can only reduce the protection limits Xp+(t) independent of the transducer but based on assumptions and Xp-(t) according to Eq. (24) if such a behavior is and limitations of the state measurement, adaptive detected. The minimum values of the protection values identification and attenuation control. Table 2 gives Min(Xp+) and Min(Xp-) describe the worst case scenario. typical characteristics describing the performance of the The nonlinear adaptive control (ANC) compensates protection algorithms. In the current example all actively for this undesired behavior and keeps the coil protection schemes (LM, ALM, ANM, ANC) which are within the initial (and constant) protection limits Xp+(0) based on modeling the voice coil displacement are using and Xp-(0). a relatively large time delay τ= 3ms in the audio stream Only the non-adaptive linear modeling (LM) requires a to cope with the inertia of the coil and to keep the high margin MAC for coping with the time variant overshooting and undershooting low as discussed in mechanical compliance Cms(x=0,t) due to visco- section 3.1.1. An additional time delay cannot be elasticity, aging, climate and other influences. applied to the protection scheme based on state The activation margin Mact and the measurement/ measurement (SM) resulting in a poorer performance adaptation margin Mm are calculated by multiplying the with respect to overshooting and undershooting. The overshoot Oact and error Em, respectively, given in Table anticipation of the peak value according to section 3.1.2 2 with target peak displacement Xtarget= 0.450 mm based is not used in this example but this technique is capable on the minimum clearance in Table 1. of avoiding any additional delay in the audio signal with superior performance of the attenuation control. Table 3: Spreadsheet for calculating the protection limits and nominal amplitude Transducer Protection Total Protection Nominal Side Margins Margins Margin Limits Amplitude Protection Scheme upper M0+ MDC+ M+ Xp+(0) Min(Xp+) MAC Mact Mm XAC lower M0- MDC- M- Xp-(0) Min(Xp-) + 144 356 336 SM (state 135 9 140 measurement) - 144 306 256 LM (linear, non- + 20 10 150 22 202 298 298 106 adaptive modeling) - 50 80 302 148 148 + 20 10 97 403 403 (adaptive, ALM 22 45 200 linear modeling) - 50 80 197 253 253 ANM (adaptive, + 67 433 413 nonlinear, 22 45 227 modeling) - 67 383 333 ANC (adaptive, + 67 433 433 nonlinear 22 45 344 control) - 67 383 383 The margin Mm required to cover the temporal modeling linearizes the transducer and shifts the coil to the error before adaptive protection schemes (ALM, ANM, original rest position X . ANC) have been converged is usually larger than the 0 margin Mm representing the error in state measurement (SM). 6. CONCLUSION 5.2. Acoustical Output The theory and the practical consideration show that the The last column in Table 3 describes the nominal AC protection limits XP± and the nominal AC amplitude amplitude for each protection scheme in the worst case XAC, which describes the maximum acoustical output in scenario which corresponds with the acoustical output at the worst case depend on transducer properties and the low frequencies. performance of the protection scheme. Those characteristics can only be generated by the system The linear modeling with fixed parameters (LM) gives integrator based on reliable information received from the lowest output because it requires a large margin M AC transducer manufacturer and software provider. The to cope with aging and climate. system integrator can replace clearance values by Xmax if The state measurement (SM) without anticipation of the the audibility of the nonlinear distortion limit the peak value according to section 3.1.2 has also a maximum displacement. relatively low performance due to the high activation margin required to cope with overshooting and The most important transducer characteristics are the undershooting of the attenuation control. lumped parameters, clearance values and safety margins The nominal AC amplitude XAC found in the simple describing the variation of parameters and stability of linear modeling (LM) can be doubled by using adaptive the transducer (DC displacement). It is useful to refer all parameter identification (ALM) which requires no those information to Golden Reference Units which margin MAC for the time variance of the linear should represent the production average during end-of- parameters. Considering the transducer nonlinearities in line testing. the modeling (ANM) increases the negative initial protection limit Pp- because the margins M0- and MDC+ The most important characteristics of the protection are not required anymore. The ANM automatically algorithm are the measurement or adaptation error for reduces the negative protection limit Xp-(t) if an offset the critical state variables, overshooting and ΔX0(t) is found. However, the nominal amplitude XAC is undershooting of the activation control system and not much higher than the value found in ALM latency added by the protection systems. protection scheme because this characteristic describes the worst case scenario with a DUT having maximum Linear modeling with fixed transducer parameters is not offset ΔX0(t) and generating maximum DC capable of coping with nonlinear and time variant displacement. The adaptive nonlinear control (ANC) processes and requires large safety margins, which gives the largest nominal amplitude XAC because it reduces the acoustical output considerably. The adaptive protection schemes can be realized at low [12] A. Tokatian, “Adjustable high-speed audio cost by monitoring voltage and current at the transducer transducer protection circuit”, US patent 6201680 terminals without using a mechanical sensor. [13] B. Jensen, “Thermal protection of electro-dynamic transducers used in loudspeaker systems”, US patent US The adaptive nonlinear control (ANC) generates not 8259953 only the largest AC amplitude XAC and acoustical output but also reduces the nonlinear distortion. The active [14] C. Luo, et. all, “Method and system for temperature linearization and stabilization of the transducer also protection of a speaker”, US patent 8983080 needs a reliable mechanical protection system because [15] S. 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