Green Speaker Design (Part 2: Optimal Use of Transducer Resources) Wolfgang Klippel, KLIPPEL GmbH, Mendelssohnallee 30, 01277 Dresden, Germany
Green speaker design is a new concept for developing active loudspeaker systems that generate the desired sound output with minimum size, weight, cost and energy. This paper focuses on the optimization of the transducer by exploiting the new opportunities provided by digital signal processing. Nonlinear adaptive control can compensate for the undesired signal distortion, protect the transducer against overload, stabilize the voice coil position and cope with time varying properties of the suspension. The transducer has to provide maximum efficiency of the electro-acoustical conversion and sufficient voltage sensitivity to cope with the amplifier limitations. The potential of the new concept is illustrated using a transducer intended for automotive application.
1 Introduction • reducing linear and nonlinear signal Although enclosure and other mechanical and distortion [4], acoustical elements determine the size, shape and • reliable protection against thermal and weight of the audio product, the electro-acoustical mechanical overload [5], [6] and transducer usually limits the voltage sensitivity and • stabilization of the voice coil position [7], efficiency in loudspeaker systems. In small, direct while coping with aging, climate and other external radiating loudspeakers almost 100 % of the electrical influences and generating a desired linear transfer power will heat up the voice coil [1]. Doubling the behavior over the life time of the audio device. input power is not possible in most professional This paper continues the discussion on the optimal applications because it would damage the voice coil use of all hardware resources in the first paper [2] but or it consumes too much energy in mobile focusses on the transducer. After analyzing applications with limited battery capacity. Voltage consequences for the power amplifier, the potential of sensitivity is a second weakness of the electro- the new design concept will be illustrated by slight dynamical transducer because the back modification of a loudspeaker intended for a electromagnetic force (EMF) generated by the voice passenger warning system in electric cars. coil velocity makes it hard to feed electrical energy Voltage Sensitivity(f) @ 1Vrms, 1 m 90 into the transducer at the fundamental resonance at fs. 7 N/A 85 Power efficiency and voltage sensitivity are different dB characteristics, and this becomes obvious when the 80 75 3.5 N/A spectrum Gw(t) of the audio stimulus w(t) is 70 considered in the modeling. Bl(x=0) 65 amplifier transducer 1.7 N/A z(t) u(t) 60 w(t) DSP p(t) 55 audio 50 stimu lus i(t) current 45 Enclosure sensor 0.05 0.1 0.5 1 0.4 Frequency [kHz] Figure 1: Active loudspeaker system with adaptive, Efficiency η(f) nonlinear control of the transducer based on voltage 1 7 N/A and current monitoring % A new concept for designing an active 0.1 3.5 N/A loudspeaker system has been presented in the first part of the Green Speaker Design [2]. Digital signal 0.01 Bl(x=0) processing (DSP) applied to the electrical input signal 1.7 N/A u(t) of the passive system (transducer + box) as shown 0.001 in Figure 1 opens up new degrees of freedom in the design of the hardware components. A software solution based on adaptive nonlinear control with 0.0001 current sensing [3] is superior to any hardware solution with respect to 0.05 0.1 0.5 1 0.4 Frequency [kHz]
Figure 2: Voltage sensitivity SPL1V,1m(f) and generated on-axis at the distance rref=1m by a defined efficiency η(f) of an electro-dynamical transducer rms voltage uref at the transducer terminals. For mounted in a baffle versus frequency f of a single defining the peak voltage requirement of the amplifier tone stimulus using three different values of the and selecting the transducer with optimum nominal force factor Bl(x=0) at the rest position. input impedance ZN, the voltage sensitivity shall be compared at the same reference voltage (e.g. uref = 1
Vrms). In the passband there is a close relationship 2 Transducer Modeling between efficiency ηPB and voltage sensitivity Lumped parameter modeling is a convenient basis 2 ZW1 SPL =10lgH ( f , r ) N for modeling transducers used in loudspeakers and PB,, uref r ref ref p0 other audio devices. The interested reader is referred to the first part [2] where the equivalent circuit and ηPB1W Z N =10lg −8dB (3) the parameters for the electro-dynamical transducer 100%Π0 RE have been discussed. η Z This paper here neglects the influences of =10lgPB N +112dB 100% RE generator resistance Rg and load impedance ZL(f) representing the electro-mechanical system (box, using a particular reference rms voltage passive radiator, panel…) and operates the transducer uref= ZW N 1 (usually 2 or 2.8 V) that generates 1W in an infinite half-space which is usually a baffle. input power at the nominal impedance ZN of the Figure 2 shows the efficiency η(f) and voltage device under test (usually 4 or 8 Ohm). Eqs. (2) and sensitivity SPL1V,1m(f) on-axis at distance rref = 1m of -5 (3) also use the reference sound pressure p0 = 2∙10 an electro-dynamical loudspeaker mounted in an −12 Pa and the standard reference power Π=10 W . infinite baffle assuming omnidirectional radiation 0 into the half space for a sinusoidal tone of frequency f and terminal voltage uref = 1Vrms. The frequency 2.2 Fundamental Resonance responses of efficiency η(f) and voltage sensitivity The efficiency of the loudspeaker at the SPL1V,1m(f) have a similar shape if the motor uses a fundamental resonance frequency fs can be calculated small magnet that provides a low force factor Bl, as by shown for the dotted curves for Bl = 1.7 N/A. For a 2 22 (Bl) SDsρπ0 2 f . η()f = larger magnet generating a force factor Bl= 7 N/A, the s 2 (4) Bl+ R R R c curves are significantly different [9]. (( ) E MS) MS The relationship between the lumped transducer For woofers and other similar transducers, where parameters and the two important characteristics will the electrical resistance transformed to the 2 be discussed in three main frequency bands in the mechanical domain (Bl) / R is much larger than the following chapters. E mechanical resistance RMS and the electrical damping dominates the total damping, the efficiency η(fs) is 2.1 Passband described as The efficiency η(f) is almost constant in the 22 SfDsρπ0 2 s s passband of the transducer with 2f < f < 5f , where ka η()fs = (5) < 1, the back EMF is not active and the effect of the RcMS inductance LE is negligible. A frequency independent and becomes independent of force factor Bl and DC value called passband efficiency ηPB is defined as resistance RE. The small value of the mechanical 2 Bl ρ 2 resistance RMS generates a distinct maximum of the ( ) 0SD ηPB = 100% (1) efficiency at resonance (η(fs) > ηPB). However, a high RM2 2π c E MS force factor value Bl will reduce the voltage using the lumped parameter modeling [2], the density sensitivity at the resonance to of air ρ0 and assuming omni-directional radiation into ρ fS uref . the half-space [8]. SPL( f )= 20lg 0 sD (6) urref, ref s The passband efficiency ηPB rises with force factor r Bl p0 ref Bl and the effective radiation area SD but falls with Contrary to the passband region where efficiency DC resistance RE and moving mass MMS. The passband voltage sensitivity can be calculated and voltage sensitivity are rising with the force factor, as the sound pressure level a low force factor Bl would improve the voltage sensitivity at resonance. That means a subwoofer ρ BlS u SPL = 20lg 0 D ref designed for a narrow audio band close to the PB,, u r (2) ref ref 2π r RME MS p0 fundamental resonance can use a weak motor with a ref
small force factor Bl and would be the best choice for system design, see section 7.2 in [2], but is less high efficiency and high voltage sensitivity [10]. relevant for transducer optimization discussed here. The other lumped transducer parameters RE, RMS, 2.3 Low Frequencies Bl, MMS and KMS determine the frequency dependency A transducer mounted in a large baffle provides, of η(f) and SPL1V,1m(f) and the interaction with voltage spectrum GU(f) generating the efficiency η and at low frequencies f < fs, the efficiency SPL1V,1m when a broadband audio signal is ()Bl22 S ρπ2 f 2 η <≈ D 0 reproduced. ()ffs 2 (7) RKE MS c Thus, the optimization of the transducer also and the voltage sensitivity: depends on the voltage spectrum GU(f) and the load
2 impedance ZL(f) of the mechano-acoustical system. If ρπBlS2 f uref SPL( f<≈ f ) 20lg 0 D (8) the system design requires an improvement of urref, ref s r RK p0 ref E MS transducer efficiency Δη/η and voltage sensitivity Both characteristics rise with the frequency ΔSPL as defined in Eqs. (43) and (44) in [2], it is useful to focus the optimization on the lumped squared, whereas force factor Bl and resistance RE have the same influence as in the passband. A lower transducer parameters that have the highest influence in the particular application. stiffness KMS of the suspension would increase the efficiency and sensitivity in this frequency band. Table 2: Optimization of voltage sensitivity
Table 1: Optimization of efficiency Application Maximize in Use Application Maximize in Design Transducer Design Transducer Rules Design Rules Design A1: Full band A1: Full band loudspeaker using Bl 1 D1, D2, loudspeaker using sealed, Bl 2 1 D2, D4- sealed, vented box or 2 RME MS D4-D7 vented box or passive RME MS D7 passive radiator system radiator system (f0/2 < f ) (f0/2 < f ) A2: Woofer using small A2: Woofer using small 2 closed-box, vented-box or Bl D3, D4- closed-box, vented-box Bl D1, D3,
passive radiator system RE D7 or passive radiator RE D4-D7 (f < 2f0) system (f < 2f0) A3: Subwoofer in large 2 A3: Subwoofer in large sealed-box Bl D3, D4- Bl D1, D3, RK2 D7, D9 sealed-box (f0/3 < f < 2f0) E MS RKE MS D4-D7,D9 (f0/3 < f < 2f0) A4: Narrow-band A4: Narrow-band subwoofer in sealed-box 1 D11-D13 subwoofer in sealed- 1 system D10-D13 RMS box system Bl (0.75f0 < f < 1.25f0) (0.75f0 < f < 1.25f0)
A5: Woofer with 2 Bl D3, D4- A5: Woofer with bandpass system Bl D1, D3, RE D7 bandpass system (fp/2 < f < 2f0) RE D4-D7 (fp/2 < f < 2f0) A6: Micro-speaker with 2 small rear volume and Bl 1 D2, D4- A6: Micro-speaker with Bl 1 2 RE + small rear volume and D1, D3, side-fire port (MMMS MP ) D7 RE (MMMS+ MP ) side-fire port D4-D7 (f0 < f < 2fp) 2 (f0 < f < 2fp) A7: Flat panel with Bl 1 D2, D4- exciter (f0/2 < f ) 2 A7: Flat panel with D1, D2, RME MS D7 Bl 1 exciter (f0/2 < f ) D4-D7, RM E MS D16-D21 3 Transducer Requirements
The previous discussion shows that the effective The tables 1 and 2 illustrate the parameter ratio for radiation area SD increases efficiency η(f) and voltage seven applications (A1-A7) that should be maximized sensitivity SPL1V,1m(f) at all frequencies in the same in the transducer design to improve power efficiency way. This is only true for the transducer mounted in and voltage sensitivity, respectively. The right the baffle, but SD may change the frequency responses column gives a reference to practical design η(f) and SPL1V,1m(f) if the transducer drives additional considerations (D1-D20) listed in Table 3. acoustical elements (e.g. closed box). Finding the It is beneficial to maximize the motor efficiency 2 optimal radiation size SD is an important step in the factor (Bl) /RE in such applications where a high force
is required for driving the load of the mechano- Use a lower damping ratio for the radiator acoustical system coupled to the transducer [11]. The D21 material (cone, panel) moving mass MMS shall be minimized, while keeping 2 the efficiency factor (Bl) /RE as high as possible, in 4 Transducer Design all applications (A1, A6, A7), where the transducer is After presenting the fundamental relationships operated dominantly in the passband region and the between efficiency and lumped transducer crossover frequency is high ( fXO >> f0). parameters, this section discusses the influence of the Only in a particular application (A4) such as a geometry, choice of the material and other design subwoofer operated in a narrow band (0.75f0 < f < considerations. 1.25f0) would a low mechanical resistance RMS and a weak motor with low force factor Bl provide more efficiency and voltage sensitivity [10]. 4.1 Gap-Coil Topology For an electro-dynamical transducer, the Table 3: Design considerations for improving relationship between the gap depth hg and the voice efficiency and sensitivity in system design coil height hc is a good starting point in our search for Optimal Design Considerations maximum efficiency in sound reproduction. Shorten wire length and increase diameter D1 gap depth voice coil to reduce DC resistance RE while keeping coil 2 pole plate the same motor efficiency factor Bl /RE height D2 Use aluminum coil wire to reduce moving pole magnet mass MMS piece D3 Use copper coil wire to improve motor 2 efficiency factor Bl /RE equal-length configuration D4 Use coil height hcoil ≈ 2Xmax to keep 50 % of the windings in the gap at maximum excursion Xmax D5 Keep magnetic fringe field outside gap as small as possible D6 Use small voice coil overhang to exploit over-hung coil under-hung coil the fringe field Figure 3: Common topologies for configuring the D7 Use nonlinear force factor Bl(x) to reduce gap-depth and voice coil height in electro-dynamical electrical damping at higher amplitudes transducers D8 Reduce effective radiation area SD D9 Use soft suspension in the intended Figure 3 shows typical configurations to working range x < Xmax (not progressive maximize either efficiency or linearity of the electro- KMS(x) dependency) dynamical transducer. The so-called equal-length configuration uses a minimum voice coil overhang to D10 Reduce airflow in the gap to decrease RMS exploit the magnetic fringe field outside the gap. This D11 Reduce losses in suspension to decrease configuration gives the highest force factor value RMS Bl(x=0) at the voice coil rest position, which is D12 Use mass and stiffness to tune the cut-off beneficial for maximizing the effective force factor frequency fc of the loudspeaker D13 Use a small magnet to reduce electrical Bl when reproducing common audio signals at high damping amplitudes (as discussed in [2]). D14 Use absorbing filling in the rear enclosure Unfortunately, the equal-length configuration D15 Shorten and widen the side-fire port to without nonlinear control generates significant harmonic and intermodulation distortion and other reduce acoustical mass MAP D16 Increase the number and density of undesired nonlinear symptoms (DC-displacement, vibrations modes instabilities…) at larger voice coil displacement x D17 Place the actuator at the optimal excitation [12]. Figure 4 shows the nonlinear force factor characteristic Bl(x) calculated by a magnetic finite point re element model where the gap depth hg was varied D18 Clamp the exciter or use a higher magnet between 5, 10, 15 and 20 mm while assuming the coil mass Mmag height hc=10 mm and magnet size are constant [13]. D19 Reduce the moving mass MMS of the exciter D20 Generate a mode shape that minimizes acoustical cancellation
constant coil height 10 mm offset of the voice coil rest position caused by Bl(x) production variances and aging, the equal-length 10 mm gap (equal length coil) N/A configuration is sensitive to an offset and may 15 mm gap 5 mm gap generate a significant DC displacement by rectifying (underhang coil) (overhang coil) the AC audio signal. Nevertheless, the equal-length configuration is
20 mm gap the best candidate for active systems where the (underhang coil) passive transducer provides the highest efficiency over a wide audio band and digital signal processing can be used to cancel the nonlinear loudspeaker distortion [4] and actively stabilize the voice coil voice coil displacement X mm position [7]. For this reason, the remaining parts of this section focus on the optimal design of the equal- Figure 4: Force factor Bl(x) versus displacement x of length configuration. an equal-length, an overhung and an underhung configurations using a constant voice coil height and 4.2 Motor Efficiency Factor different gap depths. The efficiency at low frequencies and in the
The overhung configuration shown in Figure 3 passband in Eqs. (1) and (7) depends on the squared uses spare windings below and above the gap that are effective force factor divided by the DC resistance, which can be interpreted as a motor efficiency factor used when the voice coil is moved. This generates a 2 (Bl) /RE. plateau in the Bl(x) characteristic (hg = 5 mm in Figure Expressing DC resistance as 4), giving more linearity and less nonlinear distortion 2 for moderate excursion. ll REE=ρρ = E (9) The underhung configurations in Figure 4 use 15 AVww and 20 mm thick pole plates to generate a wider linear with the length l, cross-sectional area Aw and the plateau in the nonlinear Bl(x) characteristics. electrical resistivity ρE of the wire, and neglecting the The price paid for less Bl(x)-variation and lower magnetic fringe field outside the gap allows the motor nonlinear distortion is a loss of force factor, illustrated efficiency factor to be written as 2 as shaded area in Figure 4. 2 ()Bl Vw = B (10) R ρ Topology Equal- Over- Under- EE 2 length hang hang using B to represent the mean induction seen by the Motor efficiency High low low conductive wire material of the volume Vw. Eq. (10) 2 shows that the motor efficiency factor is independent factor Bl/ RE of the length l and cross-sectional area Aw of the wire. Moving mass MMS medium high low This fact gives the loudspeaker designer some Bl(x)-nonlinearity Strong weak weak freedom in realizing the desired voltage sensitivity, as L(x)-nonlinearity medium strong weak discussed in section 5, by trading force factor Bl DC-Stability critical robust robust against DC resistance RE. Weight, size cost Low medium high The volume Vw can be increased by maximizing Table 4: Overview of benefits and drawbacks of the fill factor in the coil winding area [14] by using selected motor topologies using different ratios rectangular wire and an efficient winding layout, between voice coil height and depth length which usually increases the manufacturing effort and cost. In practice, there is not much freedom to Table 4 summarizes the properties of the common increase volume Vw by using a thinner bobbin motor topologies. The equal-length configuration has material and reducing the clearance in the gap, which been used for consumer applications where maximum is required to cope with rocking modes and voice coil output, efficiency, cost, size and weight require a rubbing. compromise in linearity. The overhung configuration is attractive for subwoofer applications where the Material Resistivity ρE Density ρD moving mass and inductance nonlinearities L(x) and Copper 1.68×10−8 Ωm 8.96 g/cm3 L(i) are less important. The underhung coil is an Aluminum 2.65×10−8 Ωm 2.7 g/cm3 interesting topology for all high-frequency applications (e.g. tweeter) where the coil mass limits Table 5: Resistivity and density of common wire the overall efficiency. While both the overhung and material underhung configurations are relatively robust to an
4.3 Coil Material of a loudspeaker reproducing common (broadband)
The electrical resistivity ρE and the density ρD of audio signals with a Gaussian-like probability density the wire material given in Table 5 affect the DC function pdf(x) [2]. In this case, there is no increase in resistance RE and the total moving mass MMS, power consumption and only a moderate increase in respectively. peak voltage requirement. This has a significant influence on the passband efficiency 4.5 Gap Depth 2 BVρ S2 After defining the voice coil height hc, the optimal η = wD0 PB 2 (11) gap depth hg shall be determined in order to exploit ρρVM+ 2πc E( D w add ) the magnetic fringe field outside the gap. The considering the additional mass Madd, representing the induction B within the gap and in the fringe field, as contribution of other moving loudspeaker parts such illustrated in Figure 5, can be calculated by using a as suspension, diaphragm, bobbin and moving air. magnetic finite element simulation tool. Choosing the volume Vw and the proper material B(x, hg) of the wire depend on the ratio between additional fringe fringe field field mass and coil mass: Bmax M add M ratio = (12) 0.7Bmax ρ V Dw coil hc If the mass ratio Mratio >> 1, a larger wire volume gap Vw increases the passband efficiency. Using copper instead of aluminum as coil wire would increase the hg -0.5hc 0.5hc passband efficiency ηPB by half if the coil mass is x negligible compared to the total mass MMS because Figure 5: Voice coil overhang exploits the magnetic aluminum has a higher resistivity. If the mass ratio fringe field in the magnetic induction B(x, hg) outside Mratio << 1 and the coil mass dominates the total the magnetic gap with the gap depth hg. moving mass MMS, an aluminum coil provides 6 times more passband efficiency than a copper coil. The optimal value hg for maximizing the motor efficiency factor can be found by a gap geometry at 4.4 Voice Coil Height which the induction at both ends of the voice coil The voice coil height hc limits the maximum Bx(=±= 0.5 hcg , h ) 0.7 Bmax (14) displacement XBl in an equal-length configuration.
According to IEC standard 62458 [15], the force is 70% of the maximum induction Bmax in the gap. For factor Bl(XBl) referred to the force factor value at the a smaller value of the gap depth hg, the windings at rest position Bl(x=0) drops at the peak displacement both ends of the voice coil would generate a lower XBl to a given force factor ratio Blmin: contribution to the squared Bl value while increasing Bl(x) the electrical resistance RE, giving a lower motor min ⋅100% = Bl (13) 2 − < < min X Bl x X Bl Bl(0) efficiency factor Bl /RE. For example, moving the coil to a force factor ratio Blmin = 82 % generates about 10 % inter- 4.6 Magnet Geometry modulation distortion for a two-tone signal [16]. If After defining the clearance between the voice nonlinear control can be applied to the loudspeaker coil and the pole plates, the gap width wg and the pole and the nonlinear distortion can be actively canceled, plate surface Ag can be determined, giving the gap the force factor ratio can be reduced to Blmin = 50 %, volume Vg=Agwg. In order to generate the highest giving a larger maximum displacement XBl ≈ hc/2. At induction Bg in the gap, the optimal working point in this point, half of the coil is out of the gap if the fringe the demagnetization curve shown in Figure 6 must be field is small and there is no offset in the voice coil used. rest position. Theoretically, the nonlinear control could be applied to even larger peak displacements where the force factor ratio is much lower but the compensation of the Bl(x) distortion would increase the crest factor CFu of the pre-distorted signal, which has to be provided by the power amplifier. Exploiting peak displacement where the force factor ratio Blmin decays to 50% is a good compromise for active linearization
However, a mechanical suspension becomes demagnetization curve softer during the product life due to break-in, climate Br optimum and fatigue in the rubber, fabric, foam and suspension materials. Mechanical overload may also speed up the Bmax natural aging process [18]. External forces generated by gravity and a static air pressure difference between Bmag front and rear side of the diaphragm (e.g. as caused (BH)max by the air stream in cars when a window is open) may also change the voice coil position. This is critical in transducers with an equal-length configuration, where a small coil offset leads to a significant Hk Hmag Hmax asymmetry in the Bl(x)-nonlinearity. Figure 6: Optimal working point in the Asymmetries in the loudspeaker nonlinearities demagnetization curve of the magnet. also generate a DC force that works against the mechanical stiffness KMS(x=0). If the mechanical The induction Bmag and field strength Hmag in the suspension is too soft, a significant DC displacement magnet should be close to the optimal values Bmax and might be generated, leading to bifurcation and other Hmax, giving the maximum product unstable behavior as well as excessive distortion [12]. ! The surround is the most critical part in Max( Bmag H mag )= Bmax H max = ( BH ) (15) max loudspeakers because voice coil displacement and air with the maximum energy product (BH)max, which is pressure in the rear enclosure generate significant an important material parameter of the magnet. deformation, which also affects the modal vibration Neglecting the iron in the pole piece and plates, at higher frequencies [2]. the maximum value of the induction in the gap for a Adaptive nonlinear control can cope with those given magnet volume Vm=hmAm can be estimated by problems. Active stabilization [7] and distortion µ (BH) V cancelation [4] keep the voice coil at the optimal 0 max m . Bg = (16) voice coil rest position and ensure maximum AC Vg displacement and sound pressure output. An active This value can be realized if the magnet height protection system [6] more reliably prevents an overload and provides more output than a suspension Bwgg hm = (17) with a progressive stiffness characteristic. µ0H max and the cross-sectional area 5 Optimizing Voltage Sensitivity BAgg The voltage sensitivity is a useful characteristic to A = (18) m B decide whether the peak voltage capabilities of the max power amplifier are sufficient to generate the target correspond to the gap width wg and the pole plate SPL output at all frequencies of interest. surface Ag of the gap. Modern finite element magnetic It is possible to modify the voltage sensitivity simulation tools simplify this optimization process without significantly degrading the efficiency, which while considering the saturation of the iron material was the primary design goal so far. For example, and the fringe field outside the gap. changing the DC resistance RE of the voice coil while 2 maintaining the same motor efficiency factor (Bl) /RE 4.7 Suspension will not change the efficiency η(f) in Eqs. (1), (4) and The total stiffness KMS in the denominator in Eq. (7) as long as the volume VC of the wire material is (7) reduces the efficiency and voltage sensitivity at constant. The difference in the voltage sensitivity of frequencies below resonance. It would be desirable to two designs with only different DC resistances RE and further reduce the transversal stiffness KMS while RE’ becomes: ensuring an optimal voice coil rest position, keeping SPL() f− SPL () f urref,, ref urref ref enough radial stiffness Krad to center the coil in the RREE' gap and sufficient rotational stiffness to suppress R ' (19) rocking modes generating voice coil rubbing [17]. =10lg E R This is important for flat loudspeakers where the E distance between spider and surround is small or in Practically speaking, reducing the DC resistance headphones, micro-speakers, compression drivers to half of its value gives 3dB more voltage sensitivity. and other transducers in which no spider is used.
Nominal impedance 6 Amplification 4 2 -50% The power amplification (amplifier, power [Ω] supply, cables, …) uses critical hardware components Gap depth dg [mm] 5 5 0% that determine the size, energy consumption, heat Coil height hc [mm] 11 5.75 -47% development and cost of the product. The long-term maximum output power is the most popular Resistance RE[Ω] 3.31 1.74 -47% Force factor Bl(0) characteristic of the amplifier. It is usually measured 4.6 3.5 -24% by using a sinusoidal test signal (e.g. chirp) and a [N/A] resistor corresponding to the nominal impedance ZN Bl limited peak of the transducer [19]. The long-term power displacement 4.5 3.5 -40% capability of the amplifier is usually not a limiting XBl [mm] factor for a common audio signal (e.g. music) where Motor efficiency factor 2 6.39 7.04 +10% the crest factor (CFu > 12 dB) is much higher than for Bl(0) /RE[Ns/m] a sinusoidal signal (CFu = 3dB) and where the Compliance Cms 0.66 0.67 +1% transducer has a complex and frequency dependent [mm/N] input impedance ZE(f) [20]. The back EMF and the Moving mass MMS [g] 10.4 8.6 -17% voice coil inductance LE reduce the voltage Mass ratio Mratio 1.5 3 +100% sensitivity, especially in efficient transducers having 2 Resonance frequency a high motor efficiency factor (Bl) /RE see Figure 2. 61 67 +10% fs [Hz] Reducing the DC resistance RE of the coil is a Passband efficiency practical solution but requires shorter cables and a 0.267 0.433 +62% low output impedance of the power amplifier. ηPB [%] However, reducing RE will increase the current and Voltage sensitivity in the heating of the amplifier output stage. Even if the passband 81.2 85.9 +4.7dB amplifier can provide the RMS current and long-term SPLPB,1Vrms, 1m [dB] power to the speaker, the high crest factor of common Table 6: Characteristics of the original transducer (A) audio signals generates high current peaks which may and the optimized transducer (B) with reduced voice lead to a critical temperature in the amplifier output coil height hc. stage after a short time [21]. Thus, the thermal protection of the amplifier is a 8 Transducer Characteristics similar problem to the thermal protection of the voice Force Factor Bl (X) coil in the transducer, although there are significant 4,5 original differences in the heat flow, the cooling mechanisms 4,0 transducer A and the thermal time constants. 3,5 Combining the protection of both FET output 3,0 ] A
/ 2,5 N
stage and coil in a common control block would [
l improve the maximum short-term power capacity of B 2,0 1,5 modified the amplifier. transducer B 1,0
0,5 << Coil In Coil Out >> 7 Case Study 0,0 -6 -4 -2 0 2 4 6 The freedom provided by nonlinear adaptive X [mm] control shall be illustrated using an existing 4.5” woofer A developed for automotive applications. A Figure 7: Force factor characteristic Bl(x) of the minor modification has been performed in transducer original speaker A with an overhung configuration B by shorting the voice coil to half of the height found (dashed line) and the modified speaker B with an in the original transducer A while using the same coil equal-length configuration (solid line). wire, magnetic system, suspension and diaphragm. Figure 7 shows that the original transducer A with This change did not increase the cost and was voice coil overhung of 6 mm almost has a plateau accomplished without redesigning the motor region where the force factor Bl(x) is constant for structure. Although the modified transducer B has not small displacement |x| < 3 mm. A significant fringe been optimized to the maximum efficiency, this small field outside the gap also gives 24 % more force modification improves the total performance of the factor Bl(x=0) at the rest position than the modified transducer with nonlinear control significantly. speaker B with the shorter coil height hc ≈ hg. The
shorter coil height causes an earlier decay in the Transducer A B Change Bl(x)-nonlinearity and already generates 10 % IM- Parameters distortion at Bl-limited peak displacement XBl = 3.5
mm [15]. However, the reduced DC resistance RE= 8.1 Audio Performance 1.74 Ω leads to a 10 % higher motor efficiency factor A typical music stimulus (Tracy Chapman, 2 Bl /RE in the modified speaker B. The same Crossroads, This Time) has been used to evaluate the improvement can be found in the efficiency η(f
the crest factor of the input signal by about 1 dB 2nd Harmonic compared to linear control (B+LC). However, this 10 increase is similar to the effect of the equalization at 9 B+LC low frequencies. The different alignment of the 8 original and modified speaker (A+LC) and (B+LC) 7 generates an increase of the crest factor in the 6 % terminal voltage by 0.5 dB and 1.3 dB, respectively, 5 due to the difference in the transducer resonance 4 frequency fs in free air. This increase is caused by 3 boosting low-frequency components having a higher 2 1 crest factor (CFx ≈ 16 dB) than the full band audio B+NC 0 signal. 40 60 80 100 200 This small increase in the crest factor can easily Frequency [Hz] be compensated by the much better voltage sensitivity 3rd Harmonic of the modified speaker with nonlinear control B+NC 40 compared to the original speaker A+NC, which 35 B+LC reduces the peak voltage requirement for the 30 amplifier by 33 %. 25
The shorter coil in the modified speaker under % 20 nonlinear control (B+NC) reduces the power 15 consumption and the heat development by 40%. This 10 transducer operated with reliable active protection B+NC (B+NC) can generate at least 3 dB more SPL 5 (measured as a total mean value over the stimulus) by 0 40 60 80 100 200 requiring less peak voltage than in the original Frequency [Hz] speaker A+NC. Figure 8: 2nd- and 3rd order harmonic distortion of the Exploiting the full voltage capability provided by optimized loudspeaker with linear control (B+LC) the amplifier, the mechanical protection system in the and nonlinear control (B+NC). modified speaker B+NC would reduce the bass signal
(f < fs) by 3 dB to keep the peak excursion below xprot Sound pressure spectrum p(f) of reproduced multi-tone signal = 3.5 mm. The 3 dB increase of SPL would require 80 70 17 W of real input power and would heat up the voice dB Fundamental Fundamental 60 (with linearization) coil temperature by ΔTv ≈ 120 K, which would be permissible for the speaker B. Doubling the electric 50 B+LC Distortion input power provided to the original speaker A would 40 A+LC not only require a more powerful amplifier but would 30 also generate an unacceptable increase of the coil 20 B+NC A+NC temperature ΔTv ≈ 200 K. 10 50 100 200 500 1k 2k Frequency [Hz] 8.2 Distortion Reduction Figure 8 shows the active compensation of the Figure 9: Fundamental components and nonlinear harmonic distortion generated by a single excitation distortion in a multi-tone test stimulus reproduced by tone. Since the modified transducer B is carefully the original loudspeaker (A) and the modified manufactured, the 2nd-order distortion found under loudspeaker (B) with linear (+LC) and nonlinear linear control is relatively small, indicating control (+NC). symmetrical stiffness KMS(x) and force factor Bl(x) The nonlinear control (+NC) also reduces the characteristics. The nonlinear control NC is required intermodulation distortion generated by a more for speaker B to reduce the high value (40 %) of 3rd- complex stimulus (e.g. music) as shown for a sparse order harmonic distortion by 20 dB at low multi-tone stimulus in Figure 9. The distortion frequencies. reduction achieved for the original speaker A+NC and modified speaker B+NC are shown as thin solid and thick solid lines, respectively, while the dashed lines represent the nonlinear distortion found with linear control LC. The modified speaker with linear control B+LC generates much higher distortion than the original
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