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Green Speaker Design (Part 2: Optimal Use of Transducer Resources) Wolfgang Klippel, KLIPPEL Gmbh, Mendelssohnallee 30, 01277 Dresden, Germany

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Green Speaker Design (Part 2: Optimal Use of Transducer Resources) Wolfgang Klippel, KLIPPEL Gmbh, Mendelssohnallee 30, 01277 Dresden, Germany 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 S 2 resistance RMS generates a distinct maximum of the 0 D 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
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