Maximizing Efficiency in Active Loudspeaker Systems Wolfgang Klippel, KLIPPEL GmbH, Dresden, Germany Increasing the efficiency of the electro-acoustical conversion is the key to modern audio devices generating the required sound output with minimum size, weight, cost and energy. There is unused potential for increasing the efficiency of the electro-dynamical transducer by using a nonlinear motor topology, a soft suspension and cultivating the modal resonances in the mechanical and acoustical system. However, transducers optimized for maximum efficiency are more prone to nonlinear and unstable behavior. 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 paper discusses the design of modern active systems that combine the new opportunities provided by software algorithms with the optimization of the hardware components in the transducer and power amplifier. reducing power consumption in portable 1 Introduction applications with limited battery capacity. The user of loudspeakers, headphone and other For this discussion, the paper provides new audio devices expects that the audio signal can be definitions of the efficiency to consider the influence reproduced at sufficient amplitude and quality but of the spectral properties of the complex audio prefers products which are smaller, lighter, less cost signals (e.g. music). The paper explains the intensive and provide a longer stand-alone operation difference between efficiency and voltage in personal applications. sensitivity, which is a second important Creating such an audio product requires a characteristic of the transducer required to match the combination of hardware and software components transducer with the power amplifier. as illustrated in Figure 1. After predicting the efficiency of an electro- dynamical transducer based on lumped parameter power modeling in the small and large signal domain, the DSP amplifier transducer influence of the geometry and material properties audio Nonlinear u(t) will be discussed in greater detail. Finally, the new stimulus Control w(t) z(t) concept will be applied to a case study where the P(t) i(t) effect of a simple modification of an existing voltage current transducer will be investigated. Parameter sensor Identification current 2 Loudspeaker Control Figure 1: Active loudspeaker system with adaptive, This section summarizes the new opportunities nonlinear control of the transducer based on voltage provided by digital signal processing for and current monitoring loudspeakers: Linear filtering of the electric input signal has been The next section gives an overview on the software used for a long time to equalize or align the overall algorithms that have been developed for amplitude and phase response at a receiving point loudspeakers. However, any electric control can and listening zone to a desired target curve [1]. The only manipulate the audio input signal to exploit the progress in amplification brought more power to the existing hardware components (amplifier, electric terminals than the transducer can handle. To transducer, enclosure). Additional benefits can be avoid a mechanical and thermal overload, active generated for the end user by using hardware protection systems have been developed that detect a components that are specially constructed for the critical state and attenuate the input signal before opportunities provided by digital signal processing. damage occurs. In order to combine reliable This paper searches for new degrees of freedom in protection with maximum output, an accurate the hardware design to use all resources such as modeling of voice coil displacement and material, energy and manufacturing effort more temperature at high amplitude is required [2]. Only a efficiently (Green Speaker Design). The electro- nonlinear model can explain the dynamic generation acoustical efficiency is the important criterion for of a DC-displacement in the transducers which evaluating the final product and identifying weak moves the coil away from the optimal position for points in the transducer design. For example, a maximum AC displacement [3]. Since the nonlinear typical micro-speaker converts the most of the behavior is predictable [4], it is obvious to use this electric energy into heat but only 0.01 % into sound knowledge in nonlinear controllers that generate a power. Increasing efficiency is the key to generate pre-distorted audio signal containing compensation more output by smaller loudspeaker systems and distortion that cancels for the nonlinear distortion generated in the following loudspeaker. This leads to a linear transfer behavior between control input and using the specific acoustic impedance ρ0c, the sound pressure output. The mirror filter [5] has a transfer function H(f,rref) between terminal voltage feed-forward structure and can be operated with u(t) and sound pressure p(t,rref) at the reference point fixed parameters, but any deviation between the rref (usually on-axis at 1 m distance from the source) control and transducer parameters will deteriorate and the directivity factor 2 the distortion cancelation. Therefore, loudspeakers Sp(, fr ) require a self-learning control system that dispenses ref Qf(,rref ) with a sophisticated tuning process and can react 2 (4) pf(,)r dS adaptively on production variances, aging of the suspension, changing climate conditions and other S which describes the ratio between the power radiated external influences [6]. Monitoring the input current by a virtual source generating the same sound and terminal voltage, as shown in Figure 1, provides pressure p(f,r ) on the reference point at all points reliable information [7] to identify the linear and ref on a spherical surface S and the real power nonlinear transducer parameters, the maximum integrated over S. excursion and the absolute rest position of the coil. The total efficiency in Eq. (1) can also be If the power amplifier is DC coupled, the control approximated by a more convenient integral system stabilizes the transducer [8] and keeps the expression coil at the optimal position, giving maximum AC displacement and sound output. The continuously ()f Sfdf () updated transducer parameters are valuable uu information for transducer diagnostics to detect a (5) deterioration process and anticipate a damage in Sfdf() uu order to initiate proper actions in time. Nowadays, the cost generated by hosting software using a frequency dependent efficiency factor 2 algorithms in silicon can compete with the benefits Hf(,rr ) Qf (, ) S and cost savings generated on the transducer side, (f )ref ref 100% (6) 1 even in low-cost consumer applications. 0cZfE () weighted by the auto power spectrum Suu(f) of 3 Efficiency voltage u(t) at the loudspeaker terminals. The The electro-acoustical efficiency of a loudspeaker, approximation error is negligible for broadband headphone or any other transducer is defined as ratio stimuli and vanishes for a single tone completely. P The frequency dependent efficiency factor η(f) a 100% (1) P corresponds with previous discourse on loudspeaker e efficiency based on linear modeling valid in the between electric input power Pe and the acoustic small signal domain [20]-[23]. output power Pa for any stimulus such as a test This concept can also be applied to larger signal or common audio signals. amplitudes where nonlinearities inherent in the The real input power Pe can be calculated in the time loudspeaker and other time variant properties due to domain as the product of input current i(t) and heating, aging and other visco-elastic properties voltage u(t) averaged over a measurement interval or cause a dependency of the transfer function H(f,rref), in the frequency domain as the integral of the cross- directivity factor Q(f) and impedance ZE(f) on the power density function Sui(f): particular input signal u(t). In other words, the frequency responses are used as effective parameters Putit()() Sfdf ( ) eui of a relatively simple (linear) model approximating a much more complex problem. (2) Sf() Zf ()1 df uu E 4 Voltage Sensitivity which is equivalent to the auto power spectrum of Most power amplifiers provide a low output the stimulus Suu(f) divided by the real part of the impedance, and the terminal voltage u(t) electric input impedance ZE(f). The acoustic output corresponds with the audio input signal. The voltage power Pa can be determined by integrating the far sensitivity defined as the sound pressure level field sound pressure over a closed surface S around u SPL() f 20log H (, f r ) ref (7) the transducer and expressing the result in the time urref, ref ref and frequency domain p0 in dB for given reference rms value of the input 1 2 PptdS (,r ) voltage such as u =1Vrms at a given reference a c ref 0 S point rref using the reference sound pressure (3) -5 1 2 p0=2∙10 Pa. It is necessary to introduce the voltage Suu() f H (, frr ref ) Q (, f ref ) Sdf sensitivity as a frequency dependent characteristic c 0 because a smart loudspeaker system with extensive use of equalization and linearization puts demanding requirements on the power amplifier to generate the loudspeaker mounted in a sealed enclosure output without limiting. calculated based on the lumped parameter model in Eqs. (8) and (9) assuming omnidirectional radiation 5 Moving Coil Loudspeaker into the half space for a sinusoidal tone of frequency The further investigations are performed on an f. electro-dynamic transducer using a moving coil in a static magnetic field. 5.1 Passband Performance The electro-acoustic transfer function of this The efficiency η(f) is almost constant in the transducer type can be modelled at small passband of the loudspeaker with 2fs < f < 5fs, where displacement x≈0 and at lower frequencies where the the back EMF is not active and the effect of the influence of the voice coil inductance is negligible inductance and radiation load is negligible. This by constant value is defined in standards (e.g.