# Improved Sound Radiation of Flat Panel Loudspeakers Using the Local Air Spring Effect
## 1 Introduction  
Flat-panel loudspeakers are becoming increasingly important for today's consumer market [1]. The invisible integration, wide and diffused radiation and improved room interaction are features of flat-panel loudspeakers, mentioned by [PERSON] [2], for improving the perceived audio quality. Furthermore, large and more powerful devices can be integrated without disturbing customers' views or disrupting the aesthetics of a room. However, in addition to invisible integration, flat-panel loudspeakers must posses acoustic quality that is comparable to that of conventional systems. [PERSON] [3] reported that customers of audio devices expect that the audio signal can be reproduced at a sufficient amplitude and quality. The acoustic quality can be expressed in terms of frequency limits, the maximum sound pressure level, the flatness of the pressure response, the harmonic and nonlinear distortions and the radiation characteristics [4, 5]. This study concentrates primarily on the flatness of the response, which is essential to the listener preference rating emphasized by [PERSON] [6]. Flat panel loudspeakers have higher deviations than conventional systems. In particular, in the low-frequency range, the modal density is low on the logarithmic frequency scale [7]. To optimize the spectrum of flat-panel loudspeakers, [PERSON] [8] recommended optimizing the distance between the modal frequencies to give the illusion of a continuous spectrum. However, in many cases, it is not possible to increase the modal density in the low frequency range: the material properties, the thickness of the panel and the design are fixed. Therefore, the lack of a low-frequency response needs to be resolved by construction or excitation. An example of an insufficient frequency response is shown in Figure 1. Deviations of more than 20 dB in the lower frequency range are possible. The deviations decrease for higher frequencies. Several constructive and control approaches have already been developed to improve the flatness of flat-panel loudspeaker responses. It is known that the damping of the boundary conditions, as well as the stiffness and damping of the coupled air volume (panel volume) or individual attachedconcentrated masses, have a positive influence on the pressure response [9; 10; 11; 12]. Another sufficient control variable is the position of the exciter. This can be optimized with a numerical analysis to find the best excitation positions in a fast and automatized way [13]. The achievable effect is physically limited. A single force driver is not able to excite all eigenmodes in an efficient way. Consequently, individual modes are excited with different levels of intensity, which occurs due to the superposition as a flatter pressure response. An alternative solution was presented by [PERSON] [14], who recommended the usage of an array of force drivers to selectively excite the lowest eigenmodes of the flexible panel. This construction enables the same acoustic performance as a conventional speaker within the array-addressable frequency region. However, it increases the costs and complexity due to the higher number of exciters and controlled outputs of the DSP. The last approach is known as the paneled woofer design introduced by [PERSON] [15]. A conventional woofer radiates into a small air gap between the panel and a separation plate and excites the panel uniformly. This results in a flat response, which is comparable to a conventional woofer design. This design is limited to higher frequencies and needs to be supplemented by an exciter. This paper presents a new control variable--modal related air compliance. It is known that the spring of the panel volume has a strong modal-dependent influence and can shift modes individually based on their effective radiating area [16; 17]. Furthermore, the panel volume is connected with a significant increase in the system's resonance frequency, but the air spring-related stiffness is independent of the enclosure shape, as reported by [PERSON] [18].