Reproducing Low-Pitched Signals through Small Loudspeakers*

In many sound reproduction applications it is not possible to use large loudspeakers because of size or cost constraints. Typical applications are portable audio, multimedia, TV, and public address systems, to name just a few. Hence the devices are often small in size, and therefore the transducers are inherently small as well. Needless to say, the competitive market just mentioned also dictates the highest possible audio quality of these products. However, probably the most well-known characteristic of small loudspeakers is a poor low-frequency (bass) response. In practice this means that a significant portion of the audio signal may not be reproduced (sufficiently) by the loudspeaker. For loudspeakers used in such applications reproduction below 100 Hz is usually negligible, whereas in some applications this lower limit can easily be as high as several hundred hertz. The bass portion of an audio signal contributes significantly to the sound “impact,” and depending on the bass quality, the overall sound quality will shift up or down. Therefore a good low-frequency reproduction is essential. A traditional and conceptually very simple method to increase the perceived sound level in the lower part of the audible spectrum (below the loudspeaker’s resonance frequency, which is usually the lower limit) is to amplify the low-frequency part of the audio spectrum by a fixed or a dynamic amount (depending on the signal amplitude or the reproduction level). A special system that purposefully drives a loudspeaker below resonance is the ELF system, described in Long and Wickersham [1], [2]. From an efficiency point of view these methods are unfavorable, but an even more serious problem is the high cone excursion at low frequencies (quadrupling for every octave down in frequency). For very low frequencies, the mechanical limits of the loudspeaker will limit the stroke the cone can make, leading to distortion and possibly loudspeaker overload. Thus increasing the radiated sound pressure level physically means forcing the loudspeaker to radiate sound in a frequency range for which it is not equipped. It may be better to prevent this completely by using methods to be outlined in this paper. In the process we shall discover several advantages of these methods. Because the radiation characteristics of (small) loudspeakers are at the core of the topic to be discussed, we shall review these characteristics in terms of the loudspeaker parameters. Because this is fairly well-known material (see, for example, Beranek [3], Olson [4], or Borwick [5] for extensive reviews), this will be discussed in Appendix 1. We will show that in the normal operating range of the loudspeaker (above resonance and below the transition frequency, where the wavelength becomes roughly equal to the cone diameter), the efficiency η is