Piezoelectric speakers and earpieces have several appealing features: they are thin and lightweight, their current consumption is low and they are cheap to manufacture. Despite these advantages they have been usable only in niche applications, since the performance available from them is usually well below the quality expectations; they are plagued by both strong coloration and disturbing nonlinearity. The solution proposed in this paper for these problems is to apply negative feedback. An extremely simple arrangement for achieving this is to use a part of the surface area of a piezoelectric driver as a displacement sensor and use this signal to create feedback. (The same result can be, of course, achieved through the use of an external sensing element, but at the cost of added complexity.) Since the feedback signal is proportional to the displacement, and the sound pressure radiated to the free space is approximately proportional to the acceleration of a compact source surface, either the feedback signal or the input signal has to be differentiated twice (or, in practice, passed through a second-order low-pass filter). The electronics needed for this kind of feedback is otherwise extremely simple, consisting of an input amplifier with a high input impedance for the feedback signal and a summation amplifier, in addition to the circuitry normally needed to drive the transducer.
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https://aes2.org/publications/elibrary-page/?id=8200
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