UNCORRECTED PROOF 3 Acoustic electromechanical resonance filters 4 D.K. Fragoulis, J.N. Avaritsiotis * 5 Department of Electrical and Computer Engineering, Division of Computer Science, National Technical University of Athens, 6 9 Heroon Polytechniou Street, 15 773 Zographou, Athens, Greece 7 Received 3 September 2001; received in revised form 5 December 2001; accepted 10 December 2001 8 9 Abstract 10 11 A mechanical resonator is used as the basis of an acoustically excited filter. The resonator, which is essentially a simple brass, reed-like 12 structure, is located in a magnetic field generated by a permanent magnet. In the presence of a sound field, the mechanical resonator is excited 13 and its motion is detected by measuring the induced voltage across its terminals. The frequency response, the sound pressure sensitivity and 14 the directional properties of various resonant elements were measured so as demonstrate their ability to function as resonant sound sensors. 15 The experimental results show that the proposed device may work very well as a frequency indicator since in the case of light damping it is 16 able to detect small frequency deviations. Furthermore, a reduction of the device dimensions is discussed, in order to implement a resonant 17 microsystem that functions according to an applicable electrodynamic signal pickup scheme. # 2002 Published by Elsevier Science B.V. 18 19 Keywords: Mechanical filters; Resonant filters; Acoustic filters; Electrodynamic transducers 20 21 1. Introduction 22 Mechanical sensors belong to one of the broadest and 23 most commonly used category of sensors [1]. Using a 24 mechanical sensor, such as the membrane of a microphone, 25 one can generally measure the acoustic pressure directly. In 26 this case, the resonance curve of the membrane is required to 27 have a broad flat part. However, a mechanical sensor with 28 higher frequency selectivity could be useful as a resonant 29 sensor. 30 Elements in the form of vibrating reeds may be used as 31 mechanical sensors for sound signals [2–4]. A simple can- 32 tilever beam with a pick-up at its free end exhibits a 33 resonance curve with a dominant peak and therefore, it 34 can be used as a mechanical band pass filter. However, 35 the mechanical filter must be able to collect a sufficient 36 amount of energy from the sound field. For this reason a 37 small plate is attached at the free end of a cantilever beam, 38 which operates both as a pick-up and as a sound energy 39 collector. A mechanical structure is illustrated in Fig. 1, that 40 can perform mechanical filtering. It consists of two parallel 41 cantilever beams, at the free ends of which a relative small 42 and stiff plate has been attached. 43 The measurement technique of a mechanical system’s 44 response, that is simple to visualize because the displace- 45 ments generally are very small is to convert them into an 46 electrical current or voltage because one can then make use 47 of all the signal conditioning and processing capabilities that 48 electronics provide. This conversion may be accomplished 49 using an electromechanical transducer [5,6]. 50 A commonly used type of electromechanical transducer 51 that is based on the electrostatic field variations in conden- 52 sers is the electrostatic transducer. A condenser in its 53 simplest form consists of two metal surfaces of area (S) 54 parallel to each other, one of which may be a part of a 55 mechanical sensor. For small displacements (x), the change 56 in the capacitance may be considered approximately as 57 linear, so that: C ¼ C e d d  x    C e 1 þ d x   59 60 where C e represents the equilibrium value of the capacitance 61 and d the equilibrium value of the condenser plates separa- 62 tion. However, this method exhibits important disadvantages 63 not only because the linear approximation of the capacitance 64 changes is not accurate, but also because the equilibrium 65 separation (d) degrades significantly with time and finally 66 because the unavoidable capacity changes in cables and 67 other instrumentation components can induce spurious sig- 68 nals that are similar to those produced by the mechanical 69 system. For these reasons, a more propitious approach to the 70 transducing problem is proposed by the use of an electro- 71 dynamic transducer. Sensors and Actuators A 3332 (2002) 1–7 1 0924-4247/02/$ – see front matter # 2002 Published by Elsevier Science B.V. 2 PII:S0924-4247(02)00004-3 * Corresponding author. Tel.: þ30-1-7722-547; fax: þ30-1-7722-548. E-mail address: abari@cs.ntua.gr (J.N. Avaritsiotis).