Abstract:
A piezoelectric transducer for energy-harvesting systems includes a substrate, a piezoelectric cantilever element, a first magnetic element, and a second magnetic element, mobile with respect to the first magnetic element. The first magnetic element is coupled to the piezoelectric cantilever element. The first magnetic element and the second magnetic element are set in such a way that, in response to relative movements between the first magnetic element and the second magnetic element through an interval of relative positions, the first magnetic element and the second magnetic element approach one another without coming into direct contact, and the interaction between the first magnetic element and the second magnetic element determines application of a force pulse on the piezoelectric cantilever element.

Description:
BACKGROUND 
       [0001]    1. Technical Field 
         [0002]    The present disclosure relates to a piezoelectric transducer for an energy-harvesting system and to a method for harvesting energy through a piezoelectric transducer. 
         [0003]    2. Description of the Related Art 
         [0004]    The disclosure is particularly suited to the production of piezoelectric microtransducers that may be used in miniaturized energy-harvesting systems capable of supplying, among others, electronic components and/or devices, such as low-consumption sensors and actuators, frequently used in portable electronic devices, such as cellphones, tablet computers, portable computers (laptops), video cameras, photographic cameras, consoles for videogames, and so forth. 
         [0005]    As is known, systems for collecting energy from environmental-energy sources (also referred to as energy harvesting or energy scavenging systems) have aroused and continue to arouse considerable interest in a wide range of fields of technology. Typically, energy-harvesting systems are designed to harvest (or scavenge), store, and transfer energy generated by mechanical sources to a generic load of an electrical type. In this way, the electrical load does not use batteries or other supply systems that are frequently cumbersome, have low resistance to mechanical stresses and entail maintenance costs for replacement operations. Furthermore, systems for harvesting environmental energy are of considerable interest for devices that are in any case provided with battery supply systems, which, however, have a rather limited autonomy. This is the case, for example, of many portable electronic devices that are increasingly becoming widely used, such as cellphones, tablets, portable computers (laptops), video cameras, photographic cameras, consoles for videogames, etc. Systems for harvesting environmental energy may be used for supplying components or devices in order to reduce the energy absorbed from the battery and, in practice, increase the autonomy. 
         [0006]    Environmental energy may be harvested from several available sources and converted into electrical energy by appropriate transducers. For instance, available energy sources may be mechanical or acoustic vibrations or, more in general, forces or pressures, chemical-energy sources, electromagnetic fields, environmental light, thermal-energy sources. 
         [0007]    For harvesting and conversion piezoelectric transducers may, among others, be used. 
         [0008]    Piezoelectric transducers are in general based upon a microstructure comprising a supporting body, connected to which are piezoelectric cantilever elements, having at least one portion made of piezoelectric material. The free ends of the piezoelectric cantilever elements, to which additional masses can be connected, oscillate elastically in response to movements of the supporting body or to vibrations transmitted thereto. As a result of the movements of bending and extension during the oscillations, the piezoelectric material produces a charge that can be harvested and stored in a storage element. 
         [0009]    In miniaturized transducers, however, the use of just the piezoelectric cantilever elements and the additional masses does not enable adequate levels of efficiency to be achieved. In practice, the conversion of kinetic energy is not satisfactory because the natural frequency of the system formed by the piezoelectric cantilever element and by the additional mass is too different from the typical environmental frequencies that can be transduced. 
         [0010]    To improve the efficiency of piezoelectric transducers, it has been proposed to use a movable mass separate from the piezoelectric cantilever elements and magnets that enable temporary coupling of the movable mass and piezoelectric cantilever elements. The magnets are arranged in part on the movable mass and in part on the piezoelectric cantilever elements and are oriented so as to exert attractive forces. The movable mass is constrained to the supporting body so as to be able to come into contact with the piezoelectric cantilever elements and enable coupling of the magnets. The piezoelectric cantilever elements are drawn along in motion by the movable mass and undergo deformation until the elastic return force exceeds the magnetic force. At this point, the magnets separate, and the action of the magnetic force on the piezoelectric cantilever elements ceases almost instantaneously as the movable mass moves away, allowing the elastic force alone to act. In practice, this is equivalent to applying a force pulse on the piezoelectric cantilever elements, which are hence stimulated over a wide frequency band, which also includes the resonance frequency. 
         [0011]    Albeit far better from the efficiency standpoint, the devices described present, however, some limits in terms of reliability. In fact, each oscillation of the movable mass causes impact between the magnets of the movable mass itself and the magnets of the piezoelectric cantilever elements. Even though the frequency of oscillation of the movable mass is low (generally less than about 10 Hz), in the long run repetition of the impact may cause damage to the microstructure. In particular, microcracks may be formed, which rapidly propagate until they render the transducer unserviceable. 
       BRIEF SUMMARY 
       [0012]    The present disclosure is directed to a piezoelectric transducer for an energy-harvesting system and a method for harvesting energy through a piezoelectric transducer that enables the limitations described to be overcome or at least attenuated. 
         [0013]    One embodiment of the present disclosure is a transducer that includes a substrate, a moveable mass elastically coupled to the substrate, a plurality of cantilever piezoelectric elements extending from the substrate towards the moveable mass, a plurality of first magnetic elements at free ends of respective cantilever piezoelectric elements, and a plurality of second magnetic elements on the moveable mass, each second magnetic element being aligned with cantilever piezoelectric elements in a rest condition. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0014]    For a better understanding of the disclosure, some embodiments thereof will now be described, purely by way of non-limiting example and with reference to the attached drawings, wherein: 
           [0015]      FIG. 1  is a simplified block diagram of an energy-harvesting system; 
           [0016]      FIG. 2  is a simplified top plan view of a piezoelectric transducer according to one embodiment of the present disclosure and incorporated in the energy-harvesting system of  FIG. 1 , the piezoelectric transducer being represented in a first operating configuration; 
           [0017]      FIG. 3  shows the piezoelectric transducer of  FIG. 2  in a second operating configuration; 
           [0018]      FIG. 4  shows the piezoelectric transducer of  FIG. 2  in a third operating configuration; 
           [0019]      FIG. 5  shows the piezoelectric transducer of  FIG. 2  in a fourth operating configuration; 
           [0020]      FIG. 6  is a graph that shows quantities regarding the piezoelectric transducer of  FIG. 2 ; 
           [0021]      FIG. 7  is a simplified top plan view of a piezoelectric transducer according to a different embodiment of the present disclosure, in a first operating configuration; 
           [0022]      FIG. 8  shows the piezoelectric transducer of  FIG. 7  in a second operating configuration; 
           [0023]      FIG. 9  is a top plan view, with parts removed for clarity, of a piezoelectric transducer according to a different embodiment of the present disclosure; 
           [0024]      FIG. 10  is an enlarged cross-sectional view through the piezoelectric transducer of  FIG. 9 , taken along the line X-X of  FIG. 9 ; 
           [0025]      FIG. 11  is a top plan view, with parts removed for clarity, of a piezoelectric transducer according to a further embodiment of the present disclosure; 
           [0026]      FIG. 12  is an enlarged cross-sectional view through the piezoelectric transducer of  FIG. 11 , taken along the line XII-XII of  FIG. 12 ; 
           [0027]      FIG. 13  is a top plan view, with parts removed for clarity, of a piezoelectric transducer according to a further embodiment of the present disclosure; and 
           [0028]      FIG. 14  is an enlarged cross-sectional view through the piezoelectric transducer of  FIG. 13 , taken along the line XIV-XIV of  FIG. 13 . 
       
    
    
     DETAILED DESCRIPTION 
       [0029]    With reference to  FIG. 1 , an energy-harvesting system is designated as a whole by the reference number  1 . The energy-harvesting system  1  is particularly, but not exclusively, suited to being used for supplying electronic components and/or devices, such as low-consumption sensors and actuators, which ever more frequently used in portable electronic devices, such as cellphones, tablets, portable computers (laptops), video cameras, photographic cameras, consoles for videogames, etc. 
         [0030]    Electronic components and devices supplied through the energy-harvesting system  1  are rendered self-sufficient and do not absorb energy from the main supply system (normally a battery), which hence has greater autonomy, to the advantage of users. 
         [0031]    Furthermore, in some applications the energy-harvesting system  1  may be used both as main supply source, and as auxiliary supply source for the electronic components and/or devices referred to above. In this case, the energy-harvesting system  1  may be set alongside a conventional supply system, for example a battery supply, and go into operation when the main supply system runs down or presents malfunctioning. 
         [0032]    The energy-harvesting system  1  comprises a transducer  2 , a harvesting interface  3 , a storage element  5 , a selective-connection device  6 , and a voltage regulator  7 . Furthermore, an output of the voltage regulator  7  supplies an electrical load  8 . 
         [0033]    The transducer  2  supplies a harvesting voltage V H  in response to energy provided by an environmental-energy source  4  external to the harvesting system  1 . The transducer  2  is a piezoelectric transducer that supplies a harvesting voltage V H  in response to mechanical vibrations transmitted from the outside environment and will be described in greater detail hereinafter. 
         [0034]    The harvesting interface  3 , when supplied by the storage element  5 , receives the harvesting voltage V H  from the transducer  2  and supplies a charge current I CH  to the storage element  5 . The energy stored in the storage element  5  increases as a result of the charge current I CH  and produces a storage voltage V ST . 
         [0035]    The selective-connection device  6  selectively connects and disconnects a supply input  3   a  of the harvesting interface  3  and the storage element  5  on the basis of the response of the transducer  2 . More precisely, when the harvesting voltage V H  exceeds an activation threshold V A , that represents a state in which the transducer  2  is active and receives environmental energy from outside, the selective-connection device  6  connects the harvesting interface  3  to the storage element  5 , so that the harvesting interface  3  receives the storage voltage V ST  present on the storage element  5 . 
         [0036]    The harvesting interface may thus use the harvesting voltage V H  for charging the storage element  5 . 
         [0037]    Instead, when the transducer  2  does not receive environmental energy and the harvesting voltage V H  is below the activation threshold V A , the selective-connection device  6  disconnects the harvesting interface  3  from the storage element  5 , so that the consumption of energy of the harvesting interface  3  ceases. 
         [0038]    In one embodiment, in particular, the selective-connection device comprises a switch  10  and a driving stage  11 , configured to drive the switch  10  on the basis of the comparison between the harvesting voltage V H  and the activation threshold V A . 
         [0039]    The voltage regulator  7  receives the storage voltage V ST  and supplies a regulated supply voltage V DD  to the electrical load  8 . 
         [0040]    The selective-supply device  6  substantially makes it possible to reduce to zero the consumption of the harvesting interface  3  in the absence of activity of the transducer  2  and hence prevents dissipation of energy accumulated on the storage element  5 , when the harvesting system  1  is not in a condition to receive energy from the environment. 
         [0041]    According to one embodiment of the disclosure, illustrated in  FIGS. 2-5 , the transducer  2  comprises a microstructure including a supporting body  15 , a movable mass  16 , and an oscillating piezoelectric cantilever element  17 . The supporting body  15 , the movable mass  16 , and part of the piezoelectric cantilever element  17  are made of semiconductor material, for example monocrystalline silicon. 
         [0042]    The supporting body  15  may be a monolithic semiconductor body, or else may be obtained from the union of two or more semiconductor dice, possibly with the interposition of bonding layers and/or dielectric layers. 
         [0043]    The movable mass  16  is elastically coupled to the supporting body  15  by a system of suspensions  18 , here schematically represented by a spring and a damper. The suspensions  18  are configured to enable oscillations of the movable mass  16  along one or more axes of transduction at a first resonance frequency (main resonance frequency of the movable mass  16  constrained by the suspensions  18 ), for example less than 10 Hz. In the example described, in particular, the movable mass  16  (the position of which during an oscillation is indicated by a dashed line in the graph provided by way of example in  FIG. 6 ) can translate along a transduction axis X parallel to a face  15   a  of the supporting body  15  between a first end-of-travel position X 1  and a second end-of-travel position X 2 , where there are set stop elements (not shown) in order to prevent undesirable and potentially harmful over-shooting. The movable mass  16  may comprise, in addition to semiconductor structures, also layers or portions made of heavy metals, such as lead or tungsten, in order to improve the energy-harvesting efficiency. 
         [0044]    In one embodiment, the piezoelectric cantilever element  17  is defined by a piezoelectric layer  20  formed on a face of a supporting plate  21  made of semiconductor material, integral with the supporting body  15 . The piezoelectric layer  20  and the supporting plate  21  are coupled in such a way that any bending of the supporting plate  21  causes corresponding deformations of the piezoelectric layer  20 . Furthermore, the piezoelectric layer  20  is connected to a contact pad  22  on the supporting body  15 . 
         [0045]    The piezoelectric cantilever element  17  is anchored to the supporting body  15  and projects from the supporting body  15  in the direction of the movable mass  16 , as illustrated in  FIGS. 2-4 . 
         [0046]    Furthermore, the piezoelectric cantilever element  17  extends in a direction transverse, for example substantially perpendicular, to the transduction axis X, which coincides with the direction of motion of the movable mass  16 . The length of the piezoelectric cantilever element  17  is such that a free end thereof occupies a position in the proximity of the movable mass  16  at least in an interval of positions of the movable mass  16  along the transduction axis X, without, however, any contact between the movable mass  16  and the piezoelectric cantilever element  17 . Preferably, between the movable mass  16  and the piezoelectric cantilever element  17  there is always present at least a minimum distance L G  ( FIG. 2 ). 
         [0047]    The ensemble constituted by the piezoelectric cantilever element  17  and the piezoelectric layer  20  is elastically deformable and can oscillate with respect to a rest position with a second resonance frequency (main resonance frequency of the piezoelectric cantilever element  17 ), higher than the first resonance frequency by at least one order of magnitude and preferably comprised between 1 kHz and 10 kHz. In one embodiment, the second resonance frequency is approximately 1 kHz. 
         [0048]    A first magnetic element  25  and a second magnetic element  26  are set, respectively, at the free ends of the piezoelectric cantilever element  17  and on the movable mass  16 , on an edge adjacent to the piezoelectric cantilever element  17 . The magnetic characteristics of the first magnetic element  25  and of the second magnetic element  26  are selected in such a way that a magnetic force deriving from the interaction of the first magnetic element  25  and of the second magnetic element  26  is sufficient to deform the piezoelectric cantilever element  17  upon passage of the movable mass  16  through an interval of interaction positions ΔX around a rest position X 0  of the piezoelectric cantilever element  17 . Furthermore, the magnetic characteristics of the first magnetic element  25  and of the second magnetic element  26  are selected so that, outside the interval of interaction positions ΔX, the elastic return force due to deformation of the piezoelectric cantilever element  17  prevails over the magnetic force between the first magnetic element  25  and the second magnetic element  26 . Furthermore, outside the interval of interaction positions ΔX the magnetic force rapidly decays as a result of the increasing distance. 
         [0049]    When the supporting body  15  varies its condition of motion or is subjected to impact or vibrations, the movable mass  16  oscillates along the transduction axis X. Upon passage through the interval of interaction positions ΔX, albeit in the absence of direct contact, the magnetic interaction between the first magnetic element  25  and the second magnetic element  26  causes deformation of the piezoelectric cantilever element  17 . When the movable mass  16  passes beyond the interval of interaction positions ΔX, the elastic return force prevails, and the magnetic force decays until it soon becomes negligible. The piezoelectric cantilever element  17  thus receives a force substantially of an impulsive type, which produces stimuli over a wide frequency band, including the second resonance frequency. The piezoelectric cantilever element  17  starts to oscillate as a result of the pulse received, as indicated with a solid line in  FIG. 6 , and the corresponding deformation of the piezoelectric layer  20  produces a voltage that can be picked up at the pad  22  and used for charging the storage element  5 . 
         [0050]    It is to be noted that the magnetic forces between the first magnetic element  25  and the second magnetic element  26  may be indifferently of an attractive or repulsive type, provided that the interaction determines a force pulse on the piezoelectric cantilever element  17  during traversal of the interval of interaction positions ΔX. In one embodiment, the magnetic forces may be attractive when the second magnetic element  26  is located on one side of the first magnetic element  25  and repulsive when the second magnetic element  26  is located on the opposite side. 
         [0051]    Energy harvesting is efficient because the oscillations of the movable mass  16  and the piezoelectric cantilever element  17  are decoupled, and hence the piezoelectric cantilever element  17  may vibrate at its natural resonance frequency. Furthermore, the force pulses are transmitted to the piezoelectric cantilever element  17  without direct contact with the movable mass  16  or with the first magnetic element  25  placed thereon. The parts of the microstructure are hence not subjected to impact during operation, to the advantage of reliability. 
         [0052]    According to one embodiment, illustrated in  FIGS. 7 and 8 , a piezoelectric transducer  100 , which may be used in the energy-harvesting system  1  instead of the piezoelectric transducer  2 , comprises a supporting body  115 , a movable mass  116 , and an oscillating piezoelectric cantilever element  117 . The supporting body  115 , the movable mass  116 , and part of the piezoelectric cantilever element  117  are made of semiconductor material, for example monocrystalline silicon. 
         [0053]    The movable mass  116  is elastically connected to the supporting body  115  by a system of suspensions  118 , fixed to an anchorage  119  and configured to enable oscillations of the movable mass  116  along a transduction axis X′ parallel to a face  115   a  of the supporting body  115  with a first resonance frequency, for example less than 10 Hz. 
         [0054]    The piezoelectric cantilever element  117  is defined by a piezoelectric layer  120  formed on a face of a supporting plate  121  of semiconductor material, integral with the movable mass  116 . The piezoelectric layer  120  and the supporting plate  121  are shaped so that any bending of the supporting plate  121  causes corresponding deformations of the piezoelectric layer  120 . Furthermore, the piezoelectric layer  120  is connected to a contact pad  122  on the supporting body  115  through the suspensions  118  and the anchorage  119 , which may themselves be made conductive by appropriate doping or else may be coated with a metal layer. 
         [0055]    The piezoelectric cantilever element  117  projects from the movable mass  116  in a direction parallel to a face  115   a  of the supporting body  115  and substantially perpendicular to the transduction axis X. 
         [0056]    The ensemble of the piezoelectric cantilever element  117  and the piezoelectric layer  120  is elastically deformable and can oscillate with respect to a rest position at a second resonance frequency, higher than the first resonance frequency. 
         [0057]    A first magnetic element  125  is set at the free end of the piezoelectric cantilever element  117 . 
         [0058]    A second magnetic element  126  is set on the supporting body  115 , along the path of a free end of the piezoelectric cantilever element  117 , so that the free end of the piezoelectric cantilever element  117  passes over the first magnetic element  125  or in its immediate vicinity, without in any case direct contact, however. 
         [0059]    The magnetic characteristics of the first magnetic element  125  and second magnetic element  126  are selected so that a magnetic force deriving from the interaction of the first magnetic element  125  and of the second magnetic element  126  is sufficient to deform the piezoelectric cantilever element  117  upon passage of the piezoelectric cantilever element  117  in the proximity of the second magnetic element  126 . Furthermore, the magnetic characteristics of the first magnetic element  125  and of the second magnetic element  126  are selected so that, outside of an interval of interaction positions ΔX′, the elastic return force due to deformation of the piezoelectric cantilever element  117  prevails over the magnetic force between the first magnetic element  125  and the second magnetic element  126 . Furthermore, outside of the interval of interaction positions ΔX′ the magnetic force decays rapidly as a result of the increasing distance. 
         [0060]      FIGS. 9 and 10  illustrate a piezoelectric transducer  200  according to a different embodiment of the present disclosure. The transducer  200  comprises a supporting body  215 , a movable mass  216 , and a plurality of oscillating piezoelectric cantilever elements  217 . The supporting body  215 , the movable mass  216 , and parts of the piezoelectric cantilever elements  217  are made of semiconductor material, for example monocrystalline silicon. Also illustrated in  FIG. 10  is a protective cap  250  arranged so as to cover the movable mass  216 . 
         [0061]    The supporting body  215  has a recess  215   b  accessible through a face  215   a . The recess  215   b  houses the movable mass  216 , which, in a rest configuration, is flush with the face  215   a.    
         [0062]    The movable mass  216 , which has a substantially rectangular or square shape, is elastically connected to the supporting body  215  by a system of suspensions  218 , configured so as to enable oscillations of the movable mass  216  along a transduction axis Z at a first resonance frequency. In the example described, in particular, the transduction axis Z is perpendicular to a face  215   a  of the supporting body  215 . The transducer  200  is consequently of the so-called “out of plane” type. By way of non-limiting example, the movable mass  216  may have a length and width of between 400 and 800 μm, while the thickness may reach 400 μm. 
         [0063]    The piezoelectric cantilever elements  217  are defined by piezoelectric layers  220  formed on faces of respective supporting plates  221  of semiconductor material, integral with the supporting body  215  and having faces parallel to the face  215   a  of the supporting body  215  itself. The piezoelectric layers  220  and the supporting plates  221  are shaped so that any bending of the supporting plates  221  causes corresponding deformations of the respective piezoelectric layers  320 . Furthermore, the piezoelectric layers  220  are connected to respective contact pads  222  set on the supporting body  215 . 
         [0064]    The piezoelectric cantilever elements  217  project from the supporting body  215 , in particular from the perimeter of the recess  215   b , towards the movable mass  216 , in a direction substantially perpendicular to the transduction axis Z and parallel to the face  215   a  of the supporting body  215 . In greater detail, the piezoelectric cantilever elements  217  are comb-fingered in groups, each of which faces a respective side of the movable mass  216 . The length of the piezoelectric cantilever elements  217  is such that the respective free ends are in the proximity of the movable mass  216  at least in an interval of positions of the movable mass  216  along the transduction axis Z, without, however, any contact between the movable mass  216  and the piezoelectric cantilever elements  217 . 
         [0065]    The ensemble of each piezoelectric cantilever element  217  and of the respective piezoelectric layer  220  is elastically deformable and can oscillate with respect to a rest position at a second resonance frequency, higher than the first resonance frequency. The oscillations are substantially in planes perpendicular to the face  215   a  of the supporting body  215 . 
         [0066]    First magnetic elements  225  and second magnetic elements  226  are set, respectively, at the free ends of the piezoelectric cantilever elements  217  and on the movable mass  216 . 
         [0067]    The second magnetic elements  226 , in particular, are arranged along the perimeter of the movable mass  216  and are each aligned to a respective piezoelectric cantilever element  217 . In one embodiment (not illustrated) a single second magnetic element is present and runs along the entire perimeter of the movable mass  216 . 
         [0068]    The first magnetic elements  226  are set at the free ends of respective piezoelectric cantilever elements  217  and are hence in the proximity of corresponding second magnetic elements  226  at least when the movable mass  216  is in an interval of interaction positions ΔZ around a rest position Z 0  of the piezoelectric cantilever elements  217 . 
         [0069]    The magnetic characteristics of the first magnetic elements  225  and the second magnetic elements  226  are selected in such a way that a magnetic force deriving from the interaction of the first magnetic elements  225  and of the second magnetic elements  226  is sufficient to deform the piezoelectric cantilever elements  217  upon passage of the movable mass  216  through the interval of interaction positions ΔZ. Furthermore, the magnetic characteristics of the first magnetic elements  225  and of the second magnetic elements  226  are selected so that, outside the interval of interaction positions ΔZ, the elastic return force due to deformation of the piezoelectric cantilever element  217  prevails over the magnetic force between the first magnetic elements  225  and the second magnetic elements  226 . Outside the interval of interaction positions ΔZ the magnetic force decays rapidly as a result of the increasing distance. In this way, passage of the movable mass  216  through the interval of interaction positions ΔZ transmits, through contactless interactions between the first magnetic elements  225  and the second magnetic elements  226 , a force pulse that sets the piezoelectric cantilever elements  217  in vibration. 
         [0070]    The embodiment described enables efficient exploitation of the kinetic energy associated to the movable mass  216  for conversion into electrical energy, in particular thanks to the high density of piezoelectric cantilever elements  217  that it is possible to obtain thanks to modern techniques of machining of semiconductors. 
         [0071]      FIGS. 11 and 12  illustrate a piezoelectric transducer  300  according to a different embodiment of the present disclosure. The transducer  300  comprises a supporting body  315 , a movable mass  316 , and a plurality of oscillating piezoelectric cantilever elements  317 . The supporting body  315 , the movable mass  316 , and parts of the piezoelectric cantilever elements  317  are made of semiconductor material, for example monocrystalline silicon. Also illustrated in  FIG. 12  is a protective cap  350  arranged to cover the movable mass  316 . 
         [0072]    The supporting body  315  has a recess  315   b  accessible through a face  315   a . The recess  315   b  houses the movable mass  316 , which, in a rest configuration, is flush with the face  315   a.    
         [0073]    The movable mass  316  has a substantially rectangular or square shape and is elastically connected to the supporting body  315  by a system of suspensions  318 , configured to enable oscillations of the movable mass  316  along a transduction axis Z′ at a first resonance frequency. In the example described, in particular, the transduction axis Z′ is perpendicular to a face  315   a  of the supporting body  315 . The transducer  300  is consequently of the so-called “out of plane” type. 
         [0074]    Present for each side of the movable mass  316  is a respective piezoelectric cantilever element  317 , which extends, in one direction, from the supporting body  315  as far as into the proximity of the movable mass  316  and, in the perpendicular direction, substantially along the entire respective side of the movable mass  316 . The piezoelectric cantilever elements  317  are defined by piezoelectric layers  320  formed on faces of respective flexible supporting plates  321  made of semiconductor material, integral with the supporting body  315  and having faces parallel to the face  315   a  of the supporting body  315  itself. 
         [0075]    The piezoelectric layers  320  and the supporting plates  321  are shaped so that any bending of the supporting plates  321  causes corresponding deformations of the respective piezoelectric layers  320 . Furthermore, the piezoelectric layers  320  are connected to respective contact pads  322  on the supporting body  315 . 
         [0076]    The ensemble of each piezoelectric cantilever element  317  and of the respective piezoelectric layer  320  is elastically deformable and can oscillate with respect to a rest position at a second resonance frequency, higher than the first resonance frequency. The oscillations are substantially in planes perpendicular to the face  315   a  of the supporting body  315 . 
         [0077]    First magnetic elements  325  and second magnetic elements  326  are set, respectively, at the free ends of the piezoelectric cantilever elements  317  and on the movable mass  316 . In one embodiment, the first magnetic elements  325  and second magnetic elements  326  are continuous strips. The first magnetic elements  325  extend along the entire edge of the respective piezoelectric cantilever elements  317 . The second magnetic elements  326  have a length substantially equal to the length of the respective coupled first magnetic elements  325 . 
         [0078]    The first magnetic elements  326  are set at the free ends of respective piezoelectric cantilever elements  317  and hence are in the proximity of corresponding second magnetic elements  326  at least when the movable mass  316  is within an interval of interaction positions ΔZ around a rest position Z 0  of the piezoelectric cantilever elements  317 . 
         [0079]    The magnetic characteristics of the first magnetic elements  325  and of the second magnetic elements  326  are selected so that a magnetic force deriving from the interaction of the first magnetic elements  325  and of the second magnetic elements  326  is sufficient to deform the piezoelectric cantilever elements  317  upon passage of the movable mass  316  through the interval of interaction positions ΔZ. Outside the interval of interaction positions ΔZ, instead, the elastic return force due to the deformation of the piezoelectric cantilever element  317  prevails over the magnetic force between the first magnetic elements  325  and the second magnetic elements  326 . 
         [0080]    Consequently, passage of the movable mass  316  through the interval of interaction positions ΔZ transmits, through contactless interactions between the first magnetic elements  325  and the second magnetic elements  326 , a force pulse that sets the piezoelectric cantilever elements  317  in vibration. The embodiment described enables limitation of the number of connections for harvesting of the mechanical energy and its conversion into electrical energy. Furthermore, the area of piezoelectric material available is further increased, given the same efficiency, and manufacture is simplified. 
         [0081]    Illustrated in  FIGS. 13 and 14  is a piezoelectric transducer  400  according to a further embodiment of the present disclosure. 
         [0082]    The piezoelectric transducer  400  comprises a supporting body  415 , a movable mass  416 , and a plurality of oscillating piezoelectric cantilever elements  417 . The supporting body  415 , the movable mass  416 , and part of the piezoelectric cantilever elements  417  are made of semiconductor material, for example monocrystalline silicon. Also illustrated in  FIG. 14  is a protective cap  450  arranged to cover the movable mass  416 . 
         [0083]    The supporting body  415  has a face  415   a  in which a circular recess  415   b  is provided. The recess  415   b  houses the movable mass  416 , flush with the face  415   a.    
         [0084]    Also the movable mass  416  has a circular shape and is connected to the supporting body by a system of suspensions  418  connected to a central anchorage  419 . The suspensions  418  are configured so as to enable the movable mass  416  to perform oscillating rotational movements, at a first resonance frequency, about a transduction axis Z″ perpendicular to the movable mass  416  itself (in practice, perpendicular to the face  415   a  of the supporting body  415 ). 
         [0085]    The piezoelectric cantilever elements  417  are defined by piezoelectric layers  420  formed on faces of respective supporting plates  421  made of semiconductor material, integral with the supporting body  415  and having faces perpendicular to the face  415   a  of the supporting body  415  itself. The piezoelectric layers  420  and the supporting plates  421  are shaped so that any bending of the supporting plates  421  causes corresponding deformations of the respective piezoelectric layers  420 . Furthermore, the piezoelectric layers  420  are connected to respective contact pads  422  set on the supporting body  415 . 
         [0086]    The piezoelectric cantilever elements  417  project from the perimeter of the recess  415   b  in a radial direction inwards and extend as far as into the proximity of the movable mass  416 , from which they are separated by radial gaps  401 . The piezoelectric cantilever elements  417  are hence not in direct contact with the movable mass  416 , either in a rest condition or in normal conditions of motion of the movable mass  416  itself. 
         [0087]    The ensemble of each piezoelectric cantilever element  417  and of the respective piezoelectric layer  420  is elastically deformable and can oscillate with respect to a rest position at a second resonance frequency, higher than the first resonance frequency. The plane of oscillation of the piezoelectric cantilever elements  417  is substantially parallel to the face  415   a  of the supporting body  415 . 
         [0088]    First magnetic elements  425  and second magnetic elements  426  are set, respectively, at the free ends of the piezoelectric cantilever elements  417  and on the movable mass  416 . 
         [0089]    The second magnetic elements  426 , in particular, are arranged along the perimeter of the movable mass  416  and are each aligned to a respective piezoelectric cantilever element  417 , when the movable mass  416  is in a rest angular position. 
         [0090]    The first magnetic elements  425  are set at the free ends of respective piezoelectric cantilever elements  417  and hence are in the proximity of corresponding second magnetic elements  426  at least when the movable mass  416  is in an interval of interaction angular positions Δθ around a rest position θ 0 . In one embodiment, in the rest position θ 0  of the movable mass  416 , the second magnets  426  are aligned to respective piezoelectric cantilever elements  417 , which are in turn in rest conditions. The direction of movement of the second magnetic elements  426  is moreover perpendicular to the faces of the piezoelectric cantilever elements  417  (the path of the first magnetic elements  425  is in fact circular, whereas the piezoelectric cantilever elements  417  extend in a radial direction). 
         [0091]    The magnetic characteristics of the first magnetic elements  425  and of the second magnetic elements  426  are selected so that a magnetic force deriving from the interaction of the first magnetic elements  425  and of the second magnetic elements  426  is sufficient to deform the piezoelectric cantilever elements  417  during rotation of the movable mass  416  through the interval of interaction angular positions Δθ. Furthermore, the magnetic characteristics of the first magnetic elements  425  and of the second magnetic elements  426  are selected so that, outside of the interval of interaction angular positions Δθ the elastic return force due to deformation of the piezoelectric cantilever element  417  prevails over the magnetic force between the first magnetic elements  425  and the second magnetic elements  426 . Outside of the interval of interaction angular positions Δθ the magnetic force decays rapidly as a result of the increasing distance. In this way, rotation of the movable mass  416  through the interval of interaction angular positions Δθ transmits, through contactless interactions between the first magnetic elements  425  and the second magnetic elements  426 , a force pulse that sets the piezoelectric cantilever elements  417  in vibration. 
         [0092]    Finally, it is evident that modifications and variations may be made to the system and method described herein, without thereby departing from the scope of the present disclosure. 
         [0093]    The various embodiments described above can be combined to provide further embodiments. These and other changes can be made to the embodiments in light of the above-detailed description. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by the disclosure.