Overtone piezoelectric resonantors for power conversion

Abstract

A piezoelectric resonator includes a piezoelectric element having a first surface and a second surface on an opposite side of the piezoelectric element from the first surface, a first set of electrodes electrically connected to the first surface, the first set of electrodes comprising one or more electrodes of a first polarity alternating with electrodes of a second polarity in a first sequence, and a second set of electrodes electrically connected to the second surface, the second set of electrodes comprising one or more electrodes of a first polarity alternating with electrodes of a second polarity in a second sequence opposite of the first sequence, the energizing of the electrodes causing the piezoelectric element operate in an overtone resonant mode.

Description

Patent Application U Cal No. BK-2024-159-2-PCT MN No.407869-0210 OVERTONE PIEZOELECTRIC RESONANTORS FOR POWER CONVERSION TECHNICAL FIELD

[0001] This disclosure relates to piezoelectric resonators, more particularly using overtones in piezoelectric resonators for power conversion. BACKGROUND

[0002] Demand for power electronics with smaller volume, lighter weight, and lower cost motivates investigation into alternative power passive component technologies. Miniaturization of power converters is bottlenecked by magnetics, whose power densities fundamentally reduce at small scales. Capacitors exhibit much more favorable densities at small sizes, but efficient voltage regulation and galvanic isolation are difficult to achieve without magnetics.

[0003] One promising alternative passive component technology is piezoelectric components. Single-port piezoelectric resonators (PRs) are commonly modeled using the Butterworth-Van Dyke (BVD) model shown in FIG.1, in which the RLC branch models the PR’s mechanical resonance and loss. PRs offer very high quality factors of great than 1400, which translate to high efficiency capabilities, and it has been shown that the power handling densities of PRs fundamentally increase at small sizes. In addition, PRs offer other potential advantages to power conversion including planar form factors, batch fabrication, and potential for integration. Magnetic-less power converter designs based on PRs have been demonstrated with high power density of up to 5.7kW / cm3and efficiency of up to >99%. As visualized in Fig.2, however, maximum efficiencies of these converters have been limited to applications of high load impedance.

[0004] This trend may be explained by PRs themselves having high characteristic impedances, and that they perform most efficiently when the converters’ load impedances are of similar magnitude. One way to reduce the effective characteristic impedance of PRs is to connect several PRs in parallel. Parallelization of several small PRs is also advantageous in terms of power handling density compared to a single large PR. However, parallelizationposes additional challenges, including current sharing between PRs and synchronization of PRs with slight manufacturing variations, and has been observed to cause significant additional loss. A second strategy involves parallelization of multiple PR-based power converters, which requires additional switches and increases control complexity but enables higher performance at lower load impedance as shown in FIG.2. This motivates exploration of PR design strategies that will enable such improvement at the component level. BRIEF DESCRIPTION OF THE DRAWINGS

[0005] FIG.1 shows a Butterworth-Van Dyke (BVD) model for piezoelectric resonator (PR) and its impedance.

[0006] FIG.2 shows a graph of efficiency versus load impedance of ten PR-based power converter designs.

[0007] FIG.3 shows an embodiment of a solid-electrode PR operating in the length extensional vibration mode.

[0008] FIG.4 shows generated current density profiles along the vibration direction of the length extensional vibration mode PRs.

[0009] FIG.5 shows embodiments of PRs with alternating electrodes.

[0010] FIG.6 shows an embodiment of a PR-based power converter topology.

[0011] FIG.7 shows a graph of simulation waveforms and switch signals for a switching sequence for a PR power converter.

[0012] FIG.8 shows an embodiment of a 1st-overtone, radial vibration mode PR.

[0013] FIG.9 shows a graph of comparison of measurements between impedance measurements, simulation, and BVD model of a 1st-overtone, radial vibration mode PR.

[0014] FIG.10 shows a graph of experimental efficiencies of radial vibration mode PR at different power levels with fixed Vin = 100 V.

[0015] FIG.11 shows a graph of experimental efficiencies of radial vibration mode PR at different power levels with fixed Vin= 12 V.

[0016] FIG.12 shows oscilloscope waveform for an embodiment of a 1st-overtone radial vibration mode PR at Vin = 100 V, Vout = 65 V and Pout = 15 W.

[0017] FIG.13 shows oscilloscope waveform for an embodiment of a 1st-overtone radial vibration mode PR at Vin = 12 V, Vout = 7 V and Pout = 0.45 W. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0018] While piezoelectric resonators (PRs) are typically utilized at their lowest resonant frequencies, meaning their fundamental resonant modes, they exhibit an infinite series of higher resonant frequencies referred to as “overtones.” The embodiments herein explore intentional utilization of overtones as primary resonant modes in PR designs for power conversion. These are then evaluated for the potential of overtone PRs for extending the utility of PRs to applications with lower load impedance and achieving the same efficiency as fundamental-mode PRs and achieving even greater PR power handling density than fundamental-mode PRs.

[0019] To intuitively illustrate the concept and capabilities of overtone PRs, the k31 vibration mode of a PR is first considered. As used here the “k31mode” refers to the length extensional vibration mode for a PR with top and bottom electrodes as illustrated in FIG.3. In k31 mode, the direction of the PR’s current “I” is perpendicular to the direction of its mechanical displacement. The sideview in FIG.3 shows a common single-port PR structure 10 in which the piezoelectric material 12 is sandwiched by two solid electrodes 14 and 16. As illustrated in Fig.4(i), when this solid-electrode PR resonates at its fundamental resonant frequency, ωA,the current density resulting from its charge displacement may be represented by ^^^^(^^^^1) ∙where magnitude J is a function of x1. J is greatest at the PR’s center and gradually decreases in a sinusoidal shape towards its edges.

[0020] The solid-electrode PR in FIG.3 also supports overtone resonant frequencies of hωA, where h is an odd integer. When this PR resonates at 3ωA as shown in Fig.4(ii), J has regions of opposite sign that indicate charge displacement in opposite directions. This charge displacement ultimately cancels out, depicted as white-shaded areas in Fig.4(ii), and only a small fraction of the charge displaced by the PR’s resonance contributes to net current I that may be extracted from the PR.

[0021] To productively harness all charge displaced by overtone resonant modes, the embodiments involve an “overtone PR” structure 20 shown in Fig.4(iii). The proposed overtone PR has alternating-polarity electrodes that correspond to the x1-dependent polarity of J for its intended overtone, allowing it to harness all charge displacement as net current.The alternating electrode structure also more effectively excites the PR’s mechanical resonance, resulting in a larger-amplitude J.

[0022] As shown in FIG.4(iii), the piezoelectric element comprised of a piezoelectric material has a first surface 22 and a second surface 24, which is on an opposite side of the piezoelectric material from the first surface. The first surface has an arrangement of one or more electrodes of opposite polarities, such as 18 “+” and 20 “-“. One should note that the polarity of the electrode reflects the polarity of the voltage to which the electrodes are connected and there is no implied limitation as to the composition of the different electrodes. The electrodes on the first surface 22 are arranged in a first alternating sequence. The electrodes on the second surface 24 are arranged in a second alternating sequence that is opposite the first sequence, meaning that if the first sequence is + - +, the second sequence would be - + -.

[0023] This overtone PR structure can be employed for most PR vibration modes in which the applied electric field is perpendicular to the mechanical displacement. FIG.5(i) and FIG. 5(ii) illustrate overtone PRs based on the k31 mode and kp mode, which, as used here means the radial vibration mode. Conventions for numbering overtones are mixed in literature. The discussion here defines the nth overtone as referring to the overtone with n additional standing half-waves along the direction of wave propagation compared to the fundamental mode. The nth overtone also indicates the number of additional electrode pairs in the overtone PR compared to the fundamental-mode PR for one-dimensional modes. For cases in which overtones are harmonics, meaning the integer multiples of the fundamental frequency, the nth overtone corresponds to the (n + 1)th harmonic or an order of (n + 1).

[0024] To determine the capabilities of overtone PRs, an electrical circuit model is derived for the 2nd-overtone k31 -mode PR shown in Fig.5(i). The electrodes of the same polarity are electrically connected in parallel. Due to the inherent electric field discontinuity in overtone PRs, one must first model the structure in segments according to electrode pattern. To begin, the following strain-charge constitutive equations for piezoelectric materials to each segment are applied:where mechanical strain S1 and stress T1 are defined in the x1 direction and electric displacement D3 and field E3 are defined in the x3 direction. The superscript (i) refers to the electrode segment index designated in FIG.5(i). Relevant material properties used in this discussion include density ρ, piezoelectric charge constant d31, elastic compliance under constant electric field ^^^^1^^^1^, and dielectric constant under constant mechanical stress, ^^^^3^^^^3. Combining (1) with the linear elasticity equation of motion (2) and strain-displacement relationship (3), and applying an assumed-sinusoidal boundary condition for E3 based on voltage V,the resulting wave equations for mechanical displacement u,have sinusoidal wave solutions,where A is the displacement amplitude, ω is the frequency, κ is the wave vector and φ is the phase shift with respect to the origin. To solve for the six unknowns A and φ, the six mechanical boundary conditions connecting neighboring segments are applied, and constrained for traction-free external boundaries.In which 2a′ is the length of the center electrode as visualized in FIG.5(i). Then, the displacement u1is inserted into the constitutive equations (1) to derive D3.

[0025] According to Maxwell’s equations, the time derivative of the surface integral of D3yields the current I,which leads to the total net current Itot = ∑3 (^^^^)^^^^=1 ^^^^ ,The dimensionless function in Itot,quantifies the electrode pattern’s impact on the current output. Itotattains its maximum when^^^^^^^^�^^^^′� = = a / 3. At the maximum, the expression of the function is reduced to ^^^^(^^^^′) =

[0026] Consequently, the admittance of the 2ndovertone k31-mode PR is, ^^^^^^^^^^^^^^^^^2^ = ^^^^^^^^^^^^^^^^^^^^^^, (11)This admittance expression corresponds to the BVD circuit model parameters shown in Table I for the 2nd-overtone k31mode. Likewise, one can find that an electrode length ofmaximizes the total current for nth-overtone k31-mode PR, where n ≥ 1 is an integer, and derive the admittance aswhich corresponds to the BVD model parameters of the nth-overtone k31-mode PR in Table I. The derivations above conclude that electrodes of equal length and alternating polarities best utilize k31 mode’s overtones. Notably, to best utilize the overtones of kp mode, the electrode spacing is unequal because the waveforms are in the form of Bessel functions.

[0027] Mechanical damping in linear elastic materials such as piezoelectrics is commonlymodeled by a complex multiplier to the compliance, such that ^^^^^^^^∗ ^^^^11 = ^^^^11 (1 − ^^^^^^^^), where η isthe isotropic mechanical loss factor. At the resonant frequency, the relationship between the mechanical quality factor Q and the mechanical loss factor η is η =1^^^^. Deriving the BVDmodel with ^^^^1^^^1^∗results in complex parameters C∗and L∗in the RLC branch. One can derive R to encompass the real part of the resulting impedance,Table I: BVD Model Parameters if k31-Mode Overtone PRs

[0028] By neglecting the loss terms η2and η3in (15), which are orders of magnitude smaller than the η loss terms, one obtains the following R in the BVD model for PRs:In the proximity of a resonant mode, R is a monotonically increasing function of frequency. Equation (16) is valid for some perpendicular vibration modes that start from strain-charge constitutive equations, including k31 mode, kp mode, certain configurations of k15 mode, meaning the thickness-shear mode, and contour extensional mode of a square plate. One should note that one can model other types of intrinsic material loss, such as dielectric loss and piezoelectric loss, as circuit elements.

[0029] PR-based dc-dc power converters typically utilize specific switching sequences that maximize efficiency and enable zero-voltage switching. To evaluate the capabilities of overtone PRs for power conversion, a PR converter switching sequence of either [Vin−Vout, Zero, Vout] or [Vin, Vin−Vout, Zero, Vout] are assumed, which are utilized to achieve high performance in [6]–[8],

[0012] ,

[0027] . Both sequences can be implemented by the circuit topology in FIG.6.

[0030] In FIG.6, the power converter has an input voltage 30, the PR 32, an input capacitor 34, and output capacitor 36, and a load, 38, shown as a resistor. The circuit includes transistorswitches S1, 40, S2, 42, S3, 44, and S4, 46. The microcontroller 48 could comprise any type of controller configured to control the on / off states of the switches, described below.

[0031] FIG.7 illustrates the switching sequence with simulation waveforms. Thanks to the high quality factor of PRs, one can assume that iL is sinusoidal throughout the switching sequence. The amplitude of iL, meaning the amplitude of resonance [7]) for either assumed switching sequence is,and the mechanical loss incurred by R is, ^^^^^^^^^^^^^^^^^^^^ =1 2 ^^^^^^2^^^^^^, (18) from which the optimal-efficiency and maximum-power-density design conditions can be derived respectively for a fundamental-mode PR.

[0032] The design conditions for achieving maximum efficiency and maximum power density in an overtone PR may be similarly derived. If one only considers the loss due to R, the substitution of (17) into (18) leads to the loss ratio,

[0033] For a PR of a given material and geometric dimensions, there exists an “optimal input impedance” at which the minimum loss ratio and therefore maximum efficiency occurs,

[0034] For both fundamental-mode PRs with solid electrodes and overtone PRs operating at their intended k31-mode overtones, the maximum efficiency does not depend on the geometry nor the overtone,and the optimal input impedance in (20) is directly proportional to the PR’s characteristic impedance,

[0035] where Γ is a material-dependent coefficient, Γ= 161^^^^^^^^^1^^^1 ^^^^ ^3^^^(23) ^^^2 3^−131based on the assumed high-efficiency switching sequences. The optimal input impedance approximately scales with the optimal output impedance, within 4x as constrained by the assumed switching sequences. The exact conversion ratio does not affect the maximum efficiency nor the optimal input impedance in this model, within the constraints of the switching sequences themselves. According to Table I, the characteristic impedance linearly decreases as the overtone number increases for the same PR geometry. Hence, the maximum- efficiency Poutlinearly scales up as the overtone number increases for a fixed Vinand Vout. To design an overtone PR to achieve maximum efficiency at a specific input impedance, one can re-write (22) to obtain the maximum-efficiency aspect ratio for the nth-overtone k31-mode PR,

[0036] In addition to maximum efficiency, one can design the geometry of an overtone PR to also achieve maximum power handling density at a specified operating point. The power handling density of a nth-overtone k31-mode PR can be derived from (17),

[0037] The amplitude of resonance ILcan be constrained by the stress and electric field constraints of the piezoelectric material [2]. To derive the maximum ILassociated with each constraint, one first derives the magnitude of the inductor current from (8),

[0038] The k31-mode overtone PR’s wave solution shows that the maximum stress in each segment is the same,

[0039] Substitution of V into (26) yields the maximum amplitude of resonance ^^^^^^^^,^^^^^^^^^^^^^^^^constrained by the maximum stress T1,max,^^^^which shows the linear relationship between the overtone order (n + 1) and the maximum allowable ILconstrained by the stress limit. Likewise, (4) and (26) result in the maximum amplitude of resonanceconstrained by the maximum electric field E3,max,which shows the linear relationship between the overtone order and IL,E max. It is now clear that the E or T-constrained power density in (25) for the same geometry and operating point scales up linearly with n + 1 because the maximum IL and f both do. For a given PR, one has an optimal Vinfor maximizing the power density in (25),

[0040] The maximum power handling density is, ^^^^^^^^^^^^^^^^^^^^2=^^^^,^^^^^^^^^^^^2 , 8^^^^^^^^^^^^ 32^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^where the geometry normalization is performed as IL,max = IL,max,ob. For a target operating point, one can re-write (30) to obtain the thickness c for k31-mode overtone PRs corresponding to maximum power handling density,

[0041] For a desired Vin and Pout, the optimal c for power density remains the same with respect to overtone order while the optimal b for efficiency linearly decreases with respect to overtone.

[0042] Within the framework derived above, the discussion can now turn to evaluating the optimal load impedance, amplitude of resonance, efficiency, and power density capabilities of overtone PRs compared to other PR structures listed in Table II. The fundamental-mode PR with solid electrodes serves as the baseline for comparison in the first column. All quantities are normalized with respect to the fundamental-mode PR. The power handlingdensities are constrained by maximum electric field (E) or maximum stress (T); both have the same scaling characteristics.

[0043] As shown for the solid-electrode PR structure, use of the overtone scales up the minimum loss ratio and scales down the maximum power handling density, which illustrates the disadvantages of operating at overtones in single-electrode PRs. However, scaling down the fundamental-mode PR to the size of a “miniaturized” PR results in higher power handling density at the same efficiency and characteristic impedance. Then, parallelizing such miniaturized PRs decreases the characteristic impedance while maintaining the efficiency and power handling density of the miniaturized PR. Finally, the proposed overtone PR’s capabilities are displayed in the 5th column in Table II. The overtone PR utilizes a single PR structure to achieve all the benefits of parallelization without the challenges of impedance mismatch and frequency synchronization. Thus, in comparison with the fundamental-mode PR, the proposed 2nd-overtone k31-mode PR has a 3x lower optimal load resistance and a 3x greater power handling density while maintaining the same efficiency capability. These benefits scale linearly with the overtone order for k31 mode. Table II: Comparison of k31-Mode PR Structures

[0044] One can apply the same modeling framework discussed above to other vibration modes, such as the kpmode shown in FIG.5(ii). The kpmode differs from the k31mode inthat its wave solution is best modeled by Bessel functions rather than sinusoidal functions. In FIG.5(ii), the center electrode has a length of a2, from the center of the disc-shaped PR to the end of the center electrode. The outside electrodes, in this embodiment, have a length of a1– a2, so the electrodes are not all the same length. As shown in the diagram, both a1 and a2 are much larger than c, the thickness of the piezoelectric element.

[0045] As a result, the overtone frequencies are not integer multiples of the fundamental frequency, altering the scaling of the BVD parameters. Comparing a 1st-overtone kp-mode PR with the fundamental kp -mode PR in Table III, the optimal load impedance is almost halved, accompanied by a 1.49 times higher minimum power loss ratio. Table III: Comparison of kp– Mode PR Structures

[0046] As the overtone number increases, the minimum power loss ratio converges to 1.6 times that of the fundamental-mode PR, while the scaling of the optimal input impedance converges to a linear function of overtone. The boundaries of the electrodes of the kpmode are assumed to occur at the zero crossings of the intended current profile, but these zero crossings are not equidistant. Given that kp mode is a higher-performing vibration mode compared to k31mode, this validates the theory discussed so far with experiments focused on the kp mode.

[0047] To validate the models and scaling characteristics discussed above, the inventors implemented a 100-V rated DC-DC converter prototype based on the topology in F.6, which employs the [Vin, Vin− Vout, Zero, Vout] switching sequence. This prototype features areplaceable PR with the parts shown in Table IV. The design included two kp-mode PRs with identical geometry but different electrode patterns: one with a solid electrode and the other with a 1st-overtone alternating electrode. The experiment used 650RPM 12V fan to help PRs quickly reach thermal equilibrium.

[0048] Ready-to-ship fundamental-mode PRs and custom-ordered overtone PRs were acquired. The fundamental-mode PR was selected for its material mechanical quality factor of 1400, sufficient radius to ease mounting, and minimal thickness to reduce maximum- efficiency load impedance. The overtone PR design is illustrated in FIG.8. The device incorporated pogo-pin spring-loaded connectors and flat-pin targets to mount the PRs. Once mounted, the PRs were characterized with an impedance analyzer. The PRs are mounted with quality factors ranging from 1300 to 1400 for comparison, with fitted BVD model parameters in Table IV. Except for a minor spurious mode outside of the inductive region due to top and bottom electrodes’ manufacturing mismatch, the measured impedance response of the overtone PR closely aligns with the impedance response of COMSOL simulation and the BVD model in FIG.9.

[0049] After characterizing the PRs, they were tested in the same dc-dc converter prototype. The power was swept at fixed input and output voltages. The converter was tested with an electronic load and power supply. The efficiencies were measured with power analyzer. The efficiencies are recorded under thermal equilibrium condition. The steady-state Vout was constrained to be within 1%. The consistency of quality factors of PRs was checked to be within 5% before and after performing the efficiency sweeps. The efficiency vs. power curves are shown in FIG.10 and FIG.11 for Vin = 100 V and Vin = 12 V, respectively. The waveforms of the peak-efficiency operating point when Vin = 100 V and Vout = 65 V are shown in FIG.12, while the waveforms of the peak-efficiency operating point for Vin= 12 V and Vout = 7 V are shown in FIG.13.

[0050] As observed in FIG.10, the fundamental-mode PR attains its peak efficiency 97% at 9 W when Vin= 100 V and Vout= 65 V, while the overtone PR attains its peak efficiency 97%at 15 W when Vin = 100 V and Vout = 65 V. This experimental result aligns with the model prediction that the optimal power of 1st-overtone kp-mode PR should be 1.72 times that of the fundamental-mode kpPR in Table III.

[0051] The discussion here defines “a power converter based on an overtone PR” as a power converter with switching frequency greater than 1.5x the PR’s fundamental resonant frequency, where the fundamental resonant frequency corresponds to one standing half-wave in the contiguous substrate of piezoelectric material. Overtone PRs typically have more than one standing half-wave in a single substrate of piezoelectric material, resulting in charge displacement, and therefore extracted current, in opposite directions at different locations within the substrate. The electrode pattern is typically designed to align with the directions of expected charge displacement, and therefore extracted current, for the PR overtone frequency at which the power converter is intended to operate.

[0052] The aforementioned overtone PR concept can be applied to various PR resonant modes, including but not limited to k31 mode, length extensional mode with side electrodes, thickness-shear mode with side electrodes, kp mode (radial mode) of circular plate, radial mode of circular ring, radial mode of circular rod, contour extensional mode of square plate, contour extensional mode of square ring and width extensional mode. In general, overtone PR designs can be applied to the resonant modes whose additional standing waves of overtones generate current densities of alternating polarities that are perpendicular to the electrodes. By applying overtone PR designs to these resonant modes, one can maximize the electrical current output for an arbitrary overtone given the same voltage, and minimizing the characteristic impedance to utilize it as the main resonant mode for power conversion applications.

[0053] The overtone PR designs can be applied to resonators of various piezoelectric materials, including but not limited to lead zirconate titanate (PZT), quartz crystal, zinc oxide, barium titanate, aluminum nitride, aluminum scandium nitride, gallium nitride and lithium niobate. These materials have different efficiency and density capabilities when we use them for power conversion. As one targets certain applications, one may favor certain materials over others due to safety concerns, fabrication capabilities, efficiency / density requirements and impedance limitations. Overtone PR designs can enhance the density capabilities and decrease the optimal input impedance with comparable efficiencies for PRs of different piezoelectric materials.

[0054] The electrode patterns of overtone PR designs are not restricted to completely disconnected electrodes with minimal gaps between them. To decrease the mechanical damping caused by mounting, designers can reduce the number of required electrical and mechanical connections by engineering the electrodes of the same polarity with interconnections. For example, in Fig.5(i), the electrodes designated by I(1)and I(3)can be interconnected by placing an electrical connection of negligible area across the electrode I(2), or through placing electrode on the side of the k31resonator. In this way, one can eliminate one electrical connection on this resonator that might cause undesired mechanical damping.

[0055] Accompanied with topology and resonator developments, these overtone PR designs may achieve an even better performance by toggling between the fundamental resonant mode and various overtones. For example, in Fig.5(i), one may flip the polarity of the electrode designated by I(2)and operate this resonator under the fundamental k31 mode or the 2nd- overtone k31mode. This action may be achieved by adding two bidirectional switches in the electrical circuit path of I(2). Through this operation, one may change the optimal input impedance of the PR-based power converters, and achieve the higher-efficiency operating points of either the fundamental mode or the overtones as demonstrated in FIG.12 and Fig. 13.

[0056] The overtone PR designs can be expanded to multi-port piezoelectric device designs that maximize the current output for arbitrary voltage input with any phase and amplitude. As exemplified in equation (4), for overtone PR designs, the discussion assumes 180-degree phase shifts for the voltages. However, these voltages may have different phase shifts other than 180 degree for certain applications and circuit topology. In that case, one can also apply the same design methodology to find the best electrode pattern after changing the electrical boundary condition for E3. In one embodiment, the multiport piezoelectric component comprises a piezoelectric transformer.

[0057] PR-based power converters exhibit high efficiency at high load impedances, primarily due to the high characteristic impedances of PRs. To address this, the proposed overtone PRs utilize overtones as their primary resonant modes, enabling lower PR characteristic impedance without the drawbacks of PR parallelization. Compared to fundamental mode PRs, overtone PRs are also capable of greater power density and lower optimal load impedance, both of which scale linearly with the overtone order, and comparable efficiency capability, validated via experiments. This component-level, rather than circuit-level, strategycan be similarly applied to other PR vibration modes in which the applied electric field and the resulting mechanical vibrations are perpendicular.

[0058] All features disclosed in the specification, including the claims, abstract, and drawings, and all the steps in any method or process disclosed, may be combined in any combination, except combinations where at least some of such features and / or steps are mutually exclusive. Each feature disclosed in the specification, including the claims, abstract, and drawings, can be replaced by alternative features serving the same, equivalent, or similar purpose, unless expressly stated otherwise.

[0059] Additionally, this written description makes reference to particular features. It is to be understood that the disclosure in this specification includes all possible combinations of those particular features. For example, where a particular feature is disclosed in the context of a particular aspect, that feature can also be used, to the extent possible, in the context of other aspects.

[0060] Also, when reference is made in this application to a method having two or more defined steps or operations, the defined steps or operations can be carried out in any order or simultaneously, unless the context excludes those possibilities.

[0061] Although specific aspects of this disclosure have been illustrated and described for purposes of illustration, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, the invention should not be limited except as by the appended claims.

Claims

CLAIMS 1. A piezoelectric resonator, comprising: a piezoelectric element having a first surface and a second surface on an opposite side of the piezoelectric element from the first surface; a first set of electrodes electrically connected to the first surface, the first set of electrodes comprising one or more electrodes of a first polarity alternating with electrodes of a second polarity in a first sequence; and a second set of electrodes electrically connected to the second surface, the second set of electrodes comprising one or more electrodes of a first polarity alternating with electrodes of a second polarity in a second sequence opposite of the first sequence, the energizing of the electrodes causing the piezoelectric element to operate in an overtone resonant mode.

2. The piezoelectric resonator as claimed in claim 1, wherein the one or more electrodes of a first polarity and the one or more electrodes of the second polarity comprise electrode pairs, and the number of electrodes pairs determines a number of standing half waves in the overtone resonant mode.

3. The piezoelectric resonator as claimed in claim 1, wherein the piezoelectric element has a solid rectangular shape, and the overtone resonant mode comprises one of either a length vibrational mode, width extensional mode or a thickness-shear mode with side electrodes.

4. The piezoelectric resonator as claimed in claim 2, wherein a center electrode has a length equal to twice a length of the piezoelectric element divided by the number of standing half waves plus one.

5. The piezoelectric resonator as claimed in claim 2, wherein the electrodes in the first set of electrodes and the electrodes in the second set of electrodes are all of a same length and width.

6. The piezoelectric resonator as claimed in claim 1, wherein the piezoelectric element has a planar disc shape, and the overtone resonant mode comprises one of a radial vibration mode, radial mode of circular plate, radial mode of circular ring, radial mode of circular rod, contour extensional mode of square plate, or contour extensional mode of square ring.

7. The piezoelectric resonator as claimed in claim 6, wherein a center electrode of the one or more electrodes has a length of a distance a1 from a center of the disc to the end of the center electrode, and the disc has second length a2from the center of the disc to the edge, and a1and a2are greater than a thickness of the piezoelectric component.

8. The piezoelectric resonator as claimed in claim 6, wherein one or more electrodes in each of the first set of electrodes and the second set of electrodes have different length than other electrodes in a same set of electrodes.

9. The piezoelectric resonator as claimed in claim 1, wherein the piezoelectric component comprises a material selected from the group consisting of: lead zirconate titanate (PZT), quartz crystal, zinc oxide, barium titanate, aluminum nitride, aluminum scandium nitride, gallium nitride, and lithium niobate.

10. The piezoelectric resonator as claimed in claim 1, wherein electrodes of a same polarity are interconnected.

11. A power converter, comprising: an input voltage source; a piezoelectric resonator, comprising: a piezoelectric element having a first surface and a second surface on an opposite side of the piezoelectric element from the first surface; a first set of electrodes electrically connected to the first surface, the first set of electrodes comprising one or more electrodes of a first polarity alternating with electrodes of a second polarity in a first sequence; anda second set of electrodes electrically connected to the second surface, the second set of electrodes comprising one or more electrodes of a first polarity alternating with electrodes of a second polarity in a second sequence opposite of the first sequence, the energizing of the electrodes causing the piezoelectric element to operate in an overtone resonant mode; an output load; transistor switches connected between the input voltage, the piezoelectric resonator, and the output load; and a controller to control operation of the transistor switches to convert power from the input voltage to an output voltage across the load.

12. The power converter as claimed in claim 11, further comprising switches in a current path of one electrode of one of the first set of electrodes and a center electrode of a second set of electrodes.

13. The power converter as claimed in claim 12, the controller further configured to control the switches to change the polarity of the center electrode to toggle the piezoelectric resonator between a fundamental mode and one or more overtones.

14. The power converter as claimed in claim 11, wherein a switching frequency of the transistor switches is greater than 1.5 times the piezoelectric resonators fundamental resonant frequency.

15. A power converter, comprising: an input voltage source; a multi-port piezoelectric component, comprising: a piezoelectric element having a first surface and a second surface on an opposite side of the piezoelectric element from the first surface;a first set of electrodes electrically connected to the first surface, the first set of electrodes comprising one or more electrodes of a first polarity alternating with electrodes of a second polarity in a first sequence; and a second set of electrodes electrically connected to the second surface, the second set of electrodes comprising one or more electrodes of a first polarity alternating with electrodes of a second polarity in a second sequence opposite of the first sequence, the energizing of the electrodes causing the piezoelectric element to operate in an overtone resonant mode; an output load; transistor switches connected between the input voltage, the piezoelectric resonator, and the output load; and a controller to control operation of the transistor switches to convert power from the input voltage to an output voltage across the load.

16. The power converter as claimed in claim 15, wherein the multi-port piezoelectric element comprises a piezoelectric transformer.

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