High-efficiency piezoelectric transformers for magnetic-less DC-DC power conversion

Abstract

A power converter includes a piezoelectric transformer comprising a piezoelectric material and metalized electrodes that form two or more ports, at least one of the two or more ports being an input port having an input port surface area, at least one of the at least two ports being an output port having an output port surface area, wherein, the piezoelectric transformer has a physical characteristic of a geometry term H comprised of piezoelectric transformer dimensions at least one of input port and output port measurements, including and a voltage swing across the input port, a voltage swing across the output port, a charge utilization at the input port, a charge utilization at the output port, an input voltage, an output voltage, and a transformation ratio.

Description

Patent Application U Cal No. BK-2025-062-2-PCT MN No. 407869-0230 HIGH-EFFICIENCY PIEZOELECTRIC TRANSFORMERS FOR MAGNETIC-LESS DC-DC POWER CONVERSIONTECHNICAL FIELD

[0001] This disclosure relates to piezoelectric transformer-based dc-dc converters, more particularly to piezoelectric transformer-based converters without magnetics.BACKGROUND

[0002] Magnetic components including inductors and transformers present a significant challenge to the miniaturization of power electronics. While magnetics have long been integral to power converters, they exhibit fundamentally decreasing power densities and efficiencies at low volume. This limitation is evident in recent isolated dc-dc converter designs, in which the magnetic transformer alone accounts for 20-40% of the converter volume. Further, unlike planar semiconductor devices, magnetic components are inherently three-dimensional structures with substantial height that dictates the converter’s vertical profile. Consequently, magnetics remain a critical bottleneck for power converter miniaturization.

[0003] Major advances in the miniaturization of power electronics will require passive component technologies capable of significantly greater power densities and efficiencies at small scales. Piezoelectric components have emerged as a promising candidate with quality factors of 1,000-30,000 and energy densities multiple orders of magnitude greater than those of magnetics. Piezoelectrics also offer other practical benefits to power conversion including planar form factors, batch fabrication, potential for integration, and no generation of stray magnetic fields.

[0004] Piezoelectrics have been used as electromechanical transduction elements in a diverse set of applications, from ambient energy harvesters and sensors employing the direct piezoelectric effect (mechanical energy — electrical energy) to actuators using the indirect piezoelectric effect (electrical energy — mechanical energy). Within power electronics, piezoelectric components function as energy storage elements, acquiring and releasing energy electrically but storing energy in the mechanical compliance and inertia of an acoustic wave.These components can be realized as single-port piezoelectric resonators (PRs) or multiport piezoelectric transformers (PTs).

[0005] Recent magnetic-less dc-dc converter designs based on PRs have demonstrated power stage efficiencies of >99% and PR power handling densities of up to 5.7 kW / cm3. While these demonstrations mark tremendous milestones, such performance has only been achieved in non-isolated dc-dc converters with mild voltage conversion ratios. Capacitive isolation may be realized using multiple PRs, but this approach is susceptible to capacitive coupling across the isolation barrier and is sensitive to mismatch between the PRs. The utility of piezoelectric-based power conversion is presently confined to a narrow subset of power electronics applications.

[0006] Piezoelectrics may be expanded to a broader set of applications through use of multiport PTs, which offer the same advantages as PRs but with the added potential for galvanic isolation and inherent voltage transformation, although galvanic isolation is not necessary. When AC voltage is applied to one port of a PT, it induces mechanical deformation in the piezoelectric material that cascades throughout the component as an acoustic wave and causes charge displacement at the PT’s other port(s). All energy traveling between ports is first converted from the electrical domain to the mechanical domain, stored mechanically, and then extracted from the PT electrically at the other port. Similar to magnetic coupling, this acoustic coupling provides galvanic isolation with minimal capacitance coupling, and therefore minimal direct charge flow, between ports.

[0007] While PTs have seen decades of development for power conversion, their widespread commercial adoption has primarily been limited to low-power, high-voltage step-up applications such as cold cathode fluorescent lamp (CCFL) backlight drivers. Early implementations of PT-based dc-dc converters often incorporated auxiliary magnetic components, which limited their potential to achieve high power densities. While PTs have also been utilized to develop magnetic-less PT-based dc-dc converters, these designs have achieved only modest performance. The efficiencies and power densities of non-isolated configurations have been limited to -90% and <5 W / cm3, respectively, without magnetics. The performance has been drastically lower for isolated magnetic-less PT-based dc-dc converters, where the highest reported efficiency has been limited to 68%.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] FIG. 1 shows an embodiment of a full-bridge / full-bridge dc-dc converter.

[0009] FIG. 2 shows an embodiment of a ring-dot piezoelectric transformer (PT) structure.

[0010] FIG. 3 shows a Mason lumped circuit model of an isolated PT.

[0011] FIG. 4 shows graphs demonstrating designing PT for achieving peak efficiency and for achieving zero-voltage switching (ZVS).

[0012] FIG. 5 shows a flowchart of an embodiment of a method of designing high-efficiency, radial-mode PTs.

[0013] FIG. 6 shows a graph of variation of peak efficiency with respect to port dimensions of an embodiment of a PT.

[0014] FIG. 7 shows an example of a patterned PT component with specific port dimensions.

[0015] FIG. 8 shows a graph comparing impedance responses between modeled and experimental PTs.

[0016] FIG. 9 shows an embodiment of an experimental mounting for a PT and fixture.

[0017] FIG. 10 shows an embodiment of a dc-dc converter with a mounted dc-dc radial -mode PT.

[0018] FIG. 11 shows oscilloscope waveforms of differential input and output switch node voltages of the embodiment PT topology shown in FIG. 1

[0019] FIG. 12 shows a graph of converter power efficiency for different input voltages.

[0020] FIG. 13 shows an embodiment of a PT with a square-dot structure.

[0021] FIG. 14 shows an embodiment of a PT with multiple input ports .DETAILED DESCRIPTION OF THE EMBODIMENTS

[0022] The embodiments demonstrate piezoelectric transformers to be capable of high efficiencies as primary passive components in DC-DC converters. The embodiments present a systematic framework for designing radial -mode piezoelectric transformers (PTs) by constraining their physical dimensions to simultaneously maximize PT efficiency and ensure zero-voltage switching (ZVS). The embodiments demonstrate and validate the proposed component design strategies in an isolated full-bridge / full-bridge (FB-FB) dc-dc converter asvisualized in FIG. 1. The PT 10 in FIG. 1 lies between the input full bridge 12 and the output full bridge 14. Some of this discussion focuses on isolated piezoelectric transformers in magnetic-less dc-dc converters, with the understanding that the applications of the high efficiency piezoelectric transformers are not limited to this particular embodiment.

[0023] As mentioned above, the performance has been drastically lower for isolated magnetic-less PT-based dc-dc converters, where the highest reported efficiency has been limited to 68%. Table 1 compares the embodiments to currently-available PRs and PTs.>Table 1: Comparison with Previous Magnetic-less Isolated PT-Based DC-DC Converters

[0024] Reference 1 is T. Andersen, M. Rodgaard, M. Andersen, O. Thomsen, K. Lorenzen, C. Mangeot, and A. Steenstrup, “Integrated high voltage power supply utilizing burst mode control and its performance impact on dielectric electro active polymer actuators,” 2012, 13th International Conference on New Actuators and 7th International Exhibition on Smart Actuators and Drive Systems, ACTUATOR 2012. Reference 2 is M. S. Rodgaard, M.Weirich, and M. A. Andersen, “Forward conduction mode controlled piezoelectric transformer-based pfc led drive,” IEEE Transactions on Power Electronics, vol. 28, no. 10, pp. 4841-4849, 2012. Reference 3 is M. Sanz, P. Alou, A. Soto, R. Prieto, J. Cobos, and J. Uceda, “Magnetic-less converter based on piezoelectric transformers for step-down dc / dc and low power application,” in Eighteenth Annual IEEE Applied Power Electronics Conference and Exposition, 2003. APEC ’03., vol. 2, 2003, pp. 615-621 vol.2.

[0025] PT design and modeling begin with selection of piezoelectric material and vibration mode. Power electronics demand piezoelectric materials with low dielectric and mechanical losses, and high electromechanical coupling coefficients. Hard piezoelectric formulations of lead zirconate titanate (PZT) exhibit the aforementioned characteristics, and the radial vibration mode has demonstrated some of the highest efficiencies to date in PRs. The embodiments demonstrate how the PZT radial mode may be similarly leveraged to design high-efficiency isolated PTs.

[0026] In axially poled thin circular discs (i.e., in which diameter thickness), the radial vibration mode (kPmode) is characterized by transverse electromechanical coupling resultingin axisymmetric expansion and contraction along the radial direction. The structure of a “ring-dot” radial-mode PT (kp-kp mode) is illustrated in FIG. 2. It consists of a monolithic disc 20 of PZT material uniformly poled in the thickness direction, where the top and bottom surfaces of the disc are metalized with identical patterns of conductive electrodes. The electrode pattern consists of a central circular electrode 22, or dot, defining the input port and a concentric annular electrode, ring 24, forming the output port, with these regions separated by an unmetallized gap 26 that ensures electrical isolation between ports. The radial dimensions of the electrodes being the dot radius (Z>), ring inner radius (c), and ring outer radius (a), are the geometry design parameters that determine input and output port impedances and the transformation ratio between the ports.

[0027] To derive the equivalent circuit model of the radial mode PT, one can conceptualize it as three mechanically coupled regions: input disc port, output ring port, and the isolation ring between the ports. For each of these regions, starting from the piezoelectric constitutive equations, expressions are derived for current flowing through each port and the radial force at the interface of regions as a function of applied voltage, radial velocity, port dimensions, and material properties. The relevant material properties are defined in Table II.Table 2. Material and Property Definitions.

[0028] Each region of the PT is represented by a ‘T’ impedance network that captures its electromechanical behavior. The input and output ports are modeled as disc- and ring-typePRs, respectively. The isolation region, however, lacks electrodes and thus has zero electric displacement in the isolation region (Dz=0). This manifests as a modified ‘T’ network where the electromechanical transformer (1: n) is shorted. The piezoelectric coupling creates internal electric field that effectively stiffens the material, reducing its effective compliance from sfxtoTo establish the Mason model for the complete PT, one equates the radial forces and the radial velocities of the three regions at their interfaces (r = Z>, r = c)

[0043] ,

[0029] While the PT impedance can be calculated from the combined model, a reduced Mason model with closed-form expressions is desirable for straightforward design. To achieve this, one can approximate the isolation region using the same material constants as the electroded regions (sx« sfx). This approximation effectively treats the entire PT as having uniform mechanical properties, enabling its representation as a lumped circuit model that captures its behavior near its resonant frequency. The resonant frequency is expressed as a function of the material properties and the PT radius as follows:where Kris the geometry-normalized wavenumber at the resonant frequency, (sometimes defined as K0 r), and is also a function of material properties. Kris determined by solving the following transcendental equation:

[0030] This equation has an infinite number of solutions, where the first positive solution corresponds to the fundamental resonant mode and the subsequent solutions correspond to various higher order vibration modes. We combine the impedances of the different sections of the PT and perform a Taylor series expansion around the fundamental resonance frequency, to derive the expression for the PT lumped impedance Zeq'.

[0031] The lumped impedance of PT can be modeled by aZ - C series network that corresponds to the same resonance frequency. The Taylor series expansion of anZ - Cnetwork around its resonance frequency = / [LC is expressed as ZLC« 2jL(m — mr). On equating this with (3), one can calculate the lumped inductance and capacitance values. The mechanical damping losses, which constitute the dominant loss mechanism in the PT, can be modeled by adding a resistance in series with the L - C network. Internal mechanical losses are described by the mechanical quality factor Q and the series resistance is inversely proportional to the quality factor as R = - i J / I-.

[0032] This simplified circuit results in reduced Mason Model 30 illustrated in FIG. 3, which represents the electromechanical behavior of PTs, when operating near their resonance frequencies. The Mason model comprises physical port capacitances (CPA, CPB ), an ideal voltage transformation (1 : TV), and an LCR branch modeling the PT’s mechanical resonance and loss properties.

[0033] Using the equivalent circuit model for radial PT developed above, we now derive a design framework that constrains the PT’s port dimensions so that it simultaneously achieves maximum efficiency and ZVS for a nominal operating point in an isolated dc-dc converter.

[0034] There are switching sequences that most efficiently utilize the resonant cycle of isolated PTs. Each of these switching sequences can be realized with either a half-bridge or a full-bridge at each PT port. The amplitude of resonance II (i.e., amplitude of IL) of the PT can be estimated from the charge transferred by IL during each stage of the converter’s switchingsequence. This can be calculated from the perspective of either port of the PT. With respect to the input port, IL can be mathematically expressed as follows:>

[0035] K is the charge transfer utilization factor of the switching sequence and represents the proportion of charge displaced by IL that sources energy from the supply or delivers energy to the load. Accordingly, KA and KB are the charge utilization factors corresponding to the input and output port switching sequences, respectively. The values of both KA and KB are constrained between 0 and 1, depending on the fraction of charge transfer throughout the resonant cycle for which the port is connected to the source / load. Their values can either be fixed or span a continuous range, determined by the assumed switching sequence. VPPA is the voltage swing across the input port, which also depends on the switching sequence. VPPA equals Vm for half-bridge configurations where the voltage swings between 0 toand equals ZVm for full-bridge configurations where the voltage swings between -Vtn to +Vin. This amplitude of resonance serves as a model for the PT’s behavior throughout the assumed switching sequence. With it, one can now systematically derive conditions for a PT to achieve maximum efficiency and ZVS at a nominal converter operating point .

[0036] PT efficiency can be calculated based on loss ratio (Plossasfollows:' Pout 'f 2

[0037] To maximize PT efficiency, the power loss I Pioss= -I R l in the PT must beminimized for a given output power Pout. Thelossratio can be expanded by substituting the Poutvalue of II from (4):

[0038] To minimize (6) with respect to the PT’s port dimensions, the geometry terms are separated from the PT motional resistance A and frequency-capacitance product B =fCPA expressions, as has been proposed for PRs.>One should note that B can be generally expressed by B = G*Bo, where Bo is the geometry - b2normalized B and G is a geometry term. G is — for the input port in a ring-dot structure as ina2— c2(7). For the output port of the ring-dot structure, G would be . For other structures, Gcontains the geometry terms in the frequency-capacitance product B = G*Bo = C*f.

[0039] For the radial -mode PT, Ro and Bo are normalized with respect to geometry term G = b2(Pi \— . The loss ratio expression — — can be expressed in terms of the material Cl / l ^Pout'constants Ro and Bo, geometry term G, and converter operating point as follows:

[0040] Minimizing the loss ratio with respect to G, by setting = 0, yields thefollowing PT geometry design condition for achieving maximum efficiency, and corresponding peak efficiency, at a specified converter operating point:> >>>

[0041] If a PT design adheres to the condition in (9a) for its nominal operating point, it can be expected to achieve the peak efficiency in (9b) at that operating point 40 as visualized in FIG. 4. Unlike the PR and PT design frameworks currently available, this peak efficiency itself also has dependence on geometry terms a and b. The PT may operate when the relationship in 9a is not met, but it will not be operating at peak efficiency. One should notethat the condition on Equation 9a, that the geometry term G = b2 / ah being equal to the converter output power divided by the quantity of the charge utilization at the input port (KA), the normalized frequency-capacitance product (Bo), the converter input voltageand the voltage swing at the input port (VPPA), multiplied by 2, is a physical characteristic of the PT when operating in a power converter of a particular switching sequence. The PT does not have to operate so that relationship is true, the characteristic is that if it the relationship is true it represents the peak efficiency of the PT, regardless if the relationship is true or not when operating.

[0042] This maximum efficiency condition assumes that the converter is capable of ZVS for all switches, such as switches S1-S4 on the input side, and S5-S8 on the output side in FIG. 1, as well as all-positive instantaneous power transfer. To ensure that the converter is capable of both, we derive an additional geometry condition for ZVS that translates to sizing the PT’s input and output capacitances and PT transformation ratio such that these high-efficiency behaviors are possible at a nominal converter operating point. To derive this condition, we equate the total charge that must be displaced by IL throughout the resonant cycle from the perspective of each port. These expressions consider both energy -transfer stages and dead time, assuming ZVS and all-positive instantaneous power transfer are achieved:

[0043] To achieve ZVS simultaneously with the maximum efficiency derived in (9b), the output power operating point derived from (9a) is substituted into (10). This results in the following constraint on dimensions a, b, and c for which these high-efficiency behaviors are achieved:

[0044] A PT can be expected to achieve ZVS over the range of voltage conversion ratios that can satisfy (11), as illustrated in FIG. 4. This range is fundamentally dictated by the range of KA and KB for the assumed switching sequence.

[0045] Beyond maximum efficiency and ZVS, design of high efficiency radial PT is also constrained by other interdependent geometry conditions that arise from radial mode physics, and the required isolation between the input and output ports. The disc radius a determinesthe PT’s fundamental resonant frequency, and therefore the converter’s switching frequency range, as described in (1). Higher resonant frequencies, referred to here as overtones, tend to yield higher power handling densities for a given vibration mode. However, higher switching frequencies also in-crease control and mounting complexity. To ensure pure radial mode vibration, and validity of the one-dimensional model used above, the disc thickness h is constrained to be significantly smaller than the radius (h« a). This aspect ratio suppresses the coupling of energy into other modes. Finally, the minimum isolation region width (c - Z>) is dictated by the electrical isolation requirement between the input and output ports. The isolation gap should be sized to ensure that the peak electric field across it, under the maximum operating voltage Visa), never exceeds the maximum electric field limit (Emax)' of the piezoelectric ceramic:>

[0046] The value of the limiting field is a design choice contingent upon whether the isolation region is polarized or not. The maximum field is limited by the coercive field for a polarized gap, and breakdown field for a non-polarized gap. The coercive field for hard PZT is approximately 15 kV / cm, and the breakdown field is significantly greater than the coercive limit.

[0047] To design a high-efficiency isolated PT for a given converter topology, switching sequence, and operating range, the designer may follow an iterative design process based on the constraints within this design framework as shown in FIG. 5. The designed determines the switching frequency for the PT at 50. Initially, the disc radius a is established through (1) based on the target resonance frequency at 52, which relates directly to the converter’s switching frequency range. The minimum isolation region width c - b is also determined at 54 based on the required isolation Visa and the material’s electric field limit Emax. Then, specifying the actual values of b and c is an iterative process with the simultaneous goals of maximizing peak efficiency and ensuring ZVS. A designer may begin with the value of b at 56 that maximizes the peak efficiency value specified in (9b). Having determined Z>, the value of c is then computed from the previously calculated isolation region width c - b. The designer may then evaluate whether these values of b and c are capable of satisfying the ZVS condition outlined in (11) across the entire operational range of-^ at 58. If not, the designer inmay iteratively decrease the value of b at 60 and adjust the value of c until (11) is satisfied-liacross the entire operating region at 62. Finally, the value of disc thickness h is determined in accordance with the maximum efficiency geometry condition G derived in (9a) at 64. One should note that the resulting value of disc thickness must also satisfy the radial mode constraint h« a at 66. If this condition is not satisfied, the value of a may be increased at 68, which also modifies the initial frequency specification.

[0048] One can now apply the design framework proposed in above to design a high-efficiency isolated PT for a dc-dc converter prototype. With this design, the goal is to demonstrate the potential of isolated PTs to achieve high efficiency, so efficiency is prioritized over other design considerations such as isolation voltage, conversion ratio, and operating point.

[0049] For this design, the FB-FB topology visualized in FIG. 1 is assumed to be operating with a version of the high-efficiency, isolated switching sequence [Vin, -Vin\Vout, -Vout, Zero}. Within this switching sequence, the input bridge is operated with 50% duty cycle. To regulate the output voltage, the output bridge is controlled to short-circuit the PT’s output port (rather than send energy to the load) for a brief period of time during the switching cycle. This period is referred to as a “Zero” stage. The “Zero” stage is split between both halves of the cycle to simplify control. For this switching sequence, KA =1 since the input port is always connected to the source. The value of KB varies between 0 and 1, where KB =1 corresponds to the unregulated sequence with no “Zero” stage, and KB < 1 corresponds to the output port spending part of its cycle in a “Zero” stage for voltage regulation purposes.

[0050] To demonstrate a maximum efficiency PT design, a disc of radius a = 12.7 mm was chosen, which corresponds to a resonant frequency of 88 kHz. This switching frequency range allows for simple mounting and control. Once a has been determined, an iterative design process was employed to determine the PT’s port dimensions b and c. The process systematically varies the value of b and evaluates the corresponding theoretical peak efficiency using (9). As shown in FIG. 6, the peak efficiency increases with increasing values of b. However, the maximum permissible value of b / a is constrained by the converter’s ability to achieve ZVS. From (11), one can determine the range of b that satisfies the ZVS condition based on the range of KB for the assumed switching sequence. The upper bound on b / a for which ZVS is achieved occurs when KB approaches the extremum of its range (KB =1), beyond which ZVS cannot be maintained. This critical boundary is indicated by the dashed line 70 in FIG. 6.

[0051] The embodiments herein constrain the port dimensions to demonstrate maximum PT efficiency regardless of operating point. A conversion ratio Vout of 0.4 was found to correspond to a ZVS region that allows for high efficiency in FIG. 6. To maximize efficiency while ensuring reliable ZVS operation, c was selected, which may be considered an upper bound for b to correspond to the ZVS boundary for b. This amounts to a c / a =0.46, which corresponds to c =5.8 mm.

[0052] Having determined the value of c, an isolation width was selected of (c - Z>) = 0.4 mm, which corresponds to Viso of 600 V based on the coercive field of 15 kV / cm, or 3 kV assuming a breakdown field of 75 kV / cm. This also provides an adequate range of KB (0.85 <KB < 1) for which ZVS is maintained, allowing the “Zero” stage time duration to be varied within the assumed switching sequence. This enables regulation of the converter’s output voltage while maintaining the desired high-efficiency behaviors such as ZVS.

[0053] Once a, b and c have been selected, a designer may constrain disc thickness h according to (9a) so that the PT achieves its maximum efficiency at a desired operating point. The embodiments here use a PZT part that has a thickness of h =0.7 mm, which corresponds to the converter reaching its maximum efficiency at P out 0.4 mW / V2. This value of h satisfies the constraint h« a, which is important for ensuring primarily radial mode vibration.

[0054] In an experiment, the inventors acquired axially poled piezoelectric discs of 25.4 mm diameter and 0.7 mm thickness from Fuji Ceramics Corporation (C213 PZT Material), featuring pre-deposited silver electrodes of 15-10 pm thickness on both faces. The electrodes were patterned via selective etching to define the isolation ring with dimensions specified above. The patterning process was performed in a cleanroom environment through standard photolithography and wet etching steps.

[0055] The patterning process began with cleaning the surface of the pre-deposited silver electrodes on both faces to eliminate all particulate contamination that could compromise the subsequent photolithography steps. The disc underwent sequential cleaning in acetone to remove organic contaminants and residual oils, followed by transfer to deionized water for rinsing of acetone residues. The substrates were then blow-dried with nitrogen gun. The photolithography process began with the application of a positive-tone photoresist (MicroChem MIR900) by mounting the disc on a vacuum chuck spin coater. The coated surface was left undisturbed at ambient temperature for a few hours, allowing the viscous resist to solidify through natural solvent evaporation. The conventional soft-bake and hard-bake steps implemented in traditional photolithography were omitted to prevent any possibility of partial depolarization of the PZT disc.

[0056] The pattern transfer step required precise alignment of the photomask containing the isolation ring pattern with the ceramic disc using a Karl Suss MA6 mask aligner equipped with a 365 nm mercury vapor lamp. During exposure, the UV radiation initiated photochemical reactions in the exposed regions of the photoresist, creating a differential solubility that enables its selective removal during development. Following UV exposure, the exposed substrate was immersed in a bath of developer solution (MF-26A) with gentle agitation for 60 seconds. The development process allows the exposed positive photoresist to dissolve in the alkaline developer solution, selectively removing the exposed regions while leaving the un-exposed areas intact as a protective mask. After development, the disc underwent a rinse in deionized water for 30 seconds to remove any residual developer followed by nitrogen blow-drying.

[0057] The exposed silver electrode regions were selectively removed using a potassium iodide-based etchant. The opposite face of the disc was protected using chemically resistant Kapton polyimide tape. The ceramic disc was immersed vertically in the etchant solution using teflon tweezers, and the etching process was conducted at room temperature with gentle stirring to ensure uniform etchant distribution and removal of dissolved silver from the interface. Upon completion of electrode etch in the isolation region, the disc was immediately transferred to a bath of deionized water to arrest the etching reaction. The photoresist mask was subsequently stripped using Microposit Remover 1165, followed by the standard cleaning sequence of acetone and deionized water rinses with final nitrogen drying. The entire photolithography and etching sequence was repeated for the opposite face of the ceramic disc to create symmetric isolation rings on both electrodes. FIG. 7 shows the resulting patterned PT component with labeled dimensions for the input 24, the output ring 24 and the gap 26.

[0058] The Mason model parameters for the patterned PT component are calculated using the expressions derived in Table III and are provided in Table IV. The fundamental radial-mode resonance of the PT was verified via an eigen-frequency analysis performed in COMSOL Multiphysics 6.1. The corresponding mode shape illustrated in FIG. 8 exhibits the radial vibration profile. The simulated radial resonance (~ 90 kHz) agrees closely with the analytically calculated value (88 kHz) in Table IV, with the slight discrepancy resulting fromthe difference in material properties between the PZT-4 material in COMSOL library and that of the C-213 PZT material offered by Fuji Ceramics.Table III: Ring-Dot PT Mason Model Parameters(Ji(x) represents the first order Bessel function of the first time.Table IV: Calculated PT Parameters

[0059] To characterize the PT’s experimental performance and validate the theoretical Mason model, a mounting configuration that minimizes mechanical pressure on the PT was employed while ensuring reliable electrical connection. The mounting fixture 90 shown in FIG. 9 consists of two parallel FR-4 printed circuit boards (PCBs) 92 and 94, each having pads positioned to align with the PT’s input and output ports. The PT 20 is suspended between these PCBs. The separation between the boards should be precisely controlled. In the embodiment shown three screws such as 96 equipped with compression springs provide the separation. Spring contacts 98 are soldered to each PCB for making contact with the inner and outer ports of the PT.

[0060] The impedance response of the mounted PT was measured using a Keysight E4990A impedance analyzer configured for 1600-point logarithmic frequency sweep around the calculated resonance frequency. The impedance response across the input port is measured by short circuiting the output port. The experimental impedance response aligns closely with the theoretical Mason model near the fundamental radial-mode resonant frequency, as shown in FIG. 8.

[0061] After characterizing the PT, it was implemented in a dc-dc converter topology of FIG.1 on a four-layer PCB as shown in FIG. 10. The PT 20 was mounted onto the PCB as shown, with a wire 100 connected to the input port and a wire 102 connected to the output port. All switching times were tuned manually for each operating point, and the converter was tested with a constant-voltage electronic load. Since the PT parameters are temperature dependent, a 650 RPM 12V fan was used to ensure that the PT remains at a relatively constant temperature during testing.

[0062] To evaluate the prototype’s performance, data sweeps were conducted over various voltage and power levels, keeping a constant Vout conversion ratio of 0.4. For a given inputand output voltage, the output power was varied by modulating the switching frequency, taking advantage of the PT’s frequency-dependece as phase shift and dead time for high-efficiency behaviors. Efficiency measurements were obtained by recording the input and output power values with a Key sight PA2201 A power analyzer, which provides an estimated efficiency measurement accuracy of ±0.2%.

[0063] FIG. 12 displays the converter’s experimental power stage efficiency vs. output power. The PT attains its peak efficiency of 98.3% at 0.4 W for Vin = 30 V, and achieves efficiencies as high as 97.4% at Vm = 100 V. The waveforms of the peak efficiency operating point at Vin = 30 V, Vout = 12 V, and Pout = 0.4 W are shown in FIG. 11 and demonstrate ZVS and all-positive instantaneous power transfer. The modeled peak efficiency for this PT design is calculated using the design framework established in (9). To consider the effect of switch capacitances on the PT performance, CPA and CPB were modeled to include parasitic switch capacitance for each relevant segment when computing efficiency capability. The modeled peak efficiency for this prototype is 98.4%, which is expected to occur at a power level of 0.42 W for Vin = 30 V. This aligns closely with the measured peak efficiency. The peak experimental efficiency values decline at higher values of operating input voltages, and this discrepancy can be attributed to the decrease in the PT’s large-signal mechanical quality factor with respect to the amplitude of resonance.

[0064] A power-stage loss breakdown estimate at the peak efficiency operating point shown revealed that the dominant small loss (conduction ~ 5.3 mW) losses occurred in the switches ( ~ 0.4 mW). The losses in the input and output bus capacitors are negligible compared to these dominant losses.

[0065] When comparing the peak efficiency versus output power of the embodiments against state-of-the-art magnetic-less PT-based dc-dc converters, the proposed design outperforms prior isolated and non-isolated converter implementations. This converter demonstrates the highest peak efficiency to date for PT-based magnetic-less dc-dc converters and achieves a 29x reduction in loss ratio compared to previous magnetic-less dc-dc converter designs based on isolated PTs, validating the proposed models and framework for designing high-efficiency isolated PTs.

[0066] Various modifications and variations exist. FIG. 13 shows an embodiment of a PT with a square-dot structure. For square dot PTs, where the outer structure is a square or rectangle, a is half the length of one side of the square, and will be referred to more generally as the transformer size. The dot may not be round, so the dot radius may be referred to as theinput port measurement. The outer structure not being round means that the inner radius may be referred to as the output port measurement.

[0067] FIG. 14 shows an embodiment of a PT in which the input port is segmented into multiple ports that are electrically connected. The embodiment shows the ports electrically connected in series, they could also be electrically connected in parallel. In this structure, the sub-ports for the input may have different shapes than rings. Input port measurements may include the dimensions of subports as well as the dimensions taken up by multiple subports corresponding to the input port.

[0068] Variations and modifications exist and are considered to be encompassed by the embodiments. One variation incorporates multiple isolation gap regions at the center, ring-dot interface and at the disc boundaries. An isolation region can be added at the center of the piezoelectric disc to minimize electric field induced damping by mitigating the peak stress in the PT component, enhancing the device’s efficiency and lifetime. The isolation gap at the ring-dot interface provides galvanic isolation between the input and output ports. To establish stress-free boundaries, an isolation gap can be incorporated at the circumference of the disc at the outside of the radius a shown in FIG. 2, This circumferential isolation also enables the optimization of the electrode area, thereby maximizing electromechanical coupling and boosting the PT efficiency. The width of all these isolation gaps can be engineered to optimize the PT transformation ratio.

[0069] Another variation involves the higher resonant frequencies. The main embodiment was stimulated at the fundamental radial resonant mode, it exhibits an infinite series of higher resonant frequencies, called overtones. Some embodiments may utilize the overtones as primary resonant modes. Leveraging overtone resonant frequencies rather than the fundamental mode introduces a novel pathway to enhance performance in power conversion applications. Operating PTs at overtone frequencies enables a reduction in optimal load impedance and increase power handling density, as higher resonant modes support greater energy transfer within the same physical footprint.

[0070] In addition to structural and resonant frequency design variations, further improvement in PT performance can be achieved through material and electrode optimization. The embodiments here employed PZT as a material. The PT could be comprised of one or a variety of piezoelectric materials, depending upon the desireddielectric, mechanical properties, quality factor, and electromechanical coupling factor, allowing customization for specific applications.

[0071] The embodiments herein reveal isolated PTs to be capable of significantly greater efficiencies than previously demonstrated in magnetic-less dc-dc converters. Such high efficiency is achieved through selection of a high-performance PT vibration mode and specific PT geometry design conditions for simultaneously achieving maximum efficiency and ZVS at a nominal converter operating point. A dc-dc converter based on a PT designed using the proposed framework demonstrates a peak PT efficiency of 98.3%, which represents a significant reduction in loss ratio compared to previous isolated PT-based dc-dc converter designs without magnetics. The design framework of the embodiments extends the utility of piezoelectrics to a wide variety of power conversion applications requiring galvanic isolation.

[0072] 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.

[0073] 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.

[0074] 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.

[0075] 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

IN THE CLAIMS:

1. A power converter, comprising:a piezoelectric transformer comprising a piezoelectric material and metalized electrodes that form two or more ports, at least one of the two or more ports being an input port having an input port surface area, at least one of the at least two ports being an output port having an output port surface area, wherein,the piezoelectric transformer has a physical characteristic of a geometry term H comprised of piezoelectric transformer dimensions and at least one of input and output port measurements, andacross the input port, VPPB is avoltage swing across the output port, KA is a charge utilization at the input port, KB is a charge utilization at the output port, Vm is an input voltage, Vout is an output voltage, and N is a transformation ratio.

2. The power converter as claimed in claim 1, wherein H = where a is atransformer size measurement, b is an input port measurement, and c is an output port measurement.

3. The power converter as claimed in claim 1, wherein H is a ratio between an output port capacitance CPB, and an input port capacitance CPA .

4. The power converter as claimed in claim 1, whereinthe piezoelectric transformer has a physical characteristic of a geometry term G comprised of piezoelectric transformer dimensions and / or input and output port measurements, and,G = - where P is an input or output power of the converter, K is a quantity 2 K BQ W-p pof charge utilization at the input or output port of the transformer, Bo is a normalized frequency-capacitance product, I 'is an input or output voltage of the converter, and (VPP) is a voltage swing at the input or output port of the transformer.b2a2— c25. The power converter as claimed in claim 1, wherein G = — or G = - where a is a ah ah transformer size measurement, Z> is a transformer input port measurement, c is a transformer output port measurement, and A is a distance between transformer electrodes.

6. The power converter as claimed in claim 1, wherein the piezoelectric transformer has a ring-dot structure.

7. The power converter as claimed in claim 1, wherein the piezoelectric transformer has a square-dot structure.

8. The power converter as claimed in claim 1, wherein the input port or the output port is split into multiple sub-ports that are electrically connected.

9. The power converter as claimed in claim 1, wherein the piezoelectric transformer is structured to vibrate at a fundamental resonant frequency of the piezoelectric transformer.

10. The power converter as claimed in claim 1, wherein the piezoelectric transformer is structured to vibrate at an overtone resonant frequency.

11. The power converter as claimed in claim 1, wherein the piezoelectric transformer has multiple isolation gap regions.

12. The power converter as claimed in claim 1, wherein the piezoelectric transformer is galvanically isolated.

13. The power converter as claimed in claim 1, wherein the piezoelectric transformer is not galvanically isolated.

14. The power converter as claimed in claim 1, wherein the power converter has no magnetic components.

15. The power converter as claimed in claim 1, wherein the power converter includes one or more switches, and the piezoelectric transformer is structured to achieve zero-voltage switching of all switches.

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