Active inductor based on a piezoelectric resonator

Abstract

An active inductor includes a piezoelectric element, and switches electrically connected to the piezoelectric element configured to cause the piezoelectric element to act as an active inductor.

Description

ACTIVE INDUCTOR BASED ON A PIEZOELECTRIC RESONATORTECHNICAL FIELD

[0001] This disclosure relates to piezoelectric resonators, more particularly to piezoelectric resonators emulating an inductor.BACKGROUND

[0002] Most power electronics systems rely heavily on magnetic components such as inductors for processing electrical energy. To power converters, inductors offer periodic energy storage, filtering of high-frequency currents, and lossless acceptance of instantaneous terminal voltage changes. Further, inductors enable high-efficiency switching behaviors, such as zero-voltage (ZVS) or zero-current switching, through current-source-like behavior and / or resonance with capacitive elements. However, the power densities and performance capabilities of inductors and other magnetics fundamentally decrease at small scales, which poses a significant challenge to power converter miniaturization. This motivates the exploration of alternative passive component technologies that can provide similar functionalities as magnetics but with improved scalability to small sizes.

[0003] Piezoelectric components have emerged as compelling alternative passive components for power electronics. Piezoelectric resonators (PRs), which store energy in the mechanical compliance and inertia of a piezoelectric material, offer various advantages to power conversion including high quality factors, planar form factors, opportunity for batch fabrication, and potential for integration. Contrary to magnetic components, PRs have increased power handling densities at small scales, making them highly suitable for miniaturized power conversion. Further, the high quality factors of PRs result in lower energy losses, and their planar structures allow for more straightforward integration into modern electronic systems. Noteworthy advances have been made in magnetic-less, PR-based power converter designs, demonstrating significant power densities (up to 5.7 kW / cm3) and efficiencies, up to greater than 99%. PRs make attractive candidates for replacing magnetic components in power conversion to enable more compact, efficient, and integrated solutions.

[0004] While PRs provide promising alternative passive components for power conversion, they cannot be used as drag-and-drop replacements for magnetics. Consequently, achievinghigh performance in a PR-based converter requires complex control of multi-stage switching sequences. These switching sequences require specific circuit topologies, which limit their applicability to a narrow range of power con-version applications and distance their design considerations from widely used approaches in power electronics. These complexities can hinder the practical implementation and widespread adoption of PR-based converters. Thus, there is a need for more practical ways to leverage piezoelectrics in power conversion without such added complexity.BRIEF DESCRIPTION OF THE DRAWINGS

[0005] FIG. 1 shows an embodiment of a circuit schematic of a piezoelectric-based active inductor.

[0006] FIG. 2 shows a graph of resonator current with the states of switches Si - S4 from the circuit of FIG. 1.

[0007] FIG. 3 shows an embodiment of a buck converter with a piezoelectric-based active inductor in place of a traditional inductor.

[0008] FIG. 4 shows a graph of an expected active inductor waveform in a buck converter.

[0009] FIGs. 5A and 5B show alternative topologies for a buck converter with a piezoelectric active inductor.

[0010] FIG. 6 shows a graph of an ideal active inductor period.

[0011] FIGs. 7A and 7B show graphs of synchronization error detection in an active inductor.

[0012] FIGs. 8A and 8B show graphs of dead time error detection in an active inductor.

[0013] FIG. 9 shows an embodiment of a closed-loop controller for an active inductor.

[0014] FIGs. 10A-10C show simulated piezoelectric resonator voltage in an embodiment of a buck converter using a piezoelectric-based active inductor.

[0015] FIG. 11 shows simulated current for an embodiment of an active inductor.

[0016] FIG. 12 shows experimental waveforms of an active inductor buck converter switch node voltage, piezoelectric resonator voltage, and absolute value of the piezoelectric resonator current.

[0017] FIG. 13 shows embodiments of a resonant circuit and an anti-resonant circuit for an active inductor.

[0018] FIG. 14 shows a diagram of an active inductor control strategy.DETAILED DESCRIPTION OF THE EMBODIMENTS

[0019] The embodiments herein leverage a piezoelectric component to directly emulate the steady state and dynamic behaviors of a magnetic component, creating an “active inductor” that can serve as a drag-and-drop replacement for bulky magnetic inductors in power converters. This active inductor consists of a circuit containing piezoelectric component(s) and active switching devices, and the circuit is controlled to directly emulate the dynamics of a magnetic component with high efficiency. The embodiments present a model that provides the effective inductance of the active inductor and includes a feedback-loop control strategy for efficient performance. The model was verified by experimentally testing the active inductor in a classic buck converter.

[0020] A piezoelectric resonator (PR) is commonly modeled with the Butterworth- Van Dyke (BVD) circuit model, which includes a static capacitance between its two terminals in parallel with an LCR branch modeling its mechanical resonance and loss properties. PRs inherently have high quality factors, causing the resonant current, ZL, to be primarily sinusoidal.

[0021] A PR may be leveraged to emulate the dynamics of an inductor using the H-bridge switching cell 12 shown in FIG. 1. This “active inductor” 12 comprises a piezoelectric resonator 10 controlled to have the switching sequence visualized in FIG. 2, where SI and S4 are switched together at times complementary to S2 and S3 so that IAL = \IL\ at all times, excluding dead time. This switching sequence is synchronized to the PR’s resonant cycle, and its switching frequency is assumed to be significantly higher than that of the surrounding power converter.

[0022] FIG. 2 shows the resonator current, L, active inductor current, IAL, and gate pulses. Depending on the polarity of the active inductor voltage, the dead time may shift from immediately before the IL zero-crossings, when VAL > 0, to immediately after the IL zerocrossings, when VAL < 0. This shift ensures that IL has the correct polarity to charge / discharge the PR’s parallel capacitance CPand achieve ZVS.

[0023] As used here the term Tin means the “inner period” of the active inductor’s switching cycle, and Tout means the “outer” period of the switching cycle of the power converterutilizing the active inductor. Throughout Tin, the surrounding system delivers and extracts a certain amount of charge, q, and energy, E, to / from the PR. These quantities are related by En= VALqn, where the subscripts correspond to the stage order of the active inductor’s switching sequence, and VAL is the active inductor’s terminal voltage. One should note that qs is a negative value due to the polarity of E at that time, as illustrated in FIG. 2. In steady-state operation, the net charge and net energy exchanged is zero, as shown in Equation (l)-(2). These expressions can be combined into (3) to derive a VAL condition for inner-period steady state, shown in (4). The active inductor reaches inner-period steady-state operation only when its terminal voltage is zero, just like an inductor whose current does not change. This is an important property of the active inductor’s switching sequence, enabling it to emulate the behavior of an inductor.Qi + q2= 0 (2)VAL I + (- vAL~)q3= 2q vAL= 0 (3) = vAL= 0 (4)

[0024] Although the active inductor reaches inner-period steady-state operation only for VAL = 0, most practical power conversion applications have non-zero inductor voltage, meaning VAL # 0) throughout most or all the switching cycle. Consequently, one would expect the PR of an active inductor to regularly be in a dynamic state, gaining or losing energy as different voltage levels are applied, even if the outer converter reaches steady-state operation, meaning outer-period steady state. As such, the PR’s amplitude of resonance, II, the amplitude of E, varies with time.

[0025] One can derive the rate at which II varies by first calculating the net energy transferred from the outer converter to the active inductor during Tin, shown in (5). Note that this is a non-zero value because the active inductor is in a dynamic state where VAL * 0. Additionally, one can represent the PR’s energy by considering the instance at which E reaches its maximum, II. At this time, all the PR’s energy in the resonant branch of the BVD model is in the inductor, L, as shown in (6). In (7), one can compare (5) with the derivative of (6), accounting for II being a time-varying value. These equations show that is a functionof qi, which is solved in (9), assuming the dead time is negligible compared to Tin. Hence, one finds the rate at which II changes when VAL 0, and therefore, the governing equation of the active inductor, shown in (10).

[0026] The voltage-current relationship of the active inductor is remarkably similar to that of a traditional inductor, only differing by a scalar value. Note that L refers to the modeled inductance from the BVD model. Additionally, one can see that outer-period steady state is reached when VAL) = 0, just like a traditional inductor that achieves volt-second balance.

[0027] When the active inductor is in a dynamic state, dead time is inserted between switch transitions to aid zero-voltage switching (ZVS) and soft charging of the PR’s capacitance. For soft charging, the placement of the dead time within Tin is critical. When VAL > 0, the dead time should occur immediately before the IL zero-crossing to ensure IL has the correct polarity to charge / discharge CPthrough resonance, as shown in FIG. 2. Conversely, when VAL < 0, the dead time should occur immediately after the IL zero-crossing.

[0028] To further describe the behavior of the active inductor and its model, consider replacing the traditional inductor in a buck converter, as shown in FIG. 3. A buck converter provides an example of power converters that typically include a magnetic inductor. Buck converters, or step-down converters, are typically a DC-to-DC converter that increases current while decreasing voltage from the supply / input to the load / output, often found in power supplies. While the below discussion uses a buck converter example, one should note that any type of power converter using magnetic inductors may use the active inductor disclosed herein.

[0029] The “AL” as shown here is the active inductor 10 from FIG. 1. Based on the quality factor of PRs and the voltage-current relationship from (10), one can predict the active inductor current, IAL, to be a rectified sinusoid with its amplitude varying at a rate proportional to the applied voltage. Similar to a traditional inductor’s current in a buck converter, which is triangular, one expects IAL to have a triangular envelope, as shown in FIG.

[0030] FIGs. 5A and 5B show alternative circuit topologies for a buck converter using an active inductor. If one were to take the active inductor 12 of FIG. 1 and insert it into the buck converter of FIG. 3, the circuit may require ten transistors. Each switch in FIG. 1 may require two transistors, one for each direction at each location, assuming that bi-directional components are not available. This results in eight transistors for the active inductor. As can be seen in FIG. 3, there are two more switches 14 and 16 needed for the buck converter, totaling ten transistors. The circuits of FIGs. 5 A and 5B only require up to eight transistors.

[0031] When the high-frequency components of the active inductor current, the frequency components greater than the outer frequency, fout, are filtered, one is left with an inductor-like current equal to the moving average of IAL. This effective inductor current,represents the ideal current of the traditional inductor that is being emulated. As such, one may use the ripple of the filtered active inductor current to calculate its effective inductance Z . In (11)- (12) one can calculate the effective inductor current ripple considering normal operation of a buck converter during time t = 0 to DTout. As shown in (13) the active inductor emulates a traditional inductor of value ~ 2.47x larger than its BVD modeled inductance.

[0032] Similar to calculating an average inductor current, the PR’s average amplitude of resonance is a function of the converter’s operating point and circuit parameters. As shown in (14), the average amplitude of resonance, {II), is a function of the total charge transferred through the active inductor’s PR in one inner period — this is simply the definition of the amplitude of a rectified sine wave. In (15), one converts the total charge transferred during Tin to a value that represents a portion of the total charge transferred during Tout. Subscripts for the charges within the inner period represent their respective portion of Tin. One can find the total charge transferred during Tout as the summation of all qi, qs, energy-transfer stages, and q2, q4, dead time, shown in (17).total,out conn,out T dead,out (17)

[0033] The expression in (17) can be evaluated using the relevant parameters of the converter in which the active inductor is being used. In the buck converter example, the total charge associated with the energy-transfer stages is from the current drawn by the load of the buck converter, and the total charge associated with the dead time is a result of soft charging Cp, as shown in (18). Note that CPshould include the active inductor’s switch capacitances to achieve ZVS. The term Al), represents the roundtrip voltage difference to which the parallel capacitance must be charged / discharged for efficient operation. This voltage difference is equal to twice the active inductor voltage because the PR voltage polarity flips between dead times, meaning that CPmay need to discharge from +VAL to -VAL, which is a total of 2VAL. Its average value is simply a weighted average of the voltage differences during each segment of the outer converter cycle as shown in (19) for the buck converter. Therefore, one can find the average PR amplitude of resonance for an active-inductor-based buck converter in (20). Ideally, the charge used during the dead time for soft charging and ZVS, qdead, is significantly less than the charge transferred to the load. When this is the case, excluding the second term offers a close approximation.

[0034] Because the PR’s parallel capacitance and the switch capacitances are soft charged at all inner-period transitions, one can assume the only source of loss comes from the PR’s inherent mechanical loss. This is represented in the BVD model by the resistor, R, and we treat its associated loss like the conduction loss of a resistor as shown in (21). As described previously, IL can be well-represented as a sine wave with a time-varying amplitude. The PR’s true rms current is shown in (22), assuming negligible dead time. The equations below use integration by parts in (24), and after simplifying, the second term can be canceledbecause 7L(0) = I Tout), shown in (25). In (27) has further simplification assuming — « Tout, and one can see that the numerator is the amplitude of resonance squared at a specific time within the outer period, in this case t = Tout. However, this point within Tout is arbitrary. For the efficiency calculation, one can use the mean of the square of the amplitude of resistance, resulting in a root mean squared (rms) value of II over 2, show in (29).Pioss ~rms(21)

[0035] The power loss of the active inductor is approximated as a function of the rms value of the time-varying II. It is important to note that this loss model does not consider abrupt voltage changes corresponding to the outer period, as in the transition of the buck converter states at time t = DTout. If this transition occurs during an energy-transfer stage, there will be loss associated with hard charging the PR’s parallel capacitance.

[0036] An active inductor will reach outer-cycle periodic steady state if vAL) = 0, but will but will only reach inner-cycle stead stat if VAL = 0. The latter is rarely the case for power converters that depend on magnetics to absorb voltage changes in the circuit. Maximizing the power performance of an active inductor requires careful control of its switching signals for high-efficiency behaviors, even as VAL and IAL change. To introduce the control strategy of the active inductor, first consider the first inner-half period shown in FIG. 6, from to to t2. During this half-period, switches Si and S4 are on for a certain duration, ton, and off for a certain duration, toff, dead time. Without proper control of ton and toff, the active inductor will exhibit synchronization and / or soft charging errors resulting in unwanted circulating current and / or reduced efficiency.

[0037] For PR-based power circuits, synchronizing switching signals to the PR’s resonant cycle typically requires detection of the IL zero-crossing. To avoid current sensing of IL, theprocess detects a synchronization error by observing the PR voltage, vP, throughout the dead time. During the dead time, CPis in series with L, and therefore, vPlags IL by 90°. As such, the active inductor detects a synchronization error by observing whether or not vPreaches a local maximum before the end of the dead time, which would correspond to an IL zerocrossing as shown in FIGs. 7A-7B. FIG. 7A shows a graph of the resonator turning on too late, and FIG. 7B shows when it turns on too early. If such a peak is observed during the dead time, then the turn-on time of the relevant switches is too late. Likewise, if a peak is not observed, the turn-on time is too early.

[0038] In addition to synchronization, the active inductor regulates the duration of its dead time by observing soft charging errors at each turn-on transition. If |vp| is greater than | VAL| at the turn-on time, the duration of the dead time must decrease, and vice versa, as shown in FIGs. 8A-8B. FIG. 8A shows the situation when the resonator turns off too early, so the dead time should decrease. In FIG. 8B, the resonator turned off too late, so the dead time should increase. In this manner, the active inductor achieves ZVS and soft charging of CP.

[0039] For a given active inductor switching frequency,amplitude of resonance, and voltage difference from one stage to the next, AFp, one can calculate the ideal dead time to achieve exact soft charging and ZVS, shown in (30). However, it has been established that when VAL * 0, the amplitude of resonance, II, is a time-varying value. Consequently, the ideal dead time is a time-varying value. Moreover, (31) shows the approximate PR frequency, fin, which is function of the dead time, and also time-varying. The terms fir and far represent the resonant and antiresonant frequencies of the PR, respectively.

[0040] In this embodiment, then, the two control parameters of switching frequency and dead time are ideally time-varying, never settling to a steady-state value. This interdependence helps describes the dynamic behavior of the active inductor and poses a challenge for its closed-loop control.

[0041] Because of the constantly-dynamic behavior of the active inductor, the controller must adjust the frequency and the dead time before each switch transition (i.e., twice per inner period). As such, the control loop incorporates a predictive component, in which the active inductor learns from previous imperfections in order to adjust for future periods, hoping to predict the ideal frequency and dead time. In this control strategy, both the synchronizationloop (modulating frequency) and the soft charging loop (modulating dead time) have the same feedback loop structure but different bandwidths.

[0042] FIG. 9 depicts an embodiment of a feedback controller of the active inductor, using the generic variable, X, which either represents Tin or tdead for the synchronization loop and soft charging loop, respectively. A phase-locked loop (PLL) 20 determines the duration of Tout by integrating VAL to identify the period over which volt-second balance is achieved, meaning (VAL) = 0. As outputs, the PLL generates two instantaneous phase angles. The first, 0m, is the phase angle of the active inductor’s switching sequence at the beginning of the outer period. For example, if at the beginning of the buck converter’s outer period, at high- side switch turn-on, the active inductor is halfway through its switching sequence, L in FIG. 2, then 0m=TT. The second, On, is the phase angle within the outer period. For example, if a buck converter with a 75% duty cycle just transitioned from the high-side switch being on to the low-side switch being on, corresponding to t = DTout, then On = 3TC / 2.

[0043] Based on 0mand 0n, the controller 22 selects the corresponding inner period, Tn[m,n], and dead time, tdead[m,n], stored in memory. The controller 22 detects synchronization and soft charging errors with the newly selected frequency and dead time. These errors are integrated by integrator 24 and used to update the frequency and dead time values in preparation for the next time the converter has the same 0mand 0nconditions. This process occurs for every switch transition, twice per inner period. The integration rate of the synchronization loop may be lOx larger than that of the soft charging loop to avoid quarreling control loops.

[0044] To validate the active inductor as a concept, it was first simulated in the context of a buck converter, as shown in FIG. 3, with Vin = 100 V and D = 0.7. The PR model used for this simulation has the following values: L = 1.5 mH, C = 75.2 pF, R = 4.45 Q, and CP= 457 pF. FIGs. 10A-10C display vPwithin the active inductor and confirms that the switching frequency and dead time are appropriately modulated for synchronization to the PR’s resonant cycle and soft charging of CP. FIG. 10A shows the PR voltage in a buck converter over one outer period. FIGs. 10B and 10C shows zoomed in views to validate the soft charging behavior with VAL > 0 in FIG. 10B and VAL < 0 FIG. 10 C.

[0045] The raw and filtered waveforms of IAL are displayed in FIG. 11 and demonstrate a linear ripple that compares closely with that of its modeled trajectory based on a traditional inductor of value Leff= I - I L = 3.7 mH. The simulated average amplitude of resonance, {II), is 1.081 A, and the expected value from the model given in (20) is 1.083 A, which iswithin 0.2% of the simulated value. The simulated 0.72315 A compared to the expected value from the model given in (23) of 0.72316 A. These simulations validate the active inductor’s functionality and the proposed models, and the closed-loop control scheme embodiment discussed above.

[0046] Next, the active inductor in a classic buck converter as visualized in FIG. 3 was experimentally demonstrated. This active-inductor-based buck converter is implemented on a 1-oz copper PCB. The active inductor’s PR is selected to be an APC 841 PZT disc with a radial-mode resonant frequency of 115 kHz, which dictates the approximate value of fin to be the same. The buck converter operates at approximately 14 kHz to satisfy the assumption that fin » fout. Because the active inductor must block voltage in both directions, each of its switches is implemented with two back-to-back FETs in a common-source configuration, similar as to what was discussed above about FIG. 1.

[0047] The FETs are driven by two isolated half-bridge gate drivers, in this experiment Infineon 2EDB7259KXUMA1, one for SI, S3, and one for S2, S4. The experimental prototype was operated with open-loop switch signals generated by a Texas Instruments C2000 microcontroller and a constant-voltage load at Vout = 35 V, Vin = 50 V, and Pout = 15 W. The active inductor’s switch signals were actively tuned according to the synchronization and dead time requirements for high efficiency discussed above. To avoid capacitive losses in the switches and PR at the buck converter switch transitions, the active inductor’s switch signals were tuned to ensure that the buck converter transitions occur during the active inductor’s dead time.

[0048] FIG. 12 illustrates the active-inductor-based buck converter’s operation with experimental waveforms for vp, \IL\, and the buck converter’s switch node, v™. The converter reaches outer-period steady state, and II, the amplitude of iu has a triangular wave shape comparable to that of FIG. 4. The minimum and maximum values for / z. reveal an / z. ripple of 0.27 A, which corresponds to an experimentally observed Z = 4.62 mH. This is within 3% of the modeled value of 4.49 mH based on (13). As observed, the active inductor’s switching sequence is appropriately synchronized with the IL cycle, and the active inductor achieves soft charging of CPand ZVS. In summary, the PR-based active inductor successfully emulates the desired dynamics of an inductor in the experimental prototype and validates the concepts proposed herein.

[0049] Another embodiment uses a dynamic feed forward (DFF) term as part of the active inductor’s control strategy. Because each inner half-period has a different ton and toff whenVAL * 0, the DFF term predicts the ideal ton and toff values during operation. FIG.13 shows two circuits. The resonant circuit 30 consists of on L and C and makes up the effective resonant tank during ton. The anti-resonant circuit 32 consists of / ., C, and CPacts as the effective resonant tank during toff.

[0050] Because an inductor’s current is continuous by definition, as is a capacitor’s voltage, one can use the inductor current, ZL, and capacitor voltage, vc , as mathematical constraints at the moment the active inductor switches from the resonant circuit to the anti-resonant circuit, at the transition between ton and toff. These constraints allow one to create a system of equations, (33)-(35), that describe the ideal behavior of an active inductor that achieves synchronization and soft charging / ZVS. The inductor current at a transition is denoted as iLand the capacitor voltage at a transition is denoted as VCQ. Note that these equations include an additional amplitude of resonance corresponding to the anti -resonant circuit lLIL is the actual amplitude of resonance observed during operation, which occurs during ton, the resonant circuit. ILaris the amplitude of resonance that would be observed if the anti-resonant tank were allowed to continue resonating until its current reached a maximum / minimum.To simplify this system of equations, one can substitute xi in place of sin , andshown in (36)-(38). This allowsderivation of the ratio of ILarto II, shown in (39). The below equations assume both {xi,X2}« 1 because Z is ideally much less than ton and Son is ideally 7t.These simplifications and assumptions result in the following approximate-ideal on and off times for an active inductor’s half-period, (40) and (41).Now using these values as dynamic feed forward (DFF) terms, changing as A Vp and IL change, one can eliminate the need to detect synchronization errors as previously described, thus solely utilizing soft charging errors to drive a compensated feedback loop.

[0051] Assuming the proposed DFF terms result in accurate switching times for synchronization and ZVS, the challenge lies in measuring or estimating A Vp and II. Voltage sensing circuits are used to capture A Vp. However. IL cannot be directly measured without current sensing. Nevertheless, the rate of change for II is known from (10),and cantherefore one can track its value over time as long as it has an accurate starting point. This starting point, chosen to be the average amplitude of resonance, ( / L), can be regulated with a feedback loop. To do this, one simply varies the II used in the DFF terms in a manner that minimizes soft charging errors. For example, if the soft charging error detection indicates that the dead time is too long, | vpr\ > | VAL| at turn-on, the amplitude of resonance, IL , used in the DFF terms must be too large, and therefore should decrease. In this manner a feedback loop is created with an integrator compensator 36, as shown in FIG. 14. FIG. 14 shows the DFF term used to control the active inductor 12 from FIG. 1.

[0052] In this manner, piezoelectric resonator-based active inductors are provided. These PR active inductors can replace traditional magnetic inductors. Feedback loops may be employed to synchronize the switching sequence with the PR resonant cycle, soft charge the PRs capacitance, and achieve ZVS. The active inductors here represent a significant advantage in the miniaturization of power converters and other circuits that currently rely on bulky magnetic components.

[0053] 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 anycombination, 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.

[0054] Additionally, this written description refers 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. vAL

[0055] 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.

[0056] 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

WHAT IS CLAIMED IS:

1. An active inductor, comprising: a piezoelectric element; and switches electrically connected to the piezoelectric element configured to cause the piezoelectric element to act as an inductor.

2. The active inductor as claimed in claim 1, wherein the switches comprises a first switch and a second switch connected to an input voltage and one side of the piezoelectric element, and a third switch and a fourth switch connected to the input and another side of the piezoelectric element, such that the first and fourth switches are closed, the piezoelectric element stores energy, and when the second and third switches are closed the piezoelectric element discharges energy.

3. The active inductor as claimed in claim 1, wherein the active inductor has a switching cycle synchronized to a resonant cycle of the piezoelectric element.

4. The active inductor as claimed in claim 3, wherein the switching cycle has a frequency equal to a resonant frequency of the piezoelectric element.

5. The active inductor as claimed in claim 2, wherein the first and fourth switches are closed when a resonant current of the piezoelectric element is positive, and the second and third switches are closed when the resonant current of the piezoelectric element current is negative.

6. The active inductor as claimed in claim 5, wherein the active inductor has an off time in between transitions of the switches during which all switches are off to allow the resonant current of the piezoelectric element to either charge or discharge capacitance for at least one of either soft charging or zero voltage switching7. A power converter comprising an active inductor, the active inductor comprising: a piezoelectric element; andswitches electrically connected to the piezoelectric element configured to cause the piezoelectric element to act as an inductor.

8. The power converter as claimed in claim 7, wherein the active inductor switches comprises a first switch and a second switch connected to an input voltage and one side of the piezoelectric element, and a third switch and a fourth switch connected to the input and another side of the piezoelectric element, such that when the first and fourth switches are closed, the piezoelectric element stores energy, and when the second and third switches are closed the piezoelectric element discharges energy.

9. The power converter as claimed in claim 7, wherein the active inductor switching frequency is greater than two times the switching frequency of the power converter10. The power converter as claimed in claim 7, wherein the active inductor has a positive voltage across it during some portion of a switching cycle of the converter and a negative voltage across it during another portion of the switching cycle of the converter.

11. The power converter as claimed in claim 7, wherein the active inductor serves as a filter component.

12. The power converter as claimed in claim 7, further comprising a controller configured to control an on time for the switches and an off time for the switches based on at least one of synchronization errors and soft charging errors.

13. The power converter as claimed in claim 12, wherein the controller is further configured to detect errors in at least one of synchronization or soft charging of the piezoelectric element.

14. The power converter as claimed in claim 12, wherein the controller is further configured to use a dynamic feed forward term to predict the on time and off time.

15. The power converter as claimed in claim 12, wherein the controller includes a feedback loop for the piezoelectric resonator current.

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