Piezoelectric resonators in DC-DC converters: current status and limits

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Increasing power density and reducing the size of inductors and transformers at small volumes and high frequencies is a big challenge in the design of DC-DC converters. To circumvent such difficulties piezoelectric resonators (PRs) have been used to store energy in vibrational mode instead of electric mode by exploiting the underlying piezoelectric effect.

Even if the use of PRs has led to improved power converter designs in terms of efficiency and power density, a more accurate model of their operation is needed to investigate non-linearities along with an assessment of their physical limits.

The paper titled “Nonlinear Losses and Material Limits of Piezoelectric Resonators for DC-DC Converters” was presented at the IEEE Applied Power Electronics Conference and Exposition in February 2024. In this work, the authors delve into the fascinating world of piezoelectric materials, exploring their nonlinear behavior and material constraints.

Piezoelectric effect in resonators

Piezoelectric materials allow for a low-loss coupling between the mechanical and electrical domains. This coupling provides an energy storage mechanism for power converters that is theoretically more efficient and more power-dense than what is achievable with magnetic components. The piezoelectric effect enables the circuit to electrically couple to mechanical resonators which can have a quality factor Q some orders of magnitude beyond what can be realized by discrete capacitors and inductors. For a generic resonator, a high Q indicates a lower rate of energy loss, meaning the oscillations die out less rapidly.

PRs are characterized by a figure-of-merit expressed as k²Q_M where k is the electromechanical coupling coefficient, which specifies the conversion efficiency between electrical and mechanical energies for a given vibration mode and Q_M is the mechanical quality factor. The coupling coefficient equals the ratio of the coupled piezoelectric energy, U_m, to the geometric mean value of the stored elastic energy, U_e, and electrical energy, U_d,that is, k . The performance of a PR can vary based on its material, vibration mode, geometric dimensions, electrode pattern, mechanical mounting structure, and electrical contacts.

An equivalent circuit model (Butterworth Van-Dyke or BVD model) translates the piezoelectric resonator’s electrical response near its mechanical resonance into a simple circuit consisting of a series RLC motional branch in parallel with an input capacitance C₀, formed by the electrodes, see Figure 1 where impedance vs. frequency has also been shown.

The BVD circuit exhibits a low impedance series resonance  (f_r) from the motional branch resonance and a high impedance parallel resonance  (f_ar) from the motional branch resonating with the capacitance C₀. The PR exhibits inductive behavior in region B between f_r and f_ar frequencies; this region is important in power conversion as inductive loading enables zero-voltage switching (ZVS).

Accuracy of BVD models

The BVD model, derived from a small-signal measurement of its impedance, does not completely capture a resonator’s behavior. First, the C₀ branch assumes no dielectric loss, thus, more realistically, the modified BVD (MBVD) circuit with a series resistor R₀ is needed. Furthermore, resonators can exhibit secondary, low-coupling resonances called spurious modes, described by additional LCR branches. As actual demonstrators have attained higher power density, efficiency has begun to diverge from the performance predicted by the BVD model. An impressively high-power density of 1.01 kW/cm³ at 493 kHz in a DC-DC converter with a piezoelectric resonator has been recorded in a radial PZT (Lead Zirconate Titanate) resonator operating from 275 V to 150 V at 12 W.

At this operating point, the converter has a theoretical efficiency of 98.2% based on the resonator’s k and Q_M. The converter approaches this modeled efficiency mark at lower voltage and power, but the efficiency falls to 93.3% at the highest power operating point. These deviations suggest that nonlinear effects occur which prevent the small-signal resonator characterization from accurately modeling large-signal performance. The observed density of 1.01 kW/cm³ represents a substantial increase over other recent piezoelectric-based prototypes: 148 W/cm³, 176.8 W/cm³, and 128 W/cm³.

How temperature affects PRs

The Curie temperature in piezoelectric material represents the highest operating temperature limit. The Curie temperatures for PZT and LN (lithium niobate, LiNbO₃) are 320°C and 1,150°C, respectively. As performance degradation may occur at much lower temperatures, it is customary for suppliers to set the maximum operating temperature at half the Curie temperature. Also, both k² and Q_M decrease as temperature increases.

As shown by some researchers of Stanford University at the 2024 APEC conference¹, k^2, and Q_M decrease by 25% and 80%, respectively, in a PZT resonator from 25°C to 150°C. By contrast, k² stays constant and Q_M decreases by only 21% in LN materials.

It is worth mentioning that the LN resonator exhibits many spurious modes, therefore its Q_M is fit to the lowest resistance in the inductive band. High-temperature environment may induce permanent damage due to dipole depolarization and this effect can be monitored by measuring the resonator’s impedance after a burn-in test. The LN device showed no such permanent deterioration though. In a power converter application, a marked decrease in k² and Q_M for the lower Curie temperature resonators translates into a lower efficiency, demanding careful thermal handling.

Voltage bias effect

Piezoelectric materials exhibit a unique property: when subjected to mechanical stress or an electric field, their internal structure is modified, resulting in the re-orientation of microscopic domains. These domains can be visualized as regions inside the material where the polarization direction aligns in a specific way. The switching of these domains plays a crucial role in the piezoelectric response of the material. In some converter topologies, the PR must operate under a DC bias and this requirement can force the material to show nonlinear behavior as the electric field approaches the material coercive field. The coercive field is the maximum electric field that a piezoelectric material can withstand before undergoing depolarization with consequent loss of its basic properties. The DC bias will impact certain parameters such as frequency, output power, and efficiency and is very critical to handle in all topologies with multiple resonators to be matched.

The authors of the paper evaluated the effects of steady-state bias on the resonator frequency response. When a positive voltage bias is applied to a 1777 PZT resonator, we observe a reduction in coupling and a shift of the spurious mode to a lower frequency. If a negative bias is applied, the impedance curve moves upwards. An LN resonator has a higher coercive field vs. PZT, so only small changes in impedance have been recorded.

Large signal analysis

Large signal measurements have been performed with the Vector Network Analyzer Bode 100 from Omicron Lab with the aid of an external coupler and a power amplifier. When plotting the impedance of the PZT resonator (Z_PZT) at different power levels, the series resonant frequency shifts left at high power and the quality factor at resonance degrades causing non-linearity. An interesting measurement consists of plotting the amplitude and the real part of Z_PZT at a single frequency and increasing power. At 54 dBm an increase of both values occurs leading eventually to a failure at 66 dBm with a current density above 0.03 A/mm².

For an LN resonator, unlike PZT, a single-frequency pulse swept from low to high power shows that impedance amplitude │Z_PZT│stays constant whereas Re(Z_PZT) increases as a function of power. The first sweep did not lead to failure of the material (cracking) but produced arcing that was non-destructive. Going to lower impedance allowed for enough current to provoke destructive failure of the LN at 57 dBm with a current density exceeding 0.58 A/mm².

In conclusion, when testing to failure, increased power resulted in Q_M degradation, changes in impedance for both PZT and LN, and concomitant voltage and current waveform distortion in PZT. As power converters using PRs are operated under different conditions including temperature range, voltage bias, and power levels, it is inevitable that nonlinearity effects will arise which must properly be addressed so as not to compromise the converter performance.

References

¹ Clarissa Daniel, Eric Stolt, Weston Braun, Ruochen Lu, Juan Rivas-Davila “Nonlinear Losses and Material Limits of Piezoelectric Resonators for DC-DC Converters” IEEE Applied Power Electronics Conference and Exposition, Feb 2024

The post Piezoelectric resonators in DC-DC converters: current status and limits appeared first on Power Electronics News.

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