Comparison of BSPT and PZT Piezoelectric Ceramic Transformers for High-Temperature Power Supplies

High-temperature power electronics is an advancing area of research, especially given the widespread availability of wide bandgap semiconductors. Herein, a suitability analysis of (1 (cid:1) x)BiScO 3 (cid:1) xPbTiO 3 (BSPT) as a material for high-temperature piezoelectric transformers (PTs) is presented and compared to state-of-the-art Pb(Zr 1 (cid:1) x Ti x )O 3 (PZT). Initially, both materials are compared using a variety of metrics to prove the suitability of BSPT as a material for constructing PTs speci ﬁ cally for high-temperature applications. PTs based on the two materials are designed and fabricated

d 33 ¼ 450 pC/N, and electromechanical coupling factor, k p ¼ 0.58, but, most importantly, undoped MPB BSPT possesses a higher T C (%450°C at x ¼ 0.64) which makes BSPT a promising material for use in the range 200-350°C. Given the properties of BSPT piezoelectric ceramics, there is great potential for its usage in PTs designed to operate at higher temperatures than those based on PZT.
The objective of the work presented here is to demonstrate the effectiveness of BSPT as a material for high-temperature PTs for use in resonant power supplies. Additionally, the work will compare the performance of BSPT to state-of-the-art PZT ceramics and prove the effectiveness of PT-based resonant converters for high-temperature applications requiring up to 1 W in power. To achieve this, sample BSPT-and PZT-based PTs are fabricated and characterized using a variety of metrics at several temperatures, to evaluate the performance of BSPT compared to the current optimum PZT compositions when applied to PT applications.

PT Topology
Although the choice of PT topology is important for specific applications, when comparing two materials the PT topology choice will have a minimal impact on the results.
The ring-dot type PT, Figure 1, was chosen as the basis for this study since it is one of the simplest topologies to construct, requiring only a single piezoelectric disc, no bonding/glue, and a minimal number of electrodes. Its simple construction makes it relatively straightforward to produce two similarly dimensioned devices from different piezoelectric materials thereby allowing a fair comparison. The performance differences between PTs made of different materials, therefore, predominantly arise because of the materials alone. Ring-dot PTs are versatile, they can be used in both step-up or step-down applications; they exhibit high power densities and show minimal spurious vibration modes. [20,21] Owing to the electromechanical nature of PTs, it is common for electrical engineers to approximate the PT using an equivalent circuit, namely the Mason equivalent circuit shown inside the dashed box in Figure 2. The input and output capacitance ðC in , C out Þ, model the physical plate capacitances generated between the input and output electrodes (located on the upper face in Figure 1), and the common ground electrode (located on the lower face). The ideal transformer (1:N 1 ) models the conversion between electrical and mechanical energy. Finally, the resistor-inductor-capacitor tank circuit models the mechanical resonance of the PT, with a resonant frequency ω 0 ¼ 1= ffiffiffiffiffiffiffiffiffiffi and R 1 representing the losses.

PT-Based Resonant Converters
Resonant power conversion is one of the most popular applications of PTs. Resonant converters rely on energy oscillating between parts of a "resonant tank," traditionally constructed using discrete capacitors and inductors, which results in a sinusoidal current being generated. Resonant converters have displaced traditional "hard-switched" non-resonant electronic power converters in many applications because their continuously varying current allows semiconductor switches to be activated at instants of zero voltage or zero current, dramatically reducing switching energy losses and thereby increasing efficiency. Due to their natural vibration modes, PTs can provide the "resonant tank" for such a converter. While several topologies of PT-based resonant converter have been studied, the choice of topology is typically related to a specific application and will have minimal impact on the performance comparison between PTs. Therefore, we relate our work only to the popular inductorless half-bridge inverter topology, [22] as shown in Figure 2.
The half-bridge inverter uses two high-frequency metaloxide-semiconductor field-effect transistor (MOSFET) switches, S 1 and S 2 , which operate at a frequency close to the resonant frequency of the piezoelectric transformer, as shown in Figure 3. Correct operation results in a high-frequency trapezoidal waveform at the input to the PT ðv C in Þ. Due to the high Q factor bandpass filter characteristic of the PT, the resonant current is approximately sinusoidal, as is the output voltage. It should also be noted that the current through the resonant circuit i 1 is proportional to the vibration velocity of the PT and v C in is proportional to the electric field across the device. A full description of the operation of this converter can be found in ref. [22,23]    One of the main advantages of resonant converters is that they allow zero-voltage switching (ZVS) to be achieved, avoiding switching loss in the MOSFETs. During the deadtime interval (shown as DT in Figure 3) resonant current i 1 charges or discharges the input capacitor so that, at the point of turn-on, there is zero voltage across the relevant MOSFET. When ZVS is not achieved, C in charges or discharges quickly through the switch causing energy loss. To evaluate the zero-voltage switching performance of the converter, k ZVS is introduced where ZVS is achieved if v C in ð@S 2 turn onÞ ≥ V DC , in which case k ZVS ≥ 1. When k ZVS < 1, the switching losses in the MOSFETs are proportional to ð1 À k ZVS Þ 2 . If the PT is designed correctly and the switching waveforms displayed in Figure 3 are achieved, ZVS should be guaranteed. [23]

Electrical Efficiency
A key performance metric for all power converters is electrical efficiency, defined as where P out is the power delivered to the load, P in is the input power to the converter, and P loss is the power loss in the converter, mainly consisting of switching and conduction losses in the MOSFETs and losses in the PT. Ideally, the efficiency of the converter should be maximized and thus losses are minimized. As discussed, with the appropriate design of the PT and control circuitry, ZVS is achieved, and thus switching losses can be avoided. Therefore, the electrical efficiency of an inverter is directly related to the losses in each PT during operation and is proportional to resistance R 1 (and thus the quality factor) in the Mason equivalent circuit (assuming MOSFET conduction loss is much smaller than PT loss).

Output Power
Output power is a key consideration when designing a converter, as it informs several of the design choices. In PT-based power converters, the output power of the converter is typically limited by the temperature rise, with a 30°C rise in temperature over ambient being a typical limit. [24] Some work has been done to model the effects of ambient temperature on temperature rise for other PT topologies, [25] however, there is no available metric to determine the power limit of a PT at raised ambient temperatures and developing such as metric is beyond the scope of this work. As a result, we use output power to give context to the efficiency values that are achieved ensuring the results of the study are representative of a real-world application. Figure 1 shows the design of a ring-dot PT with a ring and a dot electrode on the upper side and a full electrode on the lower side. The dimensions are as follows: radius a ¼ 8 mm, thickness www.advancedsciencenews.com www.aem-journal.com h ¼ 1.1 mm, r a ¼ 3.4 mm and r b ¼ 6 mm. The radius and thickness were selected to achieve a radius/thickness ratio of %7, ensuring that the PT avoids interaction with spurious vibration modes, [26] even though, as Erhart suggests, these modes are not excited in this PT topology. [21] Second, r a and r b were chosen to achieve a capacitance ratio (C N ¼ C in =ðN 2 1 C out Þ) of less than 2=π, to agree with the criterion presented by Foster et al. [23] This ensures that an inductorless half-bridge power inverter constructed with this PT should achieve ZVS irrespective of the load (if the driving conditions presented in ref. [23] are adhered to). Identically dimensioned PTs based on this design were fabricated from both BSPT and PZT materials.

Ceramic Preparation
0.64(PbTiO 3 )-0.36(BiScO 3 ) (BSPT-64) ceramics were prepared by the conventional solid-state route using PbO (99%, Sigma-Aldrich), Bi 2 O 3 (99.9%, Sigma-Aldrich), Sc 2 O 3 (99%, Sigma-Aldrich), and TiO 2 (99.9%, Sigma-Aldrich) as raw materials. Raw materials were pre-dried (300°C for PbO, Bi 2 O 3 and 800°C for Sc 2 O 3 , TiO 2 ) for 8 h before weighing then ball-milled in isopropanol with yttria-stabilized zirconia milling media for 6 h. The mixture was then calcined twice at 800 and 900°C followed by drying and sieving. Green pellets were formed using a uniaxial steel die and then cold-isostatically pressed at 200 MPa. Throughout this article, the term pellet was used to refer to the PT disc with or without full-face electrodes, and the term PT refers to a poled disc with the ring-dot electrodes. Pellets were sintered at 1200°C for 2 h in a closed environment. During sintering, green pellets were buried in calcined powder of the same composition to minimize volatilization.
Pb(Zr,Ti)O 3 (PZT-P85) ceramics were prepared from commercial powder (P85, Weifang Jude Electron). Green pellets were formed using a uniaxial press and then cold-isostatically pressed under the same conditions as BSPT. Pellets of PZT-P85 were sintered at 1250°C for 2 h in a closed environment with sacrificial powder to minimize volatilization.

X-Ray Diffraction and Scanning Electron Microscopy
The X-ray powder diffraction (XRD) analysis was performed on a high-resolution STOE STADI-P diffractometer (Cu Kα emitter, STOE & Cie GmbH) using sintered and crushed samples. Microstructure and elemental compositions were determined by scanning electron microscope (SEM, Philips XL 30S FEG) and energy-dispersive X-Ray spectroscopy (EDX, Oxford Link ISIS) on polished surface/fracture surfaces of bulk ceramics.

Electrical Measurements of Material
Impedance spectroscopy and relative permittivity measurements were performed using either a Solartron Modulab or Hewlett Packard 4284A precision inductor-capacitor-resistor (LCR) meter. Au-paste electrodes were coated on the upper and lower faces of the pellets. Results were corrected for sample geometry (thickness/area) and high-frequency data was corrected for instrument error. For ferroelectric polarization-field (P-E) measurements, ceramics were ground to a thickness of %1 mm and gold-sputtered. Bipolar P-E loops were obtained using an aixACCT TF 2000E ferroelectric tester at 1 Hz.

Fabrication of PTs
BSPT-64 and PZT-P85 pellets were coated at room temperature with an Ag electrode and poled for 30 mins at 40 kV cm À1 at 120°C. The Ag electrode was removed and the Au ring-dot/full electrode was sputtered onto both sides to form the PT samples, as shown in Figure 4.

PT Testing and Equivalent Circuit
An Elite tube furnace was used to vary the ambient temperature of the PT samples, from 25 to 200°C for PZT-P85 samples and up to 250°C for BSPT-64 samples. Each PT was suspended from a ceramic rod, allowing it to freely vibrate whilst in the furnace. An n-type thermocouple was placed %1 cm away from the PT and the temperature was logged 4 times per second using a Pico TC-08 datalogger. The temperature was adjusted, and the transient was allowed to settle until no change in temperature was observed for at least 20 min, before any small-or large-signal measurement was taken.

Small-Signal-Impedance Testing
The small-signal input impedance, Z in , of each PT was measured using a 1 V excitation from an Omicron Bode 100 vector network analyzer. The output electrode of the PT is short-circuited to the ground electrode, and the impedance between the input electrode and ground electrode is measured. Similarly, the small-signal output impedance, Z out , was measured between the output electrode and ground electrode, with the input electrode shorted to the ground electrode. Each impedance measurement was performed over a range of frequencies around the radial resonant frequency. From these measurements, the equivalent circuit components of the PT, shown in the Mason equivalent circuit (Figure 2) are extracted using a high damping component extraction method presented by Forrester et al. [27]  www.advancedsciencenews.com www.aem-journal.com

Large-Signal-Power Converter Testing
Efficiency and power measurements of each converter are taken using a Yokogawa PX8000 power oscilloscope. The input power is measured across the V DC supply to the converter and the output power is measured across the R L load resistance. From these measurements, the PX8000 calculates the overall electrical efficiency of each converter. An image of this measurement setup is shown in Figure 5.
The power electronic converter was operated with an 80 V DC input and a dedicated ZVS controller, based on the frequency doubler phased-locked loop control system described in ref. [22], which ensures the converter is operated at the correct frequency. By automatically adjusting the frequency, this controller ensures that the switch S 1 turns off at the zero-crossing of i 1 thereby allowing the greatest opportunity for i 1 to charge the voltage on capacitor C in from 0 to 80 V before switch S 2 turns on after π=2 radians. In this way, ZVS is achieved.
To ensure a fair comparison between PT samples, the load resistance is matched to the output capacitor impedance. This "matched load" maximizes power transfer and can be calculated using [28] where ω is the angular switching frequency. The PT parameters including C out are temperature-dependent and thus both the operating frequency and matched load change with frequency. It is, therefore, impractical to use the exact matched load at each temperature step. Therefore, the measurement for each temperature was repeated for each of the load resistors 220 Ω, 500 Ω, and 1 kΩ. Values for the matched load, which depend on temperature, vary from 450 to 950 Ω. Results will be presented for the most efficient load, which is normally the load closest to the matched load at that temperature.

Material Properties
The room temperature XRD patterns of sintered and crushed BSPT-64 and PZT-P85 pellets are shown in Figure 6. The presence of rhombohedral and tetragonal phases (the encircled 200 peak is split into three peaks in each pattern), characteristic of MPB compositions, were observed in the XRD patterns with no secondary phase peaks. A backscattered electron SEM image of a polished sample of BSPT-64 showed a homogeneous surface with no secondary phases present, Figure 7a, consistent with the XRD data. Fracture surfaces reveal a grain size of 3-5 μm and 1-2 μm for BSPT-64 and PZT-P85, respectively, Figure 7b,c. The relative permittivity (ε r ) and dielectric loss (tan δ) of BSPT-64 and PZT-P85 are shown in Figure 8. ε r of BSPT-64 and PZT-P85 are both ≅950 at RT. The maximum value of ε r (ε r,max ) is ≅12 000 at ≅340°C and 31 000 at ≅430°C for PZT-P85 and BSPT-64, respectively. ε r,max gives the approximate temperature of the phase transition to the paraelectric cubic phase and represents the point of depolarization at zero field. tan δ is less than 0.1 for both samples below 400°C, but then increases steeply with increasing temperature for PZT-P85. In contrast, tan δ of BSPT-64 only exceeds 0.1 above ≅630°C. ε r under high voltage (5 kV) and low frequency (1 Hz) is also calculated at 5 kV cm À1 where both BSPT-64 and PZT-P85 possess a linear capacitor response. The results are higher compared to those obtained at low voltage and high frequency using an LCR meter, Figure 8b.
The bipolar polarization and strain hysteresis of BSPT-64 and PZT-P85 ceramics were measured at 120°C under an electric field of 1 Hz and 40 kV cm À1 , Figure 9. The coercive fields  www.advancedsciencenews.com www.aem-journal.com (E C ) and remnant polarizations (P r ) were ≅17 kV cm À1 and 40 μC cm À2 for BSPT-64 and ≅12 kV cm À1 and 23 μC cm À2 for PZT-P85, respectively. The bi-polar strain is higher in PZT-P85 (≅0.23%) compared to BSPT-64 (≅0.18%) at 120°C. A complex impedance plane (Z*) plot for BSPT-64 and PZT-P85 at 450°C is shown in Figure 10a. Both samples consist of a single arc from %250 to 900°C. To a first approximation, the arc could be modeled with a single parallel resistor-capacitor (RC) element as shown in Figure 10b inset. The associated capacitance for the arc is 80 pF cm À1 for BSPT-64 and 90 pF cm À1 for PZT-P85. These are consistent with values obtained from LCR measurements, thereby confirming them to be a bulk response.  (a) (b) Figure 9. a) Polarization-electric field hysteresis curves and b) bipolar strain-electric field curves obtained at 120°C for sintered pellets of BSPT-64 and PZT-P85 at a frequency of 1 Hz.

Half-bridge & controller PT inside furnace
www.advancedsciencenews.com www.aem-journal.com The temperature dependence of the bulk (grain) resistance, R b , was extracted from Z* plots for both samples and summarized in an Arrhenius plot of the bulk conductivity, Figure 10b. The difference in σ b between BSPT-64 and PZT-P85 is around 2 orders of magnitude whereas the activation energy, E a , associated with the bulk conductivity is similar, 1.16 eV for PZT-P85 and 1.11 eV for BSPT-64.

Small-Signal Impedance Measurements
The loss (R 1 ) and Q factor extracted for both BSPT-64 and PZT-P85 PTs are shown in Figure 11a,b, respectively. Damping resistance of the PZT-P85 PT increased from 15 Ω at room temperature to 35 Ω at 200°C, with a peak of 61 Ω at 100°C. Conversely, the BSPT-64 PT exhibited a decrease in R 1 from 380 Ω at room temperature to 82 Ω at 250°C. The Q-factor of the PZT-P85 PT decreased from 909 to 220 and the Q-factor of the BSPT-64 PT increased from 35 to 68 over the temperature range tested. For both PZT and BSPT, the ratio QR 1 ¼ ffiffiffiffiffiffiffiffiffiffiffiffi ffi L 1 =C 1 p decreases by a factor of about 2 over the studied temperature range, which by itself will suggest that the Q factor decreases with temperature. R 1 follows a different trend for each material. For BSPT, it changes roughly linearly by a factor of about 6, whereas for PZT it peaks before reducing. In both cases, it is the trend in R 1 that dominates the trend in Q factor.
The input ðC in Þ and output ðC out Þ capacitances extracted from both BSPT-64 and PZT-P85 PTs are shown in Figure 12, normalized to their room temperature value. Both PTs exhibit increases in both capacitances with temperature, agreeing with the ε r results presented in Figure 8b. The capacitances of the BSPT-64 PT increased by a factor of 1.82 and the capacitances of the PZT-P85 PT increased by a factor of 1.39 across the range of temperatures. The larger increase in capacitance of BSPT-64 compared to PZT-P85, also agrees with the ε r measurements shown in Figure 8b.
The resonant frequencies extracted from both BSPT-64 and PZT-P85 PTs are shown in Figure 13. The resonant frequency of the BSPT-64 PT decreases from 134.2 to 123.7 kHz, a decrease of 10.5 kHz across the temperature range. Conversely, the resonant frequency of the PZT-P85 PT increases from 136.6 www.advancedsciencenews.com www.aem-journal.com to 141.5 kHz, a 4.9 kHz increase across the temperature range, less than half that exhibited by the BSPT-64 PT.

Efficiency and Power
The efficiency and output power achieved by both BSPT-64 and PZT-P85 PT-based inductorless half-bridge inverters (section 0) driven at the correct frequency, with an 80 V input voltage and when driving the most efficient load, are shown in Figure 14.   www.advancedsciencenews.com www.aem-journal.com

ZVS Factor k ZVS
The v C in voltage at the input to each PT during operation with a 500 Ω load is shown in Figure 15. As shown in Figure 15b, the voltage at the input to the PZT-P85 PT reaches V DC before the high side MOSFET, S 2 , turns on at all temperature steps. Therefore, the PZT-based inverter achieves k ZVS ≥ 1 and thus achieves ZVS across the temperature range. In contrast, Figure 15a shows the voltage at the input to the BSPT-64 PT doesn't reach V DC before S 2 turns on for temperature <200°C. Therefore, ZVS (k ZVS ≥ 1) is only achieved by the BSPT-64 PT for temperatures >200°C, thus this has some impact on the efficiency of the BSPT-64-based inverter at low temperatures as shown in Figure 14.

Discussion
The testing performed here shows that a PT made from BSPT-64 can be effectively used in a power converter and validates the performance of BSPT-64 PTs at temperatures up to 250°C. Inverters made with BSPT-64 PTs show both improved output power and efficiency at elevated temperatures when compared to room temperature, mainly due to a reduction in the damping resistance R 1 and thus a reduction in the losses in this PT. However, PZT-P85 PTs clearly outperform the BSPT PTs in this application at temperatures less than 200°C. This is primarily due to the low damping these PTs exhibit, giving rise to lower losses and better ZVS performance. BSPT-64 PTs have one clear advantage over PZT-P85 PTs, as the Curie temperature of BSPT-64 is around 100°C higher than PZT-P85, thus allowing them to be used at temperatures greater than 200°C without depoling. Therefore, for temperatures up to 250°C, unlike PZT-P85, BSPT-64 can successfully operate and with only a 25% performance degradation compared to PZT-P85 at 200°C. Since the operating temperature of many magnetic components is limited to 100°C, the higher temperature range of BSPT could translate to PT power supplies finding application in industries such as aerospace or oil, where temperatures in the range of 200-300°C are common. However, they would need to be used with high-temperature electronic devices, such as silicon carbide, which are also an area of intense research. [29] The BSPT PT properties show improvement with increasing temperature. Therefore, at temperatures greater than 250°C it is likely that BSPT-64 converter would achieve higher powers with similar levels of efficiency. The BSPT-64 PT-based converter presented here achieves around 60% efficiency at just under 0.7 W output power at 250°C, achieving results similar to high-temperature power supplies presented in the literature, while being much simpler to implement. [30] Observing the large efficiency differences between the PZT-P85 and BSPT-64 inverters, it is clear the PT is responsible for most of the losses, due to the relatively high damping resistance of the BSPT-64 PT. This larger damping resistance causes increased I 2 R losses compared to the PZT-P85 PT and additionally, the larger output capacitance of the BSPT-64 PT also causes higher increases in resonant current, thus increases in I 2 R losses. These issues can be attributed to the low Q factor (% 50) and the rapid increase in permittivity with temperature exhibited by the BSPT-64 material. Further improvements to the BSPT material to improve on these characteristics, would lead to significant performance improvements.
Another factor in the increased efficiency observed in the PZT-P85 inverter compared to the BSPT-64 PT is the improvement in k ZVS . Whereas the PZT-P85 inverter achieves ZVS across the temperature range, BSPT-64 does not achieve ZVS at low temperatures. As Foster et al discuss, ZVS should always be achieved when C in =ðN 2 1 C out Þ < 2=π, assuming 100% efficiency. [23] However, at low temperatures, this relation no longer holds as the BSPT-64 PT's efficiency is significantly lower than 100%, owing to the large I 2 R losses. The results presented in Figure 11 for BSPT-64 show that R 1 decreases with temperature providing a significant improvement in PT efficiency by helping to reduce the I 2 R losses. Therefore, with increased temperature, k ZVS increases, where at temperatures greater than 200°C, k ZVS ≥ 1 and ZVS is achieved. If improvements to the design were made to either reduce the damping resistance or to lower the C in =N 2 1 C out ratio, improved inverter efficiency at lower temperatures could be achieved.
It should be noted that traditional silicon-based components were used for the additional circuitry in the experimental work and as these components cannot perform at high temperatures www.advancedsciencenews.com www.aem-journal.com (>150°C), only the PT was kept in the furnace during testing. Consequently, lengthy wires were used to connect the PT to the main circuitry (≅30 cm) and testing equipment (≅100 cm). This causes unwanted resonances and additional parasitic elements which likely affected the performance of both converters.

Conclusions
A suitability analysis for the use of BSPT-64 based PTs in hightemperature resonant power inverters is presented. A similar state-of-the-art PZT-P85-based PT is also fabricated for comparison. A detailed description of the design and fabrication of both samples is presented. XRD, SEM, impedance spectroscopy, and relative permittivity-temperature measurements on samples of the two materials are presented and discussed. Impedance analysis was performed on the resulting PTs allowing their equivalent circuit properties to be characterized. Finally, resonant inverters were constructed with both PTs, and power and efficiency measurements were taken at several temperatures. The results of this testing have shown that although the performance of the BSPT-64-based PT is not as good as the PZT-P85 PT, the BSPT-64 based PT performs effectively at temperatures well in excess of that possible to achieve with PZT-P85 and with comparable results to high-temperature traditional converters.