Power Improvement of Piezoelectric Transformer- Based DC/DC Converter

Transcription

1 Power Improvement of Piezoelectric Transformer- Based DC/DC Converter Y. H. Su a,b, Y. P. Liu a,b, D. Vasic *a,c, F. Costa b,d,w.j. Wu a,c.k. Lee a,e,f a Department of Engineering Science & Ocean Engineering, National Taiwan University, Taipei, Taiwan; b Lab. SATIE, ENS Cachan, 9435 Cachan, France; c Université de Cergy-Pontoise, Neuville/Oise, France ; d IUFM, Université Paris Est Créteil (UPEC), Place du 8 mai 1945, 93 St Denis, France ; e Institute of Applied Mechanics, National Taiwan University, 1617 Taipei, Taiwan; f Institute for Information Industry, 1617 Taipei, Taiwan * dejan.vasic@satie.ens-cachan.fr Abstract-By using the heat transfer equipment, a novel strategy to increase output power of piezoelectric transformer-based DC/DC converter is presented in this paper. The commercial thermal pads which are directly attaching to the piezoelectric transformer as the dissipaters can efficiently dissipate the heat of PT and enhance the power capacities of piezoelectric transformer and DC/DC converter. In fact, the piezoelectric transformer generates heat until it cracks when the vibration velocity is too large. To explain the relationship between vibration velocity and resulting heat of piezoelectric transformer, we also propose the theoretical-phenomenological model which can be described the relationships between the equivalent dissipation resistances and the input voltages at different temperatures. It will be shown that the vibration velocity as well as the heat generation determines the loop gain. A large vibration velocity and heat may cause the feedback loop to enter into an unstable state. Furthermore, the zero voltage switching (ZVS) condition was considered in order to obtain the good efficiency. The input driving circuit of the PT is a half-bridge structure with a filtering inductor and the topology was completed in the secondary side with the full-wave rectifier and a filter capacitor to obtain the DC load voltage. As a result, the maximum output power of the PT based DC/DC converter can increase from 4.41W to 1. W at specific temperature. It implies that the power capacity possibly increases.5 times in the PT DC/DC converter. I. INTODUCTION Piezoelectric transformer (PT) has several advantages for DC/DC applications because of the characteristics such as good efficiency, low profile, no EMI radiation, high power density, and easier for mass production. PTs are good substitutes of electromagnetic transformers especially in high voltage/low current application, such as electronic ballasts or backlight inverters. Moreover, Liu et al. used the PTs in low voltage DC/DC applications with variable load recently [1]. In previous researches, there are also many different types of PT-based DC/DC converters to reduce the material cost and to increase the power density. However, the major drawback of the PT-based DC/DC converters is that PT is easily unstable or even breakdown with temperature rises because of the overdeveloped internal losses []. It is revealed that the internal heat generation in PTs can represent the internal losses in the steady-state and the internal loss as well as the heat generation is the physical limitation of the PTs. Uchino et al. were first discussed the internal loss divided into three parts in the equivalent circuit of the piezoelectric transducers [3]. Albareda et al. found that the dissipation resistance related to the temperature increases proportionally to the square of the vibration velocity near the resonance frequency of the PT [4]. In addition, the temperature increase changes the characteristics of the PT: the mechanical quality factor decreases, resonance frequency changes, and the operating life of the devices are shortened. To dissipate the heat efficiently, a ring-dot-shape piezoelectric transformer with a central hole was proposed for better thermal radiation [5]. This kind of design was achieved more uniform temperature distribution, larger output power and better efficiency. On the other hand, Shao et al. adopted the contact heat transfer to dissipate the heat in order to improve the power density of piezoelectric transformers [6]. In this study, we started from observing the relationships between the equivalent heat resistances and the input voltages at different temperatures to establish a phenomenological theoretical model. The proposed model can explain the relationship between vibration velocity and generated heat of the piezoelectric transformer. Then, we added commercial thermal pads and thermoelectric cooling modules on the piezoelectric transformer to dissipate the heat and it is revealed that the maximum output power capacity could increase from 4.41W to 1. W at specific temperature. Furthermore, the mechanical current of PTs can be improved from.44a to.97a at a temperature of 55 C experimentally. The theoretical model will be detailed in the section and the topology of the PT based DC/DC converter, which includes the ZVS consideration to maintain the efficiency is analyzed in the section 3 [7]. Finally, the effects of the different cooling methods of the system will be verified by the simulation and experimental results. II. THEOETICAL ANALYSIS OF MULTI-LAYE PIEZOELECTIC TANSFOME A. Equivalent circuit of piezoelectric transformers with nonlinear resistance In this study we focus on the losses in the material. A nonlinear resistance NL is introduced to take in to account the temperature effect on the characteristics of the PT. When the

2 P and and includes decreases constitutive equations of the piezoelectric material are derived, quadratic and cubic terms are typically neglected. However, these terms may decrease the quality factor of the piezoelectric material. To take into account the quadratic terms, the mechanical resistance m two terms, a low excitation resistance the non-linear resistance NL. m=+nl. (1) According to Albareda s non-linear model of piezoelectric transducers P, NL is a function of mechanical current imp P: NL= α imp. () According to equations (1) and (), the increment of the mechanical resistance is a function of the square mechanical current im a coefficient α that characterizes the material nonlinearity. The increment of the losses influences the transfer power of the PT and limits the power density. To analyze the working characteristic of PT with high vibration level, a non-linear equivalent circuit should be used. In figure 1, we introduce the non-linear resistance NL in the classical equivalent circuit with the parameters Lm, Cm,, C1, C, and N, which determined by the dimensional parameters and material properties of the piezoelectric transformers. The operating frequency is set near the resonant frequency, so the effect of the dielectric losses is small and can be neglected. Therefore, we assume that the heat is only generated from mechanical loss Pm-loss. temperature rise of the piezoelectric transformer. Then, as mentioned in last section, the mechanical resistances increase with temperature rise as shown in figure (see the red square frame). However, there are two tendencies with increasing mechanical resistances m. First, the power loss increases with increasing mechanical resistance to form a positive feedback loop. On the other hand, considering the voltage across the piezoelectric transformer is controlled as a constant, the current flowing through m to form a negative feedback loop. The red square frame in figure shows the physical loop mentioned above in the piezoelectric transformers without any cooling device. In addition, after applying the heat transfer equipment (HTE), another physical loop in the piezoelectric transformers is established in figure (see the blue square frame). The function of the HTE is to reduce the coefficient α. According to equations (1) and (), the mechanical resistance decreases with the HTE and then the mechanical loss decrease simultaneously. In such a condition, the output power is also increasing immediately. Based on the control loop of the piezoelectric transformer, the relationships between m, NL, im, temperature rise, energy loss and output power can be described clearly. Considering the voltage across the PT is a constant, it can be viewed that the passing current capacity of the piezoelectric transformers is increased owing to the decrement of the mechanical resistance (the blue square frame in figure ). Fig. 1. Nonlinear equivalent circuit of piezoelectric transformer. It can be seen that the power losses PPTloss in the piezoelectric transformer are strongly dependent on the mechanical current in Figure 1, i.e. imp Pm. Based on the experimental observation, the mechanical resistance m increases with the temperature rise. To indicate this characteristics in the theoretical model, the non-linear resistance NL can be characterized as a temperaturedependent resistance through the coefficient α, i.e. α(t C). On the other hand, we also observe that the temperature may increase with the losses increase experimentally. It implies that a positive feedback may exist between the losses and the temperature rise. This is the underlying reason that the losses may increase unstably in the high vibration level. To have the larger output power, the mechanical resistance should be insensitive to the temperature rise. The best case is that the coefficient α is independent of temperature α(t C). B. Control loop of the energy loss and output power The energy losses of the piezoelectric transformer are usually transfers into thermal energy, which leads to the Fig.. Energy loss control loops of the piezoelectric transformers. C. Measurement of the Parameters and Temperature- Dependent esistance NL in the Equivalent Circuit Except for NL, the other equivalent circuit parameters of PT could be measured by the impedance analyzer Agilent 4194A. The equivalent circuit employed for measurement is shown in figure 3(a) as compared with the equivalent circuit of PT in figure 3(b). We used the piezoelectric transformer provided by Eleceram Technology Co., Ltd., Taiwan. It is a multi-layer rectangular transformer with circular electrodes. The properties and parameters of the specimen are given in table 1. The experimental results measured by the impedance analyzer are listed in table. It is revealed that we could derive these parameters by connecting the input terminal and output terminal in short circuit respectively. It should be noted that is measured at room temperature (5 C).

3 voltage Vin. The experimental values of NL are shown in figure 5. (a) Fig. 4. The method of shortening the output terminal to measure the mechanical current and nonlinear resistance. (b) Fig. 3. (a) Equivalent circuit employed by the impedance analyzer (b) Equivalent circuit of PT. PT size : mm*mm* 4.5mm Table 1 Picture, size and material properties of the PT Input section Output section No. of layers 4 No. of layers 4 Thickness Thickness.5mm.5mm (.5*4=mm) (.5*4=mm) Input inductance 51 μh Operating frequency 94.3 khz Isolation No. of layers 1 Thickness.5mm (.5*1=.5mm) Unstable temperature of PT 55 C Material properties (PZT-QA, ELECEAM TECHNOLOGY Co., Ltd., Taiwan): K p =.58 is the electromechanical coupling coefficient N p = is the frequency constants of the plane vibration (khz mm) d 33 = 3 1P 1 P d 31 = -14 1P 1 P are the piezoelectric constants (m VP 1 P) Y 33 = 3 1P 1 P Y 31 = -14 1P 1 P are the elastic constants (N mp P) ρ m = 7.9 is the density (g cmp 3 P) ν =.16 is Poisson s ratio Q m = 18 is the mechanical quality factor S = is the permittivity at constant strain condition, i.e. constant S (F m 1) E s 11 = is the compliance constant under the constant electric field, i.e. constant E Table The experimental result obtained by impedance analyzer f r f a L m C m C 1 C N T( C) (KHz) (KHz) (Ω) (mh) (nf) (nf) (nf) (-) C NL (Ohm) PT temperature 49 C PT temperature 36 C PT temperature 8 C PT temperature 55 C Im (A rms ) Fig. 5. Characteristics between the square of mechanical current and the NL at different temperatures. D. Increasing output power of the PT To increase the output power of the PT, we must control the temperature through the coefficient α. In this research, the coefficient α was reduced by the high-quality cooling devices, including the thermal pad, radiator and thermoelectric cooling module. Once α is reduced by the heat cooling device, both the values of temperature-dependent resistance NL and mechanical loss Pm-loss can be reduced in the same mechanical current condition. Specifically, a smaller coefficient α leads to a smaller mechanical loss at a constant stable operating temperature of the PT. Based on the decreases of mechanical losses and NL by applying high-quality cooling devices, output power can be increased in this study. (a) (b) Simulation results Experimental results According to the equivalent circuit in figure 4, we know that. Iout=Nim. (3) Pin= imp Pm. (4) Combining equations (3) and (4), the following equation can be derived: NL = Pin/( Iout/N)P P-. (5) To obtain the nonlinear resistance NL in equation (5), we can measure the temperature-independent resistance () and parameter N by the impedance analyzer first. Then, obtain the temperature-dependent resistance (NL) by measuring the output short current Iout. To observe the non-linear resistance NL in different vibration level, the output short current Iout and input power Pin were measured with increasing input (c) Fig. 6. (a) Air cooling without any cooling device (b) Heat transfer equipment (HTE) (c) HTE and thermoelectric cooling module.

4 Figure 6 shows three different cooling methods to control the coefficient α, which includes: (a) Air cooling without any cooling device, (b) Contacted heat transfer equipment (HTE) and (c) HTE and thermoelectric cooling module. The HTE is an aluminum box was mounted onto a radiator, which served as a heat sink and provided an additional surface area of 16 cmp for cooling. In the third type of experimental setup, a pair of thermoelectric cooling modules was also mounted onto the radiator and thermal pad. III. PT-CONVETE CICUIT DIAGAM AND ITS OPEATION As shown in figure 7, a half-bridge circuit and an inductor were adopted as the input driving circuit and input network to excite PT vibration respectively. To get the DC voltage, a full-wave rectifier was used to connect with PT output terminal. In addition, the filtering capacitance C F is sufficiently larger than the PT output capacitor C to guarantee the load voltage V L can be viewed as a perfect DC voltage sink. We also applied the assumption that the mechanical current i m is pure sinusoidal wave in the steady state. Fig. 7. The schematic diagram of piezoelectric transformer based DC/DC converter. Based on the assumption mentioned above, the mechanical current can be viewed as the sinusoidal current source of the rectifier and the equivalent circuit can be seen in figure 8(a). The current and voltage waveforms of the PT fed full-wave rectifier are shown in figure 8(b). It should be noted that because of the large value of the output capacitor C F, the PT output voltage v rec is not a sine wave. In figure 8(b), these waveforms can be divided into four periods. In the first and third period, the diode is blocked, and thus the PT output capacitor is charging or discharging. In the second and fourth period, diode is conducted, and thus the rectifier voltage is roughly equal to the load voltage. θ is the phase angle, i.e. θ = ωt, and θ b represents the diode block angle; V L and V D represent the load voltage and diode voltage drop respectively. The characteristics of the PT fed rectifier were shown in the table. Furthermore, figure 8(c) is shown to verify the theoretical waveforms. Table The characteristics of the PT fed rectifier. PT fed full-wave rectifier Load voltage L( NI m CV D ) ectifier VL VL PD V D C losses L L Diode block 1 C angle PT L P PTloss Im b cos losses CL Optimal load * Load condition L VL C power PL L m Based on the table, the efficiency of the converter can be determined: PL PPTloss PD PL (6) (a) (c) Fig. 8. (a)the schematic diagram of PT fed full-wave rectifier (b) theoretical voltage and current waveforms of the PT fed full-wave rectifier (c) experimental waveform of PT input voltage v in (blue, V/div), PT input current i in (yellow, 1A/div), voltage at PT output terminal v rec (green, 5V/div) and current at PT output terminal i rec (purple,.5a/div). The, ZVS (Zero Voltage Switching) condition could be achieved without any additional elements (no inductor) by using specific characteristics of the PT with a half-bridge topology, but this scheme cannot be applied to wide-range load variations [8]. Therefore, we apply the method that the primary circuit includes an additional series inductor L m to achieve the ZVS condition. This method has the function which can be optimized the efficiency and gotten a wide range of load variation. The resonant circuit formed by the series inductor L m and the internal input capacitance C 1 of the PT achieves a quasi sine-wave PT input voltage v m. Moreover, this series inductor exhibits high impedance, which both limits common and differentials mode currents. IV. i in irec v in v rec (b) SIMULATION, EXPEIMENTAL ESULTS AND DISCUSSIONS A. Experimental setup Experimental setups were shown in figure 9. We incorporated an I14, IF7431, and MB36 for the gate driver, the MOSFET switches and the rectifier, respectively. The filtering capacitance was set to be 1 μf to minimize the ripple effect. The frequency of the half-bridge circuit is controlled by the connected function generator. The input inductance was set at 51 μh with the switching frequency set at 94.3 khz to achieve soft switching conditions. The multilayer piezoelectric transformer works in planar vibrating mode. Furthermore, a DC power supplies the thermoelectric cooling module in the HTE device, which the input power

5 can and can P m. is equal to 1 W, to cool down the system. A temperature sensor was used to obtain the temperature variation of PT at different driving conditions. Three different cooling devices as shown in figure 6 were used to verify the mechanical losses and nonlinear resistance NL. In such an experimental setup, we can clearly compare the relationships between the value of α, mechanical resistance, mechanical current, temperature, PT losses and output power.. Fig. 9. Experimental setup of PT based DC/DC converter. B. Effect of temperature on the equivalent circuit parameters To explain the relationship between mechanical current im (vibration velocity) and generated heat of the piezoelectric transformer, the coefficient α is determined by measuring the mechanical current and resistance NL as well as the temperature rise for the three experimental setups as shown in figure 6. The variation of mechanical current and PT temperature are obtained by applying different input voltages as shown in figure 1 and figure 11. Im (A rms) PT PT with radiator PT with radiator and thermoelectric cooling module Vin (V rms) Fig. 1. Characteristics between mechanical current and input voltage. Temperature( C) V DC =5V I DC =.A 3 PT with radiator and thermoelectric cooling module Vin (V rms) Fig. 11. Characteristics between temperature and input voltage. The simulation software PSIM is also used to verify the experimental results in comparison with the model. The relationships between temperature, mechanical resistance m and mechanical current in different cooling methods are shown in figure 1. m (Ohm) Mechanical Current (A rms) PT PT with radiator and thermoelectric cooling module 55 C PT limit temperature 55 C PT limit temperature 55 C PT limit temperature Mechanical Current (A rms) Fig. 1. Characteristics between mechanical resistance m, temperature and mechanical current (lines: PSIM simulation data, dots: experimental data). In figure 1 and figure 1, it can be seen that mechanical current increases with input voltage and temperature. Through applying the heat transfer equipment (HTE), the passing current (i m ) of the piezoelectric transformers can increase from.44a to.973a at the temperature of 55 C as shown in figure 1. At the 5 55 C temperature range, mechanical currents which were measured from the heat transfer equipment based experimental setup increased almost.5 times more than the single PT experimental setup. In addition, utilizing the impedance analyzer and the method of shortening the output terminal discussed in section, the relationship between m mechanical current is also shown in figure 1. It is clear that the resistance m efficiently decreased by applying the heat transfer equipment (HTE) at the constant mechanical current. In addition, the mechanical losses Pm-loss and m be related as: Pm-loss =imp Temperature ( C) (7) From equation (7), mechanical losses Pm-loss is also decreased by applying the heat transfer equipment (HTE) at the same mechanical current value. It is evident that the HTE successfully reduces the energy dissipation of the PT. Moreover, the relations between coefficient α, temperature and m be derived from the statistics of figures 1 shown above. In figure 13, it is shown that the coefficient α of the PT-only experimental setup is much larger than the others in the same temperature condition. α Experimental results of PT Experimental results of PT with radiator Experimental results of PT with radiator and thermoelectric cooling module Simulation results of PT Simulation results of PT with radiator Simulation results of PT with radiator and thermoelectric cooling module Temperature( ) Fig. 13. Characteristics between loop gain α(t ) value and temperature.

6 P (+α Owing to the fact that the coefficient α is proportional to the mechanical resistance and mechanical losses, the mechanical losses P m-loss and α can be related as: Pm-loss =imp imp P). (8) It is clear that large coefficient α leads to high PT losses at the same mechanical current. To enhance the power capacity of the piezoelectric transformer, the heat must be dissipated using heat transfer devices to decrease the coefficient α as shown in figure 14. α Im (A rms) Fig. 14. Characteristics between loop gain α(t ) value and mechanical current. C. esults of the enhanced output power and efficiency of PTbased DC/DC converter by applying HTE In figures 15 and 16, the measured results show that the largest output power of HTE used for PT-based DC/DC converter can move from 4.41 W to 1. W at the same temperature of 55 C with 47 Ohm load value. The output power was increased at least.5 times at good efficiency (7%+) when the load was varied from 1 to 33 Ohm. Output Power(W) Load( Ω) Load( Ω) Fig. 15. esults of output power and efficiency in different heat transfer structures. PT 55 C Operting Temperature Limit Efficiency.8 Input DC voltage 1.5V Input DC voltage V.6.4 Input DC voltage 5V Output Power(W) Fig. 16. esults of efficiency and output power with various input DC voltage VDC at the PT limit temperature. Furthermore, the experimental results in figure 15 were measured with various input DC voltage V DC at the same PT Efficiency limit temperature. In more detail, the relationships between efficiency and output power with various input DC voltage V DC are shown in figure 16. V. CONCLUSION In this paper, the cooling method was used to enhance the output power of piezoelectric transformers. According to the experimental results, all specimens remained a satisfactory efficiency even at temperature 55 C. By applying HTE, the ability of heat dissipation becomes better. The passing current of the PTs can increase from.471a to.97a, and the maximum output power of the PT based DC/DC converter can also increase from 4.41W to 1. W at specific temperature. Furthermore, we proposed a model that can explain the relationship between vibration velocity and generated heat of the PT. This study clearly indicates that it is possible to enhance the performance of the piezoelectric transformer by decreasing the loop gain α(t ) value. Moreover, the output current of the piezoelectric transformer in our design also increases, which implies that this technique allows the piezoelectric transformer to be used in low voltage-high current applications. ACKNOWLEDGMENT The authors are grateful to: ELECEAM TECHNOLOGY Co., LTD. for providing us with different types piezoelectric transformers used in the research work. The main funding of this project from National Science Council, Taiwan under Project NSC I--14 is gratefully acknowledged. EFEENCES [1] Y.P. Liu, D. Vasic, F. Costa, W.J. Wu, and C.K. Lee, Design Considerations of Piezoelectric Transformers with Voltage-Mode ectifiers for DC/DC Converter Application, in Industrial Electronics, 8. 34th Annual Conference of IEEE, 8, pp [] A. M. Flynn and S.. Sanders, Fundamental limits on energy transfer and circuit considerations for piezoelectric transformers, Power Electronics, IEEE Transactions on, vol. 17, pp. 8-14,. [3] K. Uchino and S. Hirose, Loss mechanisms in piezoelectrics: how to measure different losses separately, Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, vol. 48, pp , 1. [4] A. Albareda, P. Gonnard, V. Perrin,. Briot, and D. Guyomar, Characterization of the mechanical nonlinear behavior of piezoelectric ceramics, Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, vol. 47, pp ,. [5] K. Insung, K. Minsoo, J. Soonjong, S. Jaesung, and T. Vo Viet, Piezotransformer with ring-dot-shape for easy heat radiation and high efficiency power, in Applications of Ferroelectrics (ISAF/PFM), 11 International Symposium on and 11 International Symposium on Piezoresponse Force Microscopy and Nanoscale Phenomena in Polar Materials, 11, pp [6] S. Wei Wei, C. Li Juan, P. Cheng Liang, L. Yong Bin, and F. Zhi Hua, Power density of piezoelectric transformers improved using a contact heat transfer structure, Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, vol. 59, pp , 1. [7] T. Ninomiya, M. Shoyama, T. Zaitsu, and T. Inoue, Zero-voltageswitching techniques and their application to high-frequency converter with piezoelectric transformer, in Industrial Electronics, Control and Instrumentation, IECON '94., th International Conference on, 1994, pp vol.3. [8]. L. Lin, Piezoelectric transformer characterization and application of electronic ballast, PhD Dissertation, Virginia Polytechnic Institute and State University, USA