RESONANT CIRCUIT MODEL AND DESIGN FOR A HIGH FREQUENCY HIGH VOLTAGE SWITCHED-MODE POWER SUPPLY

Transcription

1 RESONANT CIRCUIT MODEL AND DESIGN FOR A HIGH FREQUENCY HIGH VOLTAGE SWITCHED-MODE POWER SUPPLY Gleyson L. Piazza, Ricardo L. Alves 2, Carlos H. Illa Font 3 and Ivo Barbi 3 Federal Institute of Santa Catarina, Campus Jaraguá do Sul, Av. Getúlio Vargas, 830, CEP , Jaraguá do Sul-SC, Brasil, carlosf@ifsc.edu.br, internet: 2 Federal Institute of Santa Catarina, Campus Florianópolis, Av. Mauro Ramos, 950, CEP , Florianópolis-SC, Brasil, ricardoalves@ifsc.edu.br, internet: Federal University of Santa Catarina, Power Electronics Institute, P. O. Box 59, CEP , Florianópolis-SC, Brasil, e-mai: gleyson@inep.ufsc.br; ivobarbi@inep.ufsc.br, internet: Abstract This paper presents a practical procedure for the determination of high voltage high frequency transformer parameters. Besides, the paper also presents the design of a resonant circuit for the high voltage switched-mode power supply. The non-idealities of the transformers are part of the resonant circuit, were the leakage inductance and winding capacitances of the transformers are associated with the external resonant circuit components. The practical procedure is applied in the design of a switched-mode power supply with 700W output power, 50kV output voltage and 45kHz switching frequency. Experimental results from the laboratory prototype are included. Keywords High frequency, High voltage, Resonant circuit, Switched-mode power supply. I. INTRODUCTION The number of different types of electronic equipments that use high DC voltages is increasing since the last decade. Medical and industrial X-rays, CO 2 laser-based systems and the telecommunications equipments with traveling wave tube (TWT) are typical examples of these applications [-6]. A large number of special power converters have been proposed to supply these equipments [-6]. The design of high voltage power supplies presents several problems and drawbacks that can not be observed in low voltage applications. Therefore, each particular application requires a specific solution to achieve the design specification requirements. Reliability, high efficiency and low cost and size are the aims that the designer should reach. The first topologies employed in high voltage power supplies were based on PWM (non-resonant) converters. Nevertheless, this strategy presents several problems, many of then caused by the high-voltage transformers. The large turns ratio in the transformer increases the effects of the transformer non-idealities. The principal effects that produce changes in the behavior of the power converter are voltage spikes that can damage circuit components and current spikes respectively originated by the leakage inductance and the parasitic capacitance formed between windings [7]. The resonant converter is an attractive alternative to avoid the problems caused by the non-idealities of the high voltage transformer. In this case, the non-idealities can be used as integrant part of the circuit, were the leakage inductance and capacitance of the transformer are used as part of the resonant circuit components [2-3], [5], [8-9]. This way, an accurate procedure for the determination of high voltage high frequency transformer parameters must be obtained to propitiate a good design of the resonant circuit. Theoretical approaches for the determination of high voltage high frequency transformer parameters are described in the literature [0-2]. These approaches have some disadvantages as: complexity, in most of the cases is necessary to use finite-element analysis tools; the analysis is dependent of the geometric characteristics of the transformer, insulation material, core material and the constructive aspects of the windings. In this paper a practical procedure for the determination of high voltage high frequency transformer parameters is described. This procedure is independent of the geometric characteristics of the transformer and the constructive aspects of the windings. The practical procedure is applied in the design of a switched-mode power supply with 700W output power, 50kV output voltage and 45kHz switching frequency. II. THE PROPOSED CONVERTER The proposed converter is presented in Fig.. It is composed by a single-phase full-wave rectifier with output capacitor and by a DC-DC resonant half-bridge converter. In the proposed converter, the high voltage stage is obtained by the association of five transformers, with primary sides connected in parallel and the secondary sides connected to voltage-double rectifiers, which are connected in series. The parallel connections of primary sides provide the sharing of the output power among the transformers. The series connections of the voltage-double rectifiers provide the sharing of the output voltage among the secondary-side components. This concept ensures modular design, where the output voltage requirement can be meet by adding or removing the block formed by the voltage transformer and the voltagedouble rectifier. In Fig., the inductance Lr represents the resonant inductor, the capacitance Cp represents the resonant capacitor, the capacitance Cs represents the DC current blocking capacitor and the capacitance Cb represents the voltage clamping capacitor /09/$ IEEE 326

2 S ~ ~ D D3 D2 D4 + C + C2 Lr Cp Tr Tr2 Tr3 Tr4 Tr5 Cs S2 D5 D6 Cb Tr Tr2 Tr3 Tr4 Dr Dr2 Dr3 Dr4 Dr5 Dr6 Dr7 Dr8 Co Co2 Co3 Co4 Co5 Co6 Co7 Co8 + In order to simplify the calculations in the resonant circuit design is preferable to work with the circuit referred to the primary side. Furthermore, the capacitance between primary and secondary windings, the magnetic losses and the winding resistances do not have significant influence in the resonance phenomenon. This way, the equivalent circuit can be reduced to the circuit presented in Fig. 3, were [5]: L d is the equivalent leakage inductance, obtained by the series association of the primary side and secondary side leakage inductance referred to primary side. C t is the equivalent windings capacitance obtained by the parallel association of the primary side and secondary side winding capacitor referred to primary side. L m is the magnetizing inductance. Dr9 Co9 Tr5 Dr0 Co0 Fig.. The proposed converter. - III. THE HIGH VOLTAGE TRANSFORMER MODEL To simplify the analysis, in low voltage applications, the adopted model to high frequency transformers is based only in two elements; the magnetizing and leakage inductances, both generally referred to the primary side of the transformer. However, due to the high number of turns in high voltage transformers, the parasitic capacitances distributed between turns, layers and windings that can be ignored in low voltage transformers, starts to exercise significant influence. This phenomenon become still more evident when the transformer presents a high turns ratio, because the capacitance is referred to the primary side with a square of the turns ratio. A. Generic Model to High Frequency Transformers A high frequency transformer can be generally represented by the circuit presented in Fig. 2, were [7]: R and R 2 are the resistances of the primary side and secondary side windings, respectively. L and L 2 are the leakage inductances of the primary and secondary sides, respectively. C and C 2 are the capacitances of the primary side and secondary side windings, respectively. L m is the magnetizing inductance. C 3 is the capacitance between primary side and secondary side windings. R f represents the magnetic losses in the transformer core. Fig. 3. High frequency transformer equivalent circuit. As can be observed in the Fig. 3, there are two resonance frequencies in the high frequency transformer. The series resonance frequency f s is determined by the leakage inductance (L d ) and the equivalent windings capacitance (C t ) and the parallel resonance frequency f p witch is defined by the magnetizing inductance (L m ) and the equivalent windings capacitance (C t ). The transformer frequency response depends directly of these resonance frequencies that can be mathematically expressed by the expressions () and (2). fs = () 2. π. Ld Ct f p = (2) 2. π. Lm Ct The value of the magnetizing inductance is relatively easy to obtain by analytical ways. However it depends directly of the reluctance of the magnetic circuit and this parameter is very sensible to core imperfections and external agents as ambient temperature. The other parameters are more difficult to estimate because they depend of many variables, as geometric characteristics of the transformer and constructive aspects of the windings. However, if a same transformer is constructed with the different winding techniques, the parameters can vary in a wide range. Therefore, a practical way to obtain the parameters of a specific transformer must be used. B. Practical Determination of the Transformer Parameters Fig. 2. Generic high frequency transformer model. The first step is the determination of inductances L m and L d. This task requires two considerations. The first one is that the leakage inductance can be negligible if compared with the magnetizing inductance. The other consideration is that the use of a low frequency in the measurements allows consider the effects of the winding capacitances insignificant /09/$ IEEE 327

3 Therefore, to low frequencies, the equivalent circuit to the high frequency high voltage transformer presented in Fig. 4 can be used. inductance. Thus, from the results presented in (3), the equivalent magnetizing inductance (L m ) is equal to.88mh. After this, the primary side of the transformer was connected in the HP4284A precision LCR meter with the secondary side opened. The frequency response of the five transformers is presented in Fig. 5 and Fig. 6. Fig. 4. High voltage transformer equivalent circuit to low frequency. Measuring the inductance in the primary side with the secondary opened, the value obtained is equal the sum of the leakage inductance with the magnetizing inductance. This value can be adopted as the L m inductance. The winding capacitances of a transformer can not be measured by direct ways due to the equivalent circuit configuration. One alternative method to obtain precise values of these capacitances is using an impedance analyzer to identify the parallel and series resonance frequencies. The value of C t can be obtained substituting the L m value in the expression (2) and L d is obtained substituting the C t value in the expression (). Magnitude Fig. 5. The magnitude of the transformer s frequency response. C. Experimental Procedure The high voltage switched-mode power supply were designed from the specifications presented in Table. TABLE I High voltage switched-mode power supply specifications Line voltage (V) 0/220 Line frequency (Hz) 60 Output power (W) 700 Switching frequency (khz) 45 Output voltage strike (kv) 50 Output voltage range (kv) 5 24 Output current range (ma) 8 24 The transformers were designed from the specifications presented in Table 2. TABLE II Transformer s design specifications Peak input voltage (V) 500 Turns ratio 0 Output power (W) 40 Switching frequency (khz) 45 To measure the magnetizing inductance (L m ) was used the HP4262A LCR meter. The frequency in this equipment was adjusted to khz and the result obtained in this measure is presented in (3), for the five transformers. 9.63mH 9.39mH Lmi = 9.30mH (3) 9.50mH 9.26mH The equivalent magnetizing inductance is the parallel association of each individual transformer magnetizing Phase Fig. 6. The phase of the transformer s frequency response. Analyzing the curves presented in Fig. 5, can be observed that the resonances occur in 36.4kHz and 56.kHz. This way, the values of f s and f p can be obtained by: fs = 56.kHz (4) f p = 36.4kHz (5) The value of C t was obtained substituting L m and f p in (2): Ct = = 0.2nF (6) 2* *36.4*0 3 *.88*0 3 ( π ) 2 The value of L d was obtained substituting C t and f s in (): Ld = = 9.4μH 2* *56.*0 3 *0.2*0 9 ( π ) 2 IV. THE RESONANT CIRCUIT DESIGN The aim of the resonant circuit design is the determination of the values of the resonant inductance (L r ) and the resonant capacitor (C p ) from the transformer parameters (L m, L d and C t ) and the specification of the resonant frequency (f o ). The resonant circuit configuration is presented in Fig. 7. The external resonant components are connected in the primary side of the transformer equivalent circuit. (7) /09/$ IEEE 328

4 Fig. 7. The resonant circuit configuration. As can be observed in Fig. 7, the series connection of inductances L r and L d and the parallel association of capacitances C p and C t is not possible. However, the impedance analysis of the resonant circuit presented in Fig. 7 results in the same frequency response of the impedance of the circuit presented in Fig. 8 [5]. Fig. 8. The equivalent resonant circuit configuration. Thus, the mathematical definition of the resonant frequency is presented in (8), where the equivalent resonant circuit is composed by the series connection of the resonant inductor and the equivalent leakage inductance and the parallel connection of the resonant capacitor and the equivalent winding capacitor. fo = (8) 2. π. ( Lr + Ld) ( Cp + Ct) Due the output characteristic of the converter, it was selected a resonant frequency greater than the switching frequency. Thus, the resonant frequency is equal to 56kHz. Thus, the resonant inductance (L r ) is equal to 90uH and the resonant capacitor (C p ) is equal to 66nF. The choice of resonant inductor value was based on the RMS primary current value. V. EXPERIMENTAL RESULTS To validate the mathematical analysis, the results obtained from the prototype depicted in Fig. 9 are presented in this section. The high voltage transformers and the voltagedouble rectifiers are not shown in picture. The resonant inductance (L r ) was designed with EE42/20 IP2R ferrite core and 29 turns of eight 37AWG Litz wire. The resonant capacitor (C p ) was designed with the parallel association of two 33nF/630V polypropylene capacitors. The experimental results for the current across the resonant inductor and the voltage in the resonant capacitor terminals are presented in Fig. 0. These results were obtained with the power supply operating with the maximum duty cycle and with no load condition. As expected, the behavior is a second order circuit in which the current and the voltage in the energy storage components are presenting resonant waveforms in a switching period. In the Fig. the same waveforms can be observed with more details. Fig. 9. The picture of the prototype (the high voltage transformers and the voltage-double rectifiers are not shown in picture). Fig. 0. The resonant capacitor voltage and the resonant inductor current to the power supply operating with no load. V Cp Fig.. Detail of the resonant capacitor voltage and the resonant inductor current. I Lr /09/$ IEEE 329

5 The experimental results with the converter operating with resistive load and in closed-loop mode are presented as follow. Three different values are adopted to the output current, 5mA, 0mA and 25mA. The voltage in the resonant capacitor terminals (V Cp ) and the current across the resonant inductor (I Lr ) with an output current of 5mA are depicted in Fig. 2. As can be observed, there are some oscillations due to non idealities of the system. The results with an output current of 0mA are presented in Fig. 3. The relevant waveforms to the converter operating with full load are presented in Fig. 4. As can be observed, this case corresponds to the maximum duty cycle. VI. CONCLUSIONS High voltage high frequency transformers present two particularities as follow: Large turns ratio; High isolation distances. Large turns ratio leads to a great number of turns in the secondary side and, therefore, a significant capacitance in it. This capacitance is reflected to the primary side multiplied by the squared turns ratio. High isolation distances between primary side and secondary side, and in the secondary side itself contribute for the increasing of the leakage inductance. The parameters of the high voltage high frequency transformers are very important to design a resonant circuit. A practical procedure for the determination of high voltage high frequency transformer parameters and design the resonant circuit to be used in high voltage power supplies was presented in this paper. Some transformers were constructed and submitted to the proposed approach to validate the procedure. The experimental results show that the practical procedure represents satisfactory the resonant circuit behavior. This procedure is independent of the geometric characteristics of the transformer and the constructive aspects of the windings. ACKNOWLEDGEMENT The authors would like to thank Mr. José Maria Mascheroni from Automatisa Sistemas Ltda, for his support and encouragement during the development of this work. Fig. 2. Voltage in the resonant capacitor and current across resonant inductor with 5mA output current. I Lr V Cp Fig. 3. Voltage in the resonant capacitor and current across resonant inductor with 0mA output current. I Lr V Cp Fig. 4. The resonant capacitor voltage and the resonant inductor current to the power supply operating with 25mA output current /09/$ IEEE 330

6 REFERENCES [] I. Barbi, R. Gules. "Isolated DC-DC Converters with High-Output Voltage for TWTA Telecommunication Satellite Applications", IEEE Transactions on Power Electronics, vol. 8, no. 4, pp , July [2] F. da S. Cavalcante, J. W. Kolar. "Design of a 5kW High Output Voltage Series-Parallel Resonant DC-DC Converter", in Proc. of PESC 2003, vol. 4, pp , [3] S. D. Johnson, A. F. Witulski, R.W. Erickson. "Comparison of Resonant Topologies in High-Voltage DC Application". IEEE Transactions on Aerospace and Electronic System, vol. 24, pp , May 988. [4] V. Garcia, M. Rico, J. Sebastian, M. M. Hernando, J. Uceda. "An Optimized DC-to-DC Converter Topology for High-Voltage Pulse-Load Applications", in Proc. of IEEE PESC'94, vol. 2, pp , 994. [5] G. L. Piazza. "Implementação de uma Fonte para Acionamento de Raio Laser". Master s Dissertation. Universidade Federal de Santa Catarina, Programa de Pós-Graduação em Engenharia Elétrica. Florianópolis, SC, Brasil, (in portuguese) [6] T. Filchev, D. Cook, P. Wheeler, J. Clare. Investigation of High Voltage, High Frequency Transformers/Voltage Multipliers for Industrial Applications, in Proc. of Conference on Power Electronics, Machines and Drives, pp , [7] S.-K. Chung. "Transient Characteristics of High-Voltage Flyback Transformer Operating in Discontinuous Conduction Mode", IEE Proc.-Electr. Power Appl., vol. 5, no. 5, pp , September [8] C. B. Viejo, M. A. P. García, M. R. Secades, J. C. Antolín. "A Resonant High Voltage Converter with C- Type Output Filter", in Proc. of Industry Applications Conference, vol. 3, pp , 995. [9] J. Li, Z. Niu, D. Zhou, Y. Shi. "Analysis of Series- Parallel Resonant Converter with Multipliers", in Proc. of IEEE International Symposium on Circuits and Systems, vol. 5, pp , [0] L. Dalessandro, F. da S. Cavalcante, J. W. Kolar. Self- Capacitance of High-Voltage Transformers, IEEE Transactions on Power Electronics, vol. 22, no. 5, pp , September [] J. A. Martin-Ramos, A. M. Pernia, J. Diaz, F. Nuno, J. A. Martinez. Power Supply for a High-Voltage Application. IEEE Transactions on Power Electronics, vol. 23, no. 4, pp , July [2] M. A. Perez, C. Blanco, M. Rico, F. F. Linera. A New Topology for High Voltage, High Frequency Transformers, in Proc. of APEC 995, vol. 2, pp , /09/$ IEEE 33