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The development of a high repetitive and high power Nd:YAG laser by using a zero-current switching resonant converter
Optics & Laser Technology 30 (1998) 199±203
The development of a high repetitive and high power Nd:YAG laser by using a zero-current switching resonant converter Hee-Je Kim a, *, Eun-Soo Kim b, 1, Dong-Hoon Lee a, 2 a
Department of Electrical Engineering, Pusan National University, Changjeon-dong, Kumjeng-ku, Pusan, 609-735, South Korea b Korea Electro-technology Research Institute, 28-1 Sungjoo-dong, Changwon, 641-120, South Korea Received 2 March 1998; received in revised form 18 May 1998; accepted 19 May 1998
Abstract In materials processing, the power density control of a laser beam has been considered to be signi®cant. In this study, a zerocurrent switching resonant converter as the power supply of a pulsed Nd:YAG laser was adopted to control the laser power density, which depends on ¯ashlamp current pulsewidth and pulse repetition rate. It allowed us to design and fabricate a high repetition rate and high power pulsed Nd:YAG laser system. As a result of that, the current pulsewidth could be controlled in the range 200±350 ms (step 50 ms), and the pulse repetition rate could be adjusted to 500±1150 pps (pulse per second). In addition, in the case of one laser head consisting of an Nd:YAG laser rod and two ¯ashlamps, the maximum laser output of 240 W was produced at the condition of 350 ms and 1150 pps, and that of about 480 W was generated at the same condition when two laser heads were arranged in cascade. # 1998 Elsevier Science Ltd. All rights reserved. Keywords: Zero-current switching (ZCS) resonant converter; High repetition rate and high power (HRHP) pulsed Nd:YAG laser; Current pulsewidth; Pulse repetition rate
1. Introduction The pulsed Nd:YAG laser is the most commonly used type of solid-state laser in many ®elds at present because of its good thermal and mechanical properties and easy maintenance [1, 2]. In recent studies of laser processing methods, the pulsed Nd:YAG laser, which has various advantages over the commonly used CO2 laser, has been investigated energetically. It can be focused to a smaller point, due to its shorter wavelength, than the CO2 laser, and can be easily adjusted to materials. Thereby it is broadly used in many applications such as micromachining, holography, range®nding, materials processing and so on [3±6]. Among other things, in materials processing, a suitable laser power density is required for speci®c processes, and the laser power density can be controlled by the current pulsewidth and pulse repetition rate, which are * Corresponding author. Tel.: +82-51-510-2364; Fax: +82-51-5130212; E-mail: [email protected]. 1 E-mail: [email protected] 2 E-mail: [email protected] 0030-3992/98/$19.00 # 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 0 - 3 9 9 2 ( 9 8 ) 0 0 0 3 6 - X
known to be major factors for particular properties of materials [7, 8]. In this study, a zero-current switching (ZCS) resonant converter [9, 10] as the power supply was adopted to control the laser power density. We have designed and fabricated a high repetition rate and high power (HRHP) pulsed Nd:YAG laser system applying the ZCS resonant converter. In order to investigate the operational characteristics of the HRHP pulsed Nd:YAG laser system, experiments for the laser output as a function of current pulsewidth and pulse repetition rate have been carried out.
2. Power supply The power supply was designed and fabricated to be suitable for the high frequency range and to reduce switching loss and noises. It consisted of three components such as a ZCS resonant converter unit, a recti®er unit, and a simmer-trigger unit, as shown in Fig. 1. In particular, the ZCS resonant converter was used to decrease the loss occurred by the tailing current gener-
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H.-J. Kim et al. / Optics & Laser Technology 30 (1998) 199±203
of charging capacitor, and V in the input voltage. According to this formula, it is found that there are two ways to control the power density of the resonant converter. One is to vary the input voltage V in at a constant pulsewidth and frequency, and the other is to adjust the switching frequency f. In the latter case, low frequency switching causes noises and instability. Therefore, we adopted the control method to vary the input voltage V in.
3. Operation of the ZCS converter Fig. 1. Schematic circuit of the pulsed Nd:YAG laser which consists of three components: a ZCS resonant converter unit, a recti®er unit, and a simmer-trigger unit.
ated on turning o an insulated gate bipolar transistor (IGBT). The recti®er unit consisted of a three-phase interchanging voltage regulator (IVR), a three-phase bridge diode recti®er, and a smoothing condenser as shown in Fig. 1. Because of the over-peak current which came from the resonant converter, a high power DC capacitor with a good frequency response and a smoothing condenser were connected in parallel. The change of input voltage depending on the load change could be adjusted slightly by the three-phase IVR. In Fig. 2, the pulse forming network (PFN) applied to the ZCS series resonant converter consisted of switch devices (Q1, Q2), a resonant inductor (Lr), and resonant capacitors (C1, C2). The switching loss was zero in principle, and it is adequate in high repetition rate operation because the current through Q1, Q2, C1, and C2 was forced to the sinusoidal wave, and the switch devices were turned on/o at zero current. The output of the ZCS series resonant converter is Pout 2fCV 2in
1
where f is the repetition frequency, C the capacitance
The proposed ZCS converter circuit is shown in Fig. 2. The circuit operation can be divided into two modes, whose waveforms and equivalent circuits for the modes are shown in Fig. 3. To simplify the analysis, the initial states of the circuit are assumed as follows: the voltage V c1 of capacitor C1 is initially charged to input voltage V in, the voltage V c2 of capacitor C2 is zero, switch devices Q1, Q2 are turned o, and the simmer-trigger circuit is turned on. Mode 1 (t0Rt < t1): mode 1 starts with the Q 1 turning on at time t0. The equivalent circuits are shown in Fig. 3(b). The resonant current IQ1 ¯ows through the path C1 4Q1 4Lr 4D5 4lamp1 4 C1 and the path V in 4Q1 4Lr 4D5 4lamp1 4 C1. The resonant capacitor voltage V c1, V c2 and the input voltage V in at time t1 both are equal to zero. Then the current through resonant inductor Lr ¯ows through Lr 4D5 4lamp1 4 D3 4Q1 4Lr. As a result of that, V c1 and V c2 are clamped at zero and also V in is clamped at zero. Mode 2 (t1Rt < t3): the equivalent circuit is shown in Fig. 3(b). Even though the switch Q1 is turned o at time t2, the resonant current is continuously ¯owing through Lr 4D5 4lamp1 4 D3 4V in 4D2 4L r due to the stored energy in the resonant inductor Lr. During mode 1 and mode 2, lamp2 is blocked by D6, so the energy is only provided with lamp1. Here, I D3 is a freewheeling current. The modes for lamp2 can be also divided into two modes, and these operations are just the same as in the case of lamp1. The simulated circuit waveforms of this ZCS series resonant converter are shown in Fig. 4. The simulation parameters were as follows. Input voltage (V in): DC 540 V Resonant capacitor (C1, C2): 40 mF Resonant inductor (Lr): 46 mH Switching frequency ( f): 1150 Hz Current pulsewidth: 300 ms
Fig. 2. Electrical circuit of the ZCS resonant converter which consists of switch devices (Q1, Q2), a resonant inductor (Lr), and resonant capacitors (C1, C2).
The simmer-trigger circuit creates an ionized spark streamer between two electrodes so that the main discharge can occur. In order to generate the streamer, a
H.-J. Kim et al. / Optics & Laser Technology 30 (1998) 199±203
201
Fig. 3. (a) Circuit waveforms of operation modes for the ZCS resonant converter during a switching cycle. (b) Equivalent circuits of operation modes for the ZCS resonant converter divided into two modes.
simmer current of about 20 mA to a few A is required, and it is restricted by resistance. A 0.3 mm2 nickel wire is wrapped around the ¯ashlamp for easy triggering. 4. Laser resonator A laser head was composed of a Nd:YAG laser rod and two ¯ashlamps. The double elliptical cavity inside was coated with gold, and two mirrors were dielectrically coated. In general, in a double elliptical cavity,
all rays emanating from the pumping source are transformed into the laser rod. In the case of one laser head, they had a 50 cm separation. The total mirror had a re¯ectivity of over 99.5% and a concave curvature of 2 m. The half mirror had a re¯ectivity of 85%. In addition, in order to maintain a stable laser operation, the laser rod and ¯ashlamps were liquid-cooled by circulating pure water as a coolant in ¯owtubes which surround these elements. We used two water pumps of 35 l/min. One cooled a ¯ashlamp and a rod, and the other did the rest: the lamp and the parts surrounding a re¯ector.
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H.-J. Kim et al. / Optics & Laser Technology 30 (1998) 199±203
Fig. 4. Simulated current and voltage waveforms of the ZCS resonant converter.
5. Experimental results In the case of one laser head, Fig. 5 shows the laser output obtained by varying the pulse repetition rate at a ®xed current pulsewidth of 350 ms and an input power of 8 kW. As a result, the highest output was obtained at 1150 pps. It means that the laser output per second rises with increasing repetition rate. In this experiment, the repetition rate was restricted to 1150 pps because of the properties of the Xe ¯ashlamp made in ILC. Fig. 6 shows the laser output gained by adjusting the current pulsewidth at a repetition frequency of 1150 pps and an input power of 8 kW. The longer the pulsewidth, the higher the laser output. The maximum laser output was 240 W at an input power of 12 kW. The laser output as a function of electrical input power is shown in Fig. 7. As we can see, it rises linearly from the electrical input power of about 4 kW,
Fig. 5. Laser output as a function of pulse repetition rates at a ®xed current pulsewidth of 350 ms and an input power of 8 kW.
which is the oscillating point, to the input rating. Consequently, it is expected that more laser output can be generated by increasing the input and having a better cooling device. In Fig. 8, the voltage waveform and the current waveform, which were applied across the switch devices during a switching period of ZCS series resonant converters, are shown. There are no sudden peak voltages and ringing. The current waveform became a sinusoidal wave by series resonance. In addition, we arranged two laser heads in cascade and the re¯ectivity of the half mirror was changed from 85 to 80%. The maximum average output was about 480 W. 6. Conclusions A zero-current switching resonant converter was adopted as the power supply of a pulsed Nd:YAG
Fig. 6. Laser output as a function of current pulsewidths at a repetition frequency of 1150 pps and an input power of 8 kW.
H.-J. Kim et al. / Optics & Laser Technology 30 (1998) 199±203
Fig. 7. Laser output as a function of electrical input power at a current pulsewidth of 350 ms and a repetition frequency of 1150 pps.
203
cessing. We have designed and fabricated a high repetition rate and high power pulsed Nd:YAG laser system applied to the ZCS resonant converter. In this study, in order to ®nd out operational characteristics of the HRHP pulsed Nd:YAG laser system, experiments have been performed by adjusting the current pulsewidths to 200±350 ms (step 50 ms) and the pulse repetition rate to 500±1150 pps. As a result, in the case of one laser head with a Nd:YAG laser rod and two ¯ashlamps, a maximum laser output of 240 W was obtained at a current pulsewidth of 350 ms and a pulse repetition rate of 1150 pps. An output of about 480 W for two laser heads was gained under the same conditions. References
Fig. 8. Voltage and current waveforms applied across the switch devices during a switching period of the ZCS series resonant converters.
laser in order to control the laser power density which is considered to be the major factor in materials pro-
[1] Koechner W. Solid-state laser engineering. New York: Springer, 1995. [2] Golla D, Knoke S, Schone W, Ernst G, Bode M, Tunnermann A, Welling H. 300 W cw diode-laser side-pumped Nd±YAG rod laser. Opt Lett 1995;20:1148±50. [3] Liedl G, Schroder K, Kaplan A. Excimer laser processing of ferrite video heads. Appl Surf Sci 1996;106:374±8. [4] Liu DD, Hussain F. O-axis holographic technique for particle image velocimetry using a Fourier-transform lens. Opt Lett 1995;20:327±9. [5] Hattori K, Sato Y. Accurate range®nder with laser pattern shifting. Proc 13th IEEE ICPR 1996;3:849±53. [6] Xie J, Kar A. Mathematical modeling of melting during laser materials processing. Appl Phys 1997;81:3015±22. [7] Timothy MW. Nd:YAG lasers with controlled pulse shape. Proc LAMP, 1987:75±80. [8] Hujii KM. The speci®c nature of high power Nd:YAG laser for welding [ML-2801A] [in Japanese]. Japanese Laser Association, 1991:13±18. [9] Rashid MH. Power electronics circuits, devices, and application. New Jersey: Prentice-Hall, 1993:445-451. [10] Reatti A. Analysis and design of a current-driven two-inductor ZCS low diD/dt. IEEE J Circuits and Systems 1996;43:745±52.
The development of a high repetitive and high power Nd:YAG laser by using a zero-current switching resonant converter Hee-Je Kim a, *, Eun-Soo Kim b, 1, Dong-Hoon Lee a, 2 a
Department of Electrical Engineering, Pusan National University, Changjeon-dong, Kumjeng-ku, Pusan, 609-735, South Korea b Korea Electro-technology Research Institute, 28-1 Sungjoo-dong, Changwon, 641-120, South Korea Received 2 March 1998; received in revised form 18 May 1998; accepted 19 May 1998
Abstract In materials processing, the power density control of a laser beam has been considered to be signi®cant. In this study, a zerocurrent switching resonant converter as the power supply of a pulsed Nd:YAG laser was adopted to control the laser power density, which depends on ¯ashlamp current pulsewidth and pulse repetition rate. It allowed us to design and fabricate a high repetition rate and high power pulsed Nd:YAG laser system. As a result of that, the current pulsewidth could be controlled in the range 200±350 ms (step 50 ms), and the pulse repetition rate could be adjusted to 500±1150 pps (pulse per second). In addition, in the case of one laser head consisting of an Nd:YAG laser rod and two ¯ashlamps, the maximum laser output of 240 W was produced at the condition of 350 ms and 1150 pps, and that of about 480 W was generated at the same condition when two laser heads were arranged in cascade. # 1998 Elsevier Science Ltd. All rights reserved. Keywords: Zero-current switching (ZCS) resonant converter; High repetition rate and high power (HRHP) pulsed Nd:YAG laser; Current pulsewidth; Pulse repetition rate
1. Introduction The pulsed Nd:YAG laser is the most commonly used type of solid-state laser in many ®elds at present because of its good thermal and mechanical properties and easy maintenance [1, 2]. In recent studies of laser processing methods, the pulsed Nd:YAG laser, which has various advantages over the commonly used CO2 laser, has been investigated energetically. It can be focused to a smaller point, due to its shorter wavelength, than the CO2 laser, and can be easily adjusted to materials. Thereby it is broadly used in many applications such as micromachining, holography, range®nding, materials processing and so on [3±6]. Among other things, in materials processing, a suitable laser power density is required for speci®c processes, and the laser power density can be controlled by the current pulsewidth and pulse repetition rate, which are * Corresponding author. Tel.: +82-51-510-2364; Fax: +82-51-5130212; E-mail: [email protected]. 1 E-mail: [email protected] 2 E-mail: [email protected] 0030-3992/98/$19.00 # 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 0 - 3 9 9 2 ( 9 8 ) 0 0 0 3 6 - X
known to be major factors for particular properties of materials [7, 8]. In this study, a zero-current switching (ZCS) resonant converter [9, 10] as the power supply was adopted to control the laser power density. We have designed and fabricated a high repetition rate and high power (HRHP) pulsed Nd:YAG laser system applying the ZCS resonant converter. In order to investigate the operational characteristics of the HRHP pulsed Nd:YAG laser system, experiments for the laser output as a function of current pulsewidth and pulse repetition rate have been carried out.
2. Power supply The power supply was designed and fabricated to be suitable for the high frequency range and to reduce switching loss and noises. It consisted of three components such as a ZCS resonant converter unit, a recti®er unit, and a simmer-trigger unit, as shown in Fig. 1. In particular, the ZCS resonant converter was used to decrease the loss occurred by the tailing current gener-
200
H.-J. Kim et al. / Optics & Laser Technology 30 (1998) 199±203
of charging capacitor, and V in the input voltage. According to this formula, it is found that there are two ways to control the power density of the resonant converter. One is to vary the input voltage V in at a constant pulsewidth and frequency, and the other is to adjust the switching frequency f. In the latter case, low frequency switching causes noises and instability. Therefore, we adopted the control method to vary the input voltage V in.
3. Operation of the ZCS converter Fig. 1. Schematic circuit of the pulsed Nd:YAG laser which consists of three components: a ZCS resonant converter unit, a recti®er unit, and a simmer-trigger unit.
ated on turning o an insulated gate bipolar transistor (IGBT). The recti®er unit consisted of a three-phase interchanging voltage regulator (IVR), a three-phase bridge diode recti®er, and a smoothing condenser as shown in Fig. 1. Because of the over-peak current which came from the resonant converter, a high power DC capacitor with a good frequency response and a smoothing condenser were connected in parallel. The change of input voltage depending on the load change could be adjusted slightly by the three-phase IVR. In Fig. 2, the pulse forming network (PFN) applied to the ZCS series resonant converter consisted of switch devices (Q1, Q2), a resonant inductor (Lr), and resonant capacitors (C1, C2). The switching loss was zero in principle, and it is adequate in high repetition rate operation because the current through Q1, Q2, C1, and C2 was forced to the sinusoidal wave, and the switch devices were turned on/o at zero current. The output of the ZCS series resonant converter is Pout 2fCV 2in
1
where f is the repetition frequency, C the capacitance
The proposed ZCS converter circuit is shown in Fig. 2. The circuit operation can be divided into two modes, whose waveforms and equivalent circuits for the modes are shown in Fig. 3. To simplify the analysis, the initial states of the circuit are assumed as follows: the voltage V c1 of capacitor C1 is initially charged to input voltage V in, the voltage V c2 of capacitor C2 is zero, switch devices Q1, Q2 are turned o, and the simmer-trigger circuit is turned on. Mode 1 (t0Rt < t1): mode 1 starts with the Q 1 turning on at time t0. The equivalent circuits are shown in Fig. 3(b). The resonant current IQ1 ¯ows through the path C1 4Q1 4Lr 4D5 4lamp1 4 C1 and the path V in 4Q1 4Lr 4D5 4lamp1 4 C1. The resonant capacitor voltage V c1, V c2 and the input voltage V in at time t1 both are equal to zero. Then the current through resonant inductor Lr ¯ows through Lr 4D5 4lamp1 4 D3 4Q1 4Lr. As a result of that, V c1 and V c2 are clamped at zero and also V in is clamped at zero. Mode 2 (t1Rt < t3): the equivalent circuit is shown in Fig. 3(b). Even though the switch Q1 is turned o at time t2, the resonant current is continuously ¯owing through Lr 4D5 4lamp1 4 D3 4V in 4D2 4L r due to the stored energy in the resonant inductor Lr. During mode 1 and mode 2, lamp2 is blocked by D6, so the energy is only provided with lamp1. Here, I D3 is a freewheeling current. The modes for lamp2 can be also divided into two modes, and these operations are just the same as in the case of lamp1. The simulated circuit waveforms of this ZCS series resonant converter are shown in Fig. 4. The simulation parameters were as follows. Input voltage (V in): DC 540 V Resonant capacitor (C1, C2): 40 mF Resonant inductor (Lr): 46 mH Switching frequency ( f): 1150 Hz Current pulsewidth: 300 ms
Fig. 2. Electrical circuit of the ZCS resonant converter which consists of switch devices (Q1, Q2), a resonant inductor (Lr), and resonant capacitors (C1, C2).
The simmer-trigger circuit creates an ionized spark streamer between two electrodes so that the main discharge can occur. In order to generate the streamer, a
H.-J. Kim et al. / Optics & Laser Technology 30 (1998) 199±203
201
Fig. 3. (a) Circuit waveforms of operation modes for the ZCS resonant converter during a switching cycle. (b) Equivalent circuits of operation modes for the ZCS resonant converter divided into two modes.
simmer current of about 20 mA to a few A is required, and it is restricted by resistance. A 0.3 mm2 nickel wire is wrapped around the ¯ashlamp for easy triggering. 4. Laser resonator A laser head was composed of a Nd:YAG laser rod and two ¯ashlamps. The double elliptical cavity inside was coated with gold, and two mirrors were dielectrically coated. In general, in a double elliptical cavity,
all rays emanating from the pumping source are transformed into the laser rod. In the case of one laser head, they had a 50 cm separation. The total mirror had a re¯ectivity of over 99.5% and a concave curvature of 2 m. The half mirror had a re¯ectivity of 85%. In addition, in order to maintain a stable laser operation, the laser rod and ¯ashlamps were liquid-cooled by circulating pure water as a coolant in ¯owtubes which surround these elements. We used two water pumps of 35 l/min. One cooled a ¯ashlamp and a rod, and the other did the rest: the lamp and the parts surrounding a re¯ector.
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H.-J. Kim et al. / Optics & Laser Technology 30 (1998) 199±203
Fig. 4. Simulated current and voltage waveforms of the ZCS resonant converter.
5. Experimental results In the case of one laser head, Fig. 5 shows the laser output obtained by varying the pulse repetition rate at a ®xed current pulsewidth of 350 ms and an input power of 8 kW. As a result, the highest output was obtained at 1150 pps. It means that the laser output per second rises with increasing repetition rate. In this experiment, the repetition rate was restricted to 1150 pps because of the properties of the Xe ¯ashlamp made in ILC. Fig. 6 shows the laser output gained by adjusting the current pulsewidth at a repetition frequency of 1150 pps and an input power of 8 kW. The longer the pulsewidth, the higher the laser output. The maximum laser output was 240 W at an input power of 12 kW. The laser output as a function of electrical input power is shown in Fig. 7. As we can see, it rises linearly from the electrical input power of about 4 kW,
Fig. 5. Laser output as a function of pulse repetition rates at a ®xed current pulsewidth of 350 ms and an input power of 8 kW.
which is the oscillating point, to the input rating. Consequently, it is expected that more laser output can be generated by increasing the input and having a better cooling device. In Fig. 8, the voltage waveform and the current waveform, which were applied across the switch devices during a switching period of ZCS series resonant converters, are shown. There are no sudden peak voltages and ringing. The current waveform became a sinusoidal wave by series resonance. In addition, we arranged two laser heads in cascade and the re¯ectivity of the half mirror was changed from 85 to 80%. The maximum average output was about 480 W. 6. Conclusions A zero-current switching resonant converter was adopted as the power supply of a pulsed Nd:YAG
Fig. 6. Laser output as a function of current pulsewidths at a repetition frequency of 1150 pps and an input power of 8 kW.
H.-J. Kim et al. / Optics & Laser Technology 30 (1998) 199±203
Fig. 7. Laser output as a function of electrical input power at a current pulsewidth of 350 ms and a repetition frequency of 1150 pps.
203
cessing. We have designed and fabricated a high repetition rate and high power pulsed Nd:YAG laser system applied to the ZCS resonant converter. In this study, in order to ®nd out operational characteristics of the HRHP pulsed Nd:YAG laser system, experiments have been performed by adjusting the current pulsewidths to 200±350 ms (step 50 ms) and the pulse repetition rate to 500±1150 pps. As a result, in the case of one laser head with a Nd:YAG laser rod and two ¯ashlamps, a maximum laser output of 240 W was obtained at a current pulsewidth of 350 ms and a pulse repetition rate of 1150 pps. An output of about 480 W for two laser heads was gained under the same conditions. References
Fig. 8. Voltage and current waveforms applied across the switch devices during a switching period of the ZCS series resonant converters.
laser in order to control the laser power density which is considered to be the major factor in materials pro-
[1] Koechner W. Solid-state laser engineering. New York: Springer, 1995. [2] Golla D, Knoke S, Schone W, Ernst G, Bode M, Tunnermann A, Welling H. 300 W cw diode-laser side-pumped Nd±YAG rod laser. Opt Lett 1995;20:1148±50. [3] Liedl G, Schroder K, Kaplan A. Excimer laser processing of ferrite video heads. Appl Surf Sci 1996;106:374±8. [4] Liu DD, Hussain F. O-axis holographic technique for particle image velocimetry using a Fourier-transform lens. Opt Lett 1995;20:327±9. [5] Hattori K, Sato Y. Accurate range®nder with laser pattern shifting. Proc 13th IEEE ICPR 1996;3:849±53. [6] Xie J, Kar A. Mathematical modeling of melting during laser materials processing. Appl Phys 1997;81:3015±22. [7] Timothy MW. Nd:YAG lasers with controlled pulse shape. Proc LAMP, 1987:75±80. [8] Hujii KM. The speci®c nature of high power Nd:YAG laser for welding [ML-2801A] [in Japanese]. Japanese Laser Association, 1991:13±18. [9] Rashid MH. Power electronics circuits, devices, and application. New Jersey: Prentice-Hall, 1993:445-451. [10] Reatti A. Analysis and design of a current-driven two-inductor ZCS low diD/dt. IEEE J Circuits and Systems 1996;43:745±52.