A detailed analytical analysis of a passive resonant snubber cell perfectly constructed for a pulse width modulated d.c. d.c.

Transcription

1 A detailed analytical analysis of a passive resonant snubber cell perfectly constructed for a pulse width modulated d.c. d.c. buck converter H. Bodur, A.F. Bakan, M. Baysal Electrical Engineering 85 (2003) Ó Springer-Verlag 2003 DOI /s Abstract In this paper, a detailed analytical analysis of a passive resonant snubber cell that is perfectly constructed for a pulse width modulated (PWM) d.c. d.c. buck converter is proposed. This snubber cell provides a larger overall efficiency and a wider load range than most of the active snubber cells presented previously, and has a simple structure and low cost. The operation principles and a detailed steady-state analysis of a PWM buck converter implemented with this snubber cell are presented. The theoretical analysis is verified with a prototype of a 5-kW and 50-kHz insulated gate bipolar transistor-(igbt)-pwm buck converter. All of the semiconductor devices in the converter operate under soft switching conditions. Additionally, at 80% output power, the overall efficiency of the proposed soft switching converter is increased to about 98% from the value of 91% in its counterpart hard switching version. Keywords Soft switching, Zero voltage switching, Zero current switching, Snubber cells, Resonant passive snubber cells 1 Introduction Pulse width modulated (PWM) d.c. d.c. converters have been widely used in industry because of their high power density, fast transient response and ease of control. Higher power density and faster transient response can be achieved by increasing the switching frequency. However, while the frequency rises, switching losses and electromagnetic and radio-frequency interference (EMI and RFI) noises increase. Therefore, it is required that these losses and noises decrease in order to increase the switching frequency. This aim can be realized by using the soft switching (SS) techniques provided by snubber cells instead of hard switching (HS) techniques. The soft switching concept has been increasingly attractive in recent years [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,12]. Snubber concept includes the suppression of voltage rate, voltage and current rise rates, and EMI and RFI noise Received: 21 December 2001 / Accepted: 15 July 2002 Published online: 3 January 2003 H. Bodur (&), A.F. Bakan, M. Baysal Yildiz Technical University, Besiktas, Istanbul, Turkey bodur@yildiz.edu.tr Tel.: /2236 Fax: rates, and the transfer of switching energy. There are many types of snubber cells proposed in the literature, such as, RC/RCD, polarized/nonpolarized, resonant/nonresonant, and active/passive snubbers [1]. In resonant converters, commutations take place under either zero voltage switching (ZVS) or zero current switching (ZCS), and so switching losses are significantly reduced. On the other hand, excessive voltage and current stresses occur in these converters, and power density is lower and control is harder than with normal PWM converters [3, 4, 6, 7, 8]. In recent years, a number of zero voltage transition (ZVT) and zero current transition (ZCT) PWM converters have been presented by adding resonant active snubbers to normal PWM converters, to combine the desirable features of both resonant and normal PWM techniques [3, 4, 5, 7]. In these types of converters, the turn on or off process is realized with ZVS and/or ZCS in very short time intervals provided by resonance. Because the resonance occurs over a very small part of the switching cycle, the converter operates as a conventional PWM converter during the very large remaining part of the cycle [2, 8]. In addition, most active snubber cells are seriously criticized due to their complexity, high cost, difficult control, large circulating energy, excessive voltage and current stresses, and also narrow line and load ranges [3, 10]. In recent years, passive snubber cells employing resonant technique have been seen as an alternative to the active snubber cells. Also, it has been reported that the passive snubber cells were cheaper and more reliable, and had a higher performance/cost ratio than the active ones. Passive snubber cells can be formed in very different ways concerning the type of main switch and the aim of snubber. The only energy that cannot be recovered by means of the passive snubber cells is that of the parasitic capacitor of the main switch [10]. Insulated gate bipolar transistor (IGBT) has been broadly used as a switching device in high power industrial applications. Whereas an IGBT has high switching capability, low conduction loss, and low cost, it has relatively high switching loss [2, 3]. This study presents a detailed analytical analysis of a passive resonant snubber cell that provides a larger overall efficiency and a wider load range than most of the active snubber cells proposed previously. This snubber cell is perfectly constructed for a PWM buck converter, and has a simple structure and low cost. In a converter equipped with this cell, all active and passive semiconductor devices operate under soft switching conditions. A detailed steady- 45

2 Electrical Engineering 85 (2003) 46 state analysis of a PWM d.c. d.c. buck converter implemented with the proposed snubber cell is presented. Moreover, the theoretical analysis is verified with a prototype of a 5-kW, 50-kHz IGBT-PWM buck converter. 2 Operation principles and analysis 2.1 Definitions and assumptions The circuit scheme of an IGBT-PWM buck converter equipped with a well-constructed passive resonant snubber cell is given in Fig. 1. This snubber cell consists of a snubber inductor (L S ), a snubber capacitor (C S ), a buffer capacitor ( ), and three auxiliary diodes (D S1, D S2, and D S3 ). During one switching cycle, the following assumptions are made in order to simplify the steady-state analysis of the circuit shown in Fig Input voltage V i is constant. 2. Output voltage V o is constant or output capacitor C F is large enough. 3. Output current is constant or main inductor L F is large enough. 4. Main inductor L F is much larger than snubber inductor L S. 5. Resonant circuits are ideal. 6. Semiconductor devices are ideal. 7. Reverse recovery time of all diodes except main diode D F is ignored. 2.2 Operation stages Nine stages take place in the steady-state operation during one switching cycle in the proposed converter. The equivalent circuit schemes of the operation stages are given in Fig. 2 and the key waveforms of these stages are given in Fig. 3. A detailed analysis of every stage is presented below Stage 1 (t 0 <t<t 2 : Fig. 2a) The equations i T =0, i DF =, i LS =0, v CS =0 and v CB =0 are valid at the beginning of this stage. At t=t 0, when the turn on signal is applied to the gate of the main transistor T, stage 1 begins. For this stage, the equations i LS ¼ i T ¼ i i ¼ V i L S ðt t 0 Þ i DF ¼ i LS ¼ V i ðt t 0 Þþ ð2þ L S are derived. The main transistor T is turned on under near ZCS because its current i T is limited by the snubber inductor L S. During this stage, L S current i LS rises and D F current i DF falls simultaneously and linearly. First, the current i LS reaches and the current i DF drops to zero at t 1. Then i LS continues to rise, and i DF continues to fall negatively. Consequently, at t=t 2, the D F current i DF drops to I rr, and so the main diode D F is turned off with ZCS due to L r and also ZVS because of C S and existent, and this stage stops. In this state t 01 ¼ L S V i t 12 ¼ t rr ¼ L S I rr ð4þ V i can be written. Here t rr and I rr are the reverse recovery time and the reverse recovery current of the main diode D F respectively, for the values of I F = and di/dt= V i /L S. Therefore, the output current and the reverse recovery current I rr are commutated to the snubber inductor L S at the end of this stage. ð1þ ð3þ Stage 2 (t 2 <t<t 4 : Fig. 2b) At the moment t=t 2, i T = +I rr, i DF =0, i LS = +I rr, v CS =0, and v CB =0 are valid. As soon as the main diode D F is turned off, the diode D S2 is turned on and this stage starts. In the interval of this stage, a parallel resonance occurs via the resonant path V i T L S D S2 C S under constant output current. For this resonance i LS ¼ I rr cos½x 1 ðt t 2 ÞŠþ V i sin½x 1 ðt t 2 ÞŠþ ð5þ Z 1 v CS ¼ C e f V i cos½x 1 ðt t 2 ÞŠþZ 1 I rr sin½x 1 ðt t 2 ÞŠþV i g C S ð6þ Fig. 1. An IGBT-PWM buck converter with a well-constructed passive resonant snubber cell v CB ¼ C e f V i cos½x 1 ðt t 2 ÞŠþZ 1 I rr sin½x 1 ðt t 2 ÞŠþV i g are obtained. In these equations C e ¼ C S =ðc S þ Þ pffiffiffiffiffiffiffiffiffi x 1 ¼ 1= L S C e ð7þ ð8þ ð9þ

3 H. Bodur et al.: A detailed analytical analysis of a passive resonant snubber cell perfectly constructed for a pulse width modulated d.c. d.c. buck converter 47 Fig. 2. Equivalent circuit schemes of the operation stages in the proposed soft switching converter

4 Electrical Engineering 85 (2003) 48 Fig. 3. Key waveforms concerning the operation stages in the proposed soft switching converter p Z 1 ¼ ffiffiffiffiffiffiffiffiffiffiffiffi L S =C e ð10þ are valid. Over this stage, first the current i LS reaches its maximum value at t 3, than the voltage v CS reaches the value of the input voltage V i at t 4. Just after v CS becomes V i, the diode D S1 is turned on with ZVS naturally, and this stage is finished. The following equations are achieved for this state. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi I LS max ¼ Irr 2 þ ð V i=z 1 Þ 2 þ ð11þ t 23 ¼ 1 x 1 arctg V i Z 1 I rr ð12þ t 34 ¼ 1 C S C e 1 V i arcsin p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : ð13þ x 1 þ Z1 2I2 rr V 2 i Stage 3 (t 4 <t<t 5 : Fig. 2c) At t=t 4,asi T =I LS4, i DF =0, i LS =I LS4,v CS =V i, and v CB =V CB4, the diode D S1 is turned on, i T drops to instantly, and this stage begins. A new resonance starts to resonate by the way of L S D S2 D S1 under constant load current at the same time. For this resonance i LS ¼ðI LS4 Þ cos½x 2 ðt t 4 Þ v CB ¼ V CB4 cos½x 2 ðt t 4 Þ are achieved. In these equations pffiffiffiffiffiffiffiffiffiffi x 2 ¼ 1= L S Š V CB4 Z 2 sin½x 2 ðt t 4 ÞŠþ ð14þ ŠþZ 2 ði LS4 Þ sin½x 2 ðt t 4 ÞŠ ð15þ ð16þ

5 H. Bodur et al.: A detailed analytical analysis of a passive resonant snubber cell perfectly constructed for a pulse width modulated d.c. d.c. buck converter p Z 2 ¼ ffiffiffiffiffiffiffiffiffiffiffiffi L S = ð17þ are existent. When the current i LS drops to again and the voltage v CB reaches its maximum value, the diodes D S1 and D S2 are turned off under near ZCS due to the existence of L S, and this stage stops. The time interval of this stage can be found as follows t 45 ¼ 1 arctg Z 2ðI LS4 Þ ð18þ x 2 V CB4 The excess of the energy stored in the snubber inductor L S is transferred to the buffer capacitor over this stage Stage 4 (t 5 <t<t 6 : Fig. 2d) The load is fed from the d.c. input supply through the main transistor T, and the snubber circuit is not active during the whole of this stage. The time duration of this stage is equal to about the on state duration of the conventional PWM converter, and is determined by the PWM control. For this stage i i ¼ i T ¼ i LS ¼ ð19þ can be written Stage 5 (t 6 <t<t 7 : Fig. 2e) At t 6, i T =, i DF =0, i LS =, v CS =V i and v CB =V CBmax are valid. The gate signal of the main transistor T is removed. Thus T is turned off and D S1 is turned on under ZVS due to C S charged to V i, and this stage starts at the same time. During this stage, the capacitor C S feeds the load with the current. In this case v CS ¼ ðt t 6 ÞþV i ð20þ C S is found. As the voltage v CS falls to V CBmax, the diode D S3 is turned on under ZVS naturally, and this stage is completed. The time duration of this stage, t 67 ¼ C S ðv i V CB max Þ ð21þ is derived Stage 6 (t 7 <t<t 8 : Fig. 2f) i T =0, i DF =0, i LS =, v CS =V CBmax and v CB =V CBmax are existent at the beginning of this stage. As soon as the diode D S3 is turned on, this stage begins at t 7. In this stage, a new resonance takes place by the way of L S D S3 C S D S1 under constant load current. For this state, the equations i LS ¼ 1 C e v CS ¼ C e Z 1 1 C e C S cos½x 1 ðt t 7 ÞŠþ C e sin½x 1 ðt t 7 ÞŠ ðt t 7 ÞþV CB max C S þ ð22þ ð23þ v CB ¼ C e Z 1 1 C e sin½x 1 ðt t 7 ÞŠ ðt t 7 ÞþV CB max ð24þ C S þ are derived. When the voltage v CS falls to zero, the diode D S2 is turned on with ZVS naturally, and this stage is finished at t=t 8. The snubber capacitor C S provides the turn off of the main transistor T under near ZVS and the buffer capacitor helps it. Also, the energy in capacitor C S is transferred to the load completely in this stage Stage 7 (t 8 <t<t 9 : Fig. 2g) At the moment t=t 8, the equations i T =0, i DF =0, i LS =I LS8, v CS =0 and v CB =V CB8 are valid, and this stage starts. A new resonance begins via the path L S D S2 D S1 under constant current at the same time. The following equations are obtained for this resonance. i LS ¼ ð I LS8 Þ cos½x 2 ðt t 8 ÞŠ V CB8 sin½x 2 ðt t 8 ÞŠþ ð25þ Z 2 v CB ¼ V CB8 cos½x 2 ðt t 8 Þ Š Z 2 ð I LS8 Þ sin½x 2 ðt t 8 ÞŠ ð26þ Just after the current i LS becomes zero, the diodes D S1 and D S2 are turned off with near ZCS due to L S, and this stage finishes. The time duration of this stage 2 3 t 89 ¼ 1 6 Z 2 arcsinqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi arctg Z 2ð I LS8 Þ7 4 5 x 2 Z2 2ð I LS8 Þ 2 þ VCB8 2 V CB8 ð27þ can be achieved. Therefore, the energy in the inductor L S is transferred to the load completely in this stage Stage 8 (t 9 <t<t 10 : Fig. 2h) This stage begins when i T =0, i DF =0, i LS =0, v CS =0 and v CB =V CB9 are existent at t 9. The capacitor is decharged with the current in this stage. Thus v CB ¼ ðt t 9 ÞþV CB9 ð28þ can be formed. As soon as the voltage v CB drops to zero, the diode D S3 is turned off and the main diode D F is turned on under ZVS because of simultaneously, and this stage is completed at t=t 10. The duration of this stage t 910 ¼ V CB9 ð29þ is found. Thus, the energy in the capacitor is transferred to the load completely at the end of this stage. 49

6 Electrical Engineering 85 (2003) Stage 9 (t 10 <t<t 11 =t 0 : Fig. 2i) During the whole of this stage, the load current passes through the main diode D F and the snubber circuit is not active. The duration of this stage is equal to about the off state duration of the normal PWM converter, and is determined by the PWM control. In this stage i DF ¼ ð30þ is valid. Consequently, at the moment t=t 11 =t 0, the turn on signal is applied again to the gate of the main transistor T, and so one switching cycle is completed and another cycle begins. 3 Design procedure The proposed passive resonant snubber cell provides soft switching conditions for the main transistor and the main diode, and so can significantly reduce switching losses, but causes some additional losses in the main and auxiliary circuits. Consequently, the snubber cell should be designed both to provide soft switching conditions at maximum load current and to minimize the additional losses. The following design procedure is developed by considering procedures such as those presented previously [5, 6, 7]. This procedure is mainly based on the soft switching demands of the main transistor and the main diode. Here, a detailed analysis is not done for the minimization of the additional losses. 1. Snubber inductor L S is selected to permit its current to rise up to at most the maximum output current within both t r and 3t rr max time periods during the turn on of the main transistor or the turn off of the main diode. In this case, from Eq. (1) V i L S t r max ð31þ which are stored in the snubber inductor during the turn off of the main diode and the charge of the snubber capacitor. This energy balance can be defined as follows: 1 2 C SVi 2 þ 1 2 L SIrr 2 max ffi 1 2 VCB 2 max ð34þ The value of is normally much larger than the value of C S. Consequently, the bigger the value of selected, the lower the value of V CBmax. Moreover, if the value of increases, the voltage across the main diode falls, but the time periods t 45, t 78, and t 89 on which the inductor energies are transferred to or the load rises. 4 Converter features The features of the proposed soft switching converter are briefly summarized as follows. 1. All of the active and passive semiconductor devices are turned on and off under exact or near ZVS and/or ZCS. 2. The proposed converter has a simple structure, low cost, and ease of control. 3. The converter acts as a conventional PWM converter during most of the switching cycle. 4. The converter can operate at a wide load range. 5. The presented snubber cell can be easily applied to the other basic PWM d.c. d.c. converters and to all switching converters. 6. The proposed converter has a larger total efficiency and a wider load range than most of the converters with active snubber presented previously. 7. In the converter presented, no additional voltage stresses on the main transistor and no additional current stresses on the main diode occur. On the other hand, the main transistor is subjected to a slight additional current stress, and the main diode is subjected to a higher voltage than the input voltage. V i 3t rr max max ð32þ L S can be written. Here, t r is the rise time of the main transistor, and t rr max is the reverse recovery time of the main diode for the values I F =max and di/dt= V i /L S. These equations provide near ZCS turn on for the main transistor and near ZCS turn off for the main diode respectively. 2. Snubber capacitor C S is selected to be decharged from V i to zero with the maximum output current over at least the time period t f during the turn off of the main transistor. For this state, according to Eq. (20), C S V i t f ð33þ max is achieved. Here, t f is the fall time of the main transistor. 3. Buffer capacitor is selected to be charged from zero up to at most a value decided before, such as the half the input voltage. This capacitor takes on the energies 5 Experimental results A prototype of a 5-kW and 50-kHz IGBT-PWM buck converter given in Fig. 4 was performed to prove the estimated operation principles and theoretical analysis of the PWM buck converter with the perfectly constructed passive resonant snubber cell. Fig. 4. Experimental circuit of a 5-kW and 50-kHz IGBT-PWM buck converter

7 H. Bodur et al.: A detailed analytical analysis of a passive resonant snubber cell perfectly constructed for a pulse width modulated d.c. d.c. buck converter With reference to the manufacturersõ handbooks, some nominal values of IGBT are V=1,200 V, I=35 A, t r =150 ns, and t f =700 ns. The values of D F are V=1,200 V, I=12 A, and t rr =50 ns. Also, D S1, D S2, and D S3 own V=600 V, I=8 A, and t rr =60 ns. The experimental results should be qualified by considering that the IGBT used has no good dynamic characteristics. The converter with this IGBT operates at 5 kw and 50 khz without any problems because of the existence of the proposed snubber cell. The experimental oscillograms shown in Fig. 5 are obtained from operating hard and soft switching converters with a digital camera. The experimental efficiency curves given in Fig. 6 are determined by measuring the voltage and current values of the input and output of these converters. Moreover, the results of the hard switching converter are estimated from the measurements, which are done with the circuit operated at low frequency levels. In Fig. 5a and b, it is seen that the main transistor T and the main diode D F operate with hard switching. While T is turned on and D F is turned off simultaneously, a very large short-circuit current flows through them, and then a resonance between the leakage inductor of the circuit and the parasitic capacitor of the main diode occurs with a very high frequency. Moreover, T still continues conducting by the time its voltage reaches V i during its turn-off process, and after this turn off, a similar resonance occurs with the parasitic capacitor of the main transistor. Therefore, very high switching losses take place, and these losses dominate the total loss of the circuit in the hard switching converter. When Fig. 5c f concerning the soft switching converter are observed together, it can be clearly seen that first T is turned on and than D F is turned off under near ZCS. T takes on the load current, the reverse recovery current of D F, and the charge current of the capacitors C S and respectively. C S is charged to a value bigger than V i due to the turn on delay of D S1, and than feeds the load by the time its voltage drops to V i again. This state causes a collapse on the T current and an overshoot on the D F and D S3 voltages. At last the oscillograms go back to normal. Consequently, T is turned off with near ZVS. During or after this process, first only C S is decharged, than C S together with are decharged, and after C S is decharged to near zero, only is charged. The reverse recovery current of D S1 reflects on the T voltage as a collapse. As soon as is decharged to near zero, D F is turned on under ZVS. is charged little negatively because of the turn on delay of D F, and then is decharged to zero through D F during the reverse recovery of D S3. This state causes an overshoot on the D F current. Moreover, it can be seen that the diodes D S1, D S2, and D S3 operate under soft switching conditions. Additionally, during the turn on and turn off of T and D F, a slight overlap occurs between their own voltages and currents. Therefore, the switching losses are near zero, but a little additional conduction loss takes place, and so the 51 Fig. 5. Some oscillograms obtained from the experimental circuits (a f 200 V/div, 2 ls/div; a,b 20 A/div; c f 10 A/div); a voltage (upper) and current (lower) for the main switch T with HS; b voltage (upper) and current (lower) for the main diode D F with HS; c voltage (upper) and current (lower) for the main switch T with SS; d voltage (upper) and current (lower) for the main diode D F with SS; e voltages for the diode D S1 (upper) and capacitor C S (lower); f voltages for the capacitor (upper) and the diode D S3 (lower)

8 Electrical Engineering 85 (2003) 52 Fig. 6. Efficiency curves of the hard switching and the proposed soft switching converters compared conduction losses dominate the total loss in the soft switching converter. Moreover, from Fig. 6 it can be seen that the efficiency values of the soft switching converter are relatively high with respect to those of the hard switching converter and most of the converters with active snubber cell presented previously. The efficiency values towards the minimum output power decrease naturally because the snubber cell is designed for the maximum output current. At 80% output power, the overall efficiency of the proposed converter increases to about 98% from the value of 91% in its counterpart hard switching converter. 6 Conclusion This study describes a passive resonant snubber cell perfectly designed for a d.c. d.c. buck converter. A PWM buck converter implemented with this passive snubber cell was analytically analyzed in detail. The operation principles and the theoretical analysis of this converter were entirely verified by a prototype of a 5-kW, 50-kHz IGBT-PWM buck converter. It was clearly shown that all the semiconductor devices used in the practical circuit operated under soft switching conditions. The converter operated at a wide load range without any problems. The experimentally obtained efficiency values were much higher than those in the hard switching converter and also those in most of the converters with active snubber. References 1. Ferraro A (1982) An overview of low-loss snubber technology for transistor converters. IEEE Power Electronics Specialists Conference, pp Hua G, Leu CS, Jiang Y, Lee FC (1994) Novel zero-voltage-transition PWM converters. IEEE Trans Power Electron 9: Hua G, Yang EX, Jiang Y, Lee FC (1994) Novel zero-currenttransition PWM converters. IEEE Trans Power Electron 9: Elasser A, Torrey DA (1996) Soft switching active snubbers for DC/DC converters. IEEE Trans Power Electron 11: Mao H, Lee FC, Zhou X, Dai H, Cosan M, Boroyevich D (1997) Improved zero-current-transition converters for high-power applications. IEEE Trans Ind Appl 33: Tseng CJ, Chen CL (1998) A passive snubber cell for non-isolated PWM DC/DC converters. IEEE Trans Ind Electron 45: Tseng CJ, Chen CL (1998) Novel ZVT PWM converters with active snubbers. IEEE Trans Power Electron 13: Grigore V, Kyyra J (1998) A new zero-voltage-transition PWM buck converter. 9th Mediterranean Electrotechnical Conference, MELECON 98, Tel Aviv, Israel, vol 2, pp Menegaz JMP, Co MA, Simonetti DSL, Vieira LF (1999) Improving the operation of ZVT DC-DC converters. 30th Power Electronics Specialists Conference, PESC 99, Charleston, vol 1, pp Smith KM, Smedley KM (1999) Properties and synthesis of passive lossless soft-switching PWM converters. IEEE Trans Power Electron 14: Bodur H, Sarul MH, Bakan AF (1999) A passive lossless snubber cell design for an ohmic loaded PWM IGBT chopper fed by a diode bridge from AC mains. ELECO 99 International Conference on Electrical and Electronics Engineering, Bursa, Turkey, vol 2, pp Kim TW, Kim HS, Ahn HW (2000) An improved ZVT PWM boost converter. 31st Power Electronics Specialists Conference, PESC00, Galway, Ireland, vol 2, pp