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Timestamp: 2019-04-22 16:51:11+00:00

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The quasi-resonant operation mode of the Cuk converter is characterized by discontinuities in the current of output diode and in the voltage of the intermediate capacitor. Therefore all the commutations are soft, allowing the increase of the switching fiequency maintaining an acceptable efficiency and increasing the power density. The inductors can be selected so as to have continuous input or output current, resulting in di€ferent converter behavior. This paper presents a methodology to calculate the values of the inductors and capacitor to ensure the correct operation. The converter is PWM controlled. Simulated and experimental results are reported.
The increase of the power density in switched mode power supplies asks for higher switchmg frequency, allowing the reduction of the size of filtering elements. In order to maintain the overall efficiency in acceptable values some kind of soft-switching technique must be used. The Cuk converter has a well-known capacity of softly turning-on the power transistor when operating in the Discontinuous Conduction Mode - DCM [l]. The zerovoltage switching (ZVS) takes place if the transfer capacitor (C) voltage goes down to zero (during the transistor conduction), discharged by the output current, io. Associating both characteristics one gets a fully softswitched converter [ 2 ] . Additionally PWM control is possible . The inconveniences of t h s operation mode are the high voltage and current stresses that the components have to withstand, typical of the discontinuous operation mode. Therefore the application field is practically reduced to low voltage input and when high switching frequency is mandatory. As an example of application there is the telephonic system, where different voltage sources must be obtained from the 48V supply. The use of a high-frequency transformer allows a higher output voltage, suitable for link extension and remote supplying. However, high voltage stresses are produced on the secondary side.
Fig. 1. Cuk converter. The characteristic intervals of operation vary with the duty-cycle. Figure 2 shows two sets of waveforms for dfferent duty-cycles.
Pig. 2. Simulated capacitor voltage arid input and output currents.
the capacitor will reduce its voltage.t2 At t l the diode D conducts (ZVS). t2 = 6 . the capacitor average voltage is strongly influenced by the resonances of the circuit.When the transistor is turned off the capacitor begins to be charged by the input current.t l Currents ii and io are equal. When the current becomes positive D. At t2 the duty-cycle finishes. CIRCUIT OPERATION FOR CONTINUOUS INPUT CURlRENT Let us consider the following quantities: Ii: Input current (supposed constant) T: switching period. b) Interval t l . blocks and v. c) Interval t2 . Capacitor voltage is maximum (vc=Vm). When vc reaches E. coo: output resonant frequency. 6: transistor duty-cycle. until the transistor is turned-on. falls to V. ai:input resonant frequency. D conducts and the output current flows through it. At t3 it changes its direction and at t4 it equals the input current. 662 . If it reverses. d) Interval tl . A 25% duty-cycle produces a new resonant interval that initially takes the place of the linear variation of ii .t4 After tl the output current decays linearly. At to the transistor is turned-on.For this reason this mode of operation will not be addressed in thw paper. Zo: output impedance. Zi: input impedance. When v. So Li must be determined in order to maintain ii positive. The output current decays linearly. the capacitor voltage will remain constant. Figure 3 shows the waveforms. For difTerent duty-cycles the waveforms change sigtllficantly. If the current falls to zero. The capacitor voltage decreases and reaches zero at t 1. STATIC CHARACTERISTICS Ill.T Both currents are equal. Specially for low duty-cycle. T 2 tl (for voltage discontinuity) (7) Eq. e) Interval t4 . starts to increase again. opening the transistor under zero-voltage. starts to conduct and the input current flows through it. The output voltage is actually controlled by the duty-cycle. The following time intervals can be identified: a) Interval to .=----- 1 liL0. IV. Simulated capacitor voltage and input and output currents. subject to zero current (ZCS). In this mode of operation the capacitor is charged whenever the transistor is off. At T the transistor is turned-on (ZCS). turning-off (ZCS) the output diode.T The input current charges the capacitor. affecting its controllability. (7) defines the condition to get zero voltage turn-off to the transistor. being discharged by io when ii reverses its direction. the diode D.C Fig. 3. O i -1op O I - - - = E T 7 a.. Input current rises linearly while the output one varies resonantly.
(13) it 1s possible to find Z-.: output voltage.. 7T v:.0.: maximum transistor voltage. The lower value is due the circuit losses that reduce the output 2-T voltage. must be selected in order to protect the transistor. as shown by eqs. h m eq.I:-T. (20). (9) defines the condition to current discontinuity. Po: maximum output power.T TI V m V. tl is practically constant. Nevertheless this action depends on the circuit parameters. The stress is evident. (14) and (16). a(1-a) -0. being possible also stepup operation. From the power balance. Li is obtained from eq. considering the parameters presented and used in the experimental prototype. 0 1 R. The duty-cycle at which it is expected to have Po and V. from eqs. (2) and (4). it is possible to determine CO-. max Approximate analytical expressions can be obtained if the previous equations are simplified considering that Vm>>Voand &. a.1Sm. & = + 7~ I. V i .c (15) From eq.T From eqs. the maximum capacitor voltage is also approximated by: tl T '~ * 2*0. C and Lo are determined.. using eqs. a . 6 =- =-Vm ZO (13) As l a (<<1.sin[cos-'(a)] Ii 0.>>I. for any V .T 2. .E=-=-V. = - E: input voltage. The average output current can be determined by integrating i. In this case it presents a stepdown behavior. Its maximum value is the solution of eq. V. DESIGN PROCEDURE Let us define the input parameters needed for the design: L O t4 = tl + --(Iq V O + Ii) < T (9) Eq. (15 ) . I.: duty-cycle @ Poand Vo Itma: transistor repetitive peak current.. =I-- 2.0. (12) and (14).(t) in a switching period: I. Z. 663 .T + 6. . Figure 5 displays the normalized capacitor peak voltage. (1). Vtm. the output voltage is: (16) Figure 4 shows the static characteristic of the converter. vm-v. (11) and (14) the converter Operates as power Source for a fixed du@Wcle.T (18) (11) 1 t4w--2. <T There is a minimum duty-cycle defined by eq.C .(1-S)2 2.T --. Considering additionally that t l < q ( 1-S). 6. (21). The same figure displays experimental measures. m i is determined in order to guarantee continuous input current.: - In order to guarantee DCM operation even for the S . =-2-T-V. considering 100% efficiency: a 'Onstant p =I.E V.c 2.It can be shown that the output peak current is: (8) V.
IEEE Trans.1 0.2 0. 476-490. It is evident the ZV turn-off and the operation in the discontinuous mode. VIII. of IEEE PESC. Vm/E I I I I A 0. Cuk and R.. The converter presents a stepdown characteristic and is PWM controlled although working in the quasi-resonant mode. The measured efficiency was 80% at nominal power. Cuk: "Constant-frequency control of quasi-resonant converters". Maksimovic and S. vol. D. July 1991. and capacitor current (5A/div) Time base: lps/div. on Power Electronics. The high voltage stress limits the applications to low input voltages. 1991. Figure 6 shows the currents through the inductors and through the capacitor. no.VOiE magnet cores (even though it was used high-frequency material: IP-12) and to the components conduction.5 0. VI.1 0 0.8 nF T=5 ps (200kHz) Fig. Proc.3 6 0.2 0.6 Fig. 0.4 0. transistor voltage (1OOV/div). 6. 36-57. Therefore the rated output power was obtained at a wider duty-cycle (60%). The transistor voltage is also displayed. Normalized capacitor peak voltage. CONCLUSIONS The quasi-resonant operation mode of the Cuk converter allows full soft-commutation. 664 . Normalized static characteristic. IEEE Trans. Maksimovic and S.=50% Li= 600 pH Lo= 5 pH C= 13. 6. pp. The losses can be mainly attributed to the 1977. 1. Therefore high switching frequency can be used allowing high power density. 3 .6 Measured values Fig. EXPERIMENTAL RESULTS The prototype uses the same parameters employed in the simulation: E=50 V V0=15 V P0=50 W 6. vol. Jan.5 0. Middlebrook: "A general unified approach to modeling switching dc-to-dc converters in discontinuous conduction mode". Cuk: "Aunified analysis of PWM converters in discontinuous modes". 4. The zero current transistor tum-on is not the best solution for MOSFET because it does not eliminates the losses caused by the parasitic capacitance.  D. pp. pp. 141-150. 6.4 0. Current in the inductors (5A/div). on Power Electronics.3 6 0. REFERENCES [l]S. VII.  D. no. 5.

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