CUK converter

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QUASI-RESONANT CUK CONVERTER:DESIGNAND STATIC CHARACTERISTICSJosk Antenor Pomilio

Faculty of Electrical Engineering - University ofCampinasC. P. 6101 13081-970 Campinas - SP BrazilFax.: +55.192.391395 Phone: +55.192.397631

E-mail: [email protected]

ABSTRACTThe quasi-resonant operation mode of the Cuk converter ischaracterizedby discontinuities in the current of output diode andin the voltage of the intermediate capacitor. Therefore all thecommutations are soft, allowing the increase of the switchingfiequency maintaining an acceptable efficiency and increasing thepower density. The inductors can be selected so as to havecontinuous input or output current, resulting in diferent converterbehavior. This paper presents a methodology to calculate thevalues of the inductors and capacitor to ensure the correctoperation. The converter is PWM controlled. Simulated andexperimental results are reported.

I. INTRODUCTIONThe increase of the power density in switched mode powersupplies asks for higher switchmg frequency, allowing thereduction of the size of filtering elements. In order tomaintain the overall efficiency in acceptable values somekind of soft-switching technique must be used.

The Cuk converter has a well-known capacity of softlyturning-on the power transistor when operating in theDiscontinuous Conduction Mode - DCM [l]. The zero-voltage switching (ZVS) takes place if the transfer capacitor(C) voltage goes down to zero (during the transistorconduction), discharged by the output current, io.Associating both characteristics one gets a fully soft-switched converter [ 2 ] . Additionally PWM control ispossible [3].

The inconveniences of th s operation mode are the highvoltage and current stresses that the components have towithstand, typical of the discontinuous operation mode.Therefore the application field is practically reduced to lowvoltage input and when high switching frequency ismandatory. As an example of application there is thetelephonic system, where different voltage sources must beobtained from the 48V supply. The use of a high-frequencytransformer allows a higher output voltage, suitable for linkextension and remote supplying. However, high voltagestresses are produced on the secondary side.

II. CIRCUIT OPERATION FOR CONTINUOUSOUTPUT CURRENTLet us consider the topology shown in figure 1. Supposeideal switches and constant input and output voltages.Additionally consider that the circuit operates in the DCM.In this situation, during the transistor cif state the current i;reverses and becomes equal to the output current (assumedconstant), turning off the diode. Obviously the averagecapacitor voltage is equal to @+Vo).

l i /vc i o

Fig. 1. Cuk converter.The characteristic intervals of operation vary with the

duty-cycle. Figure 2 shows two sets of waveforms fordfferent duty-cycles.

7-- =50% '11S=25o/d -

-command -io - ' 1 j -VCPig. 2. Simulated capacitor voltage arid input and output

currents.0-7803-2972-4/96$5.00@1996EEE 66


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When the transistor is turned off the capacitor begins tobe chargedby the input current, being discharged by io whenii reverses its direction. When vc reaches E, the diode D,starts to conduct and the input current flows through it.When v, falls to V,, D conducts and the output current flowsthrough it.

For difTerent duty-cycles the waveforms changesigtllficantly. A 25% duty-cycle produces a new resonantinterval that initially takes the place of the linear variation ofii . When the current becomes positive D, blocks and v, startsto increase again, until the transistor is turned-on.

Specially for low duty-cycle, the capacitor averagevoltage is strongly influenced by the resonances of thecircuit, affecting its controllability. For this reason this modeof operation will not be addressed in thw paper.

Ill. CIRCUIT OPERATIONFOR CONTINUOUSINPUT CURlRENTIn this mode of operation the capacitor is charged wheneverthe transistor is off. The output voltage is actually controlledby the duty-cycle. Figure 3shows the waveforms.

O i

-1op - - - = E T 7I

Fig. 3. Simulated capacitor voltageand input and output currents.

The following time intervals can be identified:a) Interval to - t l

Currents ii and io are equal. Capacitor voltage ismaximum (vc=Vm). At to the transistor is turned-on, subjectto zero current (ZCS). Input current rises linearly while theoutput one varies resonantly. The capacitor voltage decreasesand reaches zero at t 1.b) Interval t l - t2

At t l the diode D conducts (ZVS). The output currentdecays linearly. At t2 the duty-cycle finishes, opening thetransistor under zero-voltage.

c) Interval t2 - TThe input current charges the capacitor. If the current

falls to zero, the capacitor voltage will remain constant. If itreverses, the capacitor will reduce its voltage. So Li must bedetermined in order to maintain ii positive.d) Interval tl - t4

After tl the output current decays linearly. At t3 itchanges its direction and at t4 it equals the input current,turning-off (ZCS) the output diode.e) Interval t4 - T

Both currents are equal. At T the transistor is turned-on(ZCS).

IV.STATIC CHARACTERISTICSLet us consider the following quantities:Ii: Input current (supposed constant)T: switching period,6: transistor duty-cycle,ai: nput resonant frequency,coo: output resonant frequency,Zi: input impedance,Zo:output impedance.

1a,=--- -liL0.C

t2 =6. T 2 l (for voltage discontinuity) (7)Eq. (7) defines the condition to get zero voltage turn-off

to the transistor.

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It can be shown that the output peak current is: V. DESIGN PROCEDURELet us define the input parameters needed for the design:(8 )E: input voltage,

LOVOt4 =t l +--(Iq +Ii ) < T (9)

Eq. (9) defines the condition to current discontinuity.The average output current can be determined by

integrating i,(t) in a switching period:-, = vm-v, a ( 1 - a ) --.sin[cos-'(a)]i +Z, -0 , -T 0, .T

V,: output voltage,Po: aximum output power,6,: duty-cycle @ Po nd VoItma: transistor repetitive peak current,Vtm,: maximum transistor voltage.

The duty-cycle at which it is expected to have Poand V,must be selected in order to protect the transistor.

2 . E6,1Sm, =I-- V,maxIn order to guarantee DCM operation even for the S-from eqs. (12) and (14), it is possible to determine CO-.

h m q. (13) it 1s possible to find Z-. usi ng eqs. (2) and(4), C and Lo are determined.Approximate analytical expressions can be obtained ifthe previous equations are simplified considering that

Vm>>Voand &,>>I;:a,&=-+-

- v:.c 2.T V,.T (18)7~ VmI, = (11)

T I2-T-V,7T 1

2.0, a .0 ,t4w--- < T

VmI, =-Z OThere is a minimum duty-cycle defined by eq. (20). mi is

determined in order to guarantee continuous input current.Its maximum value is the solution of eq. (21). Li is obtainedfrom eq. (1).(13)

tl *6- =- ~T 2*0,.TAs la (


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V O i E magnet cores (even though it was used high-frequencymaterial: IP-12)and to the components conduction.

0.1 0. 2 0.3 0.4 0.5 0. 60 Measuredvalues 6

Fig.4. Normalized static characteristic.Vm/E

I I I I A

0.1 0.2 0.3 0.4 0.5 0.66

Fig. 5. Normalized capacitor peak voltage.

VI.EXPERIMENTAL RESULTSThe prototype uses the same parameters employed in thesimulation:E=50 VV0=15 VP0=50 W6,,=50%Li= 600 pHLo= 5 pHC= 13.8nFT=5 ps (200 Hz)

Figure 6 shows the currents through the inductors andthrough the capacitor. The transistor voltage is alsodisplayed. It is evident the ZV turn-off and the operation inthe discontinuous mode.

The measured efficiency was 80% at nominal power.Therefore the rated output power was obtained at a widerduty-cycle (60%). The losses can be mainly attributed to the

VII.CONCLUSIONSThe quasi-resonant operation mode of the Cuk converterallows full soft-commutation. Therefore high switchingfrequency can be used allowing high power density.

The high voltage stress limits the applications to lowinput voltages.

The converter presents a stepdown characteristic and isPWM controlled although working in the quasi-resonantmode.

The zero current transistor tum-on is not the bestsolution for MOSFET because it does not eliminates thelosses causedby the parasitic capacitance.

Fig. 6. Current in the inductors (5A/div), transistor voltage(1OOV/div), and capacitor current (5A/div)

Time base: lps/div.

VIII.REFERENCES[ l]S. Cuk and R. D. Middlebrook: "A general unified

approach to modeling switching dc-to-dc converters indiscontinuous conduction mode". Proc. of IEEE PESC,1977, pp. 36-57.

[2] D. Maksimovic and S. Cuk: "Aunified analysis of PWMconverters in discontinuous modes". IEEE Trans. onPower Electronics, vol. 6, no. 3 , July 1991,pp. 476-490.

[3] D. Maksimovic and S. Cuk: "Constant-frequency controlof quasi-resonant converters". IEEE Trans. on PowerElectronics, vol. 6, no. 1, Jan. 1991, pp. 141-150.

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