CUK TOPOLOGY

elektor electronics - 1/200522

The Cuk converter is a capacitively coupled converterthat generates an adjustable output voltage and currentby periodically charging a capacitor. As the circuit (in itssimplest form) does not provide electrical isolationbetween the input and output, it is suitable for secondary-side switched-mode power supplies or chargers.

SymmetryFigure 1 illustrates the operating principle of the Cuk con-verter. The output voltage can adjusted anywhere between0 V and a several times the input voltage by varying theduty cycle of switch S. This circuit thus combines the char-acteristics of a step-down converter and a step-up con-verter, while using only a single semiconductor switch andjust one inductor. This outstanding property gives designers

access to a wide range of highly interesting applications.If the converter is used as a battery charger, a batteryhaving any desired voltage can not only be chargedfrom a 12-V storage battery, but also discharged backinto the storage battery. It makes no difference whetherthe battery in question is (for example) a 6-V battery or a60-V battery. When the battery is discharged, the energyis fed back into the original battery with a high level ofefficiency, instead of being dissipated as heat in a resis-tor or semiconductor device in the usual manner. Notonly does this save energy, it also allows batteries to bequickly discharged at high currents.Another interesting application results from the symmetryof the circuit. If diode D is replaced by a second switchand FETs or IGBTs with integrated free-wheeling diodesare used in the implementation, the result is a bidirec-tional converter (Figure 2). When T1 is driven, energyis transferred from voltage source Uin to Uout, while whenT2 is driven, energy is transferred in the opposite direc-tion. Here again the values of Uin and Uout are not impor-tant, and the desired current level is determined by theduty cycle of whichever transistor is being driven.

Voltage isolationFor certain applications, such as primary-side switched-mode power supplies, the input and output voltages mustbe isolated from each other.This is also possible with the Cuk converter. As shown inFigure 3, the input and output can be isolated using anadditional capacitor and a high-frequency or ‘planar’transformer. A planar transformer has a core that con-tains relatively little ferrite and has an extremely largecross section. Using such a transformer, it is possible toobtain winding voltages of 100 V or more, and 5 kW ofpower in a 150-g package can easily be achievedthanks to the small number of turns required at 500 kHz(see www.paytongroup.com).This version of the circuit also retains all the other proper-ties. Any desired voltage ratio can be set using the turnsratio and capacitance ratio shown in the circuit diagram. In the isolated version of the circuit, the overall efficiency

L

Uin Uout

L

S

D

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Figure 1.The topology of the

Cuk converter…

L

S1

S2

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Uin Uout

Figure 2....is symmetrical…

Little-known but still highly interesting

The topology of the Cuk converter was first published in the1980s, but it is rarely encountered in practice even today.However, this circuit concept offers enticing advantages formany power supply applications.

Georg Gerads

is lower due to the additional magnetisation losses andconversion losses in the transformer. An efficiency ofmore than 96% can easily be achieved by the circuitwithout a transformer, but 92% or better is still possiblewith a transformer.Besides the fact that the circuit configuration is the samefor all power levels, the Cuk converter can also be usedover a wide range of powers. The topology is equallysuitable for small power supplies in the watt range andlarger power supplies in the kilowatt range.

OperationTo understand how the converter works, you need tohave a basic understanding of how inductors behave.When a dc voltage is applied to an inductor, the currentincreases linearly from an initial value of zero with aslope di/dt = U/L. When the voltage is switched off, thecurrent decreases, again with a linear slope. This isaccompanied by a negative voltage across the inductor.As an inductor cannot accumulate a dc voltage, the mag-nitude of the negative voltage assumes a level such thatthe areas of the voltage–time rectangles F1 and F2 inFigure 4 are identical.The negative voltage across the inductor depends on theduty cycle, which is the ratio of the ‘on’ and ‘off’ times ofthe switch. At a 50% duty cycle, the amplitudes of theapplied and induced voltage are the same (b); below50% the amplitude of the induced voltage is less thanthat of the applied voltage (a), and above 50% it isgreater (c).

UL– = (1 – a) / a Uin

Very high negative voltages occur at large duty cycles.This must be taken into account during circuit design byselecting suitable semiconductor devices and limiting themaximum possible duty cycle.These observations presume that there is a free-wheelingcircuit that accepts the current from the inductor after theswitch is opened. If such a circuit is not present, theamplitude of the voltage across the inductor will rise tosuch a high level that flashover will occur at the switch.Even in this case, the areas of F1 and F2 are still equal. The allowable saturation inductance (which is propor-tional to the area of F1) must also be taken into accountin designing the inductor. If the saturation inductance isexceeded, the inductor loses its inductive properties andinstead behaves like a short circuit. If this happens, thecurrent no longer increases linearly, but instead rises to avalue that is limited only by the ohmic resistance of thecoil. This means that the risk of saturation does notdepend on the power level, but only on the voltage andfrequency.

In a Cuk converter, switch S is periodically closed andopened with a duty factor a. When S is closed, the volt-age across the inductor is equal to the input voltage. Thebehaviour of the voltage and current are shown in Fig-

ure 5a. After S is opened, current ii2 continues to flowthrough the free-wheeling diode D and charges capacitorC to Uin + UL, as shown in Figure 5b. If switch S is now closed again, the capacitor at the outputis charged to UC – UL. As a result, the output voltage isequal to the inductor voltage shown in Figure 5b, whichmeans the voltage during the free-wheeling interval. Thisvoltage depends only on the duty cycle a, and as previ-ously stated, it can be adjusted to a value anywherebetween 0 V and a several times the input voltage. The circuit has the same form for all power levels. Theamplitude of the output voltage can be considerably greaterthan that of the input voltage with a high duty cycle, while

1/2005 - elektor electronics 23

FOR SWITCHED-MODE POWER SUPPLIES

L 1

1

n

nS

D

C C/n

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Uin Uout

Figure 3. ...and can also bemade to providevoltage isolation.

uin

t

u

iF1

F2

UL

b

uin

t

u

i

F1

F2

UL

a

uin

t

u

i

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F1

F2

UL

c

Figure 4. The voltage–timearea is always thesame, regardless ofthe dut cycle.

the output current can be vastly greater than the input cur-rent with a low duty cycle. The currents and applied volt-ages that the switching transistor and diode have to handlemust be taken into account in selecting suitable components

and designing the circuit. Measures must also be taken tolimit the maximum current and duty cycle, in order to pro-tect the components under all load conditions.

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Slobodan M. CukAs a professor and head of the Power Electronics Groupat the renowned California Institute of Technology(Caltech), Dr Slobodan Cuk (pronounce: “chook”) and hiscolleague Robert Middlebrook developed switched-modepower supply applications in the late 1970s based on atopology that was just as clever as it was novel. This‘CuKonverter’ technology is distinguished by constant inputand output currents, in which respect it resembles conven-

tional dc converters. Since its invention, the CuKonverterhas been marketed for industrial and military applicationsby the company TESLAco. Besides serving as head of thiscompany, Dr Cuk still gives courses on the subject ofpower electronics and switched-mode converters.

His principal ‘literary’ work consists of three practicallyoriented volumes titled Advances in Switched-Mode PowerConversion, which contain the collected working papersof the Caltech Power Electronics Group. They are avail-able from TESLAco (http://www.teslaco.com/teslaco.html)

Uin UoutS

ii1 io1

UL UL

D

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UC

Uin UoutS

ii2 io2

UL UL

D

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UCa b

Figure 5.Voltage and current

curves of the Cukconverter.