 Ćuk converter

"Cuk" redirects here. For the IdelUral festival, see Çük.
The Ćuk converter (pronounced Chook, sometimes incorrectly spelled Cuk, Čuk or Cúk) is a type of DCDC converter that has an output voltage magnitude that is either greater than or less than the input voltage magnitude.
The nonisolated Ćuk converter can only have opposite polarity between input and output. It uses a capacitor as its main energystorage component, unlike most other types of converters which use an inductor. It is named after Slobodan Ćuk of the California Institute of Technology, who first presented the design.^{[1]}
Contents
Nonisolated Ćuk converter
Operating Principle
A nonisolated Ćuk converter comprises two inductors, two capacitors, a switch (usually a transistor), and a diode. Its schematic can be seen in figure 1. It is an inverting converter, so the output voltage is negative with respect to the input voltage.
The capacitor C is used to transfer energy and is connected alternately to the input and to the output of the converter via the commutation of the transistor and the diode (see figures 2 and 3).
The two inductors L_{1} and L_{2} are used to convert respectively the input voltage source (V_{i}) and the output voltage source (C_{o}) into current sources. Indeed, at a short time scale an inductor can be considered as a current source as it maintains a constant current. This conversion is necessary because if the capacitor were connected directly to the voltage source, the current would be limited only by (parasitic) resistance, resulting in high energy loss. Charging a capacitor with a current source (the inductor) prevents resistive current limiting and its associated energy loss.
As with other converters (buck converter, boost converter, buckboost converter) the Ćuk converter can either operate in continuous or discontinuous current mode. However, unlike these converters, it can also operate in discontinuous voltage mode (i.e., the voltage across the capacitor drops to zero during the commutation cycle).
Continuous mode
In steady state, the energy stored in the inductors has to remain the same at the beginning and at the end of a commutation cycle. The energy in an inductor is given by:
This implies that the current through the inductors has to be the same at the beginning and the end of the commutation cycle. As the evolution of the current through an inductor is related to the voltage across it:
it can be seen that the average value of the inductor voltages over a commutation period have to be zero to satisfy the steadystate requirements.
If we consider that the capacitors C and C_{o} are large enough for the voltage ripple across them to be negligible, the inductor voltages become:
 in the offstate, inductor L_{1} is connected in series with V_{i} and C (see figure 2). Therefore V_{L1} = V_{i} − V_{C}. As the diode D is forward biased (we consider zero voltage drop), L_{2} is directly connected to the output capacitor. Therefore V_{L2} = V_{o}
 in the onstate, inductor L_{1} is directly connected to the input source. Therefore V_{L1} = V_{i}. Inductor L_{2} is connected in series with C and the output capacitor, so V_{L2} = V_{o} + V_{C}
The converter operates in onstate from t=0 to t=D·T (D is the duty cycle), and in off state from D·T to T (that is, during a period equal to (1D)·T). The average values of V_{L1} and V_{L2} are therefore:
As both average voltage have to be zero to satisfy the steadystate conditions we can write, using the last equation:
So the average voltage across L_{1} becomes:
Which can be written as:
It can be seen that this relation is the same as that obtained for the Buckboost converter.
Discontinuous mode
Like all DCDC converters Cuk converters rely on the ability of the inductors in the circuit to provide continuous current, in much the same way a capacitor in a rectifier filter provides continuous voltage. If this inductor is too small or below the "critical inductance", then the current will be discontinuous. This state of operation is usually not studied too much depth, as it is not used beyond a demonstrating of why the minimum inductance is crucial.
The minimum inductance is given by:
Where f_{s} is the switching frequency.
Current
Voltage
Related structures
Inductor coupling
Instead of using two discrete inductor components, many designers implement a coupled inductor Ćuk converter, using a single magnetic component that includes both inductors on the same core. The transformer action between the inductors inside that component gives a coupled inductor Ćuk converter lower output ripple than a Ćuk converter using two independent discrete inductor components.^{[2]}
Singleended primaryinductance converter (SEPIC)
Main article: SEPIC converterA SEPIC converter is able to stepup or stepdown the voltage.
References
 ^ Ćuk, Slobodan; Middlebrook, R. D. (June 8, 1976). "A General Unified Approach to Modelling SwitchingConverter Power Stages" (PDF). Proceedings of the IEEE Power Electronics Specialists Conference (Cleveland, OH.): pp.73–86. http://www.ee.bgu.ac.il/~kushnero/temp/guamicuk.pdf. Retrieved 20081231.
 ^ The Four Boostbuck Topologies
Categories: Electrical power conversion
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