Ćuk converter

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The Ćuk converter (pronounced chook; sometimes incorrectly spelled Cuk, Čuk or Cúk) is a type of DC/DC converter that has an output voltage magnitude that is either greater than or less than the input voltage magnitude. It is essentially a boost converter followed by a buck converter with a capacitor to couple the energy.

Boost converter DC-to-DC power converter with an output voltage greater than its input voltage

A boost converter is a DC-to-DC power converter that steps up voltage from its input (supply) to its output (load). It is a class of switched-mode power supply (SMPS) containing at least two semiconductors and at least one energy storage element: a capacitor, inductor, or the two in combination. To reduce voltage ripple, filters made of capacitors are normally added to such a converter's output and input.

Buck converter DC to DC converter

A buck converter is a DC-to-DC power converter which steps down voltage from its input (supply) to its output (load). It is a class of switched-mode power supply (SMPS) typically containing at least two semiconductors and at least one energy storage element, a capacitor, inductor, or the two in combination. To reduce voltage ripple, filters made of capacitors are normally added to such a converter's output and input.

Contents

Similar to the buck–boost converter with inverting topology, the output voltage of non-isolated Ćuk is typically also inverting, and can be lower or higher than the input. It uses a capacitor as its main energy-storage 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]

Buck–boost converter

The buck–boost converter is a type of DC-to-DC converter that has an output voltage magnitude that is either greater than or less than the input voltage magnitude. It is equivalent to a flyback converter using a single inductor instead of a transformer.

Capacitor Passive two-terminal electronic component that stores electrical energy in an electric field

A capacitor is a device that stores electrical energy in an electric field. It is a passive electronic component with two terminals.

Inductor Passive two-terminal electrical component that stores energy in its magnetic field

An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a coil around a core.

Non-isolated Ćuk converter

There are variations on the basic Ćuk converter. For example, the coils may share single magnetic core, which drops the output ripple, and adds efficiency. Because the power transfer flows continuously via the capacitor, this type of switcher has minimized EMI radiation. The Ćuk converter allows energy to flow bidirectionally by using a diode and a switch.

Operating principle

Fig 1: Schematic of a non-isolated Cuk converter. Cuk conventions.svg
Fig 1: Schematic of a non-isolated Ćuk converter.
Fig 2: The two operating states of a non-isolated Cuk converter. Cuk operating.svg
Fig 2: The two operating states of a non-isolated Ćuk converter.
Fig 3: The two operating states of a non-isolated Cuk converter. In this figure, the diode and the switch are either replaced by a short circuit when they are on or by an open circuit when they are off. It can be seen that when in the off-state, the capacitor C is being charged by the input source through the inductor L1. When in the on-state, the capacitor C transfers the energy to the output capacitor through the inductance L2. Cuk operating2.svg
Fig 3: The two operating states of a non-isolated Ćuk converter. In this figure, the diode and the switch are either replaced by a short circuit when they are on or by an open circuit when they are off. It can be seen that when in the off-state, the capacitor C is being charged by the input source through the inductor L1. When in the on-state, the capacitor C transfers the energy to the output capacitor through the inductance L2.

A non-isolated 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.

Transistor Basic electronics component

A transistor is a semiconductor device used to amplify or switch electronic signals and electrical power. It is composed of semiconductor material usually with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals controls the current through another pair of terminals. Because the controlled (output) power can be higher than the controlling (input) power, a transistor can amplify a signal. Today, some transistors are packaged individually, but many more are found embedded in integrated circuits.

Diode abstract electronic component with two terminals that allows current to flow in one direction

A diode is a two-terminal electronic component that conducts current primarily in one direction ; it has low resistance in one direction, and high resistance in the other. A diode vacuum tube or thermionic diode is a vacuum tube with two electrodes, a heated cathode and a plate, in which electrons can flow in only one direction, from cathode to plate. A semiconductor diode, the most commonly used type today, is a crystalline piece of semiconductor material with a p–n junction connected to two electrical terminals. Semiconductor diodes were the first semiconductor electronic devices. The discovery of asymmetric electrical conduction across the contact between a crystalline mineral and a metal was made by German physicist Ferdinand Braun in 1874. Today, most diodes are made of silicon, but other materials such as gallium arsenide and germanium are used.

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 L1 and L2 are used to convert respectively the input voltage source (Vi) and the output voltage source (Co) into current sources. 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 the 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, buck–boost 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 (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 steady-state requirements.

If we consider that the capacitors C and Co are large enough for the voltage ripple across them to be negligible, the inductor voltages become:

The converter operates in on state 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 (1-D)·T). The average values of VL1 and VL2 are therefore:

Duty cycle fraction of one period in which a signal or system is active

A duty cycle or power cycle is the fraction of one period in which a signal or system is active. Duty cycle is commonly expressed as a percentage or a ratio. A period is the time it takes for a signal to complete an on-and-off cycle. As a formula, a duty cycle (%) may be expressed as:

As both average voltage have to be zero to satisfy the steady-state conditions, using the last equation we can write:

So the average voltage across L1 becomes:

Which can be written as:

It can be seen that this relation is the same as that obtained for the buck–boost converter.

Discontinuous mode

Like all DC/DC converters Ćuk 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 inductor current slope will be discontinuous where the current goes to zero. This state of operation is usually not studied in much depth as it is generally not used beyond a demonstrating of why the minimum inductance is crucial, although it may occur when maintaining a standby voltage at a much lower current than the converter was designed for.

The minimum inductance is given by:

Where is the switching frequency.

Isolated Ćuk converter

Isolated Cuk converter with gapless AC transformer in the middle Isolated-cuk-converter.png
Isolated Ćuk converter with gapless AC transformer in the middle
Coupled inductor isolated Cuk converter Zero-IO-ripple-isolated-cuk-converter.png
Coupled inductor isolated Ćuk converter
Integrated magnetics Cuk converter Zero-ripple-isolated-cuk-converter.png
Integrated magnetics Ćuk converter

The Ćuk converter can be made in an isolated kind. An AC transformer and an additional capacitor must be added. [2]

Because the isolated Ćuk converter is isolated, the output-voltage polarity can be chosen freely.

As the non-isolated Ćuk converter, the isolated Ćuk converter can have an output voltage magnitude that is either greater than or less than the input voltage magnitude, even with a 1:1 AC transformer.

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 with lower output ripple than a Ćuk converter using two independent discrete inductor components. [3]

Zeta Converter

A zeta converter provides an output voltage that is the opposite of the output voltage of a Ćuk converter.

Single-ended primary-inductance converter (SEPIC)

A SEPIC converter is able to step-up or step-down the voltage.

Patents

Further reading

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Slobodan Ćuk is a Serbian American author, inventor, business owner, electrical engineer, and professor of electrical engineering at the California Institute of Technology (Caltech). The Ćuk switched-mode DC-to-DC voltage converter is named after Slobodan Ćuk.

References

  1. Ćuk, Slobodan; Middlebrook, R. D. (June 8, 1976). A General Unified Approach to Modelling Switching-Converter Power Stages (PDF). Proceedings of the IEEE Power Electronics Specialists Conference. Cleveland, OH. pp. 73–86. Retrieved 2008-12-31.
  2. boostbuck.com: Easy Design of the Optimum Topology Boostbuck (Cuk) Family of Power Converters: How to Design the Transformer in a Cuk Converter
  3. The Four Boostbuck Topologies
  4. U.S. Patent 4257087.: "DC-to-DC switching converter with zero input and output current ripple and integrated magnetics circuits", filed 2 Apr 1979, retrieved 15 Jan 2017.
  5. U.S. Patent 4274133.: "DC-to-DC Converter having reduced ripple without need for adjustments", filed 20 June 1979, retrieved 15 Jan 2017.
  6. U.S. Patent 4184197.: "DC-to-DC switching converter", filed 28 Sep 1977, retrieved 15 Jan 2017.