# Ćuk converter

Last updated

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.

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.

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]

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.

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

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

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.

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.

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:

${\displaystyle E={\frac {1}{2}}LI^{2}}$

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:

${\displaystyle V_{L}=L{\frac {dI}{dt}}}$

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:

• in the off-state, inductor L1 is connected in series with Vi and C (see figure 2). Therefore ${\displaystyle V_{L1}=V_{i}-V_{C}}$. As the diode D is forward biased (we consider zero voltage drop), L2 is directly connected to the output capacitor. Therefore ${\displaystyle V_{L2}=V_{o}}$
• in the on-state, inductor L1 is directly connected to the input source. Therefore ${\displaystyle V_{L1}=V_{i}}$. Inductor L2 is connected in series with C and the output capacitor, so ${\displaystyle V_{L2}=V_{o}+V_{C}}$

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:

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:

${\displaystyle {\bar {V}}_{L1}=D\cdot V_{i}+\left(1-D\right)\cdot \left(V_{i}-V_{C}\right)=\left(V_{i}-(1-D)\cdot V_{C}\right)}$

${\displaystyle {\bar {V}}_{L2}=D\left(V_{o}+V_{C}\right)+\left(1-D\right)\cdot V_{o}=\left(V_{o}+D\cdot V_{C}\right)}$

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

${\displaystyle V_{C}=-{\frac {V_{o}}{D}}}$

So the average voltage across L1 becomes:

${\displaystyle {\bar {V}}_{L1}=\left(V_{i}+(1-D)\cdot {\frac {V_{o}}{D}}\right)=0}$

Which can be written as:

${\displaystyle {\frac {V_{o}}{V_{i}}}={\frac {-D}{1-D}}}$

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:

${\displaystyle L_{1}min={\frac {(1-D)^{2}R}{2Df_{s}}}}$

Where ${\displaystyle f_{s}}$ is the switching frequency.

## Isolated 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

• US Patent 4257087, [4] filed in 1979, "DC-to-DC switching converter with zero input and output current ripple and integrated magnetics circuits", inventor Slobodan Ćuk.
• US Patent 4274133, [5] filed in 1979, "DC-to-DC Converter having reduced ripple without need for adjustments", inventor Slobodan Ćuk and R. D. Middlebrook.
• US Patent 4184197, [6] filed in 1977, "DC-to-DC switching converter", inventor Slobodan Ćuk and R. D. Middlebrook.
• Power Electronics, Vol. 4: State-Space Averaging and Ćuk Converters; Ćuk Slobodan; 378 pages; 2016; ISBN   978-1519520289.

## Related Research Articles

A rectifier is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which flows in only one direction.

In electronics a relaxation oscillator is a nonlinear electronic oscillator circuit that produces a nonsinusoidal repetitive output signal, such as a triangle wave or square wave. The circuit consists of a feedback loop containing a switching device such as a transistor, comparator, relay, op amp, or a negative resistance device like a tunnel diode, that repetitively charges a capacitor or inductor through a resistance until it reaches a threshold level, then discharges it again. The period of the oscillator depends on the time constant of the capacitor or inductor circuit. The active device switches abruptly between charging and discharging modes, and thus produces a discontinuously changing repetitive waveform. This contrasts with the other type of electronic oscillator, the harmonic or linear oscillator, which uses an amplifier with feedback to excite resonant oscillations in a resonator, producing a sine wave. Relaxation oscillators are used to produce low frequency signals for applications such as blinking lights and electronic beepers and in voltage controlled oscillators (VCOs), inverters and switching power supplies, dual-slope analog to digital converters, and function generators.

A switched-mode power supply is an electronic power supply that incorporates a switching regulator to convert electrical power efficiently. Like other power supplies, an SMPS transfers power from a DC or AC source to DC loads, such as a personal computer, while converting voltage and current characteristics. Unlike a linear power supply, the pass transistor of a switching-mode supply continually switches between low-dissipation, full-on and full-off states, and spends very little time in the high dissipation transitions, which minimizes wasted energy. A hypothetical ideal switched-mode power supply dissipates no power. Voltage regulation is achieved by varying the ratio of on-to-off time. In contrast, a linear power supply regulates the output voltage by continually dissipating power in the pass transistor. This higher power conversion efficiency is an important advantage of a switched-mode power supply. Switched-mode power supplies may also be substantially smaller and lighter than a linear supply due to the smaller transformer size and weight.

Components of an electrical circuit or electronic circuit can be connected in series, parallel, or series-parallel. The two simplest of these are called series and parallel and occur frequently. Components connected in series are connected along a single conductive path, so the same current flows through all of the components but voltage is dropped (lost) across each of the resistances. In a series circuit, the sum of the voltages consumed by each individual resistance is equal to the source voltage. Components connected in parallel are connected along multiple paths so that the current can split up; the same voltage is applied to each component.

In electronics, a voltage divider is a passive linear circuit that produces an output voltage (Vout) that is a fraction of its input voltage (Vin). Voltage division is the result of distributing the input voltage among the components of the divider. A simple example of a voltage divider is two resistors connected in series, with the input voltage applied across the resistor pair and the output voltage emerging from the connection between them.

In electronics, a chopper circuit is used to refer to numerous types of electronic switching devices and circuits used in power control and signal applications. A chopper is a device that converts fixed DC input to a variable DC output voltage directly. Essentially, a chopper is an electronic switch that is used to interrupt one signal under the control of another.

A low-dropout or LDO regulator is a DC linear voltage regulator that can regulate the output voltage even when the supply voltage is very close to the output voltage.

This article illustrates some typical operational amplifier applications. A non-ideal operational amplifier's equivalent circuit has a finite input impedance, a non-zero output impedance, and a finite gain. A real op-amp has a number of non-ideal features as shown in the diagram, but here a simplified schematic notation is used, many details such as device selection and power supply connections are not shown. Operational amplifiers are optimised for use with negative feedback, and this article discusses only negative-feedback applications. When positive feedback is required, a comparator is usually more appropriate. See Comparator applications for further information.

Ripple in electronics is the residual periodic variation of the DC voltage within a power supply which has been derived from an alternating current (AC) source. This ripple is due to incomplete suppression of the alternating waveform after rectification. Ripple voltage originates as the output of a rectifier or from generation and commutation of DC power.

The commutation cell is the basic structure in power electronics. It is composed of an electronic switch and a diode. It was traditionally referred to as a chopper, but since switching power supplies became a major form of power conversion, this new term has become more popular.

A switched capacitor is an electronic circuit element implementing a filter. It works by moving charges into and out of capacitors when switches are opened and closed. Usually, non-overlapping signals are used to control the switches, so that not all switches are closed simultaneously. Filters implemented with these elements are termed "switched-capacitor filters", and depend only on the ratios between capacitances. This makes them much more suitable for use within integrated circuits, where accurately specified resistors and capacitors are not economical to construct.

The single-ended primary-inductor converter (SEPIC) is a type of DC/DC converter that allows the electrical potential (voltage) at its output to be greater than, less than, or equal to that at its input. The output of the SEPIC is controlled by the duty cycle of the control transistor (S1).

An integrating ADC is a type of analog-to-digital converter that converts an unknown input voltage into a digital representation through the use of an integrator. In its basic implementation, the dual-slope converter, the unknown input voltage is applied to the input of the integrator and allowed to ramp for a fixed time period. Then a known reference voltage of opposite polarity is applied to the integrator and is allowed to ramp until the integrator output returns to zero. The input voltage is computed as a function of the reference voltage, the constant run-up time period, and the measured run-down time period. The run-down time measurement is usually made in units of the converter's clock, so longer integration times allow for higher resolutions. Likewise, the speed of the converter can be improved by sacrificing resolution.

The Sparse Matrix Converter is an AC/AC converter which offers a reduced number of components, a low-complexity modulation scheme, and low realization effort . Invented in 2001 by Prof Johann W. Kolar , sparse matrix converters avoid the multi step commutation procedure of the conventional matrix converter, improving system reliability in industrial operations. Its principal application is in highly compact integrated AC drives.

The forward converter is a DC/DC converter that uses a transformer to increase or decrease the output voltage and provide galvanic isolation for the load. With multiple output windings, it is possible to provide both higher and lower voltage outputs simultaneously.

The operational amplifier integrator is an electronic integration circuit. Based on the operational amplifier (op-amp), it performs the mathematical operation of integration with respect to time; that is, its output voltage is proportional to the input voltage integrated over time.

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. 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.
3. U.S. Patent 4274133.: "DC-to-DC Converter having reduced ripple without need for adjustments", filed 20 June 1979, retrieved 15 Jan 2017.
4. U.S. Patent 4184197.: "DC-to-DC switching converter", filed 28 Sep 1977, retrieved 15 Jan 2017.