Ćuk converter

As ćuk converter ( English Ćuk converter ) is referred to in the electronics an electronic circuit , a direct electric voltage may transform into another DC electric power. The amount of the output voltage can be both smaller and larger than the level of the original input voltage. In contrast to the SEPIC converter, the output voltage has a negative sign compared to the input voltage, as with the inverse converter , the output voltage is inverted. Due to this fact, the Ćuk converter becomes the group of the inverting onesDC converter counted.

The name Ćuk converter can be traced back to the name of its inventor, Slobodan Ćuk , who presented the circuit idea in 1976 together with Robert D. Middlebrook.

Structure and motivation

Block diagram of the Ćuk converter with a changeover switch

The Ćuk converter uses three active energy stores , two coils and a capacitor for voltage conversion , which are continuously charged and discharged with energy using semiconductor switches. In addition, as with any voltage converter , a charging capacitor is required both at the input and at the output in order to reduce the voltage ripple.

At ordinary voltage transformers such as the up-converter or down-converter either occurs at the input or at the output of the circuit, a discontinuous current profile on which adversely affects the respective voltage ripple. In the case of a step-up converter, the output capacitor must be particularly large, as the converter only supplies current to the output when the switch is switched off. In the case of the step-down converter, on the other hand, particular attention must be paid to the input capacitor, since current only flows from the input into the circuit when the switch is on.

It is precisely these negative properties that do not occur with the Ćuk converter topology, since both the input current and the output current run continuously here. This means that both charging capacitors can be much smaller without worsening the voltage ripple.

function

Circuit diagram of a practical implementation of the Ćuk converter with a MOSFET . In order to achieve better efficiency, the diode can also be implemented as a transistor.

If the transistor T is switched on, the inductance L1 is parallel to the supply voltage and the current I _L1 begins to increase. After turning off the transistor of this current flows due to the Lenz's law and charges the capacitor C via the diode D . The current in the inductance L1 decreases and the voltage across the capacitor increases. When the transistor is switched on again, the inductance L1 is recharged and the current I _L1 increases. At the same time, a negative current I _L2 begins to flow, which, starting from the capacitor, flows over the inductance L2 and over the load (including the charging capacitor) and draws energy from the capacitor. A negative voltage thus builds up on the charging capacitor of the output. After the transistor is switched off again, the capacitor is recharged by the current I _L1 . At the same time, also due to Lenz's rule, the current I _L2 caused by the inductance L2 continues to flow through the load and the diode.

Thus, both the input current and the output current have a continuous profile.

Mathematical description

For the following considerations, it is assumed that all capacitors are very large and that the converter has settled at a constant pulse duty factor .

The current in the two inductors fluctuates continuously around two values. The mean value of these currents is constant and the charge on the capacitor is balanced on average.

${\displaystyle \int _{t_{0}}^{t_{1}}i_{L1}\,\mathrm {d} t+\int _{t_{1}}^{t_{2}}i_{L2}\,\mathrm {d} t=0}$

If one further assumes that the current curve in the inductors is triangular, the integrals can be simplified.

${\displaystyle {\overline {i_{\mathrm {L1} }}}\cdot t_{\mathrm {on} }+{\overline {i_{\mathrm {L2} }}}\cdot t_{\mathrm {off} }=0}$

If the times are replaced by the duty cycle ( d ), the following expression is obtained.

${\displaystyle {\dfrac {\overline {i_{\mathrm {L2} }}}{\overline {i_{\mathrm {L1} }}}}={\dfrac {-d}{1-d}}}$

The voltage across an inductance results from:

${\displaystyle u_{\mathrm {L} }\left(t\right)=-L\cdot {\frac {\mathrm {d} i_{L}\left(t\right)}{\mathrm {d} t}}}$

Accordingly, the mean values ​​of the voltages across the two inductances must be zero.

The voltage at the inductance L1 results from:

${\displaystyle d\cdot U_{\mathrm {in} }+(1-d)\cdot (U_{\mathrm {in} }-U_{\mathrm {C} })=0}$

${\displaystyle U_{\mathrm {C} }={\dfrac {U_{\mathrm {in} }}{1-d}}}$

The voltage at the inductance L2 results from:

${\displaystyle d\cdot (U_{\mathrm {C} }+U_{\mathrm {out} })+(1-d)\cdot U_{\mathrm {out} }=0}$

${\displaystyle U_{\mathrm {C} }=-{\dfrac {U_{\mathrm {out} }}{d}}}$

By equating the two equations, an equation is obtained which represents the output voltage of the Ćuk converter as a function of the input voltage and the duty cycle :

${\displaystyle U_{\mathrm {out} }=-U_{\mathrm {in} }\cdot {\dfrac {d}{1-d}}}$

execution

Isolating Ćuk converter.

Coupled Inductor Isolated Cuk Converter

Integrated Magnetics Cuk Converter

The Ćuk converter can be designed both non-isolating and isolating using a transformer . With the latter, it is also possible to increase or decrease the output voltage by the transmission ratio of the transformer.

The two inductors can be coupled magnetically, which reduces the voltage ripple at the input and output. The two inductors use the same core as a magnetic coupling.

See also

• Flyback converter
• Single ended flux converter
• Push-pull flux converter

literature

• MH Rashid: Power Electronics Handbook, Second Edition: Devices, Circuits and Applications (Engineering) 2nd edition, Academic Press, Burlington, California, 2007, ISBN 978-0-12-088479-7 .

Web links

Commons : Cuk converters  - collection of images, videos and audio files

• [1] Basics of DC-DC converters
• Dimensioning of the Ćuk converter

Individual evidence

1. ^ RD Middlebrook, S. Ćuk: A general unified approach to modeling switching-converter power stages . In: Proceedings of the IEEE Power Electronics Specialists Conference, June 8-10, 1976, Cleveland, OH . 1976, p. 73–84 ( pre-printed as PDF [accessed on July 5, 2010]).