## Working principle

A Ćuk converter transforms a DC voltage at the input to a DC voltage at the output with reversed polarity. Compared to the Buck, Boost and Buck-Boost converters the Ćuk converter uses an additional inductor and capacitor to store energy. Consider the following sequence of the MOSFET conduction state:

**1. On-state**: The current through the inductor L_{1}increases linearly and the diode blocks.**2. Off-state**: Since the current through the inductor L_{1}can not abruptly change the diode must carry the current so it commutates and begins conducting. Energy is transferred from the inductor L_{1}to the middle capacitor C_{2}resulting in a decreasing inductor current.**3. On-state**: The current through the inductor L_{1}again increases linearly and the diode blocks. The middle capacitor discharges and supplies the RC load through the inductor L_{2}. The induced voltage across the resistor R has the opposite polarity of the input voltage.

The circuit has two limits of operation. For a PWM duty cycle D ➝ 0 the output voltage equals zero, and for D ➝ 1 the output voltage grows toward negative infinity. In between those limits the output voltage in continuous conduction mode is given by: V_{out} = -D/(1-D) **· **V_{in}. The combination of inductors and capacitors acts as a second order low pass filter reducing the voltage ripple at the output.

Compared to the previous DC to DC voltage converters (Buck, Boost and Buck-Boost) the Ćuk converter always allows continuous current flow through the inductors, and therefore, no discontinuous conduction mode is possible.

### Experiments

- Change the PWM duty cycle of the converter from 0.5 to 0.4 and 0.6 and observe how the average output voltage changes to 16 V and 36 V, respectively.
- Change the DC capacitor value from 10 μF to 100 μF and observe how the ripple of the output voltage is reduced.