Cuk Converter

The Cuk converter is a step-down/step-up converter based on a switching boost-buck topology. Essentially, the converter is composed of two sections, an input stage and an output stage.
The input voltage vg is fed into the circuit via inductor L1. When transistor Q1 is on, current i1 builds the
magnetic  field of the inductor in the input stage. The diode CR1 is reverse biased, and energy dissipates
from the storage elements in the output stage. When Q1 turns off, inductor L1 tries to maintain the current flowing through it by reversing polarity and sourcing current as its magnetic field collapses. It thus provides energy to the output stage of the circuit via capacitor C1. R1 and R2 are parasitic or stray resistances of inductor.

The inductor currents are the input and output currents, therefore, if the principle of conservation of energy is applied:

where Ds is the duty cycle of the switch :

The voltage ratio of a Cuk converter is the same as that of a buck-boost converter, but its main advantage over other converters is that the input and output inductors result in a filtered current on both sides of the converter, while buck, boost, and buck-boost converters have a pulsating current that occurs on at least one side of the circuit i.e either on input side or output side.
This pulsation will increase the ripple in the circuit and due to this ripple , the efficiency of battery gets lowered. To ensure good efficiency ripple should be reduced.
By controlling the duty cycle of the switch , the output voltage vo  can be controlled and can be higher or lower than the input voltage vg. By using a controller to vary the duty cycle during operation, the circuit can also be made to reject disturbances ,as second part of circuit consists of parallel resonance circuit and it work as a tank circuit for specific frequency (resonant frequency) , and during resonance current will not be allowed to enter in the circuit.