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 C1 and C2 are large enough for the voltage ripple across them to be negligible, the inductor voltages become:
The converter operates in on state from to (D is the duty cycle), and in off state from D·T to T (that is, during a period equal to ). The average values of VL1 and VL2 are therefore:
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.
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.
For isolated version of Ćuk converter, an AC transformer and an additional capacitor must be added. 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. However, the turns ratio can be controlled to reduce device stress on the input side. Additionally, the parasitic elements of the transformer, namely leakage inductance and magnetizing inductance can be used to modify the circuit into a resonant converter circuit which has much improved efficiency.
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.
A zeta converter is a non-isolated, non-inverting, buck-boost power supply topology.
A SEPIC converter is able to step-up or step-down the voltage.