The circuit of the Cuk converter is shown in Fig.1.a. It consists of dc input voltage source $V_{S},$ input inductor $L_{1}$ , controllable switch S , energy transfer capacitor $C_{1},$ diode $D,$ filter inductor $L_{2}$ , filter capacitor $C,$ and load resistance $R .$

An important advantage of this topology is a continuous current at both the input and the output of the converter.

Disadvantages of the Cuk converter are a high number of reactive components and high current stresses on the switch, the diode, and the capacitor $C_{1}$ .

The main waveforms in the converter are presented in Fig.1.b . When the switch is on, the diode is off and the capacitor $C_{1}$ is discharged by the inductor $L_{2}$ current. With the switch in the off state, the diode conducts currents of the inductors $L_{1}$ and $L_{2},$ whereas capacitor $C_{1}$ is charged by the inductor $L_{1}$ current.

To obtain the dc voltage transfer function of the converter, we shall use the principle that the average current through a capacitor is zero for steady-state operation. Let us assume that inductors $L_{1}$ and $L_{2}$ are large enough that their ripple current can be neglected. Capacitor $C_{1}$ is in steady state if

$$I_{L 2} D T=I_{L 1}(1-D) T-----(1)$$

For a lossless converter

$$P_{S}=V_{S} I_{L 1}=-V_{O} I_{L 2}=P_{O}-----(2)$$

Combining these two equations, the dc voltage transfer function of the Cuk converter is,

$$M_{V} \equiv \frac{V_{O}}{V_{S}}=-\frac{D}{1-D}-----(3)$$

This voltage transfer function is the same as that for the buck- boost converter.

The boundaries between the CCM and DCM are determined by,

for $L_{1}$

$$L_{b 1}=\frac{(1-D) R}{2 D f}-----(4)$$

and

for $L_{2}$ , $$L_{b 2}=\frac{(1-D) R}{2 f}-----(5)$$

The output part of the Cuk converter is similar to that of the buck converter. Hence, the expression for the filter capacitor C is,

$$C_{\min }=\frac{(1-D) V_{O}}{8 V_{r} L_{2} f^{2}}-----(6)$$

The peak-to-peak ripple voltage in the capacitor $C_{1}$ can be estimated as

$$V_{r 1}=\frac{D V_{O}}{C_{1} R_{f}}-----(7)$$

A transformer (isolated) version of the Cuk converter can be obtained by splitting capacitor $C_{1}$ and inserting a high- frequency transformer between the split capacitors.