A nonisolated (transformerless) topology of the buck-boost converter is shown in Fig.1.a . The converter consists of dc input voltage source $V_{S},$ controlled switch $S,$ inductor $L,$ diode $D,$ filter capacitor $C,$ and load resistance $R.$ With the switch on, the inductor current increases while the diode is maintained off. When the switch is turned off, the diode provides a path for the inductor current. Note the polarity of the diode that results in its current being drawn from the output.

The buck-boost converter waveforms are shown in Fig.1.b. The condition of a zero volt-second product for the inductor in steady state yields

$$V_{S} D T=-V_{O}(1-D) T-----(1)$$

Hence, the dc voltage transfer function of the buck-boost converter is,

$$M_{V} \equiv \frac{V_{O}}{V_{S}}=-\frac{D}{1-D}-----(2)$$

The output voltage $V_{o}$ is negative with respect to the ground. Its magnitude can be either greater or smaller (equal at $D=0.5$ ) than the input voltage as the name of the converter implies.

The value of the inductor that determines the boundary between the CCM and DCM is

$$L_{b}=\frac{(1-D)^{2} R}{2 f}-----(3)$$

The output part of the Cuk converter is similar the buck converter. Hence, the expression for capacitor C is $$C_{\min }=\frac{(1-D) V_{O}}{8 V_{r} L f^{2}}$$