This work presents a non-isolated DC-DC quadratic Cuk topology, which results from the cascade connection of two conventional Cuk converters. Using the graft scheme and rearranging the power stage, it is possible to obtain a single-switch version of the converter with fewer components when compared with its two-switch counterpart. The converter can provide both voltage stepdown and step-up by varying the duty cycle imposed to the active switch, this being an interesting solution for applications that demand a wide conversion range. Both the current drawn from the source and supplied to the output stage are non-pulsating when the converter operates in continuous conduction mode (CCM), contributing to the reduction of electromagnetic interference (EMI) levels. Both the input voltage and output voltage present the same polarity as well. A comprehensive mathematical analysis is derived for the converter operating in step-up and step-down modes, as it is possible to obtain a consistent design procedure. A laboratory prototype is also implemented and thoroughly assessed experimentally to validate the theoretical assumptions.