A nonlinear programming technique using the penalty function method,which. is especially suitable for power. converter design optimization, is utilized for the comparison of the conventional BuckBoost and Cuk converters. Detailed comparisons are made with respect to the loss and weight breakdowns. of the optimum design of the two converters for a given set of performance specifications. The comparison shows that the Cuk converter outperforms the conventional Buck-Boost converter in both operating efficiency and weight considerations for both the step up or step down modes of operation. Also, a detailed comparison of the coupled inductor version of the Cuk converter under both the balanced and unbalanced current ripple reduction modes of operation is made. From this comparison, it is shown that the unbalanced current ripple reduction is more advantageous. The effects of using different input voltages and different core materials with different saturation flux densities on the global power converter optimization were also studied. The new Cuk converter was disclosed for the first time in 1977. Since then, there are several controversies about the claims made by Cuk of the advantages. of his. converter with respect to the conventional Buck-Boost converter. The comparisons made by Cuk of the two converters did Iiot satisfy the same performance specifications. Consequently, his conclusions of the superiority of his converter cannot be fully justified. In this work the comparisons are made of these two converters based upon the optimum designs. £or a given set of performance specifications. With the detailed comparisons of the loss/weight breakdowns of these two converters, the controversies surrounding the Cuk converter are solved. / Ph. D.