Buck Converter with Cubic Static Conversion Ratio.

The paper introduces a step-down converter that exhibits a static conversion ratio of cubic nature, providing an output voltage which is much closer to the input voltage, and at the same duty cycle, compared to a wide class of one-transistor buck-type topologies. Although the proposed topology contains many components, its control is still simple, as it employs only one transistor. A dc analysis is performed, the semiconductor stresses are derived in terms of input and output voltages and output power, revealing that the semiconductor voltage stresses remain acceptable and anyway lower than in other cubic buck topology. All detailed design equations are provided. The state-space approach is used to analyze the converter in the presence of conduction losses and a procedure for calculating the individual power dissipation is provided. The feasibility of the proposed cubic buck topology is first validated by computer simulation and finally confirmed by an experimental 12 V-10 W prototype.

Fourth-Order Quadratic Buck Converter Controller Design.

This paper aims to outline the process of dimensioning a controller tailored for a fourth-order step-down converter. In order to conduct a thorough small-signal analysis, it is imperative to find the state-space model in matrices form. Given its fourth-order nature, the control-to-output transfer function also aligns with this order, although its degree is ultimately reduced to a second-order using the tfest function. It is remarkable that the design of the type III error amplifier assumes a central position in the overall controller design process. The theoretical analysis was then subjected to rigorous validation via simulation, with particular attention paid to the step response in both input voltage and output resistance. This study developed from the desire to validate the efficacy of reducing the control-to-output transfer function degree using the tfest function, aiming to highlight a fourth-order converter to which controller design theory can be applied, related to that for a second-order converter.

A Gauss-Kuzmin theorem for continued fractions associated with nonpositive integer powers of an integer m ≥ 2.

We consider a family {τ m : m ≥ 2} of interval maps which are generalizations of the Gauss transformation. For the continued fraction expansion arising from τ m , we solve a Gauss-Kuzmin-type problem.