Lenka Vukšić

The Multiresonant Converter Steady-State Analysis Based on Dominant Resonant Process

The steady-state analysis of the multiresonant converter is presented. The multiresonant converter utilizes multielement resonant network that consists of resonant inductor and switch capacitances. The resonant process between resonant inductor and capacitances across rectifiers has been found as dominant resonant process. All key circuit parameters are normalized in terms of the characteristic impedance and resonant frequency given by resonant inductor and capacitances across rectifiers. The effects of the transformer magnetizing and leakage inductances have been analyzed. It is shown that dc output values and resonant current rms value strongly depend on load and switching frequency to resonant frequency ratio. It is shown that the resonant process of the resonant inductor and MOSFET output capacitances have no significant influence on overall dc conversion ratio at heavy loads. The simplified analysis is presented and resonant tank order is reduced. The circuit utilizes four different modes of operation. In each mode of operation, the 2-D state-plane diagram is derived. The dc conversion ratio, normalized rms MOSFET, and rectifier capacitance currents have been calculated. A 2.5-kW prototype has been built and tested.

Asymptotic expansions of integral means and applications to the ratio of gamma functions

Integral means are important class of bivariate means. In this paper we prove the very general algorithm for calculation of coefficients in asymptotic expansion of integral mean. It is based on explicit solving the equation of the form B(A(x))=C(x), where asymptotic expansions of B and C are known. The results are illustrated by calculation of some important integral means connected with gamma function.

Asymptotic expansions of the gamma function and Wallis function through polygamma functions

A new view on classical asymptotic expansions of the logarithm of gamma function is given. Then general formulae for the asymptotic expansions of the logarithm of gamma function and the Wallis power function through polygamma functions are derived and analysed.