Calculating boundaries for the natural voltage balancing time-constant of the constant duty cycle single leg flying capacitor converter

Purpose - The flying capacitor converter (FFC) balances the clamping capacitor voltages naturally when phase shifted carrier modulation is used. Several models that describe this mechanism, and to estimate the time constants following a perturbation, are discussed in the literature. However, due to the model complexity, numerical methods must be used to evaluate these models. This paper aims to present a closed form expression, using a reference table, that describes a maximum bound for the voltage balancing time constant. Design/methodology/approach - The FCC is analysed in the frequency domain. A decomposition of the characteristic matrix that describes the voltage balancing mechanism is used. The resulting real symmetric matrix is factorised by using approximations of the load characteristics at the frequencies of interest. Findings - The minimum eigenvalue of the factorised matrix is used to determine a maximum bound for the time constant of the voltage balancing. Since the factorised matrix is independent of variations in switching frequency and load, the eigenvalue of interest can be calculated once and tabulated. Originality/value - The closed form expression can be used for quick calculations of the maximum time constant under different operating conditions. Furthermore, the expression provides considerable insight into the influences circuit design choices have on the balancing mechanism