A simple analysis of flying capacitor converter

TL;DR

This paper demonstrates elementary analytical techniques and software tools to analyze flying capacitor converters, deriving exact formulas for voltages and currents, and revealing new insights into their periodic behavior.

Contribution

It introduces a simple analytic method for deriving formulas for capacitor voltage and inductor current averages, highlighting the use of symbolic computation in analyzing switched systems.

Findings

Capacitor voltage averages to half of source voltage.

Inductor current period is half of switching period.

Analytical formulas are exact and useful for modeling.

Abstract

The paper aims to emphasise how switched systems can be analysed with elementary techniques which require only undergraduate-level linear algebra and differential equations. It is also emphasised how math software can become useful for simplifying analytic complications. The time domain voltage balance methodology is used for stability analysis. As for deriving formulas for the asymptotic average of both capacitor voltage and inductor current, a new simple analytic method is introduced. It was shown analytically that the time average of capacitor voltage converges to half of the source voltage. A formula for the time average of the current of the inductor is also computed. As a by-product it was discovered that the period of the current is half of the switching period. Numerical simulations are obtained to illustrate the accuracy of the results. Higher dimensional generalisations could become a bit complicated as stability analysis of higher dimensional exponential matrices are not so easy to handle. On the other hand, the new discovery on the period of the current is more likely to give new insights in handling higher dimensional systems. Analytical formulas are exact and it helps in accurately modelling flying capacitor converts in practice. FCC is well studied in engineering society. However, not much is done in obtaining exact formulas using analysis. Also, math software is much used in computation of numerical results and obtaining simulations. In this paper, one more important aspect of math software is emphasised, namely, use symbolic computations in analysis.