Flying capacitor converter is an attractive multilevel converter choice due to its natural voltage balance property. Averaged voltage balance dynamics analytical research methods reported to date are essentially based on a frequency domain analysis. They require high mathematical skills and the solutions are not truly analytical and difficult to use in an everyday practice. In this paper, a straightforward time domain approach based on stitching of analytical solutions for consecutive switching intervals is applied to a four-level single-leg converter. Small parameter analysis yields physically meaningful simple accurate closed-form expressions for averaged oscillating voltage balance dynamics revealing the dependences of voltage balance frequency and time constant on load parameters, carrier frequency, and normalized DC PWM voltage command. Averaged voltage balance dynamics for AC PWM is obtained by averaging on AC fundamental period.