In this paper, the convergence speed of the voltage balancing strategy based on logic processed CPS-PWM scheme is analyzed. The voltage balancing strategy adopts the fundamental frequency sorting algorithm(FFSA), which significantly reduces the computational burden and omits the detection of arm current direction. And the logic processing can generate driving signals with obviously different charging abilities. Thus, the discussed voltage balancing strategy can provide faster convergence speed of capacitor voltages compared with normal CPS-PWM scheme based FFSA at higher carrier frequency. However, the convergence speed of the logic processing based voltage balancing strategy is dependent on many factors, such as modulation index and power factor angle. In this paper, the convergence speed is analyzed in detail and its mathematical expression is presented. Basing on the analysis, it is found that in the applications where the modulation index is usually high, i.e., higher than 0.75, the effect of modulation index on the convergence speed is always negligible. And by comparing the convergence speed of the logic processed CPS-PWM scheme with its counterpart, normal CPS-PWM scheme with low carrier frequency, the applicable range of power factor angle is revealed. The simulation and experimental results validate the theoretical analysis.