Digital control of power converters has been an area of considerable research interest in recent times. One of the problems which arises in these systems is that of the limit cycle oscillations that occur due to quantization in the feedback loop. This paper investigates the limit cycle oscillations that occur in the digitally controlled version of the buck converter with a proportional-integral controller. The amplitude and frequency of the oscillations that may occur on two duty cycle levels are investigated and related to the controller gain parameters. The analysis shows that it is not possible to guarantee that limit cycle oscillations on two levels will not occur simply by adjusting the gain parameters, and yields a condition which will prevent oscillations on two levels from occurring.