Crystal structures having periodically arranged inclusions inside a homogeneous matrix, called Phononic Crystals (PCs), exhibit various wave phenomena such as negative refraction, wave focusing, mode splitting, etc.Especially, one of the most remarkable properties is a bandgap phenomenon, which refers to wave propagations inside a PC are forbidden in certain frequency.As the bandgap phenomenon is applied in various applications such as wave guiding and wave filtering etc., there have been growing needs for the PC having wider bandgap frequency ranges.A number of researches [1-4] have successfully designed PCs having the maximized bandgap frequency ranges.These researches have shown that the design of the unit cell of PCs can be automated.However, no earlier investigation has so far paid attentions to the singular issue which will be mainly concerned in this paper-the reduction of the spatial period.We found that the optimized unit cell may correspond to shorter spatial periods so that the initial assumption on the periodicity is no longer valid.This means that the size of the unit cell in the direct lattice originally defined in the topology optimization formulation often turns out to be reduced in the final optimized unit cell especially when the creation and maximization of a bandgap are simultaneously considered.The unit cell size reduction can occur in various lattice structures including square and rectangular unit cells.It is found that the reduction of the spatial period can be a critical problem because the reduction can lead to incorrect optimized results.Furthermore, without any control on the periodicity, maintaining the originally set-up periodicity is not guaranteed.Thus, a new technique is required to avoid the reduction of the spatial period.Before dealing with a technique to control the cell size during optimization iterations, the first part of this work is focused on the explanation of the issue in some details about the characteristic of reduced unit cells of the PC.Then, we propose a technique to maintain the size of the unit cell originally defined at the beginning of the topology optimization setting.In particular, the technique is controls branches in the first Brillouin zone of the reciprocal lattice, resulting in the maintained original cell size.As numerical examples, the bandgap creation and maximization using the proposed technique will be considered with square and rectangular unit cells.