Frequency diverse arrays (FDA) can produce a periodic S-shaped pattern due to the added frequency diversity to the array. The auto-scanning capability in FDAs is obtained by applying between the element's small frequency offsets. Contrary to conventional arrays, the auto-scanning pattern occurs in FDAs without employing phase shifters in the feeding network, although controlling the time behavior of the main beam is a serious challenge in these arrays. The FDA radiation patterns behavior in space and time are co-related, and both geometry and frequency distribution affect the scanning rate and the side lobes of the pattern. Designing FDA geometries for single or multiple steering angles can be carried out by optimization techniques, but due to the various variety of scanning angles, the same technique cannot be applied to designing the scanning pattern. One-dimensional FDAs showed a comparable scanning pattern with phased arrays, although the scanning pattern performance of planar FDAs for different geometry and frequency distribution is still unknown. In this paper, several planar geometries and frequency distributions are designed and simulated, and based on the simulation results, an efficient discular FDA with a time-invariant scanning pattern is suggested.