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In recent years, there is an increasing interest in noninvasive treatments for neurological disorders like Alzheimer and Depression. Transcranial magnetic stimulation (TMS) is one of the most effective methods used for this purpose. The performance of TMS highly depends on the coils used for the generation of magnetic field and induced electric field particularly their designs affecting depth and focality tradeoff characteristics. Among a variety of proposed and used TMS coil designs, circular coils are commonly used both in research and medical and clinical applications. In current study, we focus on changing the outer and inner sizes (diameter) and winding turns of ring coils and try to reach deeper brain regions without significant field strength decay. The induced electric field and the decay rate of the generated field with depth were studied with finite element method calculations. The results of the performed simulations indicate that larger diameter coils have a larger equivalent field emission aperture and produce larger footprint of induced electric field initially. However, their emission solid angles are smaller and, as a result, the field divergence or the decay rates of the generated field with depth are smaller as well, which give them a good potential to perform better for deep brain stimulation compared with that of smaller coil.