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Owing to the high aspect ratios and small radii of curvature, carbon nanotubes (CNTs) exhibit excellent field emission characteristics, which is very advantageous for the field emission display (FED) applications. In FED design, the triode structures are more attractive for their lower driving voltage and higher light efficiency. Recently, a new CNT-based triode structure, i.e., planar triode structures, was proposed and exhibited good characteristics. In this design, the lateral gate electrode generates the transverse electric fields to pull out the electrons from the neighboring emitters. But how the display resolution affected by the bias conditions of the gate electrode and by the electron beams diverged in the y-direction is not clear yet. In this paper, these problems are investigated via computer simulation.