Nowadays carbon nanotube field effect transistor or CNTFET is one of the promising devices for future electronic applications. These transistors are frequently simulated using non-equilibrium Green's function (NEGF) formalism. In this paper we study aspects of changes in gate parameters at different channel diameter which have not been known before. We find that in small values of diameter, increasing the dielectric constant of gate insulator doesn't help to improve the performance as value of dielectric constant reaches a certain amount. We also find that increasing the oxide thickness doesn't always decrease transistor performance. For high diameter values, increasing the thickness upto a certain value, improves the transistor performance.