A new 2D-FDTD method has been proposed to analyze the dispersion diagram of planar circuits. Traveling wave field effect transistor (TWFET) is a solid state device designed to amplify signals over a wide bandwidth. An analysis of the passive behavior of this device has been performed using mode-matching technique and assuming that the passive structure performances are affected only by the width of the T bar of the gate electrode. To verify such hypothesis and to determine the cut-off frequency of the higher order modes that limits its bandwidth, we have simplified the 2D-FDTD method with a particular normalization, that permits the analysis of the case β=0. The proposed approach was tested calculating the dispersion for some known structures and it has been used in the TWFET characterizatio