This work has as main objective is a numerical analysis the rectangular slot resonator with four layers, with photonic materials - PBG, to obtain the complex resonant frequency and radiation efficiency of this structure. The analysis developed in this work was performed using the TTL - Transverse Transmission Line method. Numerical-computational results are presented in graphical form in three dimensions for all analysis performed, and the resonance frequency depending on the length and width of the slot and the radiation efficiency as a function of resonance frequency and height of the layers of substrate structure.