In this study, we seek to analyze and numerically evaluate a plasmonic sensor. To form the sensor structure, we use several amplifiers, such as two rings attached to each other and a cavity, as well as two metal insulating metal waveguides (MIM). At the beginning of this simulation, we must examine the resonant wavelengths and the refractive index of the resonators using the finite difference time domain method. By changing the refractive index and changing the dimensions of the cavity and the rims, we seek to investigate the sensor performance and the conduction characteristics of the plasmonics and to obtain the effect of these parameters. To evaluate the sensor performance, we calculate the three factors of sensitivity coefficient S, quality factor Q and figure of merit (FOM), here we reach the sensitivity of 987.6 nm / RIU. Such a plasmonic sensor with a simple framework and high optical resolution can be very useful for sensor systems on optical circuits.