Generation of terahertz (THz) radiation has been a hot research topic in recent years. Plasmonic quantum cascade lasers (QCLs) are among the most compact and efficient sources to generate THz radiation. In this paper, we comprehensively study plasmonic QCLs designed based on the antenna-feedback structure to generate efficient radiation about the center frequency of 3 THz. By changing the geometric structure of the plasmonic cavity and using two-dimensional simulation, a minimum loss less than 5.9 cm-1 is achieved at the lasing frequency. It is also possible to control the orientation of the output beam either vertically or tilted by changing the geometry of the antenna design via chirped or non-chirped grating scheme. Moreover, the output characteristics of the QCL are simulated based on the three-level rate equations through which the dynamics of the laser, as well as the P-I curve are investigated. Also, the gain spectra for two laser designs (with chirped and non-chirped gratings) are simulated and compared to each other. The results of this paper may provide deep insight into designing efficient laser sources in the THz region.