In the modern era of science and technology, devices with more speed and efficiency are in high demand. Among the reliable options, the terahertz (THz) spectra are promising. A tunable ultrabroadband THz metamaterial absorber and a THz filter using disk graphene patterns are proposed. Simulations exploiting an analytical circuit model based on a developed transmission line method and the finite element method are performed. The analytical circuit model of two graphene patterns with the transmission line theory is utilized to obtain the input impedance of the structures to describe the graphene metamaterial structures as circuit elements. Then, exploiting a genetic algorithm, the input impedance of the structures is designed to be matched to the free space in the desired terahertz spectra using circuit principles. A parametric study of the proposed structures has been carried out to show the capability of tuning the proposed structures. The results clearly reveal the effectiveness of the suggested structures for distinct practical applications, such as filters and sensors at THz spectra. Finally, the proposed configurations can be manufactured using currently developed techniques in addition to chemical vapor deposition.