Phase-mode transformation is fundamental for fault analysis in three-phase coupled power systems. The structural differences in phase-mode transformation matrices directly affect the speed and accuracy of fault identification, as well as the effectiveness of single-mode fault type classification. To address the issue that existing phase-mode transformations fail to extract modal fault components that reflect all fault types, this paper proposes a phase-mode transformation matrix for fault components capable of representing all types of cable faults. First, based on the physical structure of the cables, a transient fault characteristic analysis is conducted to summarize the coupling characteristics between equivalent conductors. Then, considering the mathematical characteristics of uniformly transposed cable line parameters, a fault component phase-mode transformation matrix that reflects all cable fault types is proposed. The transmission paths and attenuation characteristics of each mode are also analyzed. Finally, a case study based on a distribution network system is conducted, and simulation verification is performed in PSCAD. The results show that the proposed decoupling matrix can effectively decouple the cable system, allowing a single extracted mode to reflect all cable fault types while maintaining stable wave velocity and minimum attenuation, making it suitable for cable fault location.