Impedance is an intuitive and efficient way for dynamic representation of power electronics devices. One of the evident strengths, when compared to other small-signal methods, is the natural association with circuit theory. This makes them possible to be connected through basic circuit laws. However, careful attention should be paid when making this association since the impedances obtained through linearization are local variables, often referred to locally defined reference frames. To allow the operations of these impedances using basic circuit laws, a unified reference has to be defined. Though this issue was properly addressed on the state-space models, a thorough analysis and a clarification regarding the unified impedances and stability effects are still missing. This paper aims to bridge this gap by introducing the Impedance Operator (IO) and associated properties to the development of impedance networks. First, the IO for both the AC coupled and AC/DC coupled systems are presented and verified through impedance measurements in PSCAD. Then, three types of impedance network-based stability criterions are presented along with a clarification on the consistency of stability conclusions. Finally, the Nyquist-based analysis is explored, regarding the sensitivity to partition points, to open the discussion on the identification of systems weak points.