TY - JOUR AB - This paper extends the capabilities of the 3D Smith chart for representing positive and negative differential-phase group delay and the associated loaded resonator quality factor, displayed simultaneously with scattering (S)-parameters. Here, mathematical concepts, inspired from elementary differential geometry and topology, are used to implement 3D projections. It is shown that a condition for a circuit to exploit negative differential-phase group delay is that its S-parameter winding number should be ≥ 0 (relative to its origin). Finally, exemplar network responses that exhibit both positive and negative differential-phase group delay and loaded resonator quality factor are shown with the 3D Smith chart. The convenience of being able to simultaneously display a wider range of parameters on one visualization platform, with the 3D Smith chart, may help to speed-up the design and analysis of microwave circuits by the user. AU - Muller,AA AU - Sanabria-Codesal,E AU - Moldoveanu,A AU - Asavei,V AU - Lucyszyn,S DO - 10.1109/TMTT.2016.2614931 EP - 19 PY - 2017/// SN - 0018-9480 SP - 10 TI - Extended Capabilities of the 3-D Smith Chart with Group Delay and Resonator Quality Factor T2 - IEEE Transactions on Microwave Theory and Techniques UR - http://dx.doi.org/10.1109/TMTT.2016.2614931 UR - http://ieeexplore.ieee.org/document/7738571/ UR - http://hdl.handle.net/10044/1/40806 VL - 65 ER -