Common-and Differential-Mode Loop Gains by Two Wave Probes for Closed-Loop Stability Analysis

The 8-port wave probe has been proposed and proved recently to be able to generate the correct loop gains and bi-directional reflection coefficients that is critical to closed-loop circuit stability analysis. For certain type of circuits, a pair of wave probes can be used to get the common/differential-mode loop gains to better understand the cause of the oscillation, being it intended or not. In this paper, the fundamental concept and practical usage of the common/differential-mode wave-probe loop gains will be investigated both mathematically and in simulation. This further illustrates the importance of the wave probe for microwave/ millimeter-wave circuit designs.