Unconditional Stability Criteria for Microwave Networks
This paper presents a review of unconditional stability criteria for analysis and design of microwave networks. A linear two-port network is said to be unconditionally stable (in even mode) if for all passive load and source terminations, the moduli of the input and output reflection coefficients are smaller than one. There are many stability criteria stating the necessary and sufficient conditions for such unconditional stability. One classical set of these criteria is based on the combination of Rollett condition (K > 1) together with one auxiliary condition (e.g., |△| < 1, etc.), which constitutes a family of dual-parameter stability criteria. Another family of stability criteria involves merely a single-parameter condition, which is often more convenient to analyze and utilize. Besides the popular geometrically-derived criterion (μ > 1 or μ > 1), many other single-parameter criteria can be deduced that feature various specific advantages. One such criterion that is found to be most advantageous is the quasi-invariant single-parameter criterion (Kt > 1). With its simplistic form (like K), it can be shown that Kt > 1 if and only if a two-port network is unconditionally stable. The parameter Kt can be derived from the classical matrix invariants and the familiar stability criteria, leading to the straightforward proof of its unconditional stability condition. Moreover, it is invariant under arbitrary lossless termination and reactive matching at either port when unconditional stability exists. Such invariant property is retained so long as |△| < 1, which occurs more frequently than |△| > 1 for most microwave devices. The parameter can also be aptly related to the maximum available gain of an unconditionally stable device. Application of the quasi-invariant single-parameter criterion is extended for simplified graphical analysis of linear three-port stability. In particular, only one plot of a single-parameter condition needs to be constructed in each termination reflection plane. Such plot is useful to aptly depict the terminations at each port that result in unconditional stability between the remaining two ports. The three-port stability plots are exemplified to illustrate the convenience using the single-parameter condition. These stability plots find direct application in the stabilization of potentially unstable microwave networks.
Eng Leong Tan Xiaofeng Sun Kian Sen Ang
School of EEE,Nanyang Technological University,Singapore DSO National Laboratories,20 Science Park Drive,Singapore
国际会议
Progress in Electromagnetics Research Symposium 2009(2009年电磁学研究新进展学术研讨会)(PIERS 2009)
北京
英文
1524-1528
2009-03-23（万方平台首次上网日期，不代表论文的发表时间）