不共享公共接地的振荡器的同步
Synchronization of oscillators not sharing a common ground
摘要：
研究了不共用一个接地节点的耦合LC振荡器网络。电阻耦合和电感耦合被认为是。对于电阻耦合网络，它示出的振荡器耦合器互连必须是双层的，如果振荡器电压是渐近同步。此外，对于双层架构（当电阻和电感耦合器都存在时），提出了一种方法来计算表示整体耦合的复值有效拉普拉斯矩阵。证明了当且仅当有效拉普拉斯算子在虚轴上有单个特征值时，系统才具有同步行为。
英文摘要：
Networks of coupled LC oscillators that do not share a common ground node are studied. Both resistive coupling and inductive coupling are considered. For networks under resistive coupling, it is shown that the oscillator-coupler interconnection has to be bilayer if the oscillator voltages are to asymptotically synchronize. Also, for bilayer architecture (when both resistive and inductive couplers are present) a method is proposed to compute a complex-valued effective Laplacian matrix that represents the overall coupling. It is proved that the oscillators display synchronous behavior if and only if the effective Laplacian has a single eigenvalue on the imaginary axis.
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