具有六阶模态异常简并的三梯集总电路
Triple Ladder Lumped Circuit with Sixth Order Modal Exceptional Degeneracy
摘要：
我们介绍了一种电路拓扑结构的基础上实现了一个简单的三阶梯电路与集总电抗元件，提供了一个六阶退化带边（6DBE）。6DBE是一种特殊的六阶例外点的退化在无损和无增益周期阶梯。这种简并在相位-频率色散图中提供了非常平坦的带边缘。所提出的拓扑结构具有独特的结构化的谐振功能与高负载的Q因子。利用S参数理论研究了无限长周期三阶梯结构中的Floquet-Bloch模及其色散关系。基于Puiseux级数展开，给出了简并点附近本征模和色散关系的近似解析表达式。我们调查的有限长度的结构终止与负载的滤波特性，以突出的特殊性能的6DBE相比，梯子与定期带边（RBE）和四阶退化带边（DBE）。这里介绍的6DBE电路框架可以用于设计新型高Q值振荡器、滤波器、传感器和脉冲整形网络。
英文摘要：
We introduce a circuit topology based on a simple triple-ladder circuit realized with lumped reactive components that provides a sixth order degenerate band-edge (6DBE). The 6DBE is a special kind of sixth-order exceptional point of degeneracy in a lossless and gainless periodic ladder. This degeneracy provides a very flat band edge in the phase-frequency dispersion diagram. The proposed topology exhibits unique structured resonance features associated with a high loaded Q-factor. We investigate the Floquet-Bloch modes in an infinite-length periodic triple-ladder and their dispersion relation using the S parameter formalism. We also provide the approximate analytic expressions of the eigenmodes and dispersion relation around the degenerate point based on the Puiseux series expansion. We investigate the filtering characteristics of a finite-length structure terminated with loads to highlight the special properties of the 6DBE compared to ladders with regular band edge (RBE) and fourth order degenerate band edge (DBE). The circuit framework introduced here with a 6DBE can be exploited in designing novel high Q-factor oscillators, filters, sensors, and pulse shaping networks.
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