基于回转器的电路中的奇异点与非线性高灵敏度振荡器
Exceptional Points in Gyrator-Based Circuit and Nonlinear High-Sensitivity Oscillator
AI总结：
本研究提出基于回转器耦合双LC谐振器（含负元件）简并奇异点的高灵敏度振荡器方案，利用其非线性实现稳定自激振荡，灵敏度优于同类LC谐振器及多数已发表EPD电路，且支持正负电容扰动检测，可用于高灵敏传感。
摘要：
我们提出了一种基于简并奇异点（EPD）的高灵敏度振荡器方案，该电路由两个通过回转器耦合的LC谐振器构成。振荡频率对电路元件（如电容器）的扰动非常敏感。我们假设两个谐振器之一由负值的电感器和电容器组成，给出了产生EPD的条件。通过证明EPD周围的本征频率分岔可由相关的Puiseux（分数幂）级数展开描述，我们验证了线性情况下EPD的存在性以及对扰动的灵敏度。我们还研究了系统中微小损耗的影响，表明它们会导致不稳定性。我们制作了该电路，并利用其不稳定性和非线性，在实验中观察到饱和状态下稳定的自激振荡。我们测量了电路对微小电容扰动的灵敏度。饱和后的振荡频率偏移可通过线宽为10 Hz的清晰可辨的谱峰很好地检测到，谱峰在低于峰值-70 dB的范围内仍保持干净。该灵敏度（i）高于同类简单LC线性谐振器的灵敏度，（ii）与其他已发表的EPD电路相当或更优，并且（iii）适用于电容扰动的负值和正值，这与PT对称电路中的情况不同。所提出的方案可为新一代用于测量物理、化学或生物量微小变化的高灵敏度传感器铺平道路。
英文摘要：
We present a scheme for high-sensitive oscillators based on an exceptional point of degeneracy (EPD) in a circuit made of two LC resonators coupled by a gyrator. The frequency of oscillation is very sensitive to perturbations of a circuit element, like a capacitor. We show conditions that lead to an EPD, assuming one of the two resonators is composed of an inductor and a capacitor of negative values. The EPD occurrence and sensitivity to perturbations in the linear case are demonstrated by showing that the eigenfrequency bifurcation around the EPD is described by the relevant Puiseux (fractional power) series expansion. We also investigate the effect of small losses in the system and show that they lead to instability. We fabricate the circuit, and exploit its instability and nonlinearity, observing experimentally stable self-oscillations under the saturated regime. We measure the circuit's sensitivity to a small capacitor perturbation. A shift in frequency of oscillation after saturation is well detectable with very distinct spectral peaks with 10 Hz linewidth, clean until -70 dB from the peak value. The sensitivity is (i) higher than the one of a comparable simple LC linear resonator, (ii) comparable or better than other published EPD circuits, and (iii) applicable to both negative and positive values of the capacitance perturbation, contrary to what happens in PT-symmetric circuits. The proposed scheme can pave the way for a new generation of high-sensitive sensors to measure slight variations in physical, chemical or biological quantities.
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