Mode-localized sensors have attracted significant attention due to their exceptional sensitivity and inherent ability to reject common-mode noise. This high sensitivity arises from the substantial shifts in resonator amplitudes induced by energy confinement in weakly coupled resonators. Despite their promising attributes, there has been limited research on the mechanisms of energy confinement. This paper presents both qualitative and quantitative analyses of energy confinement within weakly coupled resonators and concludes them as the concept of modal dominance. This concept elucidates that mode frequencies are predominantly dictated by the natural frequencies of the internal resonators, facilitating spatial energy confinement. Based on this modal dominance, a novel concept of virtually coupled resonators is proposed, which obviates the need for physical coupling structures. Instead, energy confinement is achieved through a frequency offset between two independent resonators, resulting in a similar amplitude ratio output and enhanced sensitivity. To further enhance performance, a double-closed-loop control scheme is developed for virtually coupled resonators, expanding the bandwidth in comparison to weakly coupled resonators. Experimental results validate the feasibility of virtually coupled resonators and the double-closed-loop control, demonstrating a 2.7-fold improvement in amplitude ratio sensitivity and at least a four-fold enhancement in bandwidth relative to weakly coupled resonators with identical parameters.

模式定位传感器因其卓越的灵敏度和固有的抑制共模噪声的能力而引起了广泛关注。这种高灵敏度是由于弱耦合谐振器中的能量限制引起的谐振器振幅的大幅变化而产生的。尽管它们具有很好的特性，但关于能量限制机制的研究有限。本文对弱耦合谐振器内的能量限制进行了定性和定量分析，并将其总结为模态优势的概念。这个概念阐明了模式频率主要由内部谐振器的固有频率决定，从而促进了空间能量限制。基于这种模态优势，提出了一种虚拟耦合谐振器的新概念，它消除了对物理耦合结构的需求。相反，能量限制是通过两个独立谐振器之间的频率偏移来实现的，从而产生相似的振幅比输出和增强的灵敏度。为了进一步提高性能，为虚拟耦合谐振器开发了一种双闭环控制方案，与弱耦合谐振器相比，它扩展了带宽。实验结果验证了虚拟耦合谐振器和双闭环控制的可行性，表明相对于具有相同参数的弱耦合谐振器，振幅比灵敏度提高了 2.7 倍，带宽至少提高了 4 倍。