Coupled Mode Theory Applied to Resonators in the Presence of Conductors

Abstract

Using the method of images, Energy Coupled Mode Theory (ECMT), a coupled mode equation in the frequency domain, is extended to deal with important cases where resonators are in close proximity to conducting surfaces. Depending on the type of conductors and the orientation of the resonators, the method of images determines the relative phases of the images. Using the formed images, the coupled frequencies and fields can be determined by applying ECMT. Two cases are studied. In the first case, it is shown that a dielectric resonator inserted in a cavity couples with both the mirror image and the cavity. The frequency behavior is described by the interaction with the image which counteracts that with the cavity. The second case is that of resonators sandwiched between conducting plates. It is shown that an infinite array of stacked images is formed. The coupling of the resonator with its images determines the coupled frequencies and fields. In this context, the main advantage of ECMT is its ability to separate the effects of the walls from the uncoupled system. This means that the system parameters are independent of the separation distances and/or the type of conductors, which renders the post processing analyses easier and predictable. Provided that the behaviors of the uncoupled resonators are known, ECMT is general and can be applied to more complex systems.

A Quantitative Analysis of Coupling for a WPT System Including Dielectric/Magnetic Materials

“…Coupling coefficient is a key parameter for many electric devices, such as microwave filters, electron paramagnetic resonance probes, stereometamaterials and WPT systems [13][14][15]. The coupling coefficient mainly describes the strength of energy exchange between the resonators.…”

Excitation of Asymmetric Resonance with Symmetric Split-Ring Resonator

“…Furthermore, the excitation of symmetric and asymmetric resonances was reported not only using metasurfaces with a large number of resonators, but also with a single resonator inside a rectangular waveguide system [ 47 , 48 , 49 ]. As a result of the coupling between the resonator inside the waveguide and its mirror images that were enabled by the metallic walls of the waveguide, the collective behavior of the full metasurface was achieved [ 50 , 51 , 52 ]. Moreover, the system was very compact, and the measurements were more robust compared with a full metasurface.…”

Magnetic and Electric Coupling Analysis for Angular Misalignment of Spiral Resonators in WPT Systems

“…No matter which coupling is utilized, it is necessary to maintain the strength of coupling between the transmitting and receiving elements at a certain level. Some research works have been reported on the study of electromagnetic coupling between RF devices [11][12][13][14][15]. Quantitative data on the electric and magnetic coupling components reveal the nature of coupling between the transmitting and receiving elements.…”