A Fundamental Limit on the Performance of Geometrically-Tuned Planar Resonators

Geometric frequency tuning in planar electromagnetic resonators is common in many applications. It comes, however, at a penalty in the resonance quality, Q₀. The literature traces the causes of such penalty often in terms of the shortcomings in the added elements and materials, which were used to achieve the tuning. In this paper, however, it is shown that another underlying source of quality degradation exists at the fundamental geometric level. This source, unlike other added sources of degradation during tuning, will always exist (even before tuning takes place) and will rely on the “modal areas” of the geometric modifications made to host the tuning mechanism. Hence, it forms an upper bound to the performance that can be achieved from a geometically-tuned planar resonator, carries an important insight to resonator design in general, and significantly helps in the understanding of the problem of geometric tuning in particular. We present the electromagnetic theory behind this limit and canonically demonstrate it using practical microwave resonator examples. The theory, finite-element method simulation, and experiment results are presented and good agreement is observed. It is shown that incorporating such understanding into the design process of tunable planar resonators can help optimize their performance against a given set of design requirements. Furthermore, the presented theory provides a useful electromagnetic model as a tool for estimating Q₀ for geometrically modified or irregular metal patches and planar resonators in general, to assist analysis, and design at any wavelength or application. The theory also asserts that, under a given mode, a planar resonator will always have its maximum Q₀ before introducing any internal subtractive geometric modifications (e.g., cuts, apertures, or slits) to its original shape.