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A fundamental limit on the performance of geometrically-tuned planar resonators

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)1491 - 1499
Number of pages9
JournalIEEE Transactions on Microwave Theory and Techniques
Journal issue6
StatePublished - Jun 2011


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.

Additional information

Publisher: IEEE Rose publication type: Article Sponsorship: This research was jointly funded by EPSRC and MobileVCE. Terms of use: Copyright © 2011 IEEE. Reprinted with permission, from - A Naji, PA Warr; paper 'A fundamental limit on the performance of geometrically-tuned planar resonators';IEEE Transactions on Microwave Theory and Techniques; June 2011. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Bristol's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

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