Inverse Modeling and Optimization of CSRR-Based Microwave Sensors for Industrial Applications

Tanveerul Haq, Slawomir Koziel

Research output: Contribution to journalArticlepeer-review


Design optimization of multivariable resonators is a challenging topic in the area of microwave sensors for industrial applications. This article proposes a novel methodology for rapid redesign and parameter tuning of complementary split-ring resonators (CSRRs). Our approach involves inverse surrogate models established using preoptimized resonator data as well as analytical correction techniques to enable rapid adjustment of geometry parameters and CSRR optimization over broad ranges of operating frequencies. The tuning process is arranged to precisely allocate the operating frequency while maximizing the quality factor of the circuit. The procedure is generic and characterized by an extremely low computational cost of up to two electromagnetic (EM) analyses of the circuit at hand (not counting the inverse model setup). The presented technique is demonstrated using a circular CSRR coupled to a microstrip transmission line (MTL) and optimized to operate between 5 and 20 GHz. The design optimized for 15 GHz is fabricated and experimentally validated using a vector network analyzer. The sensor works in the transmission mode and senses the shift in resonance frequency determined by the properties of the material under test (MUT). Furthermore, an inverse regression model is developed that allows for directly finding the unknown permittivity of the MUT based on the measured resonant frequencies of the sensor. The obtained results corroborate the design utility of the proposed optimization method, as well as the practical usefulness of the specific CSRR structure developed with the aid thereof.

Original languageEnglish
Pages (from-to)4796-4804
Number of pages9
JournalIEEE Transactions on Microwave Theory and Techniques
Issue number11
Publication statusPublished - 1 Nov 2022

Bibliographical note

Funding Information:
This work was supported in part by the Icelandic Centre for Research (RANNIS) under Grant 217771 and in part by the National Science Centre of Poland under Grant 2018/31/B/ST7/02369.

Publisher Copyright:
© 1963-2012 IEEE.

Other keywords

  • Circular complementary split-ring resonator (CSRR)
  • design optimization
  • electromagnetic (EM) simulation
  • inverse modeling
  • microwave sensor
  • permittivity


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