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Lagrangian formulation to investigate the effect of coupling on resonant microstrip transmission line

Published online by Cambridge University Press:  08 March 2022

Susanta Kumar Samanta ,
Rajib Pradhan Open the ORCID record for Rajib Pradhan [Opens in a new window]  and
Debapriyo Syam
Susanta Kumar Samanta
Affiliation:
Midnapore College, Midnapore 721101, India
Rajib Pradhan*
Affiliation:
Midnapore College, Midnapore 721101, India
Debapriyo Syam
Affiliation:
Guest Faculty, CAPSS, Bose Institute, Salt Lake, Kolkata 700091, India
*
Author for correspondence: Rajib Pradhan, E-mail: rjbpradhan@yahoo.co.in
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Abstract

An analytical and a numerical study on coupling in microstrip transmission line (MTL) are reported for different split-gap orientations of a single gap square-shaped split-ring resonator (SRR). Taking both magnetic and electric couplings and adopting Lagrangian formulation for this coupled system, mathematical relations are found for each orientation of SRR to determine the connection between coupling co-efficient and resonant mode frequency. It is shown that coupling results in higher resonance frequency when the SRR, with parallel split-gap, has the gap far from the MTL. But, a lower resonance frequency is obtained when the SRR is placed at shorter distances with parallel split-gap near to the MTL. Again, for perpendicular split-gap orientation of SRR, the resonant frequency is found in terms of an effective coupling co-efficient; at shorter distances it is found to be lower than the fundamental resonance frequency of uncoupled SRR and an opposite effect is obtained at longer distances. Using CST Microwave Studio, the resonance frequency for each split-gap orientation of SRR is also studied as a function of separation between MTL and SRR. It is observed that this phenomenon strongly depends on SRR side-length, substrate height, and separation between MTL and SRR.

Keywords

Filtersmicrostrip linemicrowavesresonancesensorssplit-ring resonatorterahertz
Type
EM Field Theory
Information
International Journal of Microwave and Wireless Technologies , Volume 15 , Issue 2 , March 2023 , pp. 298 - 310
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press in association with the European Microwave Association

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