Article
Discussion and Analysis of Dumbbell Defect-Ground-Structure
(DB-DGS) Resonators for Sensing Applications from a Circuit
Theory Perspective
Lijuan Su , Paris Vélez , Jonathan Muñoz-Enano and Ferran Martín *
Citation: Su, L.; Vélez, P.;
Muñoz-Enano, J.; Martín, F.
Discussion and Analysis of Dumbbell
Defect-Ground-Structure (DB-DGS)
Resonators for Sensing Applications
from a Circuit Theory Perspective.
Sensors 2021, 21, 8334. https://
doi.org/10.3390/s21248334
Academic Editor: Qammer
Hussain Abbasi
Received: 5 November 2021
Accepted: 9 December 2021
Published: 13 December 2021
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4.0/).
CIMITEC, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain;
Lijuan.Su@uab.cat (L.S.); Paris.Velez@uab.cat (P.V.); Jonatan.Munoz@uab.cat (J.M.-E.)
* Correspondence: Ferran.Martin@uab.cat
Abstract:
Microstrip transmission lines loaded with dumbbell defect-ground-structure (DB-DGS)
resonators transversally oriented have been exhaustively used in microwave circuits and sensors.
Typically, these structures have been modelled by means of a parallel LC resonant tank series
connected to the host line. However, the inductance and capacitance of such model do not have a
physical meaning, since this model is inferred by transformation of a more realistic model, where the
DB-DGS resonator, described by means of a resonant tank with inductance and capacitance related to
the geometry of the DB-DGS, is magnetically coupled to the host line. From parameter extraction, the
circuit parameters of both models are obtained by considering the DB-DGS covered with semi-infinite
materials with different dielectric constant. The extracted parameters are coherent and reveal that
the general assumption of considering the simple LC resonant tank series-connected to the line to
describe the DB-DGS-loaded line is reasonable with some caution. The implications on the sensitivity,
when the structure is devoted to operating as a permittivity sensor, are discussed.
Keywords:
slot resonator; dumbbell defect-ground structure (DB-DGS); microwave sensor; parame-
ter extraction; microstrip technology
1. Introduction
The dumbbell defect-ground-structure (DB-DGS) resonator [
1
,
2
] is a slot resonator
exhaustively used in microwave engineering for the implementation of circuits (mainly fil-
ters [
3
–
9
]) and sensors [
10
–
13
]. DB-DGS resonators are typically combined with microstrip
transmission lines. The typical topology of a DB-DGS-loaded microstrip line is depicted
in Figure 1, where the resonant element is transversally etched in the ground plane. This
structure exhibits a notched response with a transmission zero at the fundamental reso-
nance frequency of the DB-DGS resonator, and the structure has been typically modelled
by means of a parallel resonant tank series-connected to the host transmission line [
1
,
2
]
(see Figure 1b).
The notched response of DB-DGS-loaded microstrip lines can be exploited for the
implementation of notch and stopband filters [
3
–
6
], as well as for the design of common-
mode filters in differential lines [
7
,
9
]. However, slot resonators, including the DB-DGS
resonator, are also of interest for the implementation of planar microwave sensors devoted
to permittivity measurements, and to the characterization of materials (including solids and
liquids) [
10
–
13
]. The reason is that the resonance frequency of these slot resonators is very
sensitive to the dielectric properties of the material surrounding the resonator (in contact or
in close proximity to it). Thus, the canonical output variable in these permittivity sensors
is the resonance frequency of the resonant element (and eventually the notch magnitude)
very sensitive to the permittivity of the so-called material under test (MUT).
Sensors 2021, 21, 8334. https://doi.org/10.3390/s21248334 https://www.mdpi.com/journal/sensors
