Analysis of Hybrid Meander Structures with Additional Shields
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electronics
Article
Analysis of Hybrid Meander Structures with Additional Shields
Diana Belova-Plonienė, Audrius Krukonis and Andrius Katkevičius *
Department of Electronic Systems, Vilnius Gediminas Technical University, 03227 Vilnius, Lithuania;
d.belova-ploniene@vilniustech.lt (D.B.-P.); audrius.krukonis@vilniustech.lt (A.K.)
* Correspondence: andrius.katkevicius@vilniustech.lt; Tel.: +370-5-274-4766
Abstract: Models of hybrid meander structures with additional shields are presented in this paper.
The influence of additional shields and their grounding positions on the electromagnetic characteris-
tics of the hybrid meander structures was investigated. Three-dimensional models were created and
analyzed using the method of moments (MoM) in the Sonnet® and finite-difference time-domain
(FDTD) method in CST Microwave Studio® commercial software packages. The computer-based
modeling was verified by physical experiment. The analysis showed that it is possible to control the
delay time characteristic using different values of lumped inductive elements without the need to
change the overall size of the hybrid meander structure. The delay time varied by 1.2 ns in the range
of 1.3 ns to 2.5 ns when the inductivity changed from 1 nH to 10 nH in our investigation. On the
other hand, the passband decreased from 2.384 GHz to 0.508 GHz. The additional shields and their
grounding positions allowed for increasing the passband by up to 1.6%.
Keywords: hybrid meander structure; microwave devices; electromagnetic characteristics; addi-
tional shields
Citation: Belova-Plonienė, D.;
Krukonis, A.; Katkevičius, A.
1. Introduction
Analysis of Hybrid Meander Meander structures are used in many microwave devices [1–3]. The most common ap-
Structures with Additional Shields. plication areas for meander structures are antennas [4], antenna arrays [5], phase shifters [6],
Electronics 2021, 10, 1583. https:// filters [7], and slow-wave structures. Meander structures are also used in resonator de-
doi.org/10.3390/electronics10131583 signs [8], pulse-forming lines [9], meandered superinductors [10], and others. One of
the main reasons for using meander structures is the ability to miniaturize a microwave
Academic Editor: Massimo Donelli device. Meander structures also have other specific advantages that are specific to the field
of application.
Received: 9 June 2021 For example, the task of antenna miniaturization was solved in [11]. The authors
Accepted: 28 June 2021
presented a compact and broadband coplanar waveguide-fed meander-slot antenna. A size
Published: 30 June 2021
of 30 × 20 mm2 was achieved using a modified meander slot, which was combined with a Y-
shape monopole and trident-shaped feed strip. The antenna was designed for WiFi, WiMax,
Publisher’s Note: MDPI stays neutral
and 5G applications and could work in a 2.33–3.56 GHz frequency range. A 1.6 mm thick
with regard to jurisdictional claims in
FR4 dielectric εr = 4.4 and tanδ = 0.02 substrate was used for the design. The width of the
published maps and institutional affil-
meander conductor varied between 0.5 mm and 0.9 mm at different locations. The meander
iations.
structure allowed for reducing the dimensions of the antenna and increasing the external
slot current path length and, as a result, for shifting the first resonance frequency to lower
frequencies. The maximum gain value of the proposed antenna was about 2 dBi around
3.4 GHz. The gain did not fall below 0.6 dBi over the entire bandwidth of interest. The
Copyright: © 2021 by the authors. dimensions of the microstrip patch IoT antenna were reduced using the s-shape meander
Licensee MDPI, Basel, Switzerland.
line in [12]. The overall dimensions of the antenna were 40 × 10 × 1.6 mm3 . The resonant
This article is an open access article
frequency of the antenna was 2.4 GHz. FR4 dielectric was used for the substrate. The
distributed under the terms and
authors focused on the selection of construction parameters to obtain optimal antenna
conditions of the Creative Commons
performance characteristics, such as antenna peak gain, efficiency, and higher fractional
Attribution (CC BY) license (https://
bandwidth. The chosen structure of the antenna also allowed for getting higher efficiency
creativecommons.org/licenses/by/
4.0/).
and gain in comparison with a conventional meander shape antenna. Miniaturization is
Electronics 2021, 10, 1583. https://doi.org/10.3390/electronics10131583 https://www.mdpi.com/journal/electronics
Electronics 2021, 10, 1583 2 of 16
also relevant in devices, which work in lower frequency ranges. A traditional monopole
antenna for a 140 MHz central frequency is huge and inconvenient to use. A 46% reduction
in size using a meander line monopole was presented in [13]. Fifteen meander sections had
an overall footprint of 293 × 64.5 mm2 . The width of a meander conductor was 2.9 mm.
The gap between adjacent conductors was equal to 5.9 mm. FR4 was used for the substrate.
The antenna was designed for specific low-frequency electromagnetic surveying systems.
The bandwidth of the antenna was 13 MHz, the directivity was 1.68 dBi, and the radiation
efficiency was 80.2%.
Meander structures are also popular in filter design. Meander lines as symmetrical
shunts were used in a vialess compact metamaterial band pass filter in [14]. The filter was
designed on an FR4 epoxy glass substrate with a dielectric constant of 4.4, a loss tangent of
0.02, and a thickness of 1.6 mm. The length of the meander line influenced the operating
frequency range of the filter and the group delay time, which varied from 0.5 ns to 0.75 ns
within the passband from 1.93 GHz to 4.3 GHz. The length of the meander conductor was
9.6 mm, the width of the conductor was 0.4 mm, and the gap between adjacent conductors
was also 0.4 mm. A measured insertion loss of 0.70 dB and a return loss higher than
25 dB with a 3 dB fractional bandwidth of 50.4% at a central frequency of 2.62 GHz were
obtained. A microstrip line filter with band stop characteristics is presented in [15]. The
miniaturization was achieved with a meander structure. The authors showed that the
increasing order of the filter improves the band rejection characteristics. A second-order
meander filter with a 2.4 GHz central frequency was fabricated and verified. The size of the
meander structure was 2 × 16.3 mm2 . The width of the meander conductor was 0.7 mm.
FR4 was used for the substrate.
Another big group of devices, which include meander structures, are slow-wave
structures. A novel configuration of a Ka-band slow-wave structure is presented in [16].
The presented structure includes a V-shaped microstrip meander line. The authors paid
great attention to the shape of the meander due to peculiarities of the manufacture. An even
greater focus on the manufacture was given in [17]. The presented slow-wave structure
was designed for a miniaturized traveling wave tube amplifier, which works in a V-band
or 50–70 GHz frequency range. The focus on the manufacture was relevant due to the
small size of the meander line. The width of the conductor and the gap between adjacent
conductors was only 50 µm. The thickness of the metalized conductor was only 1 µm. The
quartz εr = 3.75 substrate had only a 0.5 mm thickness. The authors discussed the methods
of magnetron sputtering and laser ablation for the manufacture. The presented slow-wave
structure provided a high slow-down factor (c/vph ~ 7–9); therefore, it could be used for
compact low-voltage traveling wave tubes.
Despite the positive properties of the meander structures, the structure of the meander
itself and the used materials may lead to negative features, such as higher fluctuation of
frequency characteristics and undesired pass or stop bands. For example, an extra size
reduction was achieved by combining meander line and Minkowski fractal techniques
in [18]. The central frequency of the designed filter was 2.4 GHz with a 429 MHz bandwidth.
The FR4 dielectric substrate was used in the design. The thickness of the substrate was 1.6
mm. The authors achieved a 1.6 dB insertion loss and a 17 dB return loss. The meander
structure allowed the reduction of the size by 52.77% in comparison with the initial design
of the filter. On the other hand, the appearance of multi-undesired bands was a negative
feature of the usage of the meander line. In this case, the undesired bands were eliminated
with Minkowski fractal geometries. The overall dimensions of the miniaturized filter were
14.18 × 13.01 mm2 .
Some authors do not focus on a specific application, but investigate the influence
of the design parameters of the meander on the frequency characteristics. A possible
improvement of the delay time characteristics by varying the constructive characteristics
is presented in [19]. The authors presented a multilayered meander line with additional
shields, which were grounded in the shielding conductor through vias. The authors claim
that additional shields and position of vias are very important to the operation of a meander
Electronics 2021, 10, 1583 3 of 16
delay line. The additional configuration reduced the coupling between the parallel lines
in the turn-up or in other word edge sections. The overall dimension of the delay line
was 50 mm. The length of the central adjacent conductors was 24.85 mm. The width of
the conductor was 0.3 mm. The gap between conductors varied from 0.15 to 1.2 mm. The
thickness of the dielectric substrate was 0.15 mm, and permittivity was εr = 4.6. According
to the authors, the additional shields helped to reduce the coupling between adjacent
conductors, which led to the reduction of fluctuation of the frequency characteristics.
The authors also presented models of the multilayered meander and multilayered hyper-
shielded meander lines. The idea was to move every second parallel conductor to the
bottom layer and to keep the shields between parallel conductors both in the top and
bottom layers. The new configuration allowed for increasing the shielding efficiency and
the passband of the structure. Various meander geometries were investigated in [20].
The authors presented a monolithic planar spin-valve sensor for high-sensitivity compass
applications. For a good signal-to-noise ratio, the authors used a bridge, which consisted
of a group of meanders. The focus of the study was to investigate how meander geometry
influences the electromagnetic properties of a sensor and sensor sensitivity.
There are many different meander structures investigated already. Meander structures
can also have a hybrid construction when the central electrode is planar and the connecting
electrodes are replaced with 3D coils, such as in [20]. A meander structure with 3D coils
allows the increase of the values of input impedance and delay time and the reduction of
the fluctuation of the phase velocity. The biggest disadvantage of meander structures with
3D coils is the quite large occupied area. A solution was proposed to replace the spiral coils
with contact plates in the PCB and to solder the inductors to the contact plates in order to
simulate the spiral coils [21]. These changes made it possible to reduce the dimensions but
maintain similar parameters of the hybrid meander structure. The delay time and input
impedance could be adjusted by varying the values of the inductors in the peripheral parts
of the meander structure. On the other hand, the coupling between adjacent conductors
had an impact on the passband of the hybrid meander structure. The passband decreased
when the inductance increased in the peripheral parts of the meander electrode.
A possible solution is to use additional shields. The additional shields in planar
meander structures have already been investigated in detail [22]. The additional shields
and their grounding positions allowed for configuring the passband and making it wider.
On the other hand, the investigations were usually performed using computer-based
modeling. Partial cases were investigated more often with lossless conductors.
There is still lack of information about hybrid meander structures with additional
shields. Therefore, the influence of the additional shields and their grounding positions
on the operation of a hybrid meander structure is investigated in this paper. We do not
focus on a specific application. The main goal is to clarify whether additional shields and
their grounding positions could be used in order to adjust the frequency characteristics of
the hybrid meander structures. The novelty of this work is the quantitative analysis of the
computer-based and experimental results of a hybrid meander structure with additional
shields. A hybrid meander structure without additional shields as a base model is taken
from our previous research studies [21]. The computer-based modeling results will be
compared with the results of a physical experiment.
2. Materials and Methods
Models of the hybrid meander structures with additional shields were investigated
using the Sonnet® (13.52, Sonnet Software, Inc., Syracuse, NY, USA, 2011) and CST Mi-
crowave Studio® (CST 2010, Dassault Systèmes, Paris, France) software packages. Sonnet®
is based on the method of moments (MoM), while CST Microwave Studio® is based on
the finite-difference time-domain (FDTD) method. Both methods have differences but
allow the achievement of the same goal. MoM belongs to a family of techniques that use
an integral form of Maxwell’s equations, while FDTD belongs to a family of techniques
that use a differential form of Maxwell’s equations. MoM is a frequency-based technique,
the achievement of the same goal. MoM belongs to a family of techniques that use an
integral form of Maxwell’s equations, while FDTD belongs to a family of techniques that
use a differential form of Maxwell’s equations. MoM is a frequency-based technique,
while FDTD is a time-domain technique. Ideas can be found in the scientific literature that
Electronics 2021, 10, 1583
more reliable results will be achieved if the computer-based modeling is performed with 4 of 16
two different methods, which belong to different families, based on the differentiation or
integration of Maxwell’s equations [23]. Therefore, two different software packages were
while FDTD
used in order to obtain more isreliable
a time-domain
resultstechnique. Ideas can be found
of the computer-based in the scientific
modeling literature that
and better
more reliable results will be achieved if the computer-based modeling is performed with
prepare for the physical experiment. We did not single out any method as superior in our
two different methods, which belong to different families, based on the differentiation or
case, and we did not analyze the MoM and FDTD methods themselves.
integration of Maxwell’s equations [23]. Therefore, two different software packages were
The simulation results
used were
in order also verified
to obtain by the
more reliable results
results of the
of the physical experiment.
computer-based modeling and better
prepare for the physical experiment. We did not single out any method as superior in our
2.1. Models of the Hybrid Meander
case, and we didStructure
not analyze the MoM and FDTD methods themselves.
The simulation results were also verified by the results of the physical experiment.
Models of the hybrid meander structure with additional shields and different
grounding positions 2.1.are presented
Models in Figure
of the Hybrid Meander 1. Structure
First of all, these models were designed in
the Sonnet commercial
® software
Models of thepackage. The main
hybrid meander dimensions
structure of the meander
with additional shields andstructure
different ground-
with additional shields were as
ing positions arefollows:
presented thein length
Figure 1.of First
the hybrid meander
of all, these modelsstructure, L = in the
were designed
Sonnet ®
20.28 mm; the width of thecommercial softwarestructure,
hybrid meander package. The 2a =main dimensions
10 mm; of the
the length ofmeander
the addi- structure
with additional shields were as follows: the length of
tional electrodes, c = 6 mm; the width of the meander electrode, Lc = 0.35 mm; the gap the hybrid meander structure, L
= 20.28 mm; the width of the hybrid meander structure, 2a = 10 mm; the length of the
between adjacent conductors, l = 0.7 mm; the width of the shields, Ls = 0.15; the thickness
additional electrodes, c = 6 mm; the width of the meander electrode, Lc = 0.35 mm; the gap
of the substrate, hsbetween
= 0.2 mm; the thickness
adjacent conductors,ofl =the
0.7conductors,
mm; the width hcof= the
0.035 mm.LAn
shields, FR4 ma-
s = 0.15; the thickness
terial was used forofthe
thesubstrate
substrate, where
hs = 0.2εmm;
r = 4.8theand tanδ =of0.02.
thickness Copper was
the conductors, hc =used
0.035for
mm.theAn FR4
conductor, whose inductivity was equal to 5.8 × 10 S/m. r
material was used for the substrate 7
where ε = 4.8 and tanδ = 0.02. Copper was used for
the conductor, whose inductivity was equal to 5.8 × 107 S/m.
1 2
5 3
4
6
7
(a) (b)
L
2a
4
4
c b
2 Lc l d
Ls
(c) (d)
FigureFigure 1. Three-dimensional
1. Three-dimensional views
views of the of meander
hybrid the hybrid meander
structure whenstructure
additional when
shields additional
are groundedshields areend,
in (a) one
grounded
(b) both ends, (c)in
the(a) one end,
middle (b)the
and (d) both ends,of(c)
top view the meander
hybrid middle and (d) the
structure withtop view of
grounded hybrid
in the meander
middle additional
shields when L = 20.28 mm, 2a = 10 mm, c = 6 mm, Lc = 0.35 mm, l = 0.7 mm, Ls = 0.15 mm, b = 0.9 mm, d = 0.46mm,
structure with grounded in the middle additional shields when L = 20.28 mm, 2a = 10 mm, c = mm,hs =
0.2 mm, and hc = 0.035 mm and where 1 is the meander-shape conductor, 2 is the lumped element, 3 is the additionalmm
Lc = 0.35 mm, l = 0.7 mm, Ls = 0.15 mm, b = 0.9 mm, d = 0.4 mm, hs = 0.2 mm, and hc = 0.035 shield,
4 is the grounded via, 5 is the air, 6 is the dielectric substrate, and 7 is the grounded external shield.
and where 1 is the meander-shape conductor, 2 is the lumped element, 3 is the additional shield, 4
is the grounded via, 5 is the air, 6 is the dielectric substrate, and 7 is the grounded external shield.
Electronics 2021, 10, 1583 5 of 16
A model of the hybrid meander structure with grounding in one end of the additional
shields is presented in Figure 1a. The grounding in both ends of the additional shields is
presented in Figure
A model of the1b. The meander
hybrid grounding only with
structure in the middle in
grounding ofone
theend
additional shields is pre-
of the additional
sented in Figure
shields 1c. A
is presented 2D top
in Figure 1a.view of the hybrid
The grounding in bothmeander
ends of thestructure
additional with
shieldsadditional
is
shields, whichinare
presented grounded
Figure in the middle,
1b. The grounding is the
only in presented
middle ofintheFigure 1d. The
additional connecting
shields is pre- elec-
sented
trodes in Figure
of the meander1c. A were
2D topreplaced
view of the hybrid
with themeander
lumped structure withelements
inductive additional in
shields,
the periph-
which are grounded in the middle, is presented in Figure 1d. The connecting electrodes of
eral parts of the meander. A zoomed lumped inductive element is shown in Figure 1d.
the meander were replaced with the lumped inductive elements in the peripheral parts of
The hybrid meander structure was estimated based on the S21 transmission and S11
the meander. A zoomed lumped inductive element is shown in Figure 1d.
reflectionTheparameters.
hybrid meander In addition,
structure input impedance
was estimated basedZon
IN and delay
the S21 time td characteristics
transmission and S11
werereflection
presented during In
parameters. theaddition,
investigation. The values
input impedance of the
ZIN and inductive
delay components were
time td characteristics
changed from 1 to during
were presented 10 nH thewith a step of 1 The
investigation. nH.values of the inductive components were
changed from 1 to 10 nH with a step of 1 nH.
The computer-based modeling was also repeated in the CST Microwave®Studio®
The computer-based modeling was also repeated in the CST Microwave Studio
commercial software package, which is based on the finite-difference time-domain
commercial software package, which is based on the finite-difference time-domain method.
method.
The hybridhybrid
The meandermeander structure
structure with withshields,
additional additional
which shields, which
are grounded aremiddle,
in the grounded in
the middle, is presented
is presented in Figure 2.in Figure 2.
Figure 2.Figure
Three-dimensional viewview
2. Three-dimensional of hybrid meander
of hybrid meanderstructure withgrounded
structure with grounded in the
in the middle
middle additional
additional shieldsshields
in CST in CST
Microwave Studio®.
Microwave Studio®.
®
TheThe same
same design and
design and material
material parameters werewere
parameters maintained as in the as
maintained Sonnet
in thesoftware
Sonnet® soft-
package. All the design and material parameters during the computer-based modeling
warewere
package. All the design and material parameters during the computer-based mod-
selected based on the ability to repeat the experiment physically.
eling were selected based on the ability to repeat the experiment physically.
2.2. Models for Experimental Investigation
2.2. Models
Thefor Experimental
PCB meander structure was designed in the Altium Designer®
Investigation
of the hybrid
(Altium Designer 2010, Altium, La Jolla, CA, USA, 2010) software package. The design pa- ®
The PCB of the hybrid meander structure was designed in the Altium Designer (Al-
rameters were used similarly as in the modeling procedure. To be more precise, the design
tiumparameters
Designerwere
2010, Altium,
taken La Jolla,
into account CA,the
during USA, 2010) software
computer-based package.
modeling The design pa-
stage according
rameters were used similarly
to recommendations from theasmanufacturer
in the modeling
about procedure. To besizes
minimal possible moreandprecise, the design
materials.
parameters were taken into account during the computer-based modeling stage according
to recommendations from the manufacturer about minimal possible sizes and materials.
Electronics 2021, 10, 1583 6 of 16
The contact plates, which represent the positions of the lumped inductive elements,
are presented in Figure 3a. Positions of vias in the middle and ends of the additional shields
are drilled and visible in the top-view PCB image. The universal PCB is prepared with all
holes already drilled in the factory.
PEER REVIEW The overall dimensions of the prototype plate were 32 × 32 mm2 . All other parameters
6 of 16
were the same as in the modeling procedure. The length of the hybrid meander structure
was L = 20.28 mm, the width 2a = 10 mm, the length of the additional electrodes c = 6 mm,
the width of the meander electrode Lc = 0.35 mm, the gap between adjacent conductors
l = 0.7 mm, the width of the shields Ls = 0.15, the thickness of the substrate hs = 0.2 mm,
The contact plates,
andwhich represent
the thickness the positions
of the conductors of mm.
hc = 0.035 the lumped inductive
An FR4 Kingboard tg150elements,
material was
are presented in Figure 3a. Positions of viasr in the middle and ends of the additional
used for the substrate where ε = 4.8 and tanδ = 0.02. Copper was used for the conductor,
whose inductivity was 5.8 × 107 S/m. The diameter of the drilled holes was 0.3 mm. The
shields are drilled and visible in the top-view PCB image. The universal PCB is prepared
manufactured prototype of the hybrid meander structure is presented in Figure 3b. SMA
with all holes already connectors
drilled inweretheused
factory.
for the connection.
(a) (b)
Figure 3. TheFigure
(a) PCB model
3. The (a) PCBand (b)and
model manufactured
(b) manufacturedprototype
prototype ofof
thethe hybrid
hybrid meander
meander structure.structure.
Two different types of ground metallization were used during the physical investiga-
The overall dimensions
tion. Theof the
first prototype
variant plate
was made whenwere 32 × 32 mm
the grounding 2. All other parameters
was in the middle of the additional
were the same as in the modeling procedure. The length of the hybridboth
shields. The second variant was when the grounding was in ends of the
meander additional
structure
shields of the hybrid meander structure.
was L = 20.28 mm, the width 2a = 10 mm, the length of the additional electrodes c = 6 mm,
Prototypes with different values of the lumped inductive elements were made. Proto-
the width of the meandertypeselectrode
with 1 nH, 5.1LcnH,
= 0.35 mm,
and 10 the gapare
nH elements between
presentedadjacent conductors
for discussion. l=
SMD inductors
0.7 mm, the width of theof a 0402 case were
shields Ls =used. The
0.15, S11 thickness
the reflection andofS21the
transmission
substrate parameters
hs = 0.2were
mm, measured
and
using an LA19-13-04A vector network analyzer (VNA). The delay time td characteristic
the thickness of the conductors hc = 0.035 mm. An FR4 Kingboard tg150 material was used
was calculated from S21 phase characteristics. A block diagram of an experimental mea-
for the substrate where εr = 4.8ofand
surement tanδ meander
the hybrid = 0.02. Copper
structure iswas usedinfor
presented the4a.
Figure conductor, whose
A general photograph
inductivity was 5.8 × 10 S/m. The diameter of the drilled holes was 0.3 mm. The manu-
of the
7 experiment is presented in Figure 4b.
the An
factured prototype of measuring LA19-13-04A vector analyzer has an 8.5 GHz frequency range and is capable of
hybrid meander structure is presented in Figure 3b. SMA con-
the required S parameters. The calibration phase and obtaining of the results
nectors were used for were
the connection.
performed using the recommendations of the manufacturer.
Two different types of ground metallization were used during the physical investi-
gation. The first variant was made when the grounding was in the middle of the additional
shields. The second variant was when the grounding was in both ends of the additional
shields of the hybrid meander structure.
PC with USB Vector
measurement Interconnect Network
Electronics
Electronics 2021, 10, x10,
2021, FOR1583
PEER REVIEW 7 of 167 of 16
software Analyzer 4
LA19-13-04B
USB Vector 3
PC with
Interconnect Network 2
measurement
software Analyzer 4
LA19-13-04B
1
3
(a) 2 (b)
Figure 4. (a) A block diagram of an experimental measurement of the hybrid meander structure and (b) a general photo-
graph of the experiment, where 1 is the hybrid meander structure
1 with additional shields, 2 are SMA connections, 3 is a
vector network analyzer, and 4 is a computer with the measurement software.
An LA19-13-04A vector analyzer has an 8.5 GHz frequency range and is capable of
(a) (b)
measuring the required S parameters. The calibration phase and obtaining of the results
Figure
Figure (a)block
4. (a)4.A A block
diagram were
diagramofofanperformed
an using
experimental
experimental the recommendations
measurement
measurementof the
of hybrid ofmeander
the
meander
the hybrid manufacturer.
structure and (b) aand
structure general
(b) photograph
a general photo-
graphofof
thethe
experiment, where
experiment, 1 is the
where 1 ishybrid meander
the hybrid structure
meander with additional
structure shields, 2 shields,
with additional are SMA2connections, 3 is a vector 3 is a
are SMA connections,
network analyzer, and 4 3.
is a Results
computer with the measurement software.
vector network analyzer, and 4 is a computer with the measurement software.
Models of the hybrid meander structures were investigated by computer-based mod-
3. Results
elingAn LA19-13-04A
using the Sonnet®vector
and CSTanalyzer
Microwavehas an 8.5 GHz
Studio frequency
® commercial range and
software is capable
packages. The of
resultsModels
measuring of the computer-based
theof the hybridSmeander
required modeling were
structures
parameters. The compared
were investigated
calibration with
phase the
andresults
by computer-based of the
obtaining ofphysical
modeling
the results
using the Sonnet®using
experiment.
were performed and CST
the Microwave Studio® commercial
recommendations software packages. The results of
of the manufacturer.
the computer-based modeling were compared with the results of the physical experiment.
3.1.
3. Results of Computer-Based Modelling
Results
3.1. Results of Computer-Based Modelling
A comparison
Models of the results
of the hybrid meander of the hybrid meander
structures structuresby
were investigated without and with ad-
computer-based
A comparison of the results of the hybrid meander structures without and with addi- mod-
ditional
eling usingshields is presented
theisSonnet in Figure 5. The results of the S 11 , S 21 , t d,
® and CST Microwave Studio® commercial software packages. Theand ZIN characteristics
tional shields presented in Figure 5. The results of the S11 , S21 , td , and ZIN characteristics
were
results obtained using
using the computer-based
the
of the computer-based
were obtained modeling
modelingmodeling
computer-based ininthe
were compared theSonnet
Sonnet
with ®® software
the results
software package.
of the physical
package.
experiment.
Frequency (GHz)
0 0.5 3.1. Results
1 of
1.5Computer-Based
2 2.5 Modelling
3 3.5 4 4.5 5
0
A comparison of the results of the hybrid meander structures without and with ad-
ditional shields is presented in Figure 5. The results of the S11, S21, td, and ZIN characteristics
–3 were obtained using the computer-based modeling in the Sonnet® software package.
–5
Frequency (GHz)
S21 (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
2.422 GHz
1.407 GHz
–10 1.408 GHz
–3 1.415 GHz
2.384 GHz
–5 1.398 GHz
S21 (dB)
–15
Without shields: 1 nH 5 nH 10 nH.
Grounded in the midlle: 1 nH, 5 nH, 10 nH. 2.422 GHz
1.407 GHz
Grounded in both ends: 5 nH.
–10 Grounded in one end:1.4085GHz
nH.
1.415 GHz
(a) 2.384 GHz
1.398 GHz
Figure 5. Cont.
–15
Without shields: 1 nH 5 nH 10 nH.
Grounded in the midlle: 1 nH, 5 nH, 10 nH.
Grounded in both ends: 5 nH.
Grounded in one end: 5 nH.
Electronics
Electronics 10,10,
2021,
2021, 1583 PEER REVIEW
x FOR 8 of
8 16
of 16
Frequency (GHz)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
–3
–5
–10
S11 (dB)
–15
–20
–25
–30
Without shields: 1 nH 5 nH 10 nH.
Grounded in the midlle: 1 nH, 5 nH, 10 nH.
Grounded in both ends: 5 nH.
Grounded in one end: 5 nH.
(b)
2.042 ns
3.5
2.040 ns
2.039 ns
3
2.032 ns
2.5
td (ns)
2
1.328 ns
1.5 1.321 ns
1
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Frequency (GHz)
Without shields: 1 nH 5 nH 10 nH.
Grounded in the midlle: 1 nH, 5 nH, 10 nH.
Grounded in both ends: 5 nH.
Grounded in one end: 5 nH.
(c)
Figure 5. Cont.
Electronics 2021,
Electronics 10, 10,
2021, x FOR
1583PEER REVIEW 9 9of of
16 16
300
250
200
ZIN (Ω)
150
100
50
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Frequency (GHz)
Without shields: 1 nH 5 nH 10 nH.
Grounded in the midlle: 1 nH, 5 nH, 10 nH.
Grounded in both ends: 5 nH.
Grounded in one end: 5 nH.
(d)
Figure 5. Computer-based
Figure 5. Computer-based modeling
modelingresults
resultsfrom Sonnet®® of
from Sonnet of the (a)
(a) SS2121,, (b)
(b)SS1111,,(c)
(c)tdtd, ,and
and(d)
(d)ZZ characteristics
ININcharacteristics ofof
thethe
hybrid meander
hybrid structures
meander without
structures and
without andwith
withadditional
additionalshields
shields grounded
grounded in in the
the middle,
middle,one oneend,
end,ororboth
bothends
ends when
when thethe
lumped inductive
lumped elements
inductive obtain
elements values
obtain valuesofof1,1,5,5,and
and10
10nH.
nH.
First,aacomparison
First, comparison was wasperformed
performed when
whenthethe
values of the
values oflumped inductive
the lumped elements
inductive ele-
varied
ments and were
varied and wereequalequal
to 1 nH,
to 1 5nH,
nH,5 and
nH, 10
andnH,10 while the grounding
nH, while the groundingposition was in
position was
in the
themiddle.
middle.Second,
Second,the theinfluence
influenceofofthe
thegrounding
groundingpositions
positions was
was investigated
investigated with
withthethe
constant 5 nH lumped elements and grounding positions in the middle,
constant 5 nH lumped elements and grounding positions in the middle, one end, and both one end, and both
ends
ends ofof
thetheadditional
additionalshields.
shields.
First of all, the results confirm that the inductance of lumped elements affects the
First of all, the results confirm that the inductance of lumped elements affects the
passband of the hybrid meander structure. The cutoff frequency is 2.384 GHz when 1 nH
passband of the hybrid meander structure. The cutoff frequency is 2.384 GHz when 1 nH
lumped inductive elements are used. The passband is 1.398 GHz when 5 nH lumped
lumped inductive elements are used. The passband is 1.398 GHz when 5 nH lumped in-
inductive elements are used. The passband decreases to 0.508 GHz when 10 nH lumped
ductive elements
inductive elements areareused.
used.The passband
These decreases
changes are to 0.508
clearly visible GHz
in the when
5 GHz 10 nH lumped
frequency range
inductive elements are used. These changes are clearly visible in the
in Figure 5a. The curves without and with additional shields and with the same inductance 5 GHz frequency
range in Figure
of lumped 5a. The
elements curves
almost without
overlap. and with
Therefore, the additional shields
groups of curves andthe
with with
samethe1 nH
same
inductance
and 5 nH inductances of lumped elements are zoomed near the cutoff frequencies forthe
of lumped elements almost overlap. Therefore, the groups of curves with
same 1 nH
better and 5 nH inductances of lumped elements are zoomed near the cutoff frequen-
visibility.
cies forMoreover,
better visibility.
the passband varied by no more than 38 MHz when models of the hybrid
meander
Moreover, structures with andvaried
the passband withoutby additional
no more than shields werewhen
38 MHz compared.
models For
of example,
the hybrid
the passband was increased by 38 MHz up to 2.422 GHz when
meander structures with and without additional shields were compared. For example, the additional shieldsthe
were added to the hybrid meander structure with 1 nH
passband was increased by 38 MHz up to 2.422 GHz when the additional shields lumped elements. This is were
an
improvement of about 1.6% when compared with the overall
added to the hybrid meander structure with 1 nH lumped elements. This is an improve- passband of the hybrid
meander
ment structure.
of about 1.6% whenThe improvement
compared withof thethe
passband
overalldecreases
passbandwhen of thethehybrid
inductance
meanderof
lumped elements increases. The passband was increased only by 17 MHz up to 1.415 GHz
structure. The improvement of the passband decreases when the inductance of lumped
when 5 nH lumped elements were used. This is an improvement of about 1.2%. The case
elements increases. The passband was increased only by 17 MHz up to 1.415 GHz when
with 10 nH lumped elements showed an improvement of only 7 MHz, but this variant is
5 nH lumped elements were used. This is an improvement of about 1.2%. The case with
not zoomed in Figure 5a.
10 nH lumped elements showed an improvement of only 7 MHz, but this variant is not
zoomed in Figure 5a.Electronics 2021, 10, 1583 10 of 16
The influence of the grounding positions of the additional shields on the passband
of the hybrid meander structure was investigated when 5 nH lumped elements were
used. The best results with a 17 MHz improvement up to 1.415 GHz were obtained
when the additional shields were grounded in the middle. The grounding in both ends
of the additional shields gave a 10 MHz improvement. The worst result with a 9 MHz
improvement was obtained when the additional shields were grounded only in one end.
The results also confirm that the delay time td depends on the value of the inductivity
of lumped elements. A positive feature is that the inductive lumped elements allow for
changing the delay time without changing the dimensions of the hybrid meander structure.
In this particular case study, if the delay time is equal to 1.321 ns, then the inductivity is
equal to 1 nH. The delay time increases more than twice to 2.5 ns when the inductivity
increases to 10 nH. The delay time is almost constant in the entire frequency range when
1 nH lumped elements are used.
The additional shields also effected the delay time characteristic. The td decreased
by 7 ps at a 2.422 GHz cutoff frequency when 1 nH lumped elements were used. The td
decreased by 10 ps at a 1.412 GHz cutoff frequency when 5 nH lumped elements were used.
In both cases, the shields were grounded in the middle. The grounding position in one or
both ends of the additional shields gave decreases of delay time by 3 and 2 ps, respectively,
when 5 nH lumped elements were used.
To sum up, the additional shields and their grounding positions had an impact on
the frequency characteristics of the hybrid meander structure. On the other hand, the
impact was very small and not as clearly visible as in the planar meander structures. The
computer-based modeling using Sonnet® showed that a variation in the inductance of
lumped elements in the range of 1 to 10 nH allows for changing the width of the passband
only in the range of 1.6%.
We think that the main reason for this is that the lumped inductive elements affect the
characteristic impedance of the line, and there is no more matching between the meander
line, generator, and load resistors. With the initial design parameters without the lumped
elements, the characteristic impedance was matched to the generator and load resistors and
was 50 Ω. The broken matching condition can be seen from the S11 reflection parameter
in Figure 5b and the input impedance parameter in Figure 5d. The input impedance is
higher in lower frequencies up to 2 GHz. The input impedance decreases with an increase
in frequency until the stop band appears. The fluctuation of the input impedance is bigger
in lower frequencies.
3.2. Results of Physical Experiment
The computer-based modeling was also repeated in the CST Microwave Studio® soft-
ware package before moving to the physical experiment. The experimental investigation
was made according to the PCB and prototype, which are presented in Figure 3. The
procedure for the measurements is discussed in the previous section in Figure 4.
The computer-based modeling and measurements were repeated many times with
different initial parameters of lumped elements and grounding positions of the additional
shields. Results, which were obtained using the computer-based modeling in Sonnet®
and CST Microwave Studio® , were verified by the physical experiment. For clarity, the
computer-based modeling and experimental results are compared by presenting only
one separated case in Figure 6. The inductivity of lumped elements was 5 nH, and the
additional shields were grounded in the middle position in this separated case. This case
summarizes and perfectly reflects all the other cases during the investigation.
The results of S21 are presented in Figure 6a. The cutoff frequency of the physical
experiment with 5 nH lumped elements is 1.17 GHz. This is less by 180 MHz in comparison
with the results obtained using CST Microwave Studio® and less by 240 MHz in comparison
with the results obtained using Sonnet® . The differences between the results become
smaller when the inductance of lumped elements increases.Electronics 2021, 10,
Electronics2021, 10,1583
x FOR PEER REVIEW 11 of
11 of 16
16
Frequency (GHz)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
–1
–2
–3
–4
S21 (dB)
1.17 GHz
–5
1.35 GHz
–6
1.41 GHz
–7
–8
–9
–10
Measurement, 5.1 nH Sonnet®, 5 nH CST Microwave Studio®, 5 nH
(a)
Frequency (GHz)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
–3
–5
–10
S11 (dB)
–15
–20
–25
–30
Measurement, 5.1 nH Sonnet®, 5 nH CST Microwave Studio®, 5 nH
(b)
Figure 6. Cont.Electronics 2021, 10, 1583 12 of 16
Electronics 2021, 10, x FOR PEER REVIEW 12 of 16
3
2.5
2.22 ns
td (ns)
2.09 ns
2
2.03 ns
1.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Frequency (GHz)
Measurement, 5.1 nH Sonnet®, 5 nH CST Microwave Studio®, 5 nH
(c)
Figure
Figure6.6.Comparison
Comparisonofofthe
thecomputer-based
computer-basedmodeling
modelingresults
results from
from Sonnet
Sonnet®and
®
andCST
CSTMicrowave
MicrowaveStudio
Studio®with
®
withthe
theresults
results
of the physical experiment of the (a) S21, (b) S11, and (c) td characteristics of the hybrid meander structure when the lumped
of the physical experiment of the (a) S21 , (b) S11 , and (c) td characteristics of the hybrid meander structure when the lumped
inductive elements are 5 nH.
inductive elements are 5 nH.
The
Theresults
resultsof ofSthe
21 are presented in Figure 6a. The cutoff frequency of the physical
delay time characteristic are presented in Figure 6c. The td was
experiment with 5 nH
2.22 ns at a 1.17 GHz cutoff lumped elements
frequency is 1.17
during GHz.
the This experiment.
physical is less by 180TheMHz td =in2.09
compari-
ns was
son with the results obtained using CST
® Microwave Studio ® and less by 240 MHz in com-
obtained in CST Microwave Studio at a 1.35 GHz cutoff frequency and the td = 2.03 ns in
parison
Sonnet®with at a the
1.41results obtained
GHz cutoff using Sonnet
frequency. ZIN was. The
® differences
not included in between the results
the comparison be-
because
come smaller when
the influence of thethe inductance
additional of lumped
shields elements
and their increases.
grounding positions on the frequency
The resultsof
characteristics ofthe
thehybrid
delay time characteristic
meander structurearewas presented
seen from inthe
Figure 6c. The
S11 and S21 tparameters
d was 2.22
ns at a 1.17 GHz
and td characteristic. cutoff frequency during the physical experiment. The t d = 2.09 ns was
obtained in CST Microwave Studio ® at a 1.35 GHz cutoff frequency and the td = 2.03 ns in
All the results that were obtained with the computer-based modeling and the physical
Sonnet ® at a 1.41 GHz cutoff frequency. ZIN was not included in the comparison because
experiment correlate with each other. Only the additional two cases with the results of
the
theinfluence
measurement of theareadditional
presentedshields
in Figureand7 their grounding
in order to revealpositions on the
the influence frequency
of grounding
characteristics
positions on the of additional
the hybrid shields.
meander structure was seen from the S11 and S21 parameters
and tdThecharacteristic.
results of S21 when the grounding position is in the middle or in both ends of the
All the shields
additional results that were obtained
are presented with7a.
in Figure theThe
computer-based
cutoff frequency modeling
is higherandbythe 130physi-
MHz
cal
andexperiment
is 2.38 GHz correlate
when the with each other.
additional Onlyare
shields thegrounded
additionalintwothecases
middlewithin the
theresults of
case with
1 nH
the lumped element.
measurement The difference
are presented in Figureis7only 6 MHz
in order in thethe
to reveal case when 10
influence of nH lumped
grounding
elementson
positions aretheused. The td isshields.
additional higher by 90 ps and is 1.53 ns when the grounding position of
the additional shields is in the middle when 1 nH lumped elements are used. The results
of the measurements confirmed the results of the computer-based modeling. The higher
the inductance is in the lumped elements, the lower the influence of the additional shields
and their grounding positions is.Electronics 2021, 10,
Electronics 2021, 10, 1583
x FOR PEER REVIEW 13of
13 of 16
16
Frequency (GHz)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
–1
–2
–3
–4
S21 (dB)
2.25 GHz
–5 2.38 GHz
0.294 GHz
–6
0.288 GHz
–7
–8
–9
–10
Measurement, grounded in the midlle: 1 nH, 10 nH.
Measurement, grounded in both ends: 1 nH, 10 nH.
(a)
Frequency (GHz)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
–3
–5
S11 (dB)
–10
–15
–20
Measurement, grounded in the midlle: 1 nH, 10 nH.
Measurement, grounded in both ends: 1 nH, 10 nH.
(b)
Figure 7. Cont.Electronics 2021, 10, 1583 14 of 16
Electronics 2021, 10, x FOR PEER REVIEW 14 of 16
4
3.5
3
td (ns)
2.5
2.65 ns
2.644 ns 1.44 ns
2
1.53 ns
1.5
1
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Frequency (GHz)
Measurement, grounded in the midlle: 1 nH, 10 nH.
Measurement, grounded in both ends: 1 nH, 10 nH.
(c)
Figure
Figure7.7.Results
Resultsof
ofthe
thephysical
physicalexperiment
experiment of
of the
the (a)
(a) SS2121, ,(b)
(b)SS1111
, and
, and(c)
(c)tdtdcharacteristics
characteristicsofofthe
thehybrid
hybridmeander
meanderstructure
structure
when
when the lumped inductive elements have values of 1 and 10 nH and the additional shields are grounded ininthe
the lumped inductive elements have values of 1 and 10 nH and the additional shields are grounded the middle
middle or
or in both ends of the additional shields.
in both ends of the additional shields.
The results of S21 when the grounding position is in the middle or in both ends of the
4. Discussion
additional shields are presented in Figure 7a. The cutoff frequency is higher by 130 MHz
and isOur 2.38previous
GHz when research showed shields
the additional positiveare features
groundedwhere lumped
in the middleinductive
in the caseelements
with
1allow the increase
nH lumped element.of theThevalues of theisinput
difference onlyimpedance
6 MHz in the andcase
delaywhentime 10without
nH lumped changing
ele-
the dimensions of the overall structure. On the other hand, such
ments are used. The td is higher by 90 ps and is 1.53 ns when the grounding position of hybrid systems would
also
the have negative
additional shieldsproperties.
is in the middleIncreasing
when the 1 nHinductance at the edges
lumped elements of the
are used. Themeander
results
line reduces the passband because of the matching issues
of the measurements confirmed the results of the computer-based modeling. The between the line impedance
higher
and
the the generator
inductance andlumped
is in the load resistors.
elements,In thesome
lower cases, for example,
the influence of thein planar meander
additional shields
structures,
and the coupling
their grounding between
positions is. adjacent conductors could be reduced by using additional
shields. Therefore, it was necessary to research the influence of additional shields and their
4.grounding
Discussion positions on the frequency characteristics of the hybrid meander structures.
The results, which were presented in the previous section, showed that it is possible to
Our
adjust theprevious
operation research showed
of the hybrid positive
meander featuresbywhere
structure lumped
replacing inductive electrodes
the connecting elements
allow the increase of the values of the input impedance and
with lumped inductive elements. The delay time could be controlled by varying the delay time without changing
the dimensions
inductance of the overall
of lumped elements structure.
withoutOn thethe
need other hand, the
to change suchdimensions
hybrid systemsof the would
hybrid
also
meander structure. In our experiment, the delay time varied by approximately 1.2 ns inline
have negative properties. Increasing the inductance at the edges of the meander the
reduces
range ofthe 1.3passband because
to 2.5 ns when theofinductance
the matching wasissues
changedbetween
from the1 toline impedance and the
10 nH.
generator
On the andother
load hand,
resistors.
the In some cases,
increase for example,
in inductance in planar
in lumped meander
elements structures,
decreased the
the coupling between adjacent conductors could be reduced by
passband. The additional shields had an impact and increased the passband, but the in- using additional shields.
Therefore,
crease wasitnot was necessary
significant. Thetoimprovement
research theofinfluence
the passbandof additional
was no more shields and when
than 1.6% their
grounding positions on the frequency characteristics of the hybrid
compared with the overall passband of the hybrid meander structure in our measurements. meander structures.
The The results,position
grounding which were of thepresented
additional in shields
the previous
also hadsection,
a small showed
impactthat it isoperation
on the possible
toofadjust the operation
the hybrid meanderofstructure.
the hybrid Themeander
greateststructure
impact was by replacing
obtained when the connecting
the groundingelec-
trodes
was inwith lumpedThe
the middle. inductive
grounding elements.
in oneThe enddelay time could
only showed be controlled
the worst results. by varying
the inductance of lumped elements without the need to change the dimensions of theElectronics 2021, 10, 1583 15 of 16
In summary, the properties of the hybrid meander structure with additional shields
were revealed. The results of the computer-based modeling and the physical experiment
correlated both qualitatively and quantitatively.
Author Contributions: Conceptualization, D.B.-P., A.K. (Andrius Katkevičius), and A.K. (Audrius
Krukonis); methodology, A.K. (Andrius Katkevičius); software, A.K. (Andrius Katkevičius); valida-
tion, D.B.-P. and A.K. (Andrius Katkevičius); formal analysis, D.B.-P., A.K. (Andrius Katkevičius),
and A.K. (Audrius Krukonis); investigation, D.B.-P., A.K. (Andrius Katkevičius), and A.K. (Audrius
Krukonis); resources, A.K. (Andrius Katkevičius); writing—original draft preparation, D.B.-P. and
A.K. (Andrius Katkevičius); writing—review and editing, A.K. (Andrius Katkevičius); visualization,
D.B.-P. and A.K. (Andrius Katkevičius); supervision, A.K. (Andrius Katkevičius) and A.K. (Audrius
Krukonis); funding acquisition, A.K. (Andrius Katkevičius). All authors have read and agreed to the
published version of the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.
References
1. Ding, C.; Wei, Y.; Li, Q.; Lei, X.; Wu, G.; Jiang, X.; Zhang, L.; Zhao, G.; Gong, Y.; Liao, M.; et al. A Modified Microstrip
Meander-Line Slow Wave Structure for Planar Traveling Wave Tubes. In Proceedings of the 2017 Eighteenth International Vacuum
Electronics Conference (IVEC), London, UK, 24–26 April 2017.
2. Shahidul Islam, M.; Islam, M.T.; Ullah, M.A.; Kok Beng, G.; Amin, N.; Misran, N. A Modified Meander Line Microstrip Patch
Antenna with Enhanced Bandwidth for 2.4 GHz ISM-Band Internet of Things (IoT) Applications. IEEE Access 2019, 7, 2169–3536.
[CrossRef]
3. Joo, J.; Choi, H.Y.; Song, E. Design and Modeling of Hybrid Uniplanar Electromagnetic Bandgap Power Planes for Wide-Band
Noise Suppression on Printed Circuit Boards. IEEE Access 2020, 8, 31614–31621. [CrossRef]
4. Pavithra, K.; Samson Daniel, R. Metamaterial Promoted Cpw-Fed Meander Line Antenna for Multiband Operation. In Proceedings
of the 2020 International Conference on Inventive Computation Technologies (ICICT), Coimbatore, India, 26–28 February 2020.
5. Son, T.V.; Oh Heon, K.; Euntae, J.; Jinwoo, P.; Byunggil, Y.; Kichul, K.; Jongwoo, S.; Keum Cheol, H. A Low-Profile High-Gain
and Wideband Log-Periodic Meandered Dipole Array Antenna with a Cascaded Multi-Section Artificial Magnetic Conductor
Structure. Sensors 2019, 19, 4404.
6. Yang, G.; Lou, J.; Obi, O.; Sun, N.X. Novel Compact and Low-Loss Phase Shifters With Magnetodielectric Disturber. IEEE Microw.
Wirel. Compon. Lett. 2011, 21, 240–242. [CrossRef]
7. Shanthi, G.; Srinivasa Rao, K.; Girija Sravani, K. Design and analysis of a RF MEMS shunt switch using U-shaped meanders for
low actuation voltage. Microsyst. Technol. 2020, 26, 3783–3791. [CrossRef]
8. Shu, Y.-F.; Wei, X.-C.; Yu, X.-Q.; Li, Y.-S.; Li, E.-P. A Compact Meander Line-Resonator Hybrid Structure for Wideband Common-
Mode Suppression. IEEE Trans. Electromagn. Compat. 2015, 57, 1255–1261. [CrossRef]
9. Yuxin, Z.; Langning, W.; Xu, C.; Tao, X.; Hanwu, Y. Investigation of a Novel Solid-State Dual Meander Pulse-forming Line with 10
kV-Class Withstand Voltage. AIP Adv. 2020, 10, 095318.
10. Plamen, K.; Wen-Sen, L.; Konstantin, K.; Thomas, D.; Matthew, T.B.; Michael, E.G. Granular Aluminum Meandered Superinduc-
tors for Quantum Circuits. Phys. Rev. Appl. 2019, 13, 054051.
11. Fang, X.; Wen, G.; Inserra, D.; Huang, Y.; Li, J. Compact Wideband CPW-Fed Meandered-Slot Antenna with Slotted Y-Shaped
Central Element for Wi-Fi, WiMAX, and 5G Applications. IEEE Trans. Antennas Propag. 2018, 66, 7395–7399. [CrossRef]
12. Ibrahim, K.M.; Elkattan, M.; Eldamak, A.R. Design of Low Frequency Meander Line Antenna with Efficient Size Reduction. In
Proceedings of the 2018 IEEE International Conference on Aerospace Electronics and Remote Sensing Technology (ICARES), Bali,
Indonesia, 20–21 September 2018.
13. Choudhary, D.K.; Mishra, N.; Kumar, R.; Chaudhary, R.K. Compact Two Pole Metamaterial Bandpass Filter Using Inverted IDC,
Meander Line and Rectangular Stub for WiMAX Application. In Proceedings of the 2017 Progress in Electromagnetics Research
Symposium-Fall (PIERS-FALL), Singapore, 19–22 November 2017.
14. Vishnu, K.; Menon, S.K. Compact MSL Filter Using Meander Line Resonator. In Proceedings of the 2020 5th International
Conference on Communication and Electronics Systems (ICCES), Coimbatore, India, 10–12 June 2020; pp. 414–417.
15. Wang, S.; Aditya, S.; Xia, X.; Ali, Z.; Miao, J. On-Wafer Microstrip Meander-Line Slow-Wave Structure at Ka-Band. IEEE Trans.
Electron Devices 2018, 65, 2142–2148. [CrossRef]
16. Ryskin, N.M.; Rozhnev, A.G.; Starodubov, A.V.; Serdobintsev, A.A.; Pavlov, A.M.; Benedik, A.I.; Torgashov, R.A.; Torgashov, G.V.;
Sinitsyn, N.I. Planar Microstrip Slow-Wave Structure for Low-Voltage V-Band Traveling-Wave Tube with a Sheet Electron Beam.
IEEE Electron Device Lett. 2018, 39, 757–760. [CrossRef]
17. Marzah, A.A.; Aziz, J.S. Design and Analysis of High Performance and Miniaturized Bandpass filter using Meander Line and,
Minkowski Fractal Geometry. In Proceedings of the 2018 Al-Mansour International Conference on New Trends in Computing,
Communication, and Information Technology (NTCCIT), Baghdad, Iraq, 14–15 November 2018.Electronics 2021, 10, 1583 16 of 16
18. Nara, S.; Koshiji, K. Study on Delay Time Characteristics of Multilayered Hyper-Shielded Meander Line. In Proceedings of the
2006 IEEE International Symposium on Electromagnetic Compatibility, Portland, OR, USA, 14–18 August 2006.
19. Ueberschär, O.; Almeida, M.J.; Matthes, P.; Müller, M.; Ecke, R.; Rückriem, R.; Schuster, J.; Exner, H.; Schulz, S.E. Optimized
Monolithic 2-D Spin-Valve Sensor for High-Sensitivity Compass Applications. IEEE Trans. Magn. 2015, 51. [CrossRef]
20. Daškevičius, V.; Skudutis, J.; Katkevičius, A.; Štaras, S. Simulation and Properties of the Wide-band Hybrid Slow-Wave System.
Elektron. Ir Elektrotechnika 2010, 104, 43–46.
21. Plonis, D.; Katkevičius, A.; Krukonis, A.; Šlegerytė, V.; Maskeliūnas, R.; Damaševičius, R. Predicting the Frequency Characteristics
of Hybrid Meander Systems Using a Feed-Forward Backpropagation Network. Electronics 2019, 8, 85. [CrossRef]
22. Metlevskis, E.; Martavičius, R. Computer Models of Meander Slow-Wave System with Additional Shields. Electron. Electr. Eng.
2012, 119, 61–64. [CrossRef]
23. Vandenbosch, G.; Vasylchenko, A. A Practical Guide to 3D Electromagnetic Software Tools; Open Access Peer Review Chapter of
Microstrip Antenna Book; IntechOpen: London, UK, 2011; pp. 507–541.You can also read
