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Citation: Gao, P.; Li, J.; Wang, W.
Study of Ground Plane Effects on
Monopole Antenna Performance.
Electronics 2023,12, 2681. https://
doi.org/10.3390/electronics12122681
Academic Editor: Dimitra
I. Kaklamani
Received: 11 March 2023
Revised: 19 May 2023
Accepted: 12 June 2023
Published: 15 June 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
electronics
Article
Study of Ground Plane Effects on Monopole
Antenna Performance
Pengjian Gao 1,2, Jia Li 1, 2, * and Weibing Wang 1,2
1Institute of Microelectronics of the Chinese Academy of Sciences, Beijing 100029, China;
gpj8372@sina.com (P.G.); wangweibing@ime.ac.cn (W.W.)
2University of Chinese Academy of Sciences, Beijing 100049, China
*Correspondence: lijia@ime.ac.cn
Abstract:
With the continuous development of the IoT, compact wireless communication modules
have become indispensable components, and their antennas are gradually being developed from
external devices into onboard integrated devices. The serpentine antenna, a variant of the monopole
antenna known for its small size and easy integration, is often applied to engineering practices.
However, its performance has always been closely affected by the size of the surrounding grounding
plane. By conducting a characteristic mode analysis (CMA), this study explored the variation patterns
in the ground plane size and the resonant frequency. Based on the simulation results, it was clear
that when the ground plane size is less than a quarter of the working wavelength, the ground plane
will have a significant effect on the antenna’s resonant frequency. Thus, this study further analyzed a
serpentine antenna with a grounding branch, and through analysis of the basic law of the influence
of grounding structure on the antenna’s performance, we found that by adjusting the branch length,
the matching performance of the antenna can be effectively improved. Furthermore, by changing the
size of the ground plate, the antenna’s resonant frequency can be adjusted. Such a conclusion will
hopefully provide a reference for future designs of integrated antennas in engineering applications.
Keywords: characteristic mode analysis (CMA); ground plane; monopole; gains
1. Introduction
As technologies have developed rapidly in recent years, wireless networks have been
applied to many fields, including families, enterprises, and public places [
1
]. Both standards
IEEE802.11a [
2
] and IEEE802.11b [
3
] take wireless channels as communication media for
WLANs while acknowledging their contributions to the wireless transmission of data
and video signals [
4
]. Wireless communication modules are both the fundamental link in
IoT application communications, and a key link in IOT application sensing and network
layers. They are currently widely applied in vehicle monitoring, telemetry, small wireless
networks, wireless meter reading, access control systems, industrial data collection systems,
wireless tagging, identification, contactless RF smart cards, fire safety systems, bio-signal
acquisition, hydro-meteorological monitoring, robot control, digital audio, digital image
trees, etc. As a key device for sending and receiving electromagnetic waves, antennas play
a vital role in wireless networks, with their performance directly determining the quality of
a wireless communication network [
5
,
6
] and attracting significant attention from scholars.
Following the miniaturization requirements of wireless communication nodes, antennas are
also being developed into small-sized devices that are easy to integrate [
5
,
7
]. The constant
development of the IoT has prompted greater demand for product miniaturization. Against
this backdrop, integrated antennas are currently one of the main developments anticipated
to meet the demand for miniaturized and high-performance products. Therefore, the
printed monopole antenna has become a main WLAN-related research topic thanks to its
significant advantages, including its small size, low cost, and high gains [8,9].
Electronics 2023,12, 2681. https://doi.org/10.3390/electronics12122681 https://www.mdpi.com/journal/electronics
Electronics 2023,12, 2681 2 of 17
The serpentine antenna is currently the most widely used monopole antenna structure
and is found commonly in Bluetooth, Wi-Fi, and Zigbee devices, as well as in other fields.
People are attracted to serpentine antennas due to their various advantages, such as their
smaller size, lower cost, long durability, and easy whole-machine integration [
10
]. Although
their bending structure benefits miniaturization, their gains may be reduced, causing more
losses. Therefore, the optimal way in which to balance the size and gains of these antennas
has become a main concern of many designers. A common practice is to use HFSS to
design a serpentine monopole antenna structure of a specific area size. However, in terms
of the relationship between the ground plane size and the monopole antenna wavelength,
only general conclusions have been drawn stating that the impedance, center frequency,
and gains of the antenna are impacted by the ground plane size; for example, the ground
plane size and shape influence the impedance, resonant frequency, gains, and radiation
direction of the antenna [
11
]. Some articles have also pointed out that as the ground plane
size becomes smaller, the lower frequency limit of the antenna rises, resulting in a narrower
bandwidth [
12
]; however, researchers have not yet conducted in-depth analyses of why
such influences exist.
Taking the Bluetooth serpentine antenna as an example, this study applied characteris-
tic mode analysis (CMA) to first analyze the grounding plane size’s influence on resonant
frequency changes and then analyze its impact on the amplitude of the surface current
value. Lastly, HFSS was used to explore the relationship between the ground plane size and
the impedance, center frequency, gains, and wavelength of the antenna in depth. Based
on such findings, we can conclude that the matching performance of the antenna can be
significantly improved by adjusting the length of its grounding branch. Such results will
provide practical guidance for antenna designers.
The innovations in the research findings have practical engineering significance. For
example, by adjusting the ground plate size, the antenna resonance frequency can be
changed, and by adjusting the branch length, both the antenna’s matching performance
and bandwidth can be significantly improved. Such results will provide useful references
for relevant engineering applications.
2. Effect of the Ground Plane on Monopole Antennas
2.1. Factors That Affect Monopole Antenna Characteristics
Melvin M. Weiner [
13
] proposed three main parameters that affect the operating
monopole antenna’s characteristics, including length, radius, and ground plane. For
monopole antennas with determined sizes, the ground plane will be the main influencing
factor, mainly because when the antenna works, the feed point incident wave will produce
omnidirectional diffraction at the outer edge of the ground plane, and such diffraction
will affect its surface wave. The stronger the outer edge diffraction, the larger the surface
wave value. With the change in the antenna ground plane, the strength of the outer
edge diffraction also varies. The smaller the ground plane is, the stronger the outer edge
diffraction will become; conversely, the larger the ground plane, the smaller the outer edge
diffraction [14].
Therefore, compared to the infinite ground plane, the finite ground plane will affect
the operating characteristics of the antenna, including center frequency, input impedance,
and gains, because of its size.
2.2. The Serpentine Monopole Antenna Structure
Early monopole antennas were applied to an upright ground plane that was considered
“infinite” and could be used to analyze the antennas’ performance using the principle of
the method of images. However, when they are later placed on a finite metal plane
(such as a train roof, car roof, airplane surface, etc.) and form a radiation body with the
finite metal body, the metal ground plane will generate a vital impact on the antennas’
radiation characteristics (reflection coefficient, radiation pattern, etc.). There are currently
two commonly seen serpentine antenna models, including that in Figure 1a, a serpentine
Electronics 2023,12, 2681 3 of 17
antenna with no grounding branches, and that in Figure 1b, a serpentine antenna with
grounding branches.
Electronics2023,12,xFORPEERREVIEW3of16
finitemetalbody,themetalgroundplanewillgenerateavitalimpactontheantennas’
radiationcharacteristics(reflectioncoefficient,radiationpaern,etc.).Therearecurrently
twocommonlyseenserpentineantennamodels,includingthatinFigure1a,aserpentine
antennawithnogroundingbranches,andthatinFigure1b,aserpentineantennawith
groundingbranches.
(a)(b)
Figure1.Two typesoftheserpentineantennastructure.(a)aserpentineantennawithnoground-
ingbranches(b)aserpentineantennawithgroundingbranches
Taki ngaBluetoothserpentineantennawithagroundingbranchasanexample,this
studyanalyzedtheeffectiverangeofthegroundplaneofthemonopoleantenna,using
thecommercialsoftwareHFSS15.0[15].Thesimulationresultsshowedthatthedesigned
antennamettheapplicationrequirementsofthesystem[16,17].
2.3.TheSerpentineAntennaModel
Figure2illustratesthespecificstructureoftheserpentineantenna.Intermsofits
structure,here,the1-mm-thickplatemediumwasmadeofFR4,andthewholeantenna
lengthwasbetween0.25λ
0
and0.25λg[18](λ
0
=30mm,λg=15mm;λ
0
isthefreespace
wavelength,λgistheguidedwavewavelengthinthedielectriclayer;andεr=4.4).SMA
connectorswithacharacteristicimpedanceof50Ωwereusedforfeeding.Table1shows
theinitializationparametersoftheserpentineantenna
(a)(b)
Figure2.Theserpentineantennamodels.(a)viewoftheantennastructureandoveralldesignof
thelayout(b)detaileddimensionsandlayoutoftheantenna
Figure 1.
Two types of the serpentine antenna structure. (
a
) a serpentine antenna with no grounding
branches (b) a serpentine antenna with grounding branches.
Taking a Bluetooth serpentine antenna with a grounding branch as an example, this
study analyzed the effective range of the ground plane of the monopole antenna, using
the commercial software HFSS 15.0 [
15
]. The simulation results showed that the designed
antenna met the application requirements of the system [16,17].
2.3. The Serpentine Antenna Model
Figure 2illustrates the specific structure of the serpentine antenna. In terms of its
structure, here, the 1-mm-thick plate medium was made of FR4, and the whole antenna
length was between 0.25
λ0
and 0.25
λ
g [
18
] (
λ0
= 30 mm,
λ
g = 15 mm;
λ0
is the free space
wavelength,
λ
g is the guided wave wavelength in the dielectric layer; and
ε
r = 4.4). SMA
connectors with a characteristic impedance of 50
Ω
were used for feeding. Table 1shows
the initialization parameters of the serpentine antenna.
Electronics2023,12,xFORPEERREVIEW3of16
finitemetalbody,themetalgroundplanewillgenerateavitalimpactontheantennas’
radiationcharacteristics(reflectioncoefficient,radiationpaern,etc.).Therearecurrently
twocommonlyseenserpentineantennamodels,includingthatinFigure1a,aserpentine
antennawithnogroundingbranches,andthatinFigure1b,aserpentineantennawith
groundingbranches.
(a)(b)
Figure1.Two typesoftheserpentineantennastructure.(a)aserpentineantennawithnoground-
ingbranches(b)aserpentineantennawithgroundingbranches
Taki n gaBluetoothserpentineantennawithagroundingbranchasanexample,this
studyanalyzedtheeffectiverangeofthegroundplaneofthemonopoleantenna,using
thecommercialsoftwareHFSS15.0[15].Thesimulationresultsshowedthatthedesigned
antennamettheapplicationrequirementsofthesystem[16,17].
2.3.TheSerpentineAntennaModel
Figure2illustratesthespecificstructureoftheserpentineantenna.Intermsofits
structure,here,the1-mm-thickplatemediumwasmadeofFR4,andthewholeantenna
lengthwasbetween0.25λ
0
and0.25λg[18](λ
0
=30mm,λg=15mm;λ
0
isthefreespace
wavelength,λgistheguidedwavewavelengthinthedielectriclayer;andεr=4.4).SMA
connectorswithacharacteristicimpedanceof50Ωwereusedforfeeding.Table1shows
theinitializationparametersoftheserpentineantenna
(a)(b)
Figure2.Theserpentineantennamodels.(a)viewoftheantennastructureandoveralldesignof
thelayout(b)detaileddimensionsandlayoutoftheantenna
Figure 2.
The serpentine antenna models. (
a
) view of the antenna structure and overall design of the
layout (b) detailed dimensions and layout of the antenna.
Electronics 2023,12, 2681 4 of 17
Table 1. Initial dimension parameters of the serpentine antenna (unit: mm).
W H D L1L2
0.5 7.5 0.9 3.5 6
SY1SY SX1SX R
9 37.5 11 28 0.15
SX2L H2SY2
11 2 2.5 3
Figure 3shows the reflection coefficient of the antenna S11 =
−
29 dB; the center
frequency point was 2.45 GHz, and the bandwidth was between 2.38 and 2.50 GHz (the
Bluetooth antenna bandwidth ranges from 2.402 to 2.482 GHz). The gain in Figure 4was
1.17 dBi, and the antenna was omnidirectional and met the design requirements.
Electronics2023,12,xFORPEERREVIEW4of16
Table 1.Initialdimensionparametersoftheserpentineantenna(unit:mm).
WHDL1L2
0.57.50.93.56
SY1SYSX1SXR
937.511280.15
SX2LH2SY2
1122.53
Figure3showsthereflectioncoefficientoftheantennaS11=−29dB;thecenterfre-
quencypointwas2.45GHz,andthebandwidthwasbetween2.38and2.50GHz(theBlue-
toothantennabandwidthrangesfrom2.402to2.482GHz).ThegaininFigure4was1.17
dBi,andtheantennawasomnidirectionalandmetthedesignrequirements.
Figure3.ReflectioncoefficientS11oftheserpentineantenna.
Figure4.Gainsoftheserpentineantenna.
2.4.CMAoftheSerpentineAntenna
ThisstudydemonstratedtheperformanceoftheCMAoftheserpentineantennawith
CST.ThegroundplaneSYvalueontheY-axiswaschanged,andtheresultingresonant
characteristicscanbeseeninFigure5a.Ifitssizefallswithintherangeoflessthanaquar-
terwavelength,thegroundplanewillsignificantlyaffecttheantennaresonantfrequency,
andwhenitexceedstherange,thegroundplanewillthenhaveagraduallydecreasing
effectontheresonantfrequency.
Figure 3. Reflection coefficient S11 of the serpentine antenna.
Electronics2023,12,xFORPEERREVIEW4of16
Table1.Initialdimensionparametersoftheserpentineantenna(unit:mm).
WHDL1L2
0.57.50.93.56
SY1SYSX1SXR
937.511280.15
SX2LH2SY2
1122.53
Figure3showsthereflectioncoefficientoftheantennaS11=−29dB;thecenterfre-
quencypointwas2.45GHz,andthebandwidthwasbetween2.38and2.50GHz(theBlue-
toothantennabandwidthrangesfrom2.402to2.482GHz).ThegaininFigure4was1.17
dBi,andtheantennawasomnidirectionalandmetthedesignrequirements.
Figure3.ReflectioncoefficientS11oftheserpentineantenna.
Figure4.Gainsoftheserpentineantenna.
2.4.CMAoftheSerpentineAntenna
ThisstudydemonstratedtheperformanceoftheCMAoftheserpentineantennawith
CST.ThegroundplaneSYvalueontheY-axiswaschanged,andtheresultingresonant
characteristicscanbeseeninFigure5a.Ifitssizefallswithintherangeoflessthanaquar-
terwavelength,thegroundplanewillsignificantlyaffecttheantennaresonantfrequency,
andwhenitexceedstherange,thegroundplanewillthenhaveagraduallydecreasing
effectontheresonantfrequency.
Figure 4. Gains of the serpentine antenna.
2.4. CMA of the Serpentine Antenna
This study demonstrated the performance of the CMA of the serpentine antenna with
CST. The ground plane SY value on the Y-axis was changed, and the resulting resonant
characteristics can be seen in Figure 5a. If its size falls within the range of less than a quarter
wavelength, the ground plane will significantly affect the antenna resonant frequency, and
when it exceeds the range, the ground plane will then have a gradually decreasing effect
on the resonant frequency.
Electronics 2023,12, 2681 5 of 17
Electronics 2023, 12, x FOR PEER REVIEW 5 of 16
(a) (b)
(c) (d)
Figure 5. CMA of the serpentine antenna. (a) CMA along the Y-axis. (b) CMA along the X-axis. (c)
MS max. along the Y-axis. (d) MS max. along the X-axis.
Similarly, the value of SX (set SY value as 37.5 mm) was changed, and the resulting
resonant characteristics can be found in Figure 5b. If the SX falls within the range of less
than a quarter of the wavelength, the ground plane length will seemingly affect the an-
tenna’s characteristics; if the length is more than a quarter of the wavelength, the effect of
the ground plane length change on the antenna’s resonance characteristics shall be small.
According to Figure 5c,d, when the SY and SX values are relatively small, their MS
values are also small, meaning that the antenna cannot reach the resonant state.
To summarize, when the length of the ground plane is less than a quarter of the wave-
length, it will greatly impact the antenna’s resonant frequency on both the X-axis and Y-
axis.
2.5. Serpentine Antenna Surface Current Analysis
With CST, the surface current of the serpentine antenna is analyzed. Figure 6a,b
shows the schematic diagrams of the surface current of the serpentine antenna with the
variation in the X- and Y-axes. The maximum surface current amplitude that occurs when
varying the SY value of the ground plane on the Y-axis is shown in Figure 6c. Within the
range of less than a quarter of the wavelength, the influence of the ground plane size on
the surface current is large; outside of this range, the influence of the ground plane size
on the surface current becomes small, and the amplitude of the surface current trends
gradually toward a certain value.
Similarly, as is shown in Figure 6d, if the size falls into the range of less than a quarter
of the wavelength, the ground plane will significantly affect the surface current, and if
greater than this range, the ground plane will have a small effect.
Figure 5.
CMA of the serpentine antenna. (
a
) CMA along the Y-axis. (
b
) CMA along the X-axis.
(c) MS max. along the Y-axis. (d) MS max. along the X-axis.
Similarly, the value of SX (set SY value as 37.5 mm) was changed, and the resulting
resonant characteristics can be found in Figure 5b. If the SX falls within the range of
less than a quarter of the wavelength, the ground plane length will seemingly affect the
antenna’s characteristics; if the length is more than a quarter of the wavelength, the effect of
the ground plane length change on the antenna’s resonance characteristics shall be small.
According to Figure 5c,d, when the SY and SX values are relatively small, their MS
values are also small, meaning that the antenna cannot reach the resonant state.
To summarize, when the length of the ground plane is less than a quarter of the
wavelength, it will greatly impact the antenna’s resonant frequency on both the X-axis and
Y-axis.
2.5. Serpentine Antenna Surface Current Analysis
With CST, the surface current of the serpentine antenna is analyzed. Figure 6a,b shows
the schematic diagrams of the surface current of the serpentine antenna with the variation
in the X- and Y-axes. The maximum surface current amplitude that occurs when varying
the SY value of the ground plane on the Y-axis is shown in Figure 6c. Within the range of
less than a quarter of the wavelength, the influence of the ground plane size on the surface
current is large; outside of this range, the influence of the ground plane size on the surface
current becomes small, and the amplitude of the surface current trends gradually toward a
certain value.
Similarly, as is shown in Figure 6d, if the size falls into the range of less than a quarter
of the wavelength, the ground plane will significantly affect the surface current, and if
greater than this range, the ground plane will have a small effect.
Electronics 2023,12, 2681 6 of 17
Electronics2023,12,xFORPEERREVIEW6of16
(a)
(b)
(c)(d)
Figure6.Thesurfacecurrentsoftheserpentineantenna.(a)SurfacecurrentsvaryingalongtheY-
axis.(b)SurfacecurrentsvaryingalongtheX-axis.(c)Themaximumamplitudeofsurfacecurrents
varyingalongtheY-axis.(d)ThemaximumamplitudeofsurfacecurrentsvaryingalongtheX-axis.
2.6.TheEffectiveGroundPlaneRangeoftheSerpentineAntenna
ThelengthofcopperlayinginthegroundplaneontheY-axiswasvaried.Theinitial
valuewassettoSY=9mm;infact,thelengthofthegroundplaneontheY-axiswaszero
bythen(SY−SY
1
=0).AsisshowninFigure2,SYrepresentsthewholelengthoftheY-
axis,andSY
1
representsthedistancebetweenthestartingpointoftheY-axisandthe
groundplane.SYwasincreasedevery3.75mmontheY-axis,andthemaximumvalueof
SYwastakentobe69mm.ThesimulationresultscanbeseeninFigure7.
Figure 6.
The surface currents of the serpentine antenna. (
a
) Surface currents varying along the
Y-axis. (
b
) Surface currents varying along the X-axis. (
c
) The maximum amplitude of surface currents
varying along the Y-axis. (d) The maximum amplitude of surface currents varying along the X-axis.
Electronics 2023,12, 2681 7 of 17
2.6. The Effective Ground Plane Range of the Serpentine Antenna
The length of copper laying in the ground plane on the Y-axis was varied. The initial
value was set to SY = 9 mm; in fact, the length of the ground plane on the Y-axis was zero
by then (SY
−
SY
1
= 0). As is shown in Figure 2, SY represents the whole length of the
Y-axis, and SY
1
represents the distance between the starting point of the Y-axis and the
ground plane. SY was increased every 3.75 mm on the Y-axis, and the maximum value of
SY was taken to be 69 mm. The simulation results can be seen in Figure 7.
Electronics2023,12,xFORPEERREVIEW7of16
Figure7.ReflectioncoefficientcurvescorrespondingtodifferentSYvalues.
WhentheSYvaluerangesfrom[9mm,69mm](theY-axislengthofthegroundplane
rangesfrom[0,60mm]),thecenterfrequencyoftheantennadecreasesasSYbecomes
larger.However,whenSYapproachesacertaincriticalvalue,thecenterfrequencygrows
withtheincreaseinSY.InFigure8,thegroundplaneY-axislengthstartsfrom0,andthe
antennaimpedanceshowsthecapacitivereactance,whichalsodecreasedastheSYlength
grew.WhenthegroundplaneY-axislengthreachesapproximately0.25λ0,thecapacitive
reactanceis0,andtheimpedanceispureresistance,approximately50Ω.Afterthat,the
antennaimpedanceshowsinductivereactance,theimpedanceincreases,andtheantenna
impedancematchingbecomesworse.Figure9showsthattheantennagainalsoincreases
withtheincreaseintheSYvalue,beforegraduallyconvergingtoaconstantvalue.
Figure8.Theantenna’scharacteristicimpedancecorrespondingtodifferentSYvalues.
Figure9.Theantenna’sgainscorrespondingtodifferentSYvalues.
Additionally,fromtheHFSSsimulation,itisclearthatwhentheY-axislengthofthe
planeisapproximatelyequalto0.25λ0,theomnidirectionalcharacteristicsoftheantenna
willbeexcellent,asshowninFigure10a.WhentheY-axislengthofthegroundplane
Figure 7. Reflection coefficient curves corresponding to different SY values.
When the SY value ranges from [9 mm, 69 mm] (the Y-axis length of the ground plane
ranges from [0, 60 mm]), the center frequency of the antenna decreases as SY becomes
larger. However, when SY approaches a certain critical value, the center frequency grows
with the increase in SY. In Figure 8, the ground plane Y-axis length starts from 0, and the
antenna impedance shows the capacitive reactance, which also decreased as the SY length
grew. When the ground plane Y-axis length reaches approximately 0.25
λ0
, the capacitive
reactance is 0, and the impedance is pure resistance, approximately 50
Ω
. After that, the
antenna impedance shows inductive reactance, the impedance increases, and the antenna
impedance matching becomes worse. Figure 9shows that the antenna gain also increases
with the increase in the SY value, before gradually converging to a constant value.
Electronics2023,12,xFORPEERREVIEW7of16
Figure7.ReflectioncoefficientcurvescorrespondingtodifferentSYvalues.
WhentheSYvaluerangesfrom[9mm,69mm](theY-axislengthofthegroundplane
rangesfrom[0,60mm]),thecenterfrequencyoftheantennadecreasesasSYbecomes
larger.However,whenSYapproachesacertaincriticalvalue,thecenterfrequencygrows
withtheincreaseinSY.InFigure8,thegroundplaneY-axislengthstartsfrom0,andthe
antennaimpedanceshowsthecapacitivereactance,whichalsodecreasedastheSYlength
grew.WhenthegroundplaneY-axislengthreachesapproximately0.25λ0,thecapacitive
reactanceis0,andtheimpedanceispureresistance,approximately50Ω.Afterthat,the
antennaimpedanceshowsinductivereactance,theimpedanceincreases,andtheantenna
impedancematchingbecomesworse.Figure9showsthattheantennagainalsoincreases
withtheincreaseintheSYvalue,beforegraduallyconvergingtoaconstantvalue.
Figure8.Theantenna’scharacteristicimpedancecorrespondingtodifferentSYvalues.
Figure9.Theantenna’sgainscorrespondingtodifferentSYvalues.
Additionally,fromtheHFSSsimulation,itisclearthatwhentheY-axislengthofthe
planeisapproximatelyequalto0.25λ0,theomnidirectionalcharacteristicsoftheantenna
willbeexcellent,asshowninFigure10a.WhentheY-axislengthofthegroundplane
Figure 8. The antenna’s characteristic impedance corresponding to different SY values.
Electronics 2023,12, 2681 8 of 17
Electronics2023,12,xFORPEERREVIEW7of16
Figure7.ReflectioncoefficientcurvescorrespondingtodifferentSYvalues.
WhentheSYvaluerangesfrom[9mm,69mm](theY-axislengthofthegroundplane
rangesfrom[0,60mm]),thecenterfrequencyoftheantennadecreasesasSYbecomes
larger.However,whenSYapproachesacertaincriticalvalue,thecenterfrequencygrows
withtheincreaseinSY.InFigure8,thegroundplaneY-axislengthstartsfrom0,andthe
antennaimpedanceshowsthecapacitivereactance,whichalsodecreasedastheSYlength
grew.WhenthegroundplaneY-axislengthreachesapproximately0.25λ0,thecapacitive
reactanceis0,andtheimpedanceispureresistance,approximately50Ω.Afterthat,the
antennaimpedanceshowsinductivereactance,theimpedanceincreases,andtheantenna
impedancematchingbecomesworse.Figure9showsthattheantennagainalsoincreases
withtheincreaseintheSYvalue,beforegraduallyconvergingtoaconstantvalue.
Figure8.Theantenna’scharacteristicimpedancecorrespondingtodifferentSYvalues.
Figure9.Theantenna’sgainscorrespondingtodifferentSYvalues.
Additionally,fromtheHFSSsimulation,itisclearthatwhentheY-axislengthofthe
planeisapproximatelyequalto0.25λ0,theomnidirectionalcharacteristicsoftheantenna
willbeexcellent,asshowninFigure10a.WhentheY-axislengthofthegroundplane
Figure 9. The antenna’s gains corresponding to different SY values.
Additionally, from the HFSS simulation, it is clear that when the Y-axis length of the
plane is approximately equal to 0.25
λ0
, the omnidirectional characteristics of the antenna
will be excellent, as shown in Figure 10a. When the Y-axis length of the ground plane
exceeds 0.5
λ0
, multiple lobes will appear on the radiation pattern, and the antenna gain
will decrease, as in Figure 10b.
Electronics2023,12,xFORPEERREVIEW8of16
exceeds0.5λ
0
,multiplelobeswillappearontheradiationpaern,andtheantennagain
willdecrease,asinFigure10b.
(a)(b)
Figure10.(a)SY=39mm(b)SY=70mm.
Accordingtothefilteringequation𝑓
∝1
√𝐿𝐶
[19],thecapacitivereactanceformula
1
2𝜋𝑤𝑐
,andtheinductivereactanceformula𝑋2𝜋𝑤𝑙,thethenL
2
oftheantenna
isconnectedtothegroundplane.Withthegroundplane,thismaybeseenasoneradiating
body.Changesinthegroundplanealsoleadtochangesinthe𝐿and𝐶oftheantenna.
Theantennaandgroundplaneareseentogetherasafilter,whilethecenterfrequency
varieswiththechangesinthe𝐿and𝐶values.Atfirst,theimpedanceoftheantenna
showslargercapacitivereactance,andcapacitance𝐶 andcapacitivereactance are
showntobeinverselyproportional;astheabsolutevalueofcapacitivereactancede-
creases,thecapacitance𝐶 increasesgradually.Atthistime,thecenterfrequencyde-
creases,andimpedanceshowspureresistanceatapproximately0.25λ
0
ontheY-axisof
thegroundplane.Bythen,S11isthesmallest,andthebandwidthisthelargest.Afterthat,
theimpedanceencountersinductivereactanceandgraduallyincreases,atwhichtime𝐿
alsoincreases,whilethecenterfrequency𝑓
decreases.However,duetothepurere-
sistanceintheimpedanceandinductivereactance(whicharealsoincreasing),theantenna
willgeneratereflectioncoefficient,whicheventuallyleadstoagradualincreaseinS11and
anarrowingofthebandwidth.Later,theantennashowscapacitivereactanceandgradu-
allyincreases;meanwhile,theantennabandwidthbecomesnarrow,andthecenterfre-
quency𝑓
grows.Itisthusclearthatanincreaseinthegroundplanesizeinthedirection
oftheY-axiswillaffecttheimpedanceoftheentireradiatingbodyoftheantennaand
ground,andsuchchangesalsoaffectthecenterfrequencyandbandwidth.Atthesame
time,theincreaseinthegroundplane’ssizewillalsoenlargetheradiationrangeofthe
antenna,thuschangingtheantennagainsandallowingthesegainstoconvergetoacertain
extremevaluebeforedecreasing.
Toconclude,theY-axislengthchangeinthegroundplanedirectlyaffectsthereso-
nantfrequency,bandwidth,impedance,andgainsoftheantenna.
TheY-axislengthofthegroundplanewassetto0.25λ
0
(thethenimpedanceofthe
antennawasthebestmatch),andanincreaseinthelengthoftheX-axiswassimulated;
meanwhile,theantenna’simpedance,bandwidth,S11,andgainrequirementswerecom-
prehensivelyconsidered.Itisclearthattheantennameetsthedesignrequirementsonly
iftheX-axislengthfallswithintherangeof0.25λ
0
to0.5λ
0
.WhentheX-axislengthbe-
comeslargerthan0.5λ
0
,theantennashowsmultiplelobes.InFigure11a,SX=30mm,
andtheX-axislengthisapproximately0.25λ
0
;inFigure11b,SX=60mmandtheX-axis
lengthisapproximately0.5λ
0
.Thegainsofbothantennasarelargerthan1dBi.InFigure
11c,SX=80mmandtheantennaappearstohavemultiplelobes.
Figure 10. (a)SY=39mm(b) SY = 70 mm.
According to the filtering equation
f0∝1
√LC
[
19
], the capacitive reactance formula
×c=1
2πwc
, and the inductive reactance formula
Xl=
2
πwl
, the then L
2
of the antenna is
connected to the ground plane. With the ground plane, this may be seen as one radiating
body. Changes in the ground plane also lead to changes in the
L
and
C
of the antenna.
The antenna and ground plane are seen together as a filter, while the center frequency
varies with the changes in the
L
and
C
values. At first, the impedance of the antenna
shows larger capacitive reactance, and capacitance
C
and capacitive reactance
×c
are
shown to be inversely proportional; as the absolute value of capacitive reactance decreases,
the capacitance
C
increases gradually. At this time, the center frequency decreases, and
impedance shows pure resistance at approximately 0.25
λ0
on the Y-axis of the ground
plane. By then, S11 is the smallest, and the bandwidth is the largest. After that, the
impedance encounters inductive reactance and gradually increases, at which time
L
also
increases, while the center frequency
f0
decreases. However, due to the pure resistance
in the impedance and inductive reactance (which are also increasing), the antenna will
generate reflection coefficient, which eventually leads to a gradual increase in S11 and a
narrowing of the bandwidth. Later, the antenna shows capacitive reactance and gradually
increases; meanwhile, the antenna bandwidth becomes narrow, and the center frequency
f0
grows. It is thus clear that an increase in the ground plane size in the direction of the Y-axis
will affect the impedance of the entire radiating body of the antenna and ground, and such
changes also affect the center frequency and bandwidth. At the same time, the increase in
Electronics 2023,12, 2681 9 of 17
the ground plane’s size will also enlarge the radiation range of the antenna, thus changing
the antenna gains and allowing these gains to converge to a certain extreme value before
decreasing.
To conclude, the Y-axis length change in the ground plane directly affects the resonant
frequency, bandwidth, impedance, and gains of the antenna.
The Y-axis length of the ground plane was set to 0.25
λ0
(the then impedance of the
antenna was the best match), and an increase in the length of the X-axis was simulated;
meanwhile, the antenna’s impedance, bandwidth, S11, and gain requirements were com-
prehensively considered. It is clear that the antenna meets the design requirements only if
the X-axis length falls within the range of 0.25
λ0
to 0.5
λ0
. When the X-axis length becomes
larger than 0.5
λ0
, the antenna shows multiple lobes. In Figure 11a, SX = 30 mm, and the
X-axis length is approximately 0.25
λ0
; in Figure 11b, SX = 60 mm and the X-axis length
is approximately 0.5
λ0
. The gains of both antennas are larger than 1 dBi. In Figure 11c,
SX = 80 mm and the antenna appears to have multiple lobes.
Electronics2023,12,xFORPEERREVIEW9of16
(a)(b)
(c)
Figure11.(a)SX=30mm,(b)SX=60mm,(c)SX=80mm.
InFigure12,therangeofSXiswithin0.25λ0and0.5λ0,andallimpedancesmeetthe
designrequirements.WhentheSXvalueisbetween0.25λ0and0.5λ0,thegainconstantly
decreases,andwhenSXexceeds0.5λ
0,thegainshowsanupwardtrend(asshownin
Figure13).
Figure12.ImpedancescorrespondingtodifferentSXvalues.
Figure 11. (a) SX = 30 mm, (b) SX = 60 mm, (c) SX = 80 mm.
In Figure 12, the range of SX is within 0.25
λ0
and 0.5
λ0
, and all impedances meet the
design requirements. When the SX value is between 0.25
λ0
and 0.5
λ0
, the gain constantly
decreases, and when SX exceeds 0.5
λ0
, the gain shows an upward trend (as shown in
Figure 13).
Electronics 2023,12, 2681 10 of 17
Electronics2023,12,xFORPEERREVIEW9of16
(a)(b)
(c)
Figure11.(a)SX=30mm,(b)SX=60mm,(c)SX=80mm.
InFigure12,therangeofSXiswithin0.25λ0and0.5λ0,andallimpedancesmeetthe
designrequirements.WhentheSXvalueisbetween0.25λ0and0.5λ0,thegainconstantly
decreases,andwhenSXexceeds0.5λ
0,thegainshowsanupwardtrend(asshownin
Figure13).
Figure12.ImpedancescorrespondingtodifferentSXvalues.
Figure 12. Impedances corresponding to different SX values.
Electronics2023,12,xFORPEERREVIEW10of16
Figure13.GainscorrespondingtodifferentSXvalues.
Basedonthesimulationanalysisofthelengthofthegroundplaneoftheserpentine
antennaalongtheX-axisandY-axis,itcanbeconcludedthattheantenna’sgroundplane
sizehasacriticaleffectontheantenna’scharacteristics,includingthereflectioncoefficient,
gains,impedance,andbandwidth.Onlywhenthegroundplaneiswithintheeffective
rangecantheantennademonstrateoptimalperformance.Beyondtheeffectiverange,the
antennawillnotworkproperly.
2.7.TheInfluenceoftheGroundingBranchesoftheSerpentineAntennaontheAntenna’sPer‐
formance
AsisshowninFigure2,theantennabranchL2isconnectedtothegroundplane
throughanareaconsistingofbothSX2andSY2.InFigure14,itcanbeseenthatvariation
inthelengthoftheparametricantennabranchL2mainlyaffectstheimpedancematching
characteristicsoftheantenna.Figure15showstherelationshipbetweenvariationinthe
lengthofparameterSX2andthereflectioncoefficient,therebyprovingthatbychanging
thesizeofSX2,theimpedancematchingoftheantennacanbechanged.Figure16shows
therelationshipbetweenchangesinparameterSY2andthereflectioncoefficient,proving
thatchangingthesizeofSY2caneffectivelyadjusttheresonantfrequencyoftheantenna.
Later,withtheincreaseinSY2,thelocationplanegraduallyapproachestheserpentine
antennaandthecouplingeffectbecomesevenstronger,eventuallyleadingtothean-
tenna’sgainsbecomingsmallerandthedirectionalityworse,asshowninFigure17.
Figure14.ReflectioncoefficientoftheantennawithvariationinparameterL2.
Figure 13. Gains corresponding to different SX values.
Based on the simulation analysis of the length of the ground plane of the serpentine
antenna along the X-axis and Y-axis, it can be concluded that the antenna’s ground plane
size has a critical effect on the antenna’s characteristics, including the reflection coefficient,
gains, impedance, and bandwidth. Only when the ground plane is within the effective
range can the antenna demonstrate optimal performance. Beyond the effective range, the
antenna will not work properly.
2.7. The Influence of the Grounding Branches of the Serpentine Antenna on the Antenna’s
Performance
As is shown in Figure 2, the antenna branch L
2
is connected to the ground plane
through an area consisting of both SX
2
and SY
2
. In Figure 14, it can be seen that variation
in the length of the parametric antenna branch L
2
mainly affects the impedance matching
characteristics of the antenna. Figure 15 shows the relationship between variation in the
length of parameter SX
2
and the reflection coefficient, thereby proving that by changing the
size of SX
2
, the impedance matching of the antenna can be changed. Figure 16 shows the
relationship between changes in parameter SY
2
and the reflection coefficient, proving that
changing the size of SY
2
can effectively adjust the resonant frequency of the antenna. Later,
with the increase in SY
2
, the location plane gradually approaches the serpentine antenna
and the coupling effect becomes even stronger, eventually leading to the antenna’s gains
becoming smaller and the directionality worse, as shown in Figure 17.
Electronics 2023,12, 2681 11 of 17
Electronics2023,12,xFORPEERREVIEW10of16
Figure13.GainscorrespondingtodifferentSXvalues.
Basedonthesimulationanalysisofthelengthofthegroundplaneoftheserpentine
antennaalongtheX-axisandY-axis,itcanbeconcludedthattheantenna’sgroundplane
sizehasacriticaleffectontheantenna’scharacteristics,includingthereflectioncoefficient,
gains,impedance,andbandwidth.Onlywhenthegroundplaneiswithintheeffective
rangecantheantennademonstrateoptimalperformance.Beyondtheeffectiverange,the
antennawillnotworkproperly.
2.7.TheInfluenceoftheGroundingBranchesoftheSerpentineAntennaontheAntenna’sPer‐
formance
AsisshowninFigure2,theantennabranchL2isconnectedtothegroundplane
throughanareaconsistingofbothSX2andSY2.InFigure14,itcanbeseenthatvariation
inthelengthoftheparametricantennabranchL2mainlyaffectstheimpedancematching
characteristicsoftheantenna.Figure15showstherelationshipbetweenvariationinthe
lengthofparameterSX2andthereflectioncoefficient,therebyprovingthatbychanging
thesizeofSX2,theimpedancematchingoftheantennacanbechanged.Figure16shows
therelationshipbetweenchangesinparameterSY2andthereflectioncoefficient,proving
thatchangingthesizeofSY2caneffectivelyadjusttheresonantfrequencyoftheantenna.
Later,withtheincreaseinSY2,thelocationplanegraduallyapproachestheserpentine
antennaandthecouplingeffectbecomesevenstronger,eventuallyleadingtothean-
tenna’sgainsbecomingsmallerandthedirectionalityworse,asshowninFigure17.
Figure14.ReflectioncoefficientoftheantennawithvariationinparameterL2.
Figure 14. Reflection coefficient of the antenna with variation in parameter L2.
Electronics2023,12,xFORPEERREVIEW11of16
Figure15.ReflectioncoefficientoftheantennawithchangesinparameterSX2.
Figure16.ReflectioncoefficientoftheantennawithchangesinparameterSY2.
(a)(b)
(c)
Figure17.VariationinantennagainswithSY2valuechanges.(a)SY2=3mm.(b)SY2=3.5mm.(c)
SY2=4mm.
Basedontheabovediscussion,theantennabranchlengthL2andgroundinglength
SX2havebeenproventobethetwomainfactorsaffectingtheantenna’simpedance
Figure 15. Reflection coefficient of the antenna with changes in parameter SX2.
Electronics2023,12,xFORPEERREVIEW11of16
Figure15.ReflectioncoefficientoftheantennawithchangesinparameterSX2.
Figure16.ReflectioncoefficientoftheantennawithchangesinparameterSY2.
(a)(b)
(c)
Figure17.VariationinantennagainswithSY2valuechanges.(a)SY2=3mm.(b)SY2=3.5mm.(c)
SY2=4mm.
Basedontheabovediscussion,theantennabranchlengthL2andgroundinglength
SX2havebeenproventobethetwomainfactorsaffectingtheantenna’simpedance
Figure 16. Reflection coefficient of the antenna with changes in parameter SY2.
Electronics 2023,12, 2681 12 of 17
Electronics2023,12,xFORPEERREVIEW11of16
Figure15.ReflectioncoefficientoftheantennawithchangesinparameterSX2.
Figure16.ReflectioncoefficientoftheantennawithchangesinparameterSY2.
(a)(b)
(c)
Figure17.VariationinantennagainswithSY2valuechanges.(a)SY2=3mm.(b)SY2=3.5mm.(c)
SY2=4mm.
Basedontheabovediscussion,theantennabranchlengthL2andgroundinglength
SX2havebeenproventobethetwomainfactorsaffectingtheantenna’simpedance
Figure 17.
Variation in antenna gains with SY
2
value changes. (
a
) SY2 = 3 mm. (
b
) SY2 = 3.5 mm.
(c) SY2 = 4 mm.
Based on the above discussion, the antenna branch length L
2
and grounding length
SX
2
have been proven to be the two main factors affecting the antenna’s impedance match-
ing, while the length change in SY
2
is the main factor affecting the antenna’s resonance
frequency.
3. Physical Test of the Antenna
According to the simulation parameters of the simulation software, the aforementioned
Bluetooth serpentine antenna was processed with PCB technology, and the model was
tested using a multi-probe test system. A piece of 0.05-mm-thick double-sided copper
foil was used to change the dimensions of the metal ground. During the design test, the
variation in the metal ground was simulated by pasting lengths of copper foil on the surface
of the dielectric plate. The design length of the copper foil laying in the Y-axis direction
was 7.5 mm. The length of the PCB was 70 mm, and its width was 28 mm. The parameters
are shown in Table 2.
A 1.8-mm-diameter IPEX to SMA coaxial cable (RG178) with 50
Ω
impedance was
selected. The core was welded to the feed point of the Bluetooth serpentine antenna, and
the outer surface of the shielding layer was welded to the PCB ground plane. To ensure
Electronics 2023,12, 2681 13 of 17
solid contact, each PCB board and copper foil connection was soldered and tested with a
multimeter to ensure that the connection resistance value was close to zero. The effects can
be seen in Figure 18 (PCB board no. 1, 4, and 12, from left to right).
Table 2. Length of the ground plane.
PCB board no. 1 2 3 4 5 6 7 8
Ground plane length SYY/(mm) 7.5
11.25
15
18.75
22.5
26.25
30
33.75
PCB board no. 9 10 11 12 13 14 15
Ground plane length SYY/(mm) 37.5
41.25
45
48.75
52.5
56.25
60
Electronics2023,12,xFORPEERREVIEW12of16
matching,whilethelengthchangeinSY
2
isthemainfactoraffectingtheantenna’sreso-
nancefrequency.
3.PhysicalTes toftheAntenna
Accordingtothesimulationparametersofthesimulationsoftware,theaforemen-
tionedBluetoothserpentineantennawasprocessedwithPCBtechnology,andthemodel
wastestedusingamulti-probetestsystem.Apieceof0.05-mm-thickdouble-sidedcopper
foilwasusedtochangethedimensionsofthemetalground.Duringthedesigntest,the
variationinthemetalgroundwassimulatedbypastinglengthsofcopperfoilonthesur-
faceofthedielectricplate.ThedesignlengthofthecopperfoillayingintheY-axisdirec-
tionwas7.5mm.ThelengthofthePCBwas70mm,anditswidthwas28mm.Thepa-
rametersareshowninTab l e2.
Tab l e2.Lengthofthegroundplane.
PCBboardno.12345678
GroundplanelengthSYY/(mm)7.511.251518.7522.526.253033.75
PCBboardno.9101112131415
GroundplanelengthSYY/(mm)37.541.254548.7552.556.2560
A1.8-mm-diameterIPEXtoSMAcoaxialcable(RG178)with50Ωimpedancewas
selected.ThecorewasweldedtothefeedpointoftheBluetoothserpentineantenna,and
theoutersurfaceoftheshieldinglayerwasweldedtothePCBgroundplane.Toensure
solidcontact,eachPCBboardandcopperfoilconnectionwassolderedandtestedwitha
multimetertoensurethattheconnectionresistancevaluewasclosetozero.Theeffects
canbeseeninFigure18(PCBboardno.1,4,and12,fromlefttoright).
Figure18.PartsoftheserpentineantennaPCBweldedwithcoaxialcable.
Partoftheresultsofthelaboratorytestsusingthenetworkanalysisinstrument
(modelAgilentE8363B)andthecorrespondingsimulationparametersareshowninFig-
ure19;theyareshowntostaynearthecentralresonantfrequencypointof2.45GHz.This
provesthatdifferentgroundplanescanleadtodifferentS11performances.Agroundei-
thertoolargeortoosmallwillaffectthepresentationofthebestS11value,thusaffecting
theantenna’sperformance.OurresultsshowedthatwiththeincreaseintheY-axislength
SYofthegroundplane,thefrequencyoftheantennastartedtodrop,afterwhichthefre-
quencyoftheantennaroseagainwiththeincreaseinSY.Theactualtestparameter(S11)
datacurvedeviatedslightlyfromthesimulationresults,buttheoveralltrendinitscenter
frequencywasconsistentwiththeprevioussimulationresults.Duetothebeermatching
performanceofthecoaxialadaptercableused,itsmeasuredS11valuewasalsosmaller.
Figure 18. Parts of the serpentine antenna PCB welded with coaxial cable.
Part of the results of the laboratory tests using the network analysis instrument (model
Agilent E8363B) and the corresponding simulation parameters are shown in Figure 19;
they are shown to stay near the central resonant frequency point of 2.45 GHz. This proves
that different ground planes can lead to different S11 performances. A ground either too
large or too small will affect the presentation of the best S11 value, thus affecting the
antenna’s performance. Our results showed that with the increase in the Y-axis length
SY of the ground plane, the frequency of the antenna started to drop, after which the
frequency of the antenna rose again with the increase in SY. The actual test parameter (S11)
data curve deviated slightly from the simulation results, but the overall trend in its center
frequency was consistent with the previous simulation results. Due to the better matching
performance of the coaxial adapter cable used, its measured S11 value was also smaller.
Electronics2023,12,xFORPEERREVIEW13of16
Figure19.Experimentalresults.
Theantenna’scharacteristicsweretestedinthemicrowavelaboratory,asshownin
Figure20a,b.Figure21showsacomparisonbetweenthemaximumgainvaluesimulated
byHFSSandtheexperimentaltestvalue;thetestedgainvaluewasseeminglylargerthan
thesimulatedvalue.Therefore,theparameterofcoaxialcablewasaddedtothesimula-
tion,andtheresultsshowedthattheresultinggainvaluewaslargerthantheprevious
simulatedvalue.Additionally,experimentsinwhichthemetalgroundplanebelowthe
coaxiallinewaswrappedinwave-absorbingmaterialshavebeenperformed,meaning
that,theoretically,thecoaxialcablewouldnolongerradiatetheelectricfield.Themeas-
uredresultsareshowninFigure21(themeasuredcurvedenotedasusingwave-absorbing
materials);theantenna’sgainvaluewaslessthanthesimulationvalue.Therefore,we
notedthattheantenna’sgainduetotheelectricfieldradiatedbythecoaxialcablewas
greaterthanthesimulationresult[20].
(a)(b)
Figure20.ThetestPCBantenna’sperformanceinthemicrowavelab.(a)Microwaveanechoic
chamber(b)Measurementofantennaparametersinmicrowaveanechoicchamber
Figure 19. Experimental results.
The antenna’s characteristics were tested in the microwave laboratory, as shown in
Figure 20a,b. Figure 21 shows a comparison between the maximum gain value simulated
by HFSS and the experimental test value; the tested gain value was seemingly larger
than the simulated value. Therefore, the parameter of coaxial cable was added to the
simulation, and the results showed that the resulting gain value was larger than the
Electronics 2023,12, 2681 14 of 17
previous simulated value. Additionally, experiments in which the metal ground plane
below the coaxial line was wrapped in wave-absorbing materials have been performed,
meaning that, theoretically, the coaxial cable would no longer radiate the electric field.
The measured results are shown in Figure 21 (the measured curve denoted as using wave-
absorbing materials); the antenna’s gain value was less than the simulation value. Therefore,
we noted that the antenna’s gain due to the electric field radiated by the coaxial cable was
greater than the simulation result [20].
Electronics2023,12,xFORPEERREVIEW13of16
Figure19.Experimentalresults.
Theantenna’scharacteristicsweretestedinthemicrowavelaboratory,asshownin
Figure20a,b.Figure21showsacomparisonbetweenthemaximumgainvaluesimulated
byHFSSandtheexperimentaltestvalue;thetestedgainvaluewasseeminglylargerthan
thesimulatedvalue.Therefore,theparameterofcoaxialcablewasaddedtothesimula-
tion,andtheresultsshowedthattheresultinggainvaluewaslargerthantheprevious
simulatedvalue.Additionally,experimentsinwhichthemetalgroundplanebelowthe
coaxiallinewaswrappedinwave-absorbingmaterialshavebeenperformed,meaning
that,theoretically,thecoaxialcablewouldnolongerradiatetheelectricfield.Themeas-
uredresultsareshowninFigure21(themeasuredcurvedenotedasusingwave-absorbing
materials);theantenna’sgainvaluewaslessthanthesimulationvalue.Therefore,we
notedthattheantenna’sgainduetotheelectricfieldradiatedbythecoaxialcablewas
greaterthanthesimulationresult[20].
(a)(b)
Figure20.ThetestPCBantenna’sperformanceinthemicrowavelab.(a)Microwaveanechoic
chamber(b)Measurementofantennaparametersinmicrowaveanechoicchamber
Figure 20.
The test PCB antenna’s performance in the microwave lab. (
a
) Microwave anechoic
chamber (b) Measurement of antenna parameters in microwave anechoic chamber.
Electronics2023,12,xFORPEERREVIEW13of16
Figure19.Experimentalresults.
Theantenna’scharacteristicsweretestedinthemicrowavelaboratory,asshownin
Figure20a,b.Figure21showsacomparisonbetweenthemaximumgainvaluesimulated
byHFSSandtheexperimentaltestvalue;thetestedgainvaluewasseeminglylargerthan
thesimulatedvalue.Therefore,theparameterofcoaxialcablewasaddedtothesimula-
tion,andtheresultsshowedthattheresultinggainvaluewaslargerthantheprevious
simulatedvalue.Additionally,experimentsinwhichthemetalgroundplanebelowthe
coaxiallinewaswrappedinwave-absorbingmaterialshavebeenperformed,meaning
that,theoretically,thecoaxialcablewouldnolongerradiatetheelectricfield.Themeas-
uredresultsareshowninFigure21(themeasuredcurvedenotedasusingwave-absorbing
materials);theantenna’sgainvaluewaslessthanthesimulationvalue.Therefore,we
notedthattheantenna’sgainduetotheelectricfieldradiatedbythecoaxialcablewas
greaterthanthesimulationresult[20].
(a)(b)
Figure20.ThetestPCBantenna’sperformanceinthemicrowavelab.(a)Microwaveanechoic
chamber(b)Measurementofantennaparametersinmicrowaveanechoicchamber
Figure 21. Comparison between gain simulation results and measured results.
Figure 22a–c represents the 2D patterns of the simulated and measured antenna results
(SYY = 30 mm). The simulated and measured results were basically the same in trends, and
the differences between them were caused by the coaxial cables.
Electronics2023,12,xFORPEERREVIEW14of16
Figure21.Comparisonbetweengainsimulationresultsandmeasuredresults.
Figure22a–crepresentsthe2Dpaernsofthesimulatedandmeasuredantennare-
sults(SYY=30mm).Thesimulatedandmeasuredresultswerebasicallythesamein
trends,andthedifferencesbetweenthemwerecausedbythecoaxialcables.
(a)(b)(c)
Figure22.Simulatedandmeasuredantennapaern.(a)X-ZPlane.(b)Y-ZPlane.(c)X-YPlane.
Figure23showsthesimulatedandmeasuredantennaradiationefficiencygraph
(SYY=30mm)atacenterfrequencyofapproximately2.45GHz.Themeasuredefficiency
oftheantennawasclosesttothesimulationresult.Astheserpentineantennahasanarrow
bandwidth,andintheactualtest,theantennatransmissionlineandthedielectricplate
wouldincuragreatlosstotheantenna,themeasuredantennaefficiencyaenuationwas
higherthanthatinthesimulation.
Figure23.Simulatedandmeasuredradiationefficiencyresults.
Thisstudyprovidesanewapproachtoanalyzetheeffectofthegroundplane.Firstly,
CMAanalysiswasusedtoanalyzethevariationlawofthegroundplanesizeandresonant
frequency.Thisstudyfurtheranalyzedtheserpentineantennawithagroundedbranch,
andreachedtheconclusionthatthematchingperformanceoftheantennacanbeeffec-
tivelyimprovedbyadjustingthelengthofthebranch,andtheresonantfrequencycanbe
adjustedbychangingthesizeofthegroundplane.Thismethodhaspracticalimplications
forantennadesigners,especiallywhenappliedtoPCBboardantennas,effectivelysaving
designingtime.Tabl e 3showstheperformanceoftheantennadesignedinthisstudy,
comparedwiththatinsimilarstudies.
Tab l e3.Comparisonofthepreviousliteraturealongwithproposedwork.
RefAntennaTypeAntenna
Size
Gain
(dBi)
Radiation
Efficiency(%)InnovationPoints
[21]MonopoleantennasDiameter=30mm//Spiralgroundplanedesign
[22]Ellipticalplanarmonopole
antennas
R1=12mm
R2=9mm/90Theeffectsofthedimensionsoftherectangu-
largroundplane
[23]Multibandmonopolean-
tenna20×18.6mm2.0/Thegroundplaneinfluencehasbeenmini-
mizedbyadjustingthefeedline
Figure 22. Simulated and measured antenna pattern. (a) X-Z Plane. (b) Y-Z Plane. (c) X-Y Plane.
Electronics 2023,12, 2681 15 of 17
Figure 23 shows the simulated and measured antenna radiation efficiency graph
(
SYY = 30 mm
) at a center frequency of approximately 2.45 GHz. The measured efficiency
of the antenna was closest to the simulation result. As the serpentine antenna has a narrow
bandwidth, and in the actual test, the antenna transmission line and the dielectric plate
would incur a great loss to the antenna, the measured antenna efficiency attenuation was
higher than that in the simulation.
Electronics2023,12,xFORPEERREVIEW14of16
Figure21.Comparisonbetweengainsimulationresultsandmeasuredresults.
Figure22a–crepresentsthe2Dpaernsofthesimulatedandmeasuredantennare-
sults(SYY=30mm).Thesimulatedandmeasuredresultswerebasicallythesamein
trends,andthedifferencesbetweenthemwerecausedbythecoaxialcables.
(a)(b)(c)
Figure22.Simulatedandmeasuredantennapaern.(a)X-ZPlane.(b)Y-ZPlane.(c)X-YPlane.
Figure23showsthesimulatedandmeasuredantennaradiationefficiencygraph
(SYY=30mm)atacenterfrequencyofapproximately2.45GHz.Themeasuredefficiency
oftheantennawasclosesttothesimulationresult.Astheserpentineantennahasanarrow
bandwidth,andintheactualtest,theantennatransmissionlineandthedielectricplate
wouldincuragreatlosstotheantenna,themeasuredantennaefficiencyaenuationwas
higherthanthatinthesimulation.
Figure23.Simulatedandmeasuredradiationefficiencyresults.
Thisstudyprovidesanewapproachtoanalyzetheeffectofthegroundplane.Firstly,
CMAanalysiswasusedtoanalyzethevariationlawofthegroundplanesizeandresonant
frequency.Thisstudyfurtheranalyzedtheserpentineantennawithagroundedbranch,
andreachedtheconclusionthatthematchingperformanceoftheantennacanbeeffec-
tivelyimprovedbyadjustingthelengthofthebranch,andtheresonantfrequencycanbe
adjustedbychangingthesizeofthegroundplane.Thismethodhaspracticalimplications
forantennadesigners,especiallywhenappliedtoPCBboardantennas,effectivelysaving
designingtime.Tabl e 3showstheperformanceoftheantennadesignedinthisstudy,
comparedwiththatinsimilarstudies.
Tab l e3.Comparisonofthepreviousliteraturealongwithproposedwork.
RefAntennaTypeAntenna
Size
Gain
(dBi)
Radiation
Efficiency(%)InnovationPoints
[21]MonopoleantennasDiameter=30mm//Spiralgroundplanedesign
[22]Ellipticalplanarmonopole
antennas
R1=12mm
R2=9mm/90Theeffectsofthedimensionsoftherectangu-
largroundplane
[23]Multibandmonopolean-
tenna20×18.6mm2.0/Thegroundplaneinfluencehasbeenmini-
mizedbyadjustingthefeedline
Figure 23. Simulated and measured radiation efficiency results.
This study provides a new approach to analyze the effect of the ground plane. Firstly,
CMA analysis was used to analyze the variation law of the ground plane size and resonant
frequency. This study further analyzed the serpentine antenna with a grounded branch,
and reached the conclusion that the matching performance of the antenna can be effectively
improved by adjusting the length of the branch, and the resonant frequency can be adjusted
by changing the size of the ground plane. This method has practical implications for
antenna designers, especially when applied to PCB board antennas, effectively saving
designing time. Table 3shows the performance of the antenna designed in this study,
compared with that in similar studies.
Table 3. Comparison of the previous literature along with proposed work.
Ref Antenna Type Antenna
Size
Gain
(dBi)
Radiation
Efficiency (%) Innovation Points
[21] Monopole antennas Diameter = 30 mm / / Spiral ground plane design
[22]Elliptical planar
monopole antennas
R1 = 12 mm
R2 = 9 mm / 90
The effects of the dimensions
of the rectangular ground
plane
[23]Multiband monopole
antenna 20 ×18.6 mm 2.0 /
The ground plane influence
has been minimized by
adjusting the feed line
[24]Printed multiband
monopole antenna 6×4 mm 6.4 85
An air gap was set between
the proposed antenna and
system ground
Proposed
work
The serpentine
antenna 10.9 ×7.5 mm 1.17 75
The impact of ground plane
size by CMA analysis, and the
effects of the branch length.
4. Conclusions
To summarize, the ground plane of the serpentine antenna, as part of the antenna,
has a huge influence on its performance; it cannot simply be regarded as a monopole
antenna device, but as a variation of the monopole antenna. Based on such a hypothesis,
this study, taking the serpentine antenna as an example, applied the theory that the ground
plane and the antenna will together constitute the radiating body; it also adopted the CMA
to first analyze the relationship between the size of the ground plane of the serpentine
antenna and its resonant frequency, followed by a discussion of the relationship between
Electronics 2023,12, 2681 16 of 17
the size of the ground plane of the serpentine antenna and its surface currents. Finally, this
study used HFSS to discuss the effects of ground plane size and grounding branch length
on the antenna’s characteristics in detail, while also verifying simulation results through
processing tests. These research results have critical and real engineering significance;
we found, for example, that by changing the ground plane size, the antenna’s resonance
frequency can be adjusted, and by changing the branch length of the antenna, the antenna’s
matching performance and bandwidth can be effectively improved. Such findings will
hopefully provide a reference for future engineering designs.
Author Contributions:
Methodology and initial idea, P.G. and J.L.; software development and
analysis, P.G.; supervision, J.L. and W.W.; validation, J.L.; data collection, P.G.; writing, P.G. and J.L.;
read and reviewed by J.L. and W.W. All authors have read and agreed to the published version of the
manuscript.
Funding:
Funding was provided by The National Key R&D Program (2018YFB2002700), the CAS
Strategic Pioneering Science and Technology Special Project (Class A) (XDA22020100), CAS-funded
projects (201510280052 XMXX201200019933), and the CAS STS Program (2019T3015).
Data Availability Statement: Data can be provided upon request.
Acknowledgments:
The authors gratefully acknowledge the anonymous reviewers. Their valuable
comments and suggestions were very helpful in improving the presentation of this paper and of our
future work.
Conflicts of Interest: The authors declare no conflict of interest.
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