Recei ed Augus 12, 2021, accep ed Augus 26, 2021, da e o publica ion Augus 31, 2021, da e o cu en e sion Sep embe 10, 2021.
Digi al Objec Iden i ie 10.1109/ACCESS.2021.3109522
The Design o Pixela ed SIW Ho n An ennas Wi h
Nea ly Equal Beamwid hs Using Bina y Ink
S amp Op imiza ion
JAROSLAV ZECHMEISTER , (G adua e S uden Membe , IEEE),
JAROSLAV LACIK , (Membe , IEEE), AND PETR KADLEC , (Membe , IEEE)
Depa men o Radio Elec onics, Facul y o Elec ical Enginee ing and Communica ion, B no Uni e si y o Technology, 616 00 B no, Czech Republic
Co esponding au ho s: Ja osla Zechmeis e (ja osla [email p o ec ed]) and Ja osla Lacik ([email p o ec ed])
This wo k was suppo ed in pa by he In e nal G an Agency o B no Uni e si y o Technology unde P ojec FEKT-S-20-6526, and in
pa by Czech Science Founda ion unde G an 19-06049S.
ABSTRACT In his pape , linea ly and ci cula ly pola ized single-laye Subs a e In eg a ed Wa eg-
uide (SIW) ho n an ennas wi h nea ly equal hal powe beamwid hs in p incipal planes o he 24 GHz
ISM band a e designed. The uniqueness o he solu ion lies in he applica ion o a pixela ed s uc u e o
he design o hese SIW ho n an ennas. Fo he design, a no el heu is ic algo i hm called Bina y Ink S amp
Op imiza ion is p oposed. A i s , he abili y o he p oposed algo i hm is p o ed o e i een benchma k
unc ions and compa ed wi h he esul s o six s a e-o - he-a op imiza ion algo i hms. Then, he no el
algo i hm is exploi ed o he design o he pixela ed pa o he an ennas. The an ennas a e manu ac u ed
using low-cos 3D p in ing echnology. The expe imen al esul s p o e ha he linea ly pola ized an enna has
a e lec ion coe icien below −18 dB in he whole 24 GHz ISM band. A he cen e equency o his band,
he an enna gain is 14.2 dBi, and he le el o side lobes is below −15 dB in E and H-planes. In addi ion, E and
H-plane hal powe beamwid hs a e 26.5◦and 25◦, espec i ely. The ci cula ly pola ized an enna adia es a
igh -hand ci cula ly pola ized (RHCP) wa e, he e lec ion coe icien , and axial a io a e below −12 dB
and 3 dB in he whole 24 GHz ISM band, espec i ely. A he cen e equency o his band, he an enna
gain is 8.9 dBi and he le el o side lobes is below −7.4 dB in bo h p incipal planes. Fu he , he hal powe
beamwid hs in p incipal planes a e 30.6◦and 33.4◦, espec i ely.
INDEX TERMS Subs a e in eg a ed wa eguide (SIW), SIW ho n an enna, pixela ed an enna, disc e e
e olu iona y algo i hm, bina y op imiza ion.
I. INTRODUCTION
Ho n an ennas a e widely used in wi eless applica ions due
o hei simple s uc u e, high gain and e iciency, and wide
bandwid h. Howe e , since hey a e based on con en ional
wa eguides, ho n an ennas su e om la ge olume and
weigh , and high ab ica ion cos s. P omising al e na i es a e
Subs a e In eg a ed Wa eguide (SIW) ho n an ennas. They
a e elec ically simila o con en ional ho n an ennas based
on he ec angula wa eguide. Howe e , hey can be easily
in eg a ed wi h plana ci cui s and can be ab ica ed by a low-
cos p in ci cui boa d p ocess.
Un o una ely, SIW ho n an ennas ha e na ow bandwid h,
high le els o side and back adia ion lobes, and p ima ily
The associa e edi o coo dina ing he e iew o his manusc ip and
app o ing i o publica ion was Ladislau Ma eko i s .
unequal adia ion pa e ns in he E and H-plane. Se e al
echniques can be exploi ed o he pe o mance enhance-
men o SIW ho n an ennas. A highe gain and na owe
beamwid h can be achie ed by adding a dielec ic load in
on o he an enna ape u e [1]. Fu he , a highe gain can
also be achie ed by adjus ing he shape o he dielec ic load,
o by pe o a ing he load [2], [3]. P in ed me al pa allel
pla es [4] o pe iodical ansi ions [5] on op and bo om o
he load a e also easible app oaches o he gain enhancemen
o SIW ho n an ennas. Al hough hese app oaches imp o e
he adia ion p ope ies o SIW ho n an ennas, hese an ennas
s ill p o ide unequal hal powe beamwid hs (HPBW) in E
and H-plane. SIW ho n an ennas wi h almos equal E and
H-plane beamwid hs we e p esen ed in [6] and [7]. Howe e ,
he di e ence be ween bo h beamwid hs is s ill mo e han
30%. Ho n an ennas based on SIW echnology wi h equal
122216 This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/ VOLUME 9, 2021
J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO
beamwid hs in E and H-plane we e p esen ed in [8] and [9].
Un o una ely, hese s uc u es a e mul i-laye ed, he e o e
he main bene i s o single-laye ed SIW ho n an ennas, such
as ease o manu ac u ing and a low p o ile, a e de alued.
Ci cula pola iza ion (CP) p o ides se e al ad an ages
compa ed o linea pola iza ion. CP an ennas a e an impo -
an echnology o sa elli e and mobile communica ions,
na iga ion sys ems, e c. The main ad an age o CP lies
in i s immuni y o mul i-pa h in e e ences and pola iza-
ion misma ch [10]. CP SIW ho n an ennas a e mainly
composed o wo o mo e an enna elemen s o ob ain o hog-
onal modes [11]–[14]. In [15] an inhomogeneous pola -
ize is placed in on o he an enna ape u e o achie e
CP. An an ipodal ape ed s uc u e is p esen ed in [16].
I desc ibes an e ec i e app oach o designing a CP SIW ho n
an enna.
The goal o his pape is o desc ibe he design o lin-
ea ly and ci cula ly pola ized single-laye SIW ho n an en-
nas wi h equal HPBW in main o hogonal adia ion planes.
A pixela ed app oach is applied o achie e desi ed pe o -
mance. Pixela ed s uc u es p o ide high a iabili y o he
inal shape [17]–[19]. In gene al, he pixeliza ion design ech-
nique equi es no a p io i de ined an enna empla e. The e-
o e, his app oach may lead o uncon en ional solu ions o
load shapes. Howe e , wi h an inc easing numbe o pixels,
he complexi y o he op imiza ion p oblem g ows exponen-
ially. The e o e, an e icien op imiza ion p ocedu e has o
be adop ed. Pixela ed pa e ns a e exploi ed in an enna appli-
ca ions mos ly o inc ease bandwid h o dec ease an enna
dimensions. The Gene ic Algo i hm (GA) is used in he
majo i y o a ailable s udies as an op imiza ion ool. The GA
upda es a bina y ec o using selec ion, c osso e , and mu a-
ion p ocedu es. Du ing he op imiza ion p ocess, each bi
has equal signi icance. Howe e , in eal-wo ld applica ions
o bina y pa e ns, some pixels can ha e a bigge in luence on
he s uc u e p ope ies. Due o his ac , we p opose an e o-
lu iona y op imiza ion algo i hm named Bina y Ink S amp
Op imiza ion, e lec ing he signi icance o he bi s du ing he
op imiza ion p ocess. Tha is he key bene i compa ed o he
es o he algo i hms in e ms o bina y pa e n op imiza ion.
II. BINARY INK STAMP OPTIMIZATION
A. ALGORITHM DESCRIPTION
Bina y Ink S amp Op imiza ion (BISO) is a heu is ic op i-
miza ion algo i hm o bina y p oblems. BISO is inspi ed
by s amps wi h di e en ink sa u a ion. A se o s amps
co esponds o a se o so a bes indi iduals. Thei ink
sa u a ion is de e mined by hei i ness alues. The nex
gene a ion is de e mined based on a p obabili y ma ix, which
can be imagined as an imp in o all s amps o e each o he .
A da ke posi ions, he e is a highe p obabili y o gene a ing
‘‘1’’. On he con a y, ‘‘0’’ will be gene a ed mo e o en a
b igh e posi ions.
Gene al s eps o BISO a e depic ed in he low cha
in Fig. 1. The ollowing pa ame e s a e se a he s a o he
op imiza ion un:
FIGURE 1. Flow cha o he bina y ink s amp op imiza ion algo i hm.
•Npop – numbe o indi iduals in each i e a ion,
•Neli – numbe o selec ed eli is indi iduals,
•Ni e – maximal numbe o i e a ions,
•p obMin – he minimal p obabili y o gene a ing ‘‘1’’ in
he nex i e a ion,
•p obMinRST – he minimal p obabili y o gene a ing
‘‘1’’ in he nex i e a ion when he algo i hm ge s s uck
in local ex eme,
• s Coe – c i e ia o ese ing he popula ion,
•sigCoe – he s eepness o he sigmoid unc ion.
A he s a , an ini ial popula ion is andomly gene a ed
as a bina y ma ix o size Npop ×Ndim, whe e Ndim is
he numbe o op imized a iables. Rows in his ma ix
co espond o he indi iduals o he i s popula ion. A e
he i ness e alua ion, indi iduals a e so ed acco ding o
hei alue. A se o indi iduals wi h a be e ank in he
o de ed se a e selec ed. A his poin , Hamming dis ances
be ween hese eli e indi iduals a e de e mined and compa ed
wi h Ndim × s Coe . This pa is designed o a oid he
algo i hm being s uck in a local minimum. The dec easing
VOLUME 9, 2021 122217
J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO
TABLE 1. Resul s o benchma k unc ions.
Hamming dis ance be ween mul iple indi iduals indica es
ha he sub- egion o he domain space has been exhaus i ely
explo ed and he algo i hm eaches he local minimum. In he
nex s ep, he p obabili y ec o is de e mined. The ec o is
de ined as a weigh ed sum o componen s acco ding o he
bes indi iduals:
p obVec (i)
=1
Neli
Neli
X
k=1([1 −w(k)],i Eli e(k,i)=1
w(k),i Eli e(k,i)=0(1)
whe e iis he index o he a iable, Eli e is he ma ix o he
eli e indi iduals, kis he index o he indi idual in Eli e and
wdeno es he weigh o an indi idual acco ding o:
w(k)=0.5−p obMin
1+exp h−1
meanE (k)−sigCoe ×meanEi(2)
whe e meanE is he mean i ness alue o cu en eli e indi-
iduals and deno es he i ness alue. The ange o he
sigmoid unc ion (2) is om p obMin (speci ied by use ) o
0.5 – p obMin. These wo alues de e mine he minimum
122218 VOLUME 9, 2021
J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO
TABLE 2. Pa ame e s o con en ional SIW ho n an enna.
and maximum p obabili y o gene a ing ‘‘1’’. The p obMin
pa ame e has a signi ican in luence on he con e gence a e
o he algo i hm. Fo high alues o he pa ame e (p obMin
>0.1), he con e gence a e is low, and achie ing an op i-
mum equi es a high numbe o i e a ions. Howe e , o low
alues o he pa ame e , he algo i hm is s ongly descend-
ing owa d he nea es minimum. Fo his pu pose, we ha e
implemen ed he so-called ‘‘ ese ’’ ou ine. I he Hamming
dis ance be ween he eli e indi iduals o one popula ion is
below Ndim × s Coe , he alue o he pa ame e p obMin is
se o p obMinRST. In he case ha he alue o p obMinRST
is 0.5, he nex popula ion is gene a ed andomly.
The new popula ion is gene a ed acco ding o he ollowing
equa ion in e e y i e a ion:
newPop(j,i)=(1,i and ≤p obVec (i)
0,i and >p obVec (i)
j∈{1,2,...,Npop}(3)
B. BENCHMARK RESULTS
The p oposed algo i hm is es ed on 15 benchma k unc ions
wi h bina y a iables. De ini ions o he benchma k unc ions
a e summa ized in Appendix. Mos o he benchma k unc-
ions ( 1- 13) a e adop ed om [20]. The selec ed benchma k
unc ions can be di ided in o wo ca ego ies - unimodal ( 1- 7)
and mul imodal ( 8- 13) unc ions. Ano he wo es p oblems
( b1, b2) we e p oposed as bina y es unc ions which beha e
like he eal op imiza ion o ou an enna design.
We ha e es ed he BISO algo i hm on hese unc-
ions and compa ed i wi h six op imiza ion algo i hms,
Bina y Pa icle Swa m Op imiza ion (BPSO) [21], Gene ic
Algo i hm (GA) [22], Bina y Co a iance Ma ix Adap a-
ion E olu ion S a egy (BCMAES) [23], Bina y Ba Algo-
i hm (BBA) [20], Bina y D agon ly Algo i hm (BDA) [24]
and Mul i-Ve se Op imiza ion (MVO) [25]. The ob ained
alues o benchma k unc ions wi h ou di e en dimen-
sions Ndim ={30,120, 300, 900} a e shown in Table 1.
Please no e ha he alues a e a e aged o e 100 independen
op imiza ion uns. Values in pa en heses deno e he s anda d
de ia ion o he esul s. The unimodal unc ions a e use ul
in e ms o examining he con e gence a e o op imiza ion
algo i hms. The mul imodal unc ions benchma k he abili y
o algo i hms o a oid local minimums. BISO p o ides a
good capabili y in sol ing unimodal as well as mul imodal
p oblems and ou pe o ms he o he algo i hms in mos cases.
In gene al, BISO is a sui able al e na i e o op imizing
bina y p oblems, especially o hose wi h a high numbe o
a iables.
FIGURE 2. Simpli ied model o con en ional SIW ho n an enna, ins ead o
ias, e ical solid walls a e used.
FIGURE 3. No malized simula ed adia ion pa e ns o simpli ied SIW
ho n an enna a 24 GHz. HPBW is indica ed by e ical dashed lines.
III. DESIGN OF ANTENNAS
We exploi he p oposed BISO algo i hm o designing lin-
ea ly and ci cula ly pola ized SIW ho n an ennas wi h nea ly
equal beamwid hs. To ca y ou ou goal, we exploi a
SIW ho n an enna designed o maximal di ec i i y depic ed
in Fig. 2 and de ined by he pa ame e s in Table 2. The
no malized adia ion pa e ns o he simpli ied SIW ho n
an enna a e shown in Fig 3. The E and H-plane beamwid hs
o he con en ional an enna a e 138.6◦and 25.6◦, espec-
i ely. The con en ional an enna p o ides a gain o 8.2 dBi
(please no e ha he losses o he subs a e we e no consid-
e ed in his case). The pe o mance enhancemen o such an
an enna is achie ed by ex ending he an enna ape u e and
i s pixeliza ion. This s ep depends on he an enna pola iza-
ion. The e o e, i will be desc ibed in he ollowing sec ions
indi idually. The pa ame e s o he BISO algo i hm du ing
he op imiza ion we e se as shown in Table 3. Bo h an ennas
a e designed o a subs a e wi h a hickness o 3.3 mm and
a ela i e pe mi i i y o 2.75. The subs a e is made o an
XT co-polyes e 3D p in ed ilamen om Colo abb [26].
The ela i e pe mi i i y o his ma e ial is published in [27].
VOLUME 9, 2021 122219
J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO
TABLE 3. Pa ame e s se ing o BISO algo i hm du ing an enna
op imiza ion.
FIGURE 4. Simpli ied model o he p oposed linea ly pola ized pixela ed
SIW ho n an enna.
The elec omagne ic simula ions we e pe o med by CST
S udio Sui e, whe eas he p ocess o op imiza ion was
con olled by an in-house MATLAB code. Fo he sake
o he speed o he design p ocess, a simpli ied model
o he SIW ho n an enna wi h e ical solid walls was
exploi ed.
A. LINEARLY POLARIZED ANTENNA
The linea ly pola ized (LP) an enna is designed o achie e
equal HPBW in he E and H-plane o he adia ion pa e n
wi h emphasis on SLL educ ion. The an enna is axially sym-
me ical as shown in Fig. 4. The pixeliza ion is applied o e a
g id in e sec ed wi h he body o he an enna. Cells assigned
FIGURE 5. Op imized bina y pa e n o he linea ly pola ized an enna.
FIGURE 6. Op imized linea ly pola ized an enna wi h SIW s uc u e and
coaxial-SIW ansi ion.
wi h ‘‘1’’ a e illed by a subs a e ma e ial and cells wi h
‘‘0’’ a e illed by ai . The pixel g id geome y is con olled
using pa ame e s lc1-lc6, which a e in ege mul iples o he
side leng h o he pixels and he e o e e e o he numbe
o pixels in he columns. Bi s o he op imized pa e n which
a e ou side he g id become so-called dummy pixels because
hese posi ions a e de ined as illed by he subs a e ma e ial
and co e ed by a me al laye . A e a ew ials, we obse ed
ha he shape o he g id can be oughly app oxima ed wi h
a pa abolic shape, he e o e some o he pixels a e alloca ed
o de e mine he pa ame e s lc1-lc7. This app oach helps o
educe he numbe o a iables ( hese pixels a e highligh ed
wi h blue colo in Fig. 5). The a iable lc7 is used o de e mine
he leng h o he edge me alliza ion.
The o al numbe o pixels o he op imized pa e n is
6×28. The i ness unc ion is speci ied as ollows:
=q S112+ HPBW2+ SLL2+ G2(4)
122220 VOLUME 9, 2021

J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO
TABLE 4. Pa ame e s o he p oposed linea ly pola ized an enna.
FIGURE 7. No malized E- ield dis ibu ion o he linea ly pola ized
an enna a 24.125 GHz in a) H-plane and b) E-plane.
whe e pa ame e s S11, HPBW, SLL, and Ga e de ined by he
ollowing equa ions:
S11 =(S11/15 +1,i S11 ≥ −15
0,i S11 <−15 (5)
HPBW =1HPBW
10 (6)
SLL =




1,i SLL <8
−SLL/12 +5/3,i 8 ≤SLL ≤20
0,i SLL >20
(7)
FIGURE 8. Manu ac u ed p o o ype o he linea ly pola ized an enna.
FIGURE 9. Measu ed and simula ed e lec ion coe icien o he linea ly
pola ized an enna.
and
G=




1,i G<8
−G/12 +5/3,i 8 ≤G≤15
0,i G>15
(8)
whe e S11 is he e lec ion coe icien a 24 GHz in dB,
1HPBW is he di e ence be ween HPBW in he E and
H-plane, SLL is he side lobe le el a 24 GHz, and Gis he gain
in he main di ec ion a 24 GHz, espec i ely. The op imized
pixela ed pa e n is shown in Fig. 5. The simpli ied model
is ans o med o he SIW s uc u e and he coaxial-SIW
ansi ion is added (see Fig. 6). Dimensions o he op imized
model a e lis ed in Table 4. No e ha he coaxial eed p obe
leng h in he subs a e lin is 1.8 mm. Values in pa en heses a e
he ound op imal leng hs o lc1-lc7. The E- ield dis ibu ions
a he cen e equency o he 24 GHz ISM band a e shown in
Fig. 7. Ob iously, he E- ield is ocused by he pixela ed pa .
The dielec ic pa o he p oposed an enna is made o an
XT co-polyes e om Colo abb [26] using a used deposi ion
VOLUME 9, 2021 122221
J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO
TABLE 5. Compa ison o he linea ly pola ized an enna wi h s a e-o - he-a wo ks.
FIGURE 10. No malized measu ed and simula ed adia ion pa e ns o he linea ly pola ized an enna a 24.125 GHz a) E-plane and b) H-plane. Measu ed
HPBW is indica ed by e ical dashed lines.
modeling 3D p in e P usa i3 MK3S wi h a 0.25 mm nozzle.
The subs a e is ully p in ed wi hou any pos -p ocessing
s eps, such as d illing, g inding, e c. The me al laye is made
o coppe oil and i s op imized shape is cu . The e ical
walls o he SIW s uc u e a e c ea ed by a coppe wi e o
diame e 0.8 mm. The indi idual ias a e solde ed o he op
and bo om side o he an enna and he SMA connec o is
solde ed.
The manu ac u ed LP an enna (see Fig. 8) was measu ed
in an anechoic chambe o expe imen ally e i y i s pe -
o mance. The compa ison o he measu ed and simula ed
e lec ion coe icien o e he equency band 22-26 GHz is
shown in Fig. 9. The measu ed e lec ion coe icien o he
p oposed an enna is below -18 dB in he whole 24 GHz ISM
band. The measu ed adia ion pa e ns (see Fig. 10) show
good ag eemen wi h he simula ed ones. A small disc ep-
ancy be ween he measu ed and simula ed esul s is caused
by he inaccu acy o he ab ica ion echnology, and u he
by he ac ha losses o he subs a e we e no conside ed
du ing he design p ocess o he an enna. The measu ed gain
o he an enna is 14.2 dBi a he cen al equency o he
24 GHz ISM band, he SLL is below -15 dB, E and H-plane
beamwid hs a e 26.5◦and 25◦, espec i ely. The nea ly equal
TABLE 6. Pa ame e s o he op imized ci cula ly pola ized an enna.
HPBW in he E and H-plane is achie ed o he single-laye
con igu a ion o he an enna. In his scope, he p oposed
an enna ou pe o ms he s a e-o - he-a wo ks (see Table 5).
Please no e ha he SMA connec o s used o he an ennas
eeding a e a ed up o 26.5 GHz which is su icien conside -
ing he ac ha he an ennas a e designed o he 24 GHz ISM
band. The measu ed −10 dB S11 bandwid hs (BW) canno
122222 VOLUME 9, 2021
J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO
FIGURE 11. Simpli ied model o he p oposed ci cula ly pola ized SIW
ho n an enna.
be conside ed alid, because hey a e beyond he connec o s
ope a ing ange. Consequen ly, he p esen ed alues o -10 dB
S11 BW a e acco ding o he simula ed da a.
B. CIRCULARLY POLARIZED ANTENNA
The app oach o gene a e he dielec ic pa o he CP an enna
is simila o he LP one. The pixela ed g id o he CP an enna
is also axially symme ical. Howe e , he op and bo om
me al laye s a e an ipodal (see Fig. 11). We we e inspi ed
by he con igu a ion p esen ed in [16] whe e he abili y o
an ipodal s uc u e gene a ing CP is p esen ed.
The pixel g id geome y is also con olled using pa ame e s
lc1-lc6, which e e o he numbe o pixels in he columns,
plus addi ional pa ame e s lc7-lc13 ha de e mine he es o
FIGURE 12. Op imized bina y pa e n o he ci cula ly pola ized an enna.
FIGURE 13. Op imized ci cula ly pola ized an enna wi h SIW s uc u e
and coaxial-SIW ansi ion.
he adjus ed pa o he me al laye . Pixels alloca ed o de e -
mining pa ame e s lc1-lc13 a e highligh ed wi h blue colo
in Fig. 12.
The o al numbe o pixels o he op imized pa e n is
6×28. The i ness unc ion is speci ied as ollows:
=q S112+ HPBW2+ AR2+ G2(9)
whe e S11 and HPBW a e de ined as (5) and (6), espec i ely.
The i ness pa ame e o axial a io AR is de ined as:
AR =




1,i AR >10
−AR/7−3/7,i 3 ≤AR ≤10
0,i AR <3
(10)
VOLUME 9, 2021 122223
J. Zechmeis e e al.: Design o Pixela ed SIW Ho n An ennas Wi h Nea ly Equal Beamwid hs Using BISO
FIGURE 14. No malized E- ield dis ibu ion o he ci cula ly pola ized
an enna a 24.125 GHz in a) xy plane and b) yz plane.
FIGURE 15. Manu ac u ed p o o ype o he ci cula ly pola ized an enna.
whe e AR is he axial a io in he main di ec ion a 24 GHz.
The desi ed alue o gain is se as 13 dBi and Gis de ined as:
G=




1,i G<8
−G/5+13/5,i 8 ≤G≤13
0,i G>13
(11)
whe e Gis gain in he main di ec ion a 24 GHz.
FIGURE 16. Measu ed and simula ed e lec ion coe icien o he
ci cula ly pola ized an enna.
FIGURE 17. Measu ed and simula ed axial a io o he ci cula ly pola ized
an enna.
The op imized pa e n is shown in Fig. 12. and he dimen-
sions o he p oposed CP an enna a e lis ed in Table 6. Val-
ues in pa en heses deno e he ound op imal leng hs o he
pa ame e s lc1-lc13. The simpli ied model o he CP an enna
is also ans o med o he SIW s uc u e and he coaxial-SIW
ansi ion is added (see Fig. 13). The leng h o he eeding
coaxial p obe in he subs a e lin is 1.8 mm. The E- ield
dis ibu ion o he p oposed CP an enna is shown in Fig. 14.
The CP an enna p o ides a less uni o m E- ield a he ape u e
compa ed o he LP an enna.
The an enna is manu ac u ed in he same way as o he
LP an enna p esen ed in he p e ious sec ion. The ab ica ed
sample o he an enna is shown in Fig. 15. The measu ed
and simula ed e lec ion coe icien o e he equency band
22-26 GHz is shown in Fig. 16. I emains below -12 dB o
he whole 24 GHz ISM band. The measu ed and simula ed
axial a io (see Fig. 17) is below 3 dB o e he ope a ing
band. The measu ed adia ion pa e ns (see Fig. 18) in he
122224 VOLUME 9, 2021