IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL., NO., 1
Pa ame e s Cha ac e iza ion o Dielec ic Ma e ials
Samples in Mic owa e and Millime e -Wa e Bands
Ma io P´
e ez-Esc ibano, S uden Membe , IEEE, and En ique M´
a quez-Segu a, Senio Membe , IEEE
Abs ac —In his wo k, an op imized b oadband me hod
using mul ilaye ansmission lines o cha ac e ize dielec ic
pe mi i i y and loss angen o ma e ial samples is p esen ed.
Fo his pu pose, a mic os ip line loaded wi h a piece o he
selec ed dielec ic o be cha ac e ized is used. F om wo-po
measu emen s, and using di e en leng h lines, he p opaga ion
cons an can be ob ained. To minimize andom e o s and o
imp o e he accu acy, an o e de e mina ion o he me hod
inc easing he numbe o lines measu ed and a c i e ia o choose
he op imal line leng hs is conside ed. Fi s ly, he measu emen
me hod i sel is applied o unco e ed mic os ip lines and an
accu a e model o he subs a e is ob ained. Secondly, he lines
a e co e ed wi h se e al ma e ials, made by FDM addi i e man-
u ac u ing echnique, such as Ac yloni ile Bu adiene S y ene
(ABS), Polylac ic Acid (PLA), High Impac Polys y ene (HIPS),
The moplas ic Polyu e hane (TPU), Copolyes e (CPE), FLEX,
Polye hylene Te eph hala e Glycol (PETG) and Nylon. A model
o he ansmission line conside ing he co e is de eloped and
an elec omagne ic simula o is used o indi ec ly de e mine
he co e ma e ial elec ical pa ame e s. Resul s show excellen
ag eemen wi h elec omagne ic simula ions in he 0.1- o 67-
GHz equency band, so hey assess he sui abili y o he p oposed
me hod.
Index Te ms—b oadband measu emen s, dielec ic ma e ials,
EM ma e ial cha ac e iza ion, p opaga ion cons an , ansmis-
sion line measu emen s
I. INTRODUCTION
NOWADAYS, he numbe o ma e ials and manu ac u ing
echniques a e a ailable on he ma ke is inc easing
apidly. Conc e ely, addi i e manu ac u ing echnologies ha e
become one o he mos esea ched opic in many scien i ic
ields. Thei main ad an ages includes he low cos , he
possibili y o g ea cus omiza ion, he apid p o o yping, he
design lexibili y o he possibili y o combining ma e ials.
Conc e ely, in mic owa e a ea, se e al designs ha e been
p oposed o di e en pu poses [1]–[4]. Mechanical p ope ies
a e usually a ailable om manu ac u e s. Howe e , despi e
he la ge amoun o ma e ials a ailable, he e is no much
in o ma ion abou he elec omagne ic p ope ies o hese
ma e ials. Fu he mo e, he wide a ie y o manu ac u e s
and ma e ials a ailable make i e y necessa y o achie e
cha ac e iza ion echniques as simple as possible, so ha hey
can be accessible o all designe s who wan o use his kind o
This wo k has been suppo ed by he Spanish Minis e io de Econom´
ıa,
Indus ia y Compe i i idad unde P ojec ADDMATE TEC2016-76070-C3-3-
R (AEI/FEDER, UE) and by he Spanish Minis e io de Educaci´
on, Cul u a y
Depo e unde G an FPU16/00246.
M. P´
e ez-Esc ibano and E. M´
a quez-Segu a a e wi h he Depa amen o de
Ingenie ´
ıa de Comunicaciones, Escuela T´
ecnica Supe io de Ingenie ´
ıa de
Telecomunicaci´
on, Uni e sidad de M´
alaga, 29071, M´
alaga, Spain (e-mail:
[email p o ec ed]; [email p o ec ed]).
ma e ials. Manu ac u e s o addi i e manu ac u ing ma e ials
om ime o ime change he o mula ion o ma e ials o
e en di e en ba ches can p oduce di e en elec omagne ic
p ope ies. Fo hose easons and conside ing he ad an ages
and g ow h o his manu ac u ing echnology, in es iga ions on
p in ed elec omagne ic ma e ial p ope ies ha e g own in he
las ew yea s [5]. Dissipa ion ac o and dielec ic pe mi i i y
is de e mined in an ex ao dina y band wid h, o 100 MHz
up o he limi o he ec o ne wo k analyze a ailable, 67
GHz.
O e ime, nume ous pape s ha e been p oposed in he li e -
a u e o cha ac e ize he p opaga ion cons an o plana ans-
mission lines. They can be g ouped mainly in wo di e en
ca ego ies. On he one hand, esonan me hods [6], [7] allow
o ob ain e y accu a e esul s and good losses es ima ion,
apa om showing g ea e independence o he e ec s caused
by ansi ions. Howe e , hey jus p o ide alues a he eso-
nan equencies, so hey can no be use ul when b oadband
cha ac e iza ion is equi ed. Se e al o hese me hods ha e
been p oposed o he cha ac e iza ion o p in ed ma e ials [8],
[9]. On he o he hand, b oadband me hods [10], [11] p o ide
con inuous esul s wi hin he whole equency band, because
hey ely on he p opaga ion o he ansmission line modes.
Ne e heless, hei accu acy depends on he p ecision o he
expe imen s and hey show a wo s beha io p ecisely a
esonances. In gene al, b oadband echniques ex ac he p op-
aga ion cons an om he measu emen s o pa ame e ma ices
o ansmission lines wi h di e en leng hs. They ha e a signi -
ican d awback when losses in he ansmission medium unde
es a e low, because he a enua ion cons an can be hidden
by noise and andom e o s. Se e al b oadband me hods ha e
been used in mic owa e [12] and millime e bands [13] o
cha ac e ize p in ed ma e ials. Ano he no el s a egy o he
cha ac e iza ion o ma e ials is he one p oposed in [14],
based on mic os ip lines o a iable wid h. I is no ewo hy
ha mos o hese me hods need calib a ed S pa ame e s.
On he o he hand, in his pape he me hod used do no
equi e calib a ion due o i is based in ma hema ical in a ian .
Some o he s me hod, such as hose based on Nicolson-Ross-
Wie me hod, do equi e calib a ion o he S-pa ame e s o
elimina e sys ema ic e o s [15], [16]. In o de o inc ease he
pe o mance o measu emen me hods, he o e de e mina ion
o samples needed is usually conside ed [17]–[19].
I is impo an o men ion ha hese ma e ials unde con-
side a ion in his pape do no eplace con en ional low loss
ma e ials necessa y especially an millime e band as subs a e
o mic os ip an enna o ins ance. Howe e , hese ma e ials
can be used o gene a e s uc u es in p o o yping s ages and i-
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL., NO., 2
A
A B
B
li
li+1
a1a2
b1b2
e−γli
e−γli
SA
11
SA
12
SA
21
SA
22 SB
11
SB
12
SB
21
SB
22
PAPB
(a) (b)
Fig. 1. (a) Measu emen se up using wo mic os ip lines. (b) Signal- low o he model including e o wo-po ci cui s.
nal p oduc s, as cases o s uc u al pa s o suppo o se e al
de ices as ada s o senso s a mic owa e o millime e -wa e
band. The dielec ic pa ame e s should be known accu a ely
o be conside ed p ope ly in elec omagne ic simula o be o e
ab ica ion. These ma e ials can also play a unc ional ole
as ABS in [20], [21] o HIPS in [22]. Pa icula ly, HIPS
as a polys y ene a ian has demons a e o be a candida e
o millime e wa e ma e ial. O he ma e ial wi h lexibili y
mechanical p ope ies could be use ul in mic owa e band o
wea able and con o mable ci cui y.
In his a icle, a me hod o ind elec omagne ic p ope ies
o ma e ial samples, made by addi i e manu ac u ing FDM, is
p oposed. I is based on wo-po measu emen s o mic os ip
ansmission lines. Fo his pu pose, i is equi ed he use o
a wo-po ec o ne wo k analyze (VNA) wi h no need o
calib a ion. The b oadband measu emen me hod is desc ibed
in Sec ion II. In o de o achie e a be e accu acy o he
me hod, se e al line leng h di e ences a e conside ed and a
p e ious mic os ip cha ac e iza ion is ca ied ou . A piece o
he ma e ial o be cha ac e ized is placed o e he mic os ip
line. The ex ac ion o ma e ial pa ame e s o a mul ilaye
mic os ip is based on he one in [23]. This p ocedu e is shown
in Sec ion III. Sec ion IV includes expe imen al and simula ed
esul s o he dielec ic pe mi i i y and he loss angen o
he used ma e ial samples. Finally, conclusions a e p o ided
in Sec ion V.
II. BROADBAND MEASUREMENT METHOD
A. Bianco and Pa odi wo lines me hod
The me hod add essed in his wo k is based on he one
in [10]. This me hod was hen use in he es ima ion o he
p opaga ion cons an in TRL calib a ion o six po ansmis-
sion measu emen s and ec o ne wo k analyze s [24]–[27].
The measu emen se up and he signal low is depic ed in
Fig. 1. Fi s ly, i is necessa y o ake he S-pa ame e s o wo
lines unde es (LUT) wi h di e en leng hs. I is no ewo hy
ha he e o wo-po ci cui s PAand PBa e he same
h oughou he whole se o measu emen s. The S-pa ame e s
ha e o be ans o m in o T-pa ame e s, ha will be called T1
and T2. These ma ices can be ew i en as T1=PAL1PBand
T2=PAL2PB, being L1and L2 he ansmission ma ices
o he lines excluding he e ec p o oked by he ansi ions
be ween he LUT and he po s, whose e ec s a e conside ed
in PAand PB espec i ely. On he one hand, Lia e diagonal
ma ices, gi en by
Li=e−γli0
0e+γli,(1)
being L=L1L−1
2and li he leng h o he line i.
On he o he hand, he ansmission ma ices can be com-
bined as
T=T1T−1
2=PAL1L−1
2P−1
A=PALP−1
A.(2)
A his poin , i is impo an o highligh ha bo h Tand
La e simila ma ices [28], which means ha hei aces and
de e minan s coincide, and hei alue is gi en by
ace(T) = ace(L) = e−γ∆l+e+γ∆l,(3)
whe e ∆l=l2−l1. F om (3), he p opaga ion cons an can
be ob ained as
γ=1
∆lcosh−1 ace(T)
2.(4)
Conside ing Eq. (2), he use o calib a ed o aw S-
pa ame e s do no a ec he esul s. The inclusion o a new
wo-po e o box cascaded wi h PAand PB, do no a ec
simila i y be ween he new Tand Lma ices. The e o e, i
is no necessa y o elimina e sys ema ic e o s calib a ing he
ec o ne wo k analyze be o e he measu emen o ansmis-
sion lines.
B. P oblems due o he exis ence o mul iple solu ions
A p oblem associa ed wi h Eq. (4) is ha he in e se
hype bolic cosine has an ambigui y when β∆l > π/2, and
phase shi s appea . This is due o he in ini e solu ions o he
unc ion cosh−1zgwhen zgis a complex numbe . The in e se
hype bolic cosine o a complex numbe is calcula ed as
cosh−1(zg) = ln zg+q(zg+ 1)(zg−1)(5)
As he na u al loga i hm o a complex numbe has in ini e
solu ions,
ln(zp) = ln |zp|+j(a g(zp) + 2kπ)k= 0,1, ..., (6)
in ini e numbe o p opaga ion cons an s a e ob ained om
Eq. (4).
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1,5
1,7
2,4,6
1,4,7
1,3,5,7
All
F equency [GHz]
β[ ad/m]
Fig. 2. Phase cons an s using di e en line combina ions.
In o de o ix his p oblem, Eq. (4) is sol ed using an
i e a i e echnique such as New on’s me hod o ind he
complex ze o o
γ−1
∆lcosh−1 ace(T)
2= 0.(7)
Ne e heless, his has an incon enience: o achie e a good
me hod pe o mance, i is necessa y o ha e good s a ing
alues, and i is no always possible o ge he alues ha
allow o ind he co ec solu ion. S a ing om he solu ion
o he p opaga ion cons an a he lowe equency poin , his
alue is used o ini ialize he second equency poin and so o
he las equency poin s. This way, he i e a i e p ocess s a s
om a e y close poin o he co ec solu ion.
C. O e de e mina ion o he me hod
Despi e he p oblems associa ed wi h mul iple solu ions o
Eq. (4), andom e o s in oduced du ing he measu emen s
o he S pa ame e s mus be aken in o accoun . Sys ema ic
e o s could be emo ed by calib a ion, al hough i is no
s ic ly necessa y, because po e ec s a e being conside ed
in 4, by conside ing ha hey a e going o be he same in all
he measu emen s. Fo his eason, all expe imen s pe o med
in his wo k ha e been ca ied ou wi hou calib a ion, i.e.
using aw da a om he ec o ne wo k analyze .
Random e o s, howe e , a ec all he measu emen s and
a e no p edic able o emo able by calib a ion. They can
be p oduced, in pa , by he ne wo k analyze . Ne e heless,
he mos impo an sou ces o andom e o s in he p oposed
me hod a e he epea abili y o he ansi ions and he es i-
ma ion o he line leng hs used. These e o s mean ha i is
no possible o de e mine he exac alue o he p opaga ion
cons an , so he objec i e is o achie e he bes es ima ion om
he a ailable measu emen s.
To imp o e he accu acy o he me hod, i is p oposed
o inc ease he numbe o lines o be measu ed and use a
leas squa es app oxima ion. The eby, he e ec s p oduced by
andom e o s o measu emen s epea abili y a e minimized.
The p opaga ion cons an is ob ained by sol ing he equa ion
min
α,β
1
2
N
X
n=1  ace(T)−e+γ∆l+e−γ∆l
2,(8)
whe e Nis he numbe o possible combina ions be ween all
he klines, aken wo by wo. Inc easing kis a good way o
educe unce ain y, bu his inc emen should be accompanied
by di e en ∆l alues, in o de o achie e be e esul s.
Op imal line leng hs selec ion will be explained in he nex
sec ion.
Finally, i should be bo ne in mind ha a enua ion and
phase cons an s will ha e e y di e en o de o magni ude.
Fo his eason, e o s in nume ical op imiza ion will penalize
αmuch mo e han β. To a oid his, he ans o ma ion
ε ,e = (cβ/ω)2is applied in o de o make bo h a iables
ha e he same o de o magni ude, and Eq. (8) is exp essed
as
min
α,ε ,e
1
2
N
X
n=1  ace(T)−e+γ ∆l+e−γ ∆l
2,(9)
being γ =α+j ω√ε ,e /c.
In o de o demons a e how he me hod wo ks, Fig. 2
shows he phase cons an ob ained om measu emen s o
7 lines wi h HIPS as he op subs a e. The measu emen
se up will be explained in he nex sec ions, bu wha is
impo an o no e a his poin is ha phase shi s [29], [30]
occu a highe equencies as he di e ence in line leng hs is
g ea e . F om 4 lines he bandwid h o he me hod eaches he
measu emen bandwid h. Fu he mo e, andom e o s dec ease
as he numbe o lines inc eases.
D. Op imal line leng hs
Random e o s a e inhe en o any es ima ion p oblem based
on measu emen s made by eal ins umen s. Conside ing equa-
ion (4) he a enua ion and phase cons an a e ob ained om
he measu emen o di e en leng hs ∆lkand he uncalib a ed
Spa ame e s measu ed using a ec o ne wo k analyze . In
o de o minimize he e ec o hese andom e o s, special
ca e mus be aken in connec ions epea abili y, simila i y o
connec o s and leng h o lines measu emen .
O e de e mina ion o he me hod p oposed using mo e
han wo lines will help o minimize e o s signi ican ly. The
measu emen s o S pa ame e s o Nlines, N > 2, ge o M
simul aneous non-linea complex equa ion. The alue o M
is gi en by he combina ions o Nlines aken 2 a a ime:
M= 1/2·N(N−1). Inc easing sligh ly he numbe o
lines, he o al numbe o combina ions inc ease apidly and
so, he numbe o es ima ions o he p opaga ion cons an is
also inc eased. In he expe imen ha has been ca ied ou a
numbe o se en lines p o ides 21 combina ions o wo lines.
Apa om a e y good s a is ical da a p ocessing and he
epea abili y o he connec ions some o he conside a ions
mus be aken in o accoun o ge good es ima ions o he
p opaga ion cons an . One o hose is he choice o he leng hs
o he lines employed. The leng h dis ibu ion mus be chosen
so ha he di e ences be ween he inc emen s in he leng h
o he lines should be as small as possible. In addi ion, hese
inc emen s mus be he bigge he be e . In his way, he
expe imen s o de e mine he p opaga ion cons an a e mo e
insensi i e o he ela i e e o s in he de e mina ion o he
leng hs.
Cons an inc emen s in leng h be ween di e en ansmis-
sion lines concen a es esonances in disc e e numbe o
poin s. Small de ia ions om ha pa e n sp ead he eso-
nances h ough he band o in e es . The selec ed leng hs
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li(mm)
l(q)
1
l(q)
N
l1lN
l(q)
i(mm)
q= 1
q= 1.2
q= 1.4
q= 1.6
q= 1.8
q= 2
∆l1
∆l2
∆l3
∆l4
∆l5
∆l6
∆l(q)
1
∆l(q)
2
∆l(q)
3
∆l(q)
4
∆l(q)
5
∆l(q)
6
q= 1 q= 1.2
(a)
(b)
q= 1
q= 1.2
nsamples
nsamples
(GHz)
Fig. 3. (a) Quasi-linea leng hs o lines unde es . (b) His og ams o n o
di e en alues o ac o q.
ollow a quasi-linea dis ibu ion as shown in he ollowing
equa ion
li=l0+ (lN−l0)i−1
N−1q
, i = 1,2, ...N, (10)
whe e l0is he sho es line leng h and lNis he longes . The
quasi-linea ac o qjus need o be adjus o a alue di e en
o 1, q= 1.2has empi ically demons a ed ha he dis ibu ion
o esonances sp ead enough om a p ac ical poin o iew.
The equencies whe e he phase di e ence o measu ed S21
is ze o can be easily ob ained as
n=n·c
(lb−la)√ε ,e
.(11)
Figu e 3 shows he di e ence in he inc emen ∆lij o
di e en s a egies. Fig. 3.b compa es his og ams whe e he
agg ega ion o equencies whe e he phase di e ence be ween
measu ed S21 appea s. Fo q= 1.2 he dis ibu ion is homo-
geneous h ough he equency band.
E. Mic os ip cha ac e iza ion
Once he me hod has been p esen ed, i is e alua ed
h ough expe imen al alida ion and elec omagne ic simula-
ion. Fo his, 7 mic os ip lines a e manu ac u ed o e Roge s
4350B LoP o subs a e, wi h 30 mil hickness, ε = 3.66,
an δ= 0.0031, and 17.5 µm hick coppe me alliza ion. The
leng h o he lines, shown in Fig. 4 cap ion, is calcula ed
ollowing he p ocedu e explained in he p e ious sec ion.
The line wid h is se o 1.65 mm, in o de o ge a 50 Ω
cha ac e is ic impedance.
The cha ac e iza ion me hod consis s o measu ing he S-
pa ame e s o he 7 lines. La e , Eq. (9) is applied, in o de
o ob ain αand ε ,e , om which he es ima ed nominal
ε o he subs a e, including dispe sion, is ex ac ed using
he Ki schning and Jansen model [31]. Finally, he ob ained
ε is impo ed in he comme cial ull-wa e ini e-elemen
elec omagne ic simula o ANSYS HFSS and one o he 7
mic os ip lines is simula ed, ge ing i s p opaga ion cons an .
Figu e 4 shows he measu ed and simula ed e ec i e pe -
mi i i y and he a enua ion cons an ob ained h ough he
me hod applica ion o he se o 7 lines. In addi ion, he in-
o ma ion abou he subs a e dispe sion gi en by he ma e ial
manu ac u e [32] up o 50 GHz is also depic ed. As seen,
he e is an excellen ag eemen be ween he measu ed e ec i e
ela i e pe mi i i y and he one ob ained by simula ion using
manu ac u e da a. In his sense, i mus be highligh ed ha
he ela i e pe mi i i y, ob ained om he one in Fig. 4.b
using he Ki schning and Jansen model and plo ed in Fig. 4.c,
is qui e simila o he one gi en by Roge s, showing how
good is he p oposed me hod o es ima ing his pa ame e .
Fo his eason, he ob ained ε o he Roge s 4350B LoP o
subs a e will be used in he nex sec ion o he simula ion o
he p oposed s uc u e in o de o cha ac e ize mo e p ecisely,
including lowe subs a e dispe sion, he ma e ial samples.
III. ESTIMATION OF MATERIAL PARAMETERS
The se up p oposed o he es ima ion o he dielec ic
pa ame e s consis s o a mic os ip line loaded wi h a dielec ic
o e lay, made o he ma e ial ha will be cha ac e ized. The
measu emen scheme is shown in Fig. 5. As shown, mic os ip
dielec ic has a known pe mi i i y ε 1, es ima ed in he
p e ious sec ion, and a heigh h1, whe eas he o e lay has
an unknown pe mi i i y ε 2 and a heigh h2.
The p ocedu e consis s o he de e mina ion o he p opaga-
ion cons an o he loaded mic os ip, and hen, he ex ac ion
o he a enua ion and phase cons an o he dielec ic o e lay.
Se e al nume ical models has been p oposed o es ima e
he e ec i e ela i e pe mi i i y o his s uc u e, highligh -
ing [23], [33]. Bo h models a e based on nume ical me hods,
and come om [34].
The p oblem wi h hese me hods is ha he es ima ed
ela i e pe mi i i y is calcula ed using a quasi-s a ic model.
Fo ha eason, hey do no ake in o accoun he ma e ial’s
own dispe sion. As seen in Fig. 4, ela i e pe mi i i y has a
sligh downwa d end wi h equency, and his end will also
appea in p in ing ma e ials. Fo ha eason, a ma hema ical
model ha cha ac e izes his dec easing cu e be ween he
minimum and he maximum equencies ha ou analyze
allows us o measu e will be aised. This cu e model will
be de ined as
ε i =ε 1 −(ε 67 −ε 1)i−1
N−1p
, i = 1, N, (12)
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Measu emen
Simula ion
Simula ion Roge s Model
0 20 30 40 50 6010
2.5
3
3.5
Measu emen
Simula ion
Simula ion Roge s Model
0 20 30 40 50 6010
3.5
3.55
3.6
3.65
3.7
Measu emen
Roge s Model
(a)
(b)
(c)
F equency [GHz]
F equency [GHz]
α[Np/m]
ε ,e
ε
Fig. 4. Expe imen al esul s o he p opaga ion cons an using he p oposed
me hod wi h 7 line leng hs in compa ison wi h elec omagne ic simula ion
esul s. The line leng hs a e 2, 2.69, 3.60, 4.61, 5.68, 6.82 and 8 cm.
(a) A enua ion cons an . (b) Rela i e e ec i e pe mi i i y. (c) Es ima ed
subs a e pe mi i i y.
whe e ε 1 and ε 67 a e he es ima ed ela i e pe mi i i y a 1
GHz and 67 GHz espec i ely, and pis a quasi-linea ac o .
This alue can be p= 1 o a linea model, p= 2 o a
quad a ic model o a alue be ween hese alues, ha will
suppose a quasi-linea model. A e compa ing measu emen s
and simula ions, he alue p= 1.5shows ha minimal
di e ences a e achie ed, and, he e o e, i is selec ed o his
model.
To de e mine losses, he p ocess will consis o wo pa s.
On he one hand, i will be necessa y o de e mine losses in
conduc o s. Fo his p ocess, he analy ical model p esen ed
in [34] and imp o ed in [35], which includes he e ec o
su ace oughness, will be used. Once hese losses ha e been
h1
h2
ε 1, an δ1
ε 2, an δ2
Fig. 5. Co e ed mic os ip lines using nylon sc ews o laye s bonding.
Fig. 6. Pho og aph o mic os ip lines co e ed by o ange ABS and he mea-
su emen se up using ec o ne wo k analyse o S-pa ame e s measu emen .
conside ed, i is necessa y o de e mine losses in dielec ics.
This p ocess is based on inding he an δeq o bo h dielec ics.
This equi alen model was de ined in [36]. F om i , knowing
he loss angen o he lowe subs a e an δ1, i is possible o
ob ain he loss angen o he uppe subs a e an δ2.
IV. RESULTS
To alida e he de eloped me hod, a sample o RO4350B
has been made in o de o use i as op subs a e. As i is
a ma e ial whose pe mi i i y is known, i will be used o
assess he me hod pe o mance. In addi ion, pieces o HIPS, 2
di e en ABS, TPU, CPE, NYLON, FLEX, PLA and PETG
ha e been manu ac u ed and measu ed. In he p in ing p ocess,
a 100% in ill has been used, in o de o es ima e he pu e
ma e ial cha ac e is ics. I a smalle in ill had been used,
lowe pe mi i i ies and losses would ha e been ob ained [12],
because he e would be ai inside he subs a e. Howe e ,
in his poin i is impo an o ema k ha no all p in e s
manu ac u e in he same way o ollowing he same pa e ns
a 100% in ill, and p obably he e will always be a small
amoun o ai be ween he shee s o he subs a e. Fo ha
eason, p in e and p in ing se up should be speci ied when
cha ac e izing ma e ials.
A pho og aph o he manu ac u ed s uc u e is shown in
Fig. 6. In ha Figu e, i is possible o see he uncalib a ed
measu ed da a on he VNA sc een. The junc ion be ween he

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL., NO., 6
TABLE I
COMPARISON BETWEEN THE ANALYZED MATERIALS
Ma e ial ε @1 GHz ε @10 GHz ε @25 GHz ε @67 GHz an δ α@1 GHz [dB/m] ∆1∆2
Roge s 4350B LoP o 3.638 3.611 3.592 3.578 0.0039 0.67 12.1×10−36.4×10−3
HIPS 2.45 2.438 2.424 2.4 0.004 0.57 5.2×10−33.2×10−3
ABS* 2.67 2.655 2.638 2.61 0.009 1.34 6.9×10−32.1×10−3
TPU 2.67 2.645 2.618 2.57 0.032 4.75 16.7×10−36.4×10−3
CPE 2.8 2.788 2.774 2.75 0.013 1.98 4.9×10−32.2×10−3
NYLON 2.95 2.94 2.929 2.91 0.019 2.97 11.6×10−35.6×10−3
ABS2* 2.7 2.683 2.663 2.63 0.009 1.35 6.9×10−32.1×10−3
FLEX 2.65 2.633 2.613 2.58 0.036 5.33 5.2×10−33.2×10−3
PLA 2.5 2.483 2.463 2.43 0.013 1.87 5.3×10−32.4×10−3
PETG 2.85 2.83 2.808 2.77 0.022 3.38 7.2×10−33.1×10−3
TABLE II
PRINTING SETUP OF EACH MATERIAL
Ma e ial Manu ac u e P in e Filamen Size (mm) In ill (%) Ex usion empe a u e (ºC) Bed empe a u e (ºC)
HIPS O bi-Tech Ul imake 3 2.85 100 235 100
ABS* Ul imake Ul imake 3 2.85 100 250 90
TPU Ul imake Ul imake 3 2.85 100 225 70
CPE Ul imake Ul imake 3 2.85 100 245 75
NYLON Ul imake Ul imake 3 2.85 100 240 70
ABS2* Sma ma e ials3D P usa i3 MK3 1.75 100 240 100
FLEX Sma ma e ials3D P usa i3 MK3 1.75 100 240 50
PLA Sma ma e ials3D P usa i3 MK3 1.75 100 215 50
PETG Sma ma e ials3D P usa i3 MK3 1.75 100 235 75
ABS* and ABS2*: These ma e ials we e manu ac u ed wi h he p in e ully co e ed o a oid ai lows ha could cause delamina ions.
subs a e and he manu ac u ed piece is made wi h sc ews.
In o de o ensu e he epea abili y o he ansi ions and
minimize e o s in cable mo emen , he same 2 connec o s
we e used o measu ing all he lines, changing hem o
each measu emen . Fu he mo e, a o que w ench was used
o ensu e ha all connec o s a e equally igh , and a isual in-
spec ion wi h mic oscope was made be o e each measu emen .
Las ly, a igid pla e was placed unde he subs a e o ensu e
ha i emains comple ely s aigh du ing e e y measu emen .
The mic os ip line, as well as he leng h o he lines, a e he
same ha he one used du ing he mic os ip cha ac e iza ion
in sec ion II.E. S-pa ame e s o he 7 lines a e aken by using
he ne wo k analyze Agilen PNA-X (N5247A), be ween
0.1 and 67 GHz, ha is he maximum capabili y o ha
analyze . Using he elec omagne ic simula o ANSYS HFSS,
a s uc u e as shown in Fig. 5 has been simula ed o e e y
ma e ial. A 0.4 µm su ace oughness [37], conside ing he
G oisse model [38], has been used o he simula ions. The
heigh s o he subs a es a e h1= 0.762 mm and h2= 3 mm,
espec i ely. The gap be ween he subs a es will cause he
ob ained ela i e pe mi i i y o a y sligh ly. Fo his eason,
some simula ions ha e been ca ied ou in o de o assess
his a ia ion, using he maximum gap, which is he heigh
o he me alliza ion (17 µm), and he minimum gap (0 µm).
The gap wo ks as a bias in he ela i e pe mi i i y. Howe e ,
he maximum di e ence be ween ε 2 alues ob ained wi h he
a o emen ioned gaps is 0.35%, which means ha he e o
made by he sepa a ion be ween subs a es is e y small.
The dielec ic pe mi i i y o he Roge s 4350B LoP o lowe
subs a e, used in he simula ion (ε 1) is he one shown in
Fig. 4.c, ha was calcula ed by using he p oposed me hod.
The dielec ic pe mi i i y o he p in ed ma e ial (ε 2) o he
simula ion is calcula ed om he measu ed esul s, conside ing
he dispe sion model aised in Eq.(12). Speci ically, he alues
o ε o he Roge s op subs a e and he ma e ial samples
a 1, 10, 25 and 67 GHz, as well as he an δused o
he simula ions and he a enua ion cons an a 1 GHz o
a plane wa e a e depic ed in Table I. As seen, esul s o
he Roge s ma e ial a e qui e nea o he one gi en by he
manu ac u e , shown in Fig. 4.c. Small di e ences, ha a e
less han 1%, a e p obably due o he small gap be ween bo h
subs a es o pe mi i i y empe a u e dependence. Rega ding
p in ed ma e ials, esul s a e also simila o hose ound in
o he wo ks [39]–[41], e en conside ing ha p in ing ma e ials
a e no comple ely pu e ma e ials. Despi e he a ie y o he
ma e ials s udied, hey all show a ela i e pe mi i i y be ween
2.45 and 2.95. This ac is because hey a e all plas ic ma e ials
and manu ac u ed wi h he same manu ac u ing p ocess. How-
e e , he e a e signi ican di e ences in e ms o loss angen ,
which makes some ma e ials clea ly candida es o use o
mic owa e ci cui s (i.e., HIPS o ABS), while o he s a e no
as sui able (i.e., lexible ma e ials such as TPU o FLEX).
In o de o gua an ee he epea abili y o he p ocess, he
p in ing se up, including he manu ac u e o each ma e ial,
he p in e used, he ilamen size, he in ill, he ex usion
empe a u e and he bed empe a u e a e shown in Table II.
In o de o alida e he pe o mance o he dispe sion model
in Eq.(12), he ope a o ∆is de ined as
∆ = 1
N
N
X
i=1 εsim.
,e i−εmeas.
,e i
2,(13)
whe e Nis he numbe o poin s o he measu emen and
simula ion. In Table I, ∆1is ob ained by using a simula ion
whe e dispe sion is no conside ed, while ∆2is ob ained by
using he aised dispe sion model. As seen, lowe di e ences
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL., NO., 7
0 10 20 30 40 50 60
-1
0
1
2
3
4
5
6
7
0 10 20 30 40 50 60
3.1
3.15
3.2
3.25
3.3
3.35
3.4
3.45
3.5
0 10 20 30 40 50 60
3.1
3.15
3.2
3.25
3.3
3.35
3.4
3.45
3.5
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3.2
3.25
3.3
3.35
3.4
3.45
3.5
0 10 20 30 40 50 60
-1
0
1
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9
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3.2
3.25
3.3
3.35
3.4
3.45
3.5
(a) (b)
(c) (d)
(e) ( )
(g) (h)
F equency [GHz]
F equency [GHz]
F equency [GHz]
F equency [GHz]
F equency [GHz]F equency [GHz]
F equency [GHz]F equency [GHz]
Measu emen
Measu emen
Measu emen
Measu emen
Measu emen
Measu emen
Measu emen
Measu emen
Simula ion
Simula ion
Simula ion Simula ion
Simula ion
Simula ion
Simula ion
Simula ion
α[Np/m] α[Np/m] α[Np/m] α[Np/m]
ε ,e ε ,e ε ,e ε ,e
Fig. 7. Expe imen al esul s o he p opaga ion cons an using he p oposed me hod wi h 7 line leng hs in compa ison wi h elec omagne ic simula ion esul s
using: (a),(b) HIPS, (c),(d) ABS, (e),( ) TPU, (g),(h) CPE.
be ween measu emen s and simula ions a e achie ed by using
he de eloped model.
Figu es 7 and 8 show he measu ed and simula ed p opaga-
ion cons an s in e ms o a enua ion cons an and e ec i e
dielec ic pe mi i i y. Fo simplici y, conside ing ha bo h
pieces o ABS ha e simila esul s, only he one made
by Ul imake 3 has been depic ed. As seen, an excellen
ag eemen be ween measu emen s and simula ion is achie ed,
highligh ing he good accu acy in he phase cons an and
a good es ima ion o he loss angen . Unce ain y in he
measu emen o he a enua ion cons an a high equencies
is due o he high alues o he phase cons an . The e o e, he
e o s a e loca ed in he a enua ion cons an , whose o de o
magni ude is much smalle .
Losses play a e y impo an ole in he design o s uc u es
o high equency applica ions. Al hough hese me hods a e
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL., NO., 8
0 10 20 30 40 50 60
-1
0
1
2
3
4
5
6
7
0 10 20 30 40 50 60
3.3
3.35
3.4
3.45
3.5
0 10 20 30 40 50 60
3.2
3.25
3.3
3.35
3.4
3.45
0 10 20 30 40 50 60
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0
1
2
3
4
5
6
7
8
9
0 10 20 30 40 50 60
3.25
3.3
3.35
3.4
3.45
0 10 20 30 40 50 60
-1
0
1
2
3
4
5
6
7
8
9
0 10 20 30 40 50 60
3.25
3.3
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3.4
3.45
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-1
0
1
2
3
4
5
6
7
8
9
(i) (j)
(k) (l)
(m) (n)
(o) (p)
F equency [GHz]
F equency [GHz]
F equency [GHz]
F equency [GHz]
F equency [GHz]
F equency [GHz]
F equency [GHz]F equency [GHz]
Measu emen
Measu emen
Measu emen
Measu emen
Measu emen
Measu emen
Measu emen
Measu emen
Simula ion
Simula ion
Simula ion
Simula ion
Simula ion
Simula ion
Simula ion
Simula ion
α[Np/m] α[Np/m] α[Np/m] α[Np/m]
ε ,e ε ,e ε ,e ε ,e
Fig. 8. Expe imen al esul s o he p opaga ion cons an using he p oposed me hod wi h 7 line leng hs in compa ison wi h elec omagne ic simula ion esul s
using: (i),(j) NYLON, (k),(l) FLEX, (m),(n) PLA, (o),(p) PETG.
no sui able o loss cha ac e iza ion, he p oposed o e es i-
ma ion and he echnique o selec he mos app op ia e line
leng hs allow o ob ain cohe en esul s up o 40 GHz, whe e
luc ua ions o he a enua ion cons an limi he a ailable
equency ange o his me hod. Howe e , his equency ange
is qui e wide and he ob ained a enua ion cons an is mo e
accu a e han o he in he s a e-o - he-a [11]. As i can be
seen in Table I, HIPS has a low loss angen , an δ= 0.005,
and a low ela i e pe mi i i y, ε = 2.45, i i is compa ed
o he es o subs a es unde es in his pape . HIPS is
used in nume ous applica ions because o i s easy p ocessing,
pe o mance and low cos [42]. The alues o pa ame e s
es ima ed in his pape s ongly ag ee wi h published da a by
manu ac u e s [43]. This ac makes HIPS a e y good ma e ial
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL., NO., 9
o build suppo s uc u es o ci cui s and an ennas [22].
V. CONCLUSION
In his wo k, a simple echnique o de e mine he b oadband
elec omagne ic cha ac e is ics o ma e ial samples has been
de eloped. I is e y use ul because o i s simplici y and can
be applied o bo h mic os ip lines and lines co e ed wi h
p in ing ma e ials. No calib a ion is needed, and jus se e al
he epea abili y o he ansi ions will s ongly in luence he
esul s. Fu he mo e, he me hod allows o ob ain e y accu a e
esul s in e ms o a enua ion cons an and e ec i e dielec ic
pe mi i i y by using only a ew lines, whose leng h is op-
imized in o de o minimize e o s p o oked by esonances.
The achie ed esul s show an excellen ag eemen be ween
measu emen s and simula ions, which is he eason why he
p oposed p ocedu e can be conside ed as a good al e na i e
o hose o he s a e-o - he-a , due o i s simplici y and
he accu acy o he ob ained esul s. HIPS has demons a ed
excellen losses and can be es ablished as a candida e o
ab ica ion o elec omagne ic s uc u es due o i s loss angen
close o 0.004.
The p oposed me hod can be used o any p oblem wi h
ansmission lines o wa eguides. Despi e ha ing used in
his a icle an indi ec cha ac e iza ion p ocess based on he
measu emen o he S-pa ame e s o a mul ilaye s uc u e, i
has been possible o achie e models ha include he subs a e’s
dispe sion o me al su ace oughness. Howe e , i is impo an
o men ion ha one has o be ca e ul wi h he gap be ween
bo h subs a es, o ensu e ha he e o made is e y small
in he ela i e pe mi i i y ob ained. In addi ion, i mus be
conside ed ha he cha ac e iza ion ca ied ou will ake in o
accoun he cha ac e is ics o he p in ed ma e ial as i is, wi h
i s in ill, i s possible p in ing de ec s, o i s manu ac u ing em-
pe a u es. The e o e, i any o hese pa ame e s a e changed,
i would be con enien o ca y ou a new cha ac e iza ion.
ACKNOWLEDGMENT
The au ho s would like o hank Ma io Muda a, om
M3DK P in , o he help gi en by p in ing se e al subs a es
du ing he COVID-19 lockdown.
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