EMPIR – 14IND02 Plana Cal
Bes P ac ice Guide o
Plana S-Pa ame e Measu emen s
using Vec o Ne wo k Analyse s
Uwe A z, Tho s en P obs , Ka s en Kuhlmann, PTB
Nick Ridle , Xiaobang Shang, NPL
Faisal Muba ak, VSL
Johannes Ho mann, Michael Wollensack, Ma kus Zeie , METAS
Gia Ngoc Phung, Wol gang Hein ich, FVB
Kons an in Lomakin, Ge ald Gold, Klaus Helm eich, FAU
Roge Loza , FhG
Gilles Damb ine, Kamel Haddadi, Uni -Lille1
Ma co Spi i o, TUD
Roland Cla ke, ULE
h ps://plana cal.p b.de
Sep embe 2018
This Guide has been p oduced wi hin he EURAMET p ojec en i led Mic owa e mea-
su emen s o plana ci cui s and componen s. Mo e in o ma ion abou his collabo a i e
esea ch p ojec can be ound on he p ojec ’s websi e h ps://plana cal.p b.de .
Disclaime
Any men ion o comme cial p oduc s wi hin his Guide is o in o ma ion only; i does no
imply ecommenda ion o endo semen by he pa ne s in his p ojec .
The iews exp essed in his Guide a e hose o he au ho s and o he EMPIR 14IND02
p ojec eam.
Acknowledgemen o unding
The p oduc ion o his Guide was unded by he Eu opean Me ology P og amme o Inno-
a ion and Resea ch (EMPIR). The EMPIR ini ia i e is co- unded by he Eu opean Union’s
Ho izon 2020 Resea ch and Inno a ion P og amme and he EMPIR Pa icipa ing S a es.
Au ho ship
P epa a ion o his Guide was led by Uwe A z o he Physikalisch-Technische Bundesans al
(PTB), B aunschweig (Ge many) wi h ex ensi e inpu om all membe s o he EMPIR
14IND02 p ojec eam. The discussion and inpu o all he pa ne s in he p ojec and hei
colleagues a e g ea ly app ecia ed.
Sugges ion o he quo a ion o he e e ences
A z, Uwe ; P obs , Tho s en ; Kuhlmann, Ka s en ; Ridle , Nick ; Shang, Xiaobang ;
Muba ak, Faisal ; Ho mann, Johannes ; Wollensack, Michael ; Zeie , Ma kus ; Phung, Gia
Ngoc ; Hein ich, Wol gang ; Lomakin, Kons an in ; Gold, Ge ald ; Helm eich, Klaus ; Loza ,
Roge ; Damb ine, Gilles ; Haddadi, Kamel ; Spi i o, Ma co ; Cla ke, Roland. Bes P ac ice
Guide o Plana S-Pa ame e Measu emen s using Vec o Ne wo k Analyse s : EMPIR —
14IND02 Plana Cal, 2018. Physikalisch-Technische Bundesans al (PTB).
DOI: h ps://doi.o g/10.7795/530.20190424B
This documen and all pa s con ained he ein a e p o ec ed by copy igh and a e subjec o
he C ea i e Commons use license CC by 4.0 (h ps://c ea i ecommons.o g/licenses/
by/4.0/).
Bes P ac ice Guide o Plana S-Pa ame e
Measu emen s using Vec o Ne wo k Analyse s
Con en s
P e ace 4
1 In oduc ion 6
1.1 P obe and Calib a ion Subs a e Selec ion . . . . . . . . . . . . . . . . . . . 6
1.2 Selec ion o Calib a ion Algo i hm . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Selec ion Be ween Basic Calib a ion Algo i hms . . . . . . . . . . . . 8
1.2.2 Calib a ion algo i hm in ol ing eigen alue p oblems . . . . . . . . . . 8
1.3 Selec ion o Measu emen Bounda y Condi ions . . . . . . . . . . . . . . . . 9
1.4 VNACha ac e iza ion .............................. 9
1.4.1 Noise Floo /T ace Noise . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.2 Linea i y.................................. 10
1.4.3 E o Te mD i ............................. 10
1.5 CableMo emen ................................. 11
1.6 Connec ion Repea abili y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.7 DUT Unce ain y/C oss alk . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 On-wa e measu emen s up o 110 GHz 13
2.1 Resul s om a h ee-pa y on-wa e measu emen in e compa ison . . . . . . 13
2.1.1 In luence o p obe pi ch . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.2 Impo ance o measu emen speed/ins umen d i . . . . . . . . . . 14
2.2 Limi s o es ablished echniques o ans e ing unce ain ies . . . . . . . . . 15
2.2.1 Subs a e pe mi i i y compensa ion . . . . . . . . . . . . . . . . . . 15
2.2.2 Residual e o co ec ion . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 T ans e o unce ain ies wi h he aid o ISS . . . . . . . . . . . . . . . . . . 24
3 On-wa e measu emen s abo e 110 GHz 30
3.1 Recommended good p ac ice o making on-wa e measu emen s a highe
equencies..................................... 30
3.2 Summa y o high- equency pa asi ic e ec s . . . . . . . . . . . . . . . . . . 31
3.3 Su ace oughness e ec s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Impo ance o posi ioning accu acy . . . . . . . . . . . . . . . . . . . . . . . 39
4 Nanode ice measu emen s 40
4.1 Sol ing he impedance misma ch p oblem . . . . . . . . . . . . . . . . . . . 40
4.2 Add essing he scale misma ch challenge . . . . . . . . . . . . . . . . . . . . 41
4.3 In e e ome ic me hods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3.1 Passi eme hods ............................. 42
4.3.2 Ac i eMe hods.............................. 44
2
5 Unce ain ies in on-wa e measu emen s 48
5.1 In oduc ion.................................... 48
5.2 VNA Tools II on-wa e example . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2.1 In oduc ion................................ 49
5.2.2 New p ojec and basic de ini ions . . . . . . . . . . . . . . . . . . . . 49
5.2.3 Measu emen s............................... 50
5.2.4 Calib a ion con igu a ion . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.5 E o co ec ion.............................. 53
5.2.6 Da aExplo e ............................... 53
5.3 Unce ain y budge examples . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.1 Expanded unce ain ies . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.2 Unce ain y budge s . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6 Conclusions and Ou look 58
7 Acknowledgemen s 58
Re e ences 59
3
P e ace
In he Eu opean p ojec Plana Cal [1] a majo e o has been unde aken o cha ac e ise
componen s and de ices o e en ual use in high-speed and mic owa e applica ions (e.g.
wi eless communica ions, au omo i e ada and medical sensing) wi h known measu emen
unce ain ies. I is he pu pose o his Bes P ac ice Guide o gi e an o e iew o he majo
ou comes o his p ojec oge he wi h use ul in o ma ion on ecommended measu emen
p ac ice, di e en sou ces o unce ain y and he de e mina ion o unce ain ies. This Bes
P ac ice Guide is no in ended o eplace a ailable li e a u e such as [2], [3], o [4] – jus o
name a ew. All hese ex books o e comp ehensi e in oduc ions o he subjec o on-wa e
measu emen s and deembedding, which a e sui able o beginne s as well as ad anced use s
in indus y and academia. Such in o ma ion will no be eplica ed in his Guide. Ins ead,
his Guide aims o p esen use ul bes p ac ice ecommenda ions oge he wi h key akeaways
de eloped om he esea ch pe o med in Plana Cal du ing he p ojec ’s li e ime om 2015
un il 2018.
The esea ch in Plana Cal has been ocussed on passi e one- and wo-po on-wa e
measu emen s on ypical mic owa e subs a es such as GaAs, Al2O3(alumina) and used
silica o equencies up o 325 GHz, including nanode ice measu emen s. To his end,
pa asi ic modes as well as e ec s occu ing a highe equencies such as adia ion, dispe sion
and su ace oughness ha e been in es iga ed oge he wi h he impac o he p obe i sel and
i s neighbo hood. The in luence o he neighbo hood on coplana wa eguides (CPWs) used as
s anda ds o mul iline Th u-Re lec -Line (TRL) calib a ions [5] was demons a ed o CPWs
on GaAs and alumina subs a es in [6] and [7], espec i ely. The la e in es iga ion included
di e en p obe geome ies and sugges ed measu es o supp ess he occu ence o subs a e
modes. In [8], a simila in es iga ion was pe o med o hin- ilm mic os ip lines. The
impac o adia ion losses due o mul imode p opaga ions on TRL calib a ions in he WR10
band was desc ibed in [9]. All he in es iga ions con i med ha he measu emen esul
depends on he en i onmen as well as on he speci ic combina ion o subs a e ma e ial,
plana wa eguide ype, and p obes. Only o such ully speci ied combina ions, and only
when single-mode p opaga ion is ensu ed, eliable unce ain ies o on-wa e S-pa ame e s
can be s a ed.
This Bes P ac ice Guide is o ganized as ollows. In he In oduc ion we gi e an o e iew
o commonly used e minology and ecommenda ions o he choice o measu emen equip-
men . As Vec o Ne wo k Analyze s (VNAs) a e an indispensable pa o each on-wa e
measu emen se up, we also gi e ecommenda ions on how o cha ac e ize he pe o mance
o such ins umen s and gi e ypical numbe s o one speci ic se up.
In Sec ion 2 we summa ize key indings o on-wa e measu emen s pe o med in he
equency ange up o 110 GHz. In his equency ange, aceabili y was ecen ly demon-
s a ed o de ices ab ica ed in memb ane echnology [10]. A he end o he p ojec , he
me hodology o [10] could also be ex ended o used silica [11], pa ing he way o aceabili y
o mos commonly used mic owa e ma e ials. The bigges challenge emains he ans e o
he (supposedly low) unce ain ies ob ained on a e e ence subs a e o a di e en subs a e
inco po a ing he de ices unde es (DUTs) o be measu ed. Some esul s om echniques
de eloped o his end will also be gi en in his Sec ion. Finally, he Sec ion concludes
wi h a ecommenda ion o ans e ing unce ain ies om a e e ence cus om calib a ion
o indus ial DUT en i onmen s making use o comme cially a ailable impedance s anda d
subs a es (ISS).
In Sec ion 3 we add ess he di icul ies associa ed wi h measu emen s abo e 110 GHz.
This includes he conside a ion o su ace oughness, a sho summa y o high- equency
pa asi ic e ec s and an excu sion on he impo ance o p obe posi ioning accu acy. Mo e
de ails on high- equency pa asi ic e ec s can be ound in a di e en documen de eloped
in Plana Cal, named “Guidelines o he design o calib a ion subs a es, including he sup-
4

p ession o pa asi ic modes o equencies up o and including 325 GHz”, which is also
publically a ailable om he Plana Cal websi e [1].
Sec ion 4 con ains use ul ad ice o cha ac e izing nanode ices o e a wide equency
ange, looking bo h in o he di icul ies o size and impedance misma ch compa ed o o dina y
on-wa e measu emen s. Also, an o e iew o in e e ome ic me hods is gi en.
Sec ion 5 inally co e s he subjec o unce ain ies in on-wa e measu emen s. Wi hou
dedica ed so wa e, i is i ually impossible o ake in o accoun all he ele an sou ces
o unce ain y. To his end, he VNATools so wa e package [12] de eloped by METAS has
been ex ended o include unce ain ies in on-wa e measu emen s. In his Sec ion, also an
in oduc ion o he main ea u es and use o VNATools is gi en. To achie e aceabili y,
PTB has de eloped an unce ainy budge o mul iline TRL calib a ions in Ma lab based
on he same measu emen model and unce ain y p opaga ion engine [13] as he one used in
VNATools. Typical examples om he unce ain y budge calcula ions a e gi en in Sec ion
5, illus a ing he ela i e impo ance o he di e en sou ces o unce ain y in on-wa e
measu emen s.
5
1 In oduc ion
Design and cha ac e iza ion o high equency elec onics elies upon accu a ely de ining he
e e ence plane o he calib a ion p ocess, and in gene al placing i as close as possible o he
DUT o emo e all unwan ed pa asi ic. In o de o de ine such e e ence planes and emo e
all he sys ema ic e o s o he measu emen se up (i.e., cable and ecei e con e sion losses,
ampli ude and phase acking e o s, and o he e o s), a calib a ion p ocedu e [14] needs
o be ca ied ou p io o he measu emen .
Calib a ion echniques o on-wa e measu emen s ypically consis o a p obe-le el cal-
ib a ion ( i s - ie ) pe o med on a low-loss subs a e (i.e., alumina o used silica) [15, 16,
17, 5]. This p obe-le el calib a ion is hen ans e ed o he en i onmen whe e he DUT is
embedded in and o en, o inc ease he measu emen accu acy, his calib a ion is augmen ed
wi h a second- ie on-wa e calib a ion o de-embedding s ep. This allows mo ing he e e -
ence plane as close as possible o he DUT, by de-embedding he pa asi ics associa ed o he
con ac pads and he de ice-access ias [18]. The p ocess o ans e ing he i s - ie cali-
b a ion o ano he s uc u e assumes ha he del a capaci ance in oduced by changing he
subs a e unde he p obes (i.e., bounda y condi ions) is negligible. As i was shown in [19]
his capaci ance is dependen on he p obe opology and subs a e cha ac e is ic, c ea ing
a coupling which inc eases wi h equencies. To emo e he e o s a ising om neglec ing
o imp ope ly emo ing his del a capaci ance, he calib a ion ki should be implemen ed in
he same en i onmen o he DUT.
1.1 P obe and Calib a ion Subs a e Selec ion
Calib a ion subs a es a e p o ided by di e en endo s o pe o m p obe-le el calib a ion
( i s - ie ). The subs a es a e ealized as a slab o a single ma e ial p o iding low dispe sion
(i.e., pe mi i i y change e sus equency) and low dielec ic losses. The models o he
s anda ds p o ided in mos o he a ailable calib a ion subs a es a e based on simple (i.e.,
equency in a ian ) C, L and R, as shown in Fig. 1.
Figu e 1 Equi alen ci cui s o he plana open, sho and load s anda ds.
When calib a ion echniques using ull knowledge o he s anda ds a e employed (i.e.,
SOL based) he accu acy o he calib a ion can be imp o ed by using mo e accu a e ( e-
quency dependen ) s anda d models. This can be achie ed using an expe imen al app oach
as shown in [20, 21, 22], o a simula ion based (EM) one as shown in [23].
The choice o he op imum pi ch o he p obe o be employed in a gi en equency ange
is dependen on he p obe echnology implemen a ion and ollows he same equi emen s o
low dispe sion used in CPW lines. Fo his eason, assuming ha he inal pa o he p obe
ansi ion is implemen ed as a CPW line design, as is he case o he Dominion p obe shown
in Fig. 2, he choice o he max ip o ip spacing is bounded by he λ/4 a he maximum
desi able equency o ope a ion and he e ec i e pe mi i i y o he line sec ion. When
selec ing mic o-machined p obes (i.e., using silicon as ca ie ) i is impo an o conside he
high pe mi i i y o he ma e ial (i.e., 11.9) when compu ing he e ec i e pe mi i i y o
he CPW sec ion.
6
Figu e 2 SEM images o he mic o-machined p obe ips a e 3000 con ac s ( om [24]).
When some ma e ial p ope ies o he p obe ip a e known he dispe sion cha ac e is ics
o a CPW e sus gap wid h can be used as a ool o de ine he maximum p obe pi ch o be
employed.
When selec ing p obes o a gi en es ci cui s ew hings should be kep in mind:
1. The ska ing a ea wid h and leng h ex ension a e dependen on he p obe make, and
should be analysed and ound compa ible wi h he pad sizes a ailable, o op imized
when ull cus om designs a e made (see Fig. 3).
Figu e 3 Landing a ea o p obe model om company #1 o he WR10 a), WR5 b) and WR3
c) equency band, p obe model om company #2 o he WR3 d) and p obe model
om company #3 o he WR3 e).
2. When p obing on aluminium pads special p obe ip alloy should be used, i.e., nickel
alloy p obe ips, o educe he con ac esis ance and imp o e he p obe li e ime.
3. When using comme cial echnologies, he educ ion o he e ec i e pad opening due
he sc a ch p o ec ion, as shown in he ske ch gi en in Fig. 4, is educed om he
d awn pad dimension o 1-3um, depending on he echnology.
Figu e 4 C oss sec ional ske ch iew o pad opening and sc a ch p o ec ion.
7
1.2 Selec ion o Calib a ion Algo i hm
Any on-wa e measu emen equi es he applica ion o a calib a ion p ocedu e o co ec
o unwan ed bu una oidable pe u ba ion o he da a due o he en i onmen , he p obes,
and he ins umen a ion i sel . This calib a ion p ocess is supposed o e eal he “ ue”
pe o mance o he DUT. In he ollowing, basic and ad anced calib a ion algo ihms will
be e iewed.
1.2.1 Selec ion Be ween Basic Calib a ion Algo i hms
The e m basic calib a ion algo i hm e e s o calib a ion algo i hms which a e simple o
execu e. The equi emen s in e ms o s anda ds a e di e en o all conside ed me hods and
hus i is in e es ing o compa e he ield o applica ion o each algo i hm, he achie able
accu acy and esul s. Ano he ac o which has o be conside ed when choosing a calib a ion
algo i hm is he amoun o eal es a e on he wa e equi ed by each me hod.
The i s calib a ion ou ine in es iga ed in Plana Cal was he sho open load h u
(SOLT) ou ine. I equi es, as he name insinua es, sho , open, load and h u as s anda ds.
I can be qui e easily applied o low equencies (≈15 GHz) down o DC. A c ucial poin is
o en he de ini ion o he load s anda d. The SOLT echnique is mo e obus agains bad
de ini ions o s anda ds.
The second calib a ion algo i hm in es iga ed was he line e lec ma ch (LRM) algo i hm
which equi es a ansmission line, a e lec (ei he open o sho ) and a load. In e ms o
equency i has a simila ange o applica ion as he SOLT algo i hm. Again a c ucial poin
is he de ini ion o he load s anda d. The LRM echnique equi es he leas connec ions
and s anda ds compa ed o SOLT and LRRM echniques.
The hi d calib a ion algo i hm was line e lec e lec ma ch (LRRM). I equi es a
ansmission line, a i s e lec (e.g. an open), a second e lec (e.g. a sho ) and a load.
The applicable ange o equencies is om medium equencies (≈40 GHz) down o DC.
In his me hod an induc i e componen o he load is de e mined du ing calib a ion. This
induc i e componen has i s o igin in he design o he load i sel bu as well in he leng h o
he line leading o he load. This leng h is no easy o con ol because o p obe ska ing when
con ac ing he load. Thus o loads which a e no well de ined he LRRM echnique can
yield good esul s. No e ha he implemen a ion o he LRRM algo i hm can di e be ween
di e en so wa e packages, e.g. VNA Tools II [25, 12] has a di e en implemen a ion han
WinCal [26].
The p e ious ema ks a e only applicable o si ua ions whe e he de ini ion o s anda ds
o he espec i e calib a ion comes om he manu ac u e o om geome y and ma e-
ial p ope ies. All h ee ypes o calib a ions yield simila esul s in si ua ions whe e he
de ini ion o s anda ds is de i ed om ano he p e ious calib a ion.
1.2.2 Calib a ion algo i hm in ol ing eigen alue p oblems
Calib a ion algo i hms o VNAs which equi e only pa ially known s anda ds pose p oblems
o unce ain y calcula ion. Examples a e LRM and TRL calib a ions whe e he e lec i i y
o he line can no be speci ied because in he algo i hm i is assumed ha he line has a
cha ac e is ic impedance o 50 Ω. In eali y he line in use will no ha e exac ly he equi ed
cha ac e is ic impedance and hus his needs o be aken in o accoun o unce ain y compu-
a ion. The algo i hm p esen ed in [27] is a gene aliza ion o calib a ion schemes wi h pa ly
unknown s anda ds, including [5]. The gene aliza ion consis s o cons uc ing an eigen alue
p oblem o each calib a ion scheme. One ob ious ad an age is ha he same algo i hm
can be used o di e en schemes as TRM, LRM, TRL and LRL. Ano he ad an age is ha
pa ly unknown lines can now be desc ibed wi h non-ze o e lec ion and unce ain y, which is
a clea imp o emen o e he adi ional TRL algo i hm. O e -de e mined calib a ion wi h
8
2.2 Limi s o es ablished echniques o ans e ing unce ain ies
In his sec ion we epo on me hods o ans e unce ain ies om e e ence calib a ion
subs a es o wo king calib a ion subs a es. The aim is o p ese e he low unce ain ies in
S-pa ame e measu emen s achie ed on cus om-made e e ence calib a ion subs a es e en
when using low-cos wo king calib a ion subs a es, such as e.g. impedance s anda d sub-
s a es, which can be pu chased om se e al on-wa e endo s. Recommenda ions o he
ans e o unce ain ies will be gi en a he end o he sec ion.
2.2.1 Subs a e pe mi i i y compensa ion
In [33], a simple capaci ance model was de eloped o accoun o he e ec o a change
in subs a e pe mi i i y on coplana wa eguide TRL calib a ions pe o med on di e en
subs a e ma e ials. Fo all calib a ions, he e e ence plane was mo ed o he p obe ip
and he e e ence impedance was se o 50 Ω. Whe eas in [33] all c oss-sec ional dimensions
o he CPWs on he di e en subs a es we e assumed iden ical, he in es iga ion in [34]
demons a ed ha also he measu emen e o caused by di e ences in he conduc o geom-
e y can be accoun ed o . As he measu emen s in [33] and in [34] we e limi ed o he 40
GHz equency ange, we in es iga ed he pe o mance o his compensa ion echnique using
cus om-made used silica and Al2O3subs a es up o 110 GHz.
0 10 20 30 40 50 60 70 80 90 100 110
F equency (GHz)
0
0.05
0.1
0.15
0.2
0.25
Uppe bound on |Sij-Sij)|
Silica MTRL 50 Ohm s. Al2O3 MTRL 50 Ohm
Silica MTRL 50 Ohm s. Al2O3 MTRL 50 Ohm /w pe mi i i y compensa ion
Figu e 8 Wo s -case e o bounds calcula ed by calib a ion compa ison me hod [32].
Figu e 8 shows he wo s -case e o bounds calcula ed o mul iline TRL calib a ions
using [32] on he wo di e en wa e s be o e (blue) and a e ( ed) applying he subs a e
pe mi i i y compensa ion echnique o [33]. The ed cu e shows a signi ican educ ion o
he e o bound a e applying he pe mi i i y compensa ion. As he calib a ion compa ison
echnique [32] ends o o e es ima e he ac ual e o s in he measu emen s, we decided o
in es iga e he ac ual de ia ions om he e e ence measu emen esul be o e and a e
applying he subs a e pe mi i i y compensa ion.
15

To his end, we in es iga ed measu emen s o di e en de ices ab ica ed on he Al2O3
wa e in he equency ange om 1 o 110 GHz (see Figs. 9-13). The mul iline TRL cali-
b a ion on he Al2O3wa e gi es he mos accu a e esul (black cu es), while he mul iline
TRL calib a ion on he used silica wa e (b own cu es) will in oduce a sys ema ic e o
due o he di e ences in subs a e pe mi i i y and conduc o geome ies. The ed cu es
show he esul o he mul iline TRL calib a ion on he used silica wa e a e applying he
subs a e pe mi i i y compensa ion echnique o [33]. In he ollowing igu es, he e o -
co ec ed e lec ion and ansmission measu emen a e shown on he le -hand side, while
he di e ences wi h ega d o he e e ence calib a ion a e shown on he igh -hand side. In
he case o one-po de ices only he esul s o e lec ion a e shown.
In Fig. 9, he esul s o an a enua o de ice a e displayed. While he pe mi i i y
compensa ion only sligh ly imp o es he e o in magni ude o S11 and S21, he e is a angible
imp o emen in he phase o e he en i e equency ange. Fo equencies abo e 60 GHz,
he e o s in he magni ude o S21 canno be compensa ed by he simple capaci ance model
o [33].
Figu e 10 shows he esul s o a 11.4 mm long CPW line on Al2O3subs a e. Fo S11,
he pe mi i i y compensa ion does no o e any no able imp o emen o e he used silica
calib a ion. In he phase o S21, he e is a angible imp o emen o e he en i e equency
ange.
Figu e 11 shows he esul s o a misma ched CPW line on Al2O3subs a e. He e, he
pe mi i i y compensa ion leads o an imp o emen in bo h S11 and S21. As is e iden
om he le -hand side, he esonance equencies o he black and ed cu e line up a e
0 20 40 60 80 100
F equency /GHz
-20
-15
-10
|S11|/dB
0 20 40 60 80 100
F equency /GHz
-2
0
2
|S11|/dB-|S11| e /dB
0 20 40 60 80 100
F equency /GHz
-100
-50
0
S11/°
0 20 40 60 80 100
F equency /GHz
-20
-10
0
S11/°
- S11/°
e
0 20 40 60 80 100
F equency /GHz
-16
-15
-14
|S21|/dB
0 20 40 60 80 100
F equency /GHz
-0.5
0
0.5
|S21|/dB-|S21| e /dB
0 20 40 60 80 100
F equency /GHz
-200
-100
0
S21/°
0 20 40 60 80 100
F equency /GHz
-10
-5
0
5
S21/°
- S21/°
e
Figu e 9 le : e lec ion and ansmission measu emen o a enua o de ice on Al2O3subs a e
igh : measu emen no malized o MTRL esul on Al2O3
colo s: MTRL on Al2O3(black), on used silica, on used silica a e pe m. comp.
16
0 20 40 60 80 100
F equency /GHz
-60
-40
-20
0
|S11|/dB
0 20 40 60 80 100
F equency /GHz
-20
0
20
40
|S11|/dB-|S11| e /dB
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S11/°
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S11/°
- S11/°
e
0 20 40 60 80 100
F equency /GHz
-4
-2
0
|S21|/dB
0 20 40 60 80 100
F equency /GHz
-0.4
-0.2
0
0.2
|S21|/dB-|S21| e /dB
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S21/°
0 20 40 60 80 100
F equency /GHz
-5
0
5
S21/°
- S21/°
e
Figu e 10 le : e lec ion and ansmission measu emen o 11.4 mm long CPW line on Al2O3
igh : measu emen no malized o MTRL esul on Al2O3
colo s: MTRL on Al2O3(black), on used silica, on used silica a e pe m. comp.
applying he compensa ion. Again, he co ec i e e ec o he pe mi i i y compensa ion is
mo e no eable in he phase, and o equencies abo e 60 GHz, he e o s in he magni ude
o S21 canno be compensa ed by he echnique o [33].
Figu e 12 shows he esul s o a one-po de ice, an o se open. The pe mi i i y
compensa ion only imp o es he phase o S11. The compensa ion does no wo k o he
magni ude o S11, and again, o equencies abo e 60 GHz, he sys ema ic e o s in he
magni ude o S11 s a o inc ease wi h equency.
Figu e 13 shows he esul s o a 0.4 mm long h u line on Al2O3subs a e. Fo S11,
he pe mi i i y compensa ion ha dly o e s any imp o emen o e he used silica calib a-
ion. The e is a angible imp o emen in he phase o S21 o e he en i e equency ange.
Fo equencies abo e 60 GHz, he sys ema ic e o s in he magni ude o S21 canno be
compensa ed by he echnique o [33].
In summa y, one can s a e he pe mi i i y compensa ion echnique o [33] mos ly im-
p o es on he phase e o in oduced by he o -wa e calib a ion on used silica. The e ec
is gene ally mo e no eable in S21 compa ed o S11. Wi h ega d o he magni ude e o ,
which d as ically inc eases o equencies abo e 60 GHz in S21, almos no imp o emen can
be ound.
17
0 20 40 60 80 100
F equency /GHz
-60
-40
-20
0
|S11|/dB
0 20 40 60 80 100
F equency /GHz
-20
-10
0
10
|S11|/dB-|S11| e /dB
0 20 40 60 80 100
F equency /GHz
-100
0
100
S11/°
0 20 40 60 80 100
F equency /GHz
-200
-100
0
100
S11/°
- S11/°
e
0 20 40 60 80 100
F equency /GHz
-2
-1
0
|S21|/dB
0 20 40 60 80 100
F equency /GHz
-0.4
-0.2
0
0.2
|S21|/dB-|S21| e /dB
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S21/°
0 20 40 60 80 100
F equency /GHz
-10
-5
0
5
S21/°
- S21/°
e
Figu e 11 le : e lec ion and ansmission measu emen o misma ched line on Al2O3
igh : measu emen no malized o MTRL esul on Al2O3
colo s: MTRL on Al2O3(black), on used silica, on used silica a e pe m. comp.
0 20 40 60 80 100
F equency /GHz
-1
-0.5
0
0.5
|S11|/dB
0 20 40 60 80 100
F equency /GHz
-0.5
0
0.5
|S11|/dB-|S11| e /dB
0 20 40 60 80 100
F equency /GHz
-150
-100
-50
0
S11/°
0 20 40 60 80 100
F equency /GHz
-10
-5
0
S11/°
- S11/°
e
0 20 40 60 80 100
F equency /GHz
-80
-60
-40
-20
|S21|/dB
0 20 40 60 80 100
F equency /GHz
-2
-1
0
1
|S21|/dB-|S21| e /dB
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S21/°
0 20 40 60 80 100
F equency /GHz
-6
-4
-2
0
S21/°
- S21/°
e
Figu e 12 le : e lec ion and ansmission measu emen o open de ice on Al2O3
igh : measu emen no malized o MTRL esul on Al2O3
colo s: MTRL on Al2O3(black), on used silica, on used silica a e pe m. comp.
18
0 20 40 60 80 100
F equency /GHz
-80
-60
-40
-20
|S11|/dB
0 20 40 60 80 100
F equency /GHz
-20
0
20
40
|S11|/dB-|S11| e /dB
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S11/°
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S11/°
- S11/°
e
0 20 40 60 80 100
F equency /GHz
-0.4
-0.2
0
0.2
|S21|/dB
0 20 40 60 80 100
F equency /GHz
-0.4
-0.2
0
0.2
|S21|/dB-|S21| e /dB
0 20 40 60 80 100
F equency /GHz
-150
-100
-50
0
S21/°
0 20 40 60 80 100
F equency /GHz
-5
0
5
S21/°
- S21/°
e
Figu e 13 le : e lec ion and ansmission measu emen o h u line on Al2O3
igh : measu emen no malized o MTRL esul on Al2O3
colo s: MTRL on Al2O3(black), on used silica, on used silica a e pe m. comp.
19
2.2.2 Residual e o co ec ion
A mo e gene al app oach o compensa ing sys ema ic e o s in oduced by he VNA cali-
b a ion is he de e mina ion o esidual e o s and he applica ion o a second-o de e o
co ec ion a e wa ds. In [35], a me hod o de e mining complex esidual e o s o wo-po
VNA calib a ions was p esen ed which makes use o a ime-domain app oach. The esid-
ual e o s a e ex ac ed om a dis ance- equency sys em model using a special es ima ion
algo i hm based on he quasi-op imal unscen ed Kalman il e . Since he me hod equi es
only h ee measu emen condi ions, i is pa icula ly sui ed o on-wa e applica ions, as
hese condi ions can be ob ained om using only one e i ica ion line. In [36], he same
measu emen condi ions a e exploi ed, bu since he esidual e o e ms a e now es ima ed
by applying a leas -mean-squa es me hod he calcula ion ime is signi ican ly educed.
He e, we de e mined he esidual e o s o calib a ed wo-po on-wa e measu emen s up
o 110 GHz wi h he me hod o [36], u ilizing he comme cial calib a ion subs a e GGB CS5
and GGB100 mic owa e p obes. As e i ica ion line, line 10 wi h a leng h o 6600 µm was
used. As DUTs lines o di e en leng hs we e used. By analyzing he e o -co ec ed mea-
su emen s o he DUTs, we compa ed he accu acy o SOLT calib a ions wi h cha ac e ized
s anda ds o SOLT calib a ions wi h manu ac u e de ini ions and o second-o de -co ec ed
SOLT calib a ions wi h manu ac u e de ini ions. In he ollowing igu es, he e o -co ec ed
e lec ion and ansmission measu emen a e shown on he le -hand side, while he di e -
ences wi h ega d o he e e ence calib a ion (SOLT wi h cha ac e ized s anda ds) a e shown
on he igh -hand side.
Figu es 14-16 show he esul s o lines wi h leng hs in he ange 550 . . . 1500 µm. One
ob ious disad an age o he second-o de e o co ec ion becomes appa en o equen-
cies below 10 GHz: addi ional e o s a e in oduced leading o unphysical beha io in bo h
e lec ion and ansmission. Fo highe equencies, howe e , he second-o de co ec ion is
mos ly wo king as expec ed. In he measu ed e lec ions, he second-o de e o co ec ion is
bene icial in bo h magni ude and phase, as can be seen om he ed S11 cu es app oaching
he black S11 cu es in a ange o app oxima ely 20 . . . 110 GHz. In he measu ed ansmis-
sion, he e is almos no imp o emen o he magni ude o S21, while he phase o S21 e en
de e io a es sligh ly by means o he second-o de e o co ec ion.
In summa y one can s a e ha he second-o de e o co ec ion o [36] shows some
p omise bu is cu en ly limi ed by he accu acy wi h which he esidual e o s can be
de e mined. A he edges o he equency ange (ca. 5% o he equency band), he e o
o he il e ing algo i hm inc eases. This applies o measu emen s o bo h ansmission and
e lec ion coe icien s. In p inciple, he e ec can be educed by applying a e i ica ion line
wi h a longe leng h.
The cu en s udy was limi ed by he numbe o DUTs and he e i ica ion line a ailable
on he comme cial calib a ion subs a e. Fu u e in es iga ions should y o ex end he
s udy o be e unde s and and o e come he cu en limi a ions o he me hod o [36].
20

0 20 40 60 80 100
F equency /GHz
-80
-60
-40
-20
|S11|/dB
0 20 40 60 80 100
F equency /GHz
-20
0
20
40
|S11|/dB-|S11| e /dB
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S11/°
0 20 40 60 80 100
F equency /GHz
-200
-100
0
100
S11/°
- S11/°
e
0 20 40 60 80 100
F equency /GHz
-0.4
-0.2
0
0.2
|S21|/dB
0 20 40 60 80 100
F equency /GHz
-0.2
0
0.2
|S21|/dB-|S21| e /dB
0 20 40 60 80 100
F equency /GHz
-200
-100
0
S21/°
0 20 40 60 80 100
F equency /GHz
-10
-5
0
S21/°
- S21/°
e
Figu e 14 le : SOLT-co ec ed e lec ion and ansmission o 550 µm long line on GGB CS5
igh : measu emen no malized o SOLT wi h cha ac e ized s anda ds
colo s: cha ac e ized s anda ds (black), manu ac u e de ini ions, manu ac u e de i-
ni ions a e esidual e o co ec ion
21
0 20 40 60 80 100
F equency /GHz
-60
-40
-20
|S11|/dB
0 20 40 60 80 100
F equency /GHz
-20
0
20
|S11|/dB-|S11| e /dB
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S11/°
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S11/°
- S11/°
e
0 20 40 60 80 100
F equency /GHz
-0.5
0
0.5
|S21|/dB
0 20 40 60 80 100
F equency /GHz
-0.2
0
0.2
|S21|/dB-|S21| e /dB
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S21/°
0 20 40 60 80 100
F equency /GHz
-10
-5
0
S21/°
- S21/°
e
Figu e 15 le : SOLT-co ec ed e lec ion and ansmission o 1000 µm long line on GGB CS5
igh : measu emen no malized o SOLT wi h cha ac e ized s anda ds
colo s: cha ac e ized s anda ds (black), manu ac u e de ini ions, manu ac u e de i-
ni ions a e esidual e o co ec ion
22
0 20 40 60 80 100
F equency /GHz
-60
-40
-20
|S11|/dB
0 20 40 60 80 100
F equency /GHz
-20
0
20
|S11|/dB-|S11| e /dB
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S11/°
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S11/°
- S11/°
e
0 20 40 60 80 100
F equency /GHz
-1
-0.5
0
0.5
|S21|/dB
0 20 40 60 80 100
F equency /GHz
-0.2
0
0.2
|S21|/dB-|S21| e /dB
0 20 40 60 80 100
F equency /GHz
-400
-200
0
200
S21/°
0 20 40 60 80 100
F equency /GHz
-10
-5
0
S21/°
- S21/°
e
Figu e 16 le : SOLT-co ec ed e lec ion and ansmission o 1500 µm long line on GGB CS5
igh : measu emen no malized o SOLT wi h cha ac e ized s anda ds
colo s: cha ac e ized s anda ds (black), manu ac u e de ini ions, manu ac u e de i-
ni ions a e esidual e o co ec ion
23
2.3 T ans e o unce ain ies wi h he aid o ISS
In [22] i was demons a ed ha p ope ly cha ac e ized s anda ds can be used o accoun
o di e ences be ween he comme cial ISS and he a ge DUT measu emen si ua ion. The
esul s o a e e ence MTRL calib a ion using cus om s anda ds we e in essence duplica ed
wi h he aid o cha ac e ized ISS s anda ds and a much simple calib a ion, in his case
SOLT. This cons i u es a big imp o emen o e any o he app oaches discussed in he wo
p e ious subsec ions, whe e a sys ema ic e o wi h ega d o he e e ence esul emained.
The e o e, in o de o ans e unce ain ies o indus ial applica ions whe e comme cial
ISS subs a es and simple calib a ion algo i hms ha e o be used, one has o i s cha ac e ize
he s anda ds in a manne which is adequa e o he a ge applica ion. This equi es building
cus om calib a ion s anda ds on he a ge DUT wa e , which se e o cha ac e izing he
ISS calib a ion s anda ds app op ia ely. In he ollowing, we demons a e his app oach
wi h he cus om-made Al2O3wa e as he a ge DUT wa e and he GGB CS5 calib a ion
subs a e as comme cially a ailable ISS subs a e.
Recen ly, PTB de eloped a aceabili y pa h o on-wa e S-pa ame e measu emen s
based on he MTRL calib a ion algo i hm [10]. The me hodology o [10] o es ablishing a
comp ehensi e unce ain y budge can also be applied o o he subs a es, as long as he
wideband ma e ial p ope ies a e known and single-mode p opaga ion can be assumed. Fo
he cus om-made Al2O3wa e used in ou s udies, he la e condi ion is s ic ly ul illed
only o equencies below ca. 70 GHz. Fo highe equencies, he e ec s o dispe sion
and in e ac ion wi h highe -o de and o he pa asi ic modes a e cu en ly no ully cap u ed
in he unce ain y budge . None heless we used his p elimina y unce ain y budge and
ea ed he Al2O3wa e as e e ence calib a ion wa e o cha ac e izing he s anda ds on
he GGB CS5 subs a e.
Figu es 17 and 18 show he esul o cha ac e izing he Open/Sho /Load/Th u s an-
da ds by means o a e e ence mul iline TRL calib a ion on he cus om-made Al2O3wa e .
The igu es also show he expanded unce ain y in e als comp ising he in luences o MTRL
calib a ion s anda d unce ain ies, unce ain ies om he ins umen a ion used, cabling in-
luences and epea abili y e ec s. I may appea su p ising ha some o he cha ac e ized
s anda ds show gain e en hough hey a e passi e de ices. This can easily be explained by
he ac ha he dis ance be ween he p obe ips on he CS5 s anda ds was smalle han he
dis ance be ween he calib a ion e e ence planes on he Al2O3wa e . None heless he cha -
ac e ized CS5 s anda ds can be used as ans e s anda ds o accu a ely measu ing DUTs
on he Al2O3wa e .
Fig. 19 compa es he measu emen esul s o an a enua o DUT and a misma ched line
DUT ab ica ed on he Al2O3wa e . The black cu es show he e lec ion and ansmission
when using he e e ence MTRL calib a ion on he Al2O3subs a e, he ed cu es show he
co esponding esul s o he SOLT calib a ion wi h he cha ac e ized CS5 s anda ds. The
shaded a eas indica e he expanded unce ain y in e als. I can be clea ly seen ha he
nominal alues coincide o bo h calib a ions, p o ing he consis ency o he app oach. The
only di e ences appea in he expanded unce ain ies, which a e usually sligh ly inc eased
o he calib a ion wi h he cha ac e ized s anda ds.
Exempla y unce ain y budge alues o he DUTs co ec ed ia he SOLT calib a ion
wi h cha ac e ized CS5 s anda ds a e gi en in he Tables 5-8. These ables show he unce -
ain y budge composi ion o he magni ude o S11 and he phase o S21 o he DUTs a a
equency o 65 GHz. The calib a ion s anda d unce ain ies a e designa ed wi h PTB ML
in he beginning, poin ing o he ac ha he cha ac e iza ion was pe o med wi h he PTB
mul iline calib a ion. The ables clea ly show ha he budge s a e mos ly domina ed by
he calib a ion s anda d unce ain ies. Fo he phase o S21, also cable e ec s and DUT
unce ain y p o ide signi ican con ibu ions o he o al unce ain y a 65 GHz.
24
exhibi highe -o de modes abo e 50 GHz, depending on he bounda y condi ions abo e and
below he subs a e. I is good p ac ice o use an abso bing ma e ial (wi h simila dielec ic
cons an as he subs a e) be ween he me allic wa e chuck and he DUT, which will supp ess
unwan ed modes. The DUT is e ec i ely a di e en s uc u e (elec omagne ically) wi h and
wi hou his abso be , and measu emen esul s can di e widely depending on whe he o
no i is used.
Some imes he p esence o sys ema ic e o s in he measu emen s can be de ec ed espe-
cially when non-physical beha iou is obse ed – e.g. when he obse ed linea magni ude
o he e lec ion coe icien is g ea e han uni y. This is indica i e o an inapp op ia e
e e ence s anda d used du ing calib a ion. Addi ionally, he p esence o signi ican ipple
on some measu emen aces sugges pe haps he use o an in e io calib a ion echnique.
Gene ally, he choice o e e ence calib a ion subs a e can ha e a majo impac on he
achie ed measu emen s. This is because he di e en calib a ion subs a es p o ide di e -
en calib a ion e e ence alues (e.g. due o he use o di e en subs a e ma e ials o he
calib a ion subs a e). This means ha e en he same unco ec ed measu emen da a o a
gi en de ice unde es (DUT) will gi e ise o di e en co ec ed S-pa ame e alues due
o di e en e e ence alues being used du ing he calib a ion p ocess. This occu s when a
VNA is calib a ed using s anda ds ound on one wa e (e.g. a comme cial impedance s an-
da d subs a e), and hen measu emen s a e made subsequen ly o DUTs on ano he wa e
(e.g. he wa e con aining he de ices ha need es ing). Fo his eason, when making
on-wa e S-pa ame e measu emen s ha a e no SI aceable, i is e y impo an o s a e
wha e e ences we e used du ing calib a ion. In ac , as a gene al ule, i is good p ac ise o
s a e e e y hing abou he measu emen se up ha migh ha e an impac on he ob ained
measu emen esul s – e.g. VNA, p obes (including p obe pi ch) and associa ed calib a-
ion ha dwa e and so wa e (i.e. he calib a ion subs a e, he calib a ion me hod and he
calib a ion s anda ds used).
Whene e possible, i is p e e able o ab ica e some app op ia e e e ence s anda ds on
he same wa e as he DUT. As a minimum, some leng hs o CPW line and some high-
e lec ing s anda ds (usually sho -ci cui s) a e needed. These enable he use o one o
he calib a ion echniques de i ed om he TRL app oach [44, 5] which make use o he
CPW lines o acqui e a e e ence alue which is de e mined by he p ope ies o he DUT
subs a e ma e ial. These echniques a e gene ally supe io o he mo e con en ional Sho -
Open-Load-Th u (SOLT) echnique, and a e less dependen on accu a e and epea able
p obe-placemen . Fo manual p obe s a ions, his can be a signi ican sou ce o e o a
highe equencies i he calib a ion me hod equi es known alues o he phase o he
calib a ion s anda ds.
3.2 Summa y o high- equency pa asi ic e ec s
When ope a ing in he mm-wa e equency ange (i.e., in he con ex o his sec ion abo e
110 GHz), he calib a ion e o s a ising om he inaccu acy o s anda d models and mul-
imode p opaga ion s a o se e ely impac he calib a ion accu acy ha can be achie ed.
Fo his eason a guideline o in o m he eade on hese po en ial p oblems and he means
o minimize hem was compiled in he EMPIR Plana Cal p ojec , namely, “Guidelines o
he design o calib a ion subs a es, including he supp ession o pa asi ic modes o equen-
cies up o and including 325 GHz ”. The in e es ed eade is in i ed o amilia ize himsel
wi h hese e ec s using he abo e men ioned documen . In he ollowing a selec ion o he
sugges ions p o ided in he documen is gi en:
Choice o subs a e hickness (Guideline #1)
Compu e he c i ical equency ( c) o pa asi ic modes (e.g. highe o de modes and subs a e
modes) [45] o he calib a ion subs a e employed in he gi en con igu a ion (i.e., me allic
31

o dielec ic chuck) and selec hose in which cis ou side he calib a ion equency o only
occu s in he uppe calib a ion ange, o a oid excessi e coupling o powe o unwan ed
modes.
Impac o g ound- o-g ound spacing in CPWs (Guideline #4)
The in luences o CPW g ound wid h and o g ound- o-g ound spacing, a e con ibu ing
o pa asi ic e ec s in he calib a ed esul s, in his case a dip in S-pa ame e s a a ce ain
equency. To al CPW wid h de e mines he equency whe e his dip occu s, and g ound-
o-g ound spacing in luences he s eng h o he dip beha io . Thus, he bes way o mi iga e
he impac o his dip is o keep he o al CPW wid h smalle han he o mula gi en in [45],
which equi es a adeo be ween he CPW o al wid h, he used ma e ial and he uppe
equency limi max.
Chuck opology (Guideline #5)
Using o he chuck a ma e ial which has a pe mi i i y alue simila o he calib a ion
subs a e educes he e ec s which con ibu e o he deg ada ion o he accu acy o CPW
mTRL calib a ions. Fu he in es iga ions ha e shown ha his is ue also o a chuck
ma e ial wi h a pe mi i i y la ge han ha o he wa e , because such a laye ed s uc u e
does no suppo su ace wa es ei he .
In luence o in-line and side-way neighbou ing s uc u es (Guideline #6)
One should keep sensi i e egions o he p obe shadow ee o s uc u es o a oid p obe
coupling o neighbo ing s uc u es, as shown in he igu e below (in es iga ions pe o med
up o 70 GHz).
Cus om designed TRL ki (Guideline #8)
When designing cus om ki s o LRM/TRL calib a ion he e lec should be ealized as an
o se one, keeping he minimum dis ance be ween he e ec i e e lec and he cen e o he
h u line (in insic calib a ion plane) o a oid equi ing sign changes in he solu ion o he
calib a ion equa ions.
3.3 Su ace oughness e ec s
Su ace oughness is one among di e en pa asi ic e ec s ha a ec signal in eg i y o p op-
aga ing signals on ansmission lines. While adia ion mainly inc eases he a enua ion α,
dispe sion e ec s ha e a di ec in luence on he phase eloci y ph and only indi ec ly a ec
a enua ion by inc easing he line capaci ance and hus, dielec ic loss. In con as he e o,
su ace oughness has shown o di ec ly impac ing on bo h, a enua ion and phase eloci y.
The impac magni ude depends on he ac ual oughness on he one hand and he ope a-
ion equency on he o he . Al hough i is a an ine i able p ope y o eal su aces and
can be app op ia ely aken in o accoun by modeling and simula ion, o many p ac ical
applica ions an impac o only li le su ace oughness causing de ia ions be ween ough and
32
smoo h esponses wi hin <5 % in a enua ion αand <0.5 % in phase coe icien βmay be
conside ed as negligible.
Table 9 F equency Bands and Wa eguide De ini ions.
Band Wa eguide F equency Limi s
W WR10 75 −110 GHz
F WR08 90 −140 GHz
D WR06 110 −170 GHz
G WR05 140 −220 GHz
Y WR04 170 −260 GHz
Y WR03 220 −325 GHz
Y WR02 325 −500 GHz
Y WR01.5 500 −750 GHz
Fo his pu pose, his sec ion p o ides ma gins o he oo -mean-squa e (RMS) oughness
Rqwhich mee hese equi emen s o e he equency bands om W- o Y-Band as shown
in Table 9 in e ms o bo h, a gene al conside a ion and speci ic applica ion o ce ain
ansmission lines.
−0.4−0.3−0.2−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.2
0.4
0.6
0.8
1
dep h x(
µ
m)
No malized σand H
σ(x)/σDC ˆ=CDF
|B0,ideal|
|B0, ough|
Figu e 20 Conduc i i y p o ile and skin e ec on smoo h and ough su ace a 50 GHz wi h
Rq= 1
µ
m
By making use o he G adien Model [46], he pene a ing magne ic ield can be cal-
cula ed o a gi en su ace which is ep esen ed ei he by a measu ed bea ing a ea cu e
(BAC) o Rqas shown in Fig. 20. As explained in [46], hese esponses may be used o de-
i e e ec i e ma e ial pa ame e s which in u n accoun o he impac o su ace oughness
in ansmission line models such as e.g. [45] o a CPW o [47] o ec angula wa eguides
(RWG).
While he magni ude and a io o su ace oughness impac on αand ph depend on
he ype, speci ic c oss sec ion geome y and ma e ials o he ansmission line, he su -
ace impedance as desc ibed in [46] p o ides an independen app oach o illus a ion and
compa ison:
Z=1
σe δ(σe )+j1
σDCδ(µ ,e )= πµ0µ
σe
+j πµ0µ ,e
σDC
=R+jωLi,(1)
whe e σDC is he bulk conduc i i y as a ma e ial p ope y o he conduc o (e.g. 58 MS/m
in case o bulk coppe ) and σe and µ ,e deno e e ec i e, equency dependen ma e ial
33
pa ame e alues de i ed om he G adien Model app oach which ep esen he impac o
su ace oughness. While he eal pa o Za ec s he a enua ion and is he e o e ela ed
o R, i s imagina y pa in luences ph and is ela ed o Li,, which is he inne induc ance.
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
0
5
10
15
20
25
Rq(nm)
∆< {Z}(%)
110 GHz
140 GHz
170 GHz
220 GHz
260 GHz
325 GHz
500 GHz
750 GHz
Figu e 21 Rela i e de ia ion ∆< {Z}be ween ough and smoo h case in %
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
0
100
200
300
400
Rq(nm)
∆= {Z}(%)
110 GHz
140 GHz
170 GHz
220 GHz
260 GHz
325 GHz
500 GHz
750 GHz
Figu e 22 Rela i e de ia ion ∆= {Z}be ween ough and smoo h case in %
Figs. 21 and 22 show he ela i e de ia ion be ween he ough and smoo h Zdepending
on Rq o he conside ed equency band limi s. F om he eal pa , a 5 % ma gin can
he e o e be de i ed o each band, indica ing he need o lowe Rqwi h inc easing ope a ion
equencies.
Al hough he de ia ion wi hin he imagina y pa o Zin Fig. 22 exceeds 100 % o
ela i ely small Rqal eady, i is wo h o men ion, ha i only con ibu es o he inne
induc ance e m Liwhich is much smalle han he ou e induc ance Lo(LiLo) and
is he e o e only a ac ion o he o al induc ance o mos p ac ical ansmission lines.
Fu he mo e, he 5 % limi in < {Z}is no di ec ly ela ed o he a enua ion o a speci ic
ansmission line, since he conduc o ci cum e ence mus be conside ed acco ding o he
c oss sec ion geome y [48].
While he layou o a CPW allows o a ious implemen a ions depending on he subs a e
ma e ial, manu ac u ing aspec s and o he s, ec angula wa eguides a e ypically p oduced
34
in s anda dized dimensions acco ding o hei iden i ie WR-XX in Table 9. This allows o
p ecise p edic ions o he su ace oughness impac which is shown in Figs. 23 and 24.
0 5 10 15 20 25 30 35 40 45 50
0
5
10
15
20
Rq(nm)
∆α(%)
WR10
WR08
WR06
WR05
WR04
WR03
WR02
WR01.5
Figu e 23 Rela i e de ia ion ∆αbe ween ough and smoo h RWG in %.
0 5 10 15 20 25 30 35 40 45 50
0
2
4
6
8
10
Rq(nm)
∆β(o
/
oo)
WR10
WR08
WR06
WR05
WR04
WR03
WR02
WR01.5
Figu e 24 Rela i e de ia ion ∆βbe ween ough and smoo h RWG in o
/
oo.
No e, ha he de ia ion in βis p o ided in o
/
oo as i is a he small as compa ed o he
impac on α. Howe e , i comes along wi h a small shi o he cu o equency c owa ds
lowe alues.
The Rq-ma gins o CPWs can be p o ided o ce ain cases only, since CPW lines can be
ab ica ed in a much g ea e a ie y compa ed o s anda dized RWG. Exempla ily, a CPW
implemen ed on Al2O3subs a e (ε = 9.7) is conside ed wi h he c oss sec ion geome y as
p o ided in Fig. 25.
In addi ion o he phase coe icien β, in his case, also he e ec i e ela i e pe mi i i y
is conside ed acco ding o:
ε ,e =c0
ph 2
(2)
The co esponding Rqma gins a e p o ided in Figs. 26 o 31 o a enua ion and phase
coe icien o di e en subs a e hicknesses o h= 100
µ
m and h= 10 mm, espec i ely.
35
wc= 50
µ
m
wg= 270
µ
mwg= 270
µ
m
s= 25
µ
ms= 25
µ
m = 5
µ
m
h
Figu e 25 C oss sec ion geome y o a CPW s uc u e as conside ed in his compa ison.
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
0
5
10
15
Rq(nm)
∆α(%)
110 GHz
140 GHz
170 GHz
220 GHz
260 GHz
325 GHz
Figu e 26 Rela i e de ia ion ∆αbe ween ough and smoo h CPW in % o h= 100
µ
m.
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
0.2
0.4
0.6
0.8
1
Rq(nm)
∆β(%)
110 GHz
140 GHz
170 GHz
220 GHz
260 GHz
325 GHz
Figu e 27 Rela i e de ia ion ∆βbe ween ough and smoo h CPW in % o h= 100
µ
m.
36

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
0.5
1
1.5
2
Rq(nm)
∆ε ,e (%)
110 GHz
140 GHz
170 GHz
220 GHz
260 GHz
325 GHz
Figu e 28 Rela i e de ia ion ∆ε ,e be ween ough and smoo h CPW in % o h= 100
µ
m.
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
0
2
4
6
Rq(nm)
∆α(%)
110 GHz
140 GHz
Figu e 29 Rela i e de ia ion ∆αbe ween ough and smoo h CPW in % o h= 10 mm.
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
0.2
0.4
0.6
0.8
1
Rq(nm)
∆β(%)
110 GHz
140 GHz
Figu e 30 Rela i e de ia ion ∆βbe ween ough and smoo h CPW in % o h= 10 mm.
37
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
0.5
1
1.5
2
Rq(nm)
∆ε ,e (%)
110 GHz
140 GHz
Figu e 31 Rela i e de ia ion ∆ε ,e be ween ough and smoo h CPW in % o h= 10 mm.
38
3.4 Impo ance o posi ioning accu acy
Con en ional RF es s uc u es equi e p obing pads whose dimensions a e a ound 50×50 µm2
o accommoda e he p obe ip geome y (example: pi ch o 100 µm, con ac a ea o 30×30 µm2).
The manual posi ioning o he p obe on o he CPW es s uc u e gene a es misalignmen
measu emen e o s ha impac no ably on he measu ed impedance. In pa icula , hese
measu emen e o s inc ease in he millime e -wa e and sub-millime e -wa e egimes. The
posi ioning accu acy is also c ucial when measu emen o high impedance de ices such as
nanoscale s uc u es a e conside ed. Indeed, phase-shi and magni ude e o s inhe en o
he posi ioning accu acy o se he impedance o be measu ed. Consequen ly, piezo-based
nano-posi ioning (X-Y-Z con ols) and s ain-sensing (Z con ol) s a egies a e used o p o-
ide au oma ed and accu a e con ol o he p obe landing on o he es s uc u e [49, 50].
39
4 Nanode ice measu emen s
4.1 Sol ing he impedance misma ch p oblem
Vec o ne wo k analyze s ha e been in oduced in he se en ies o measu e he elec ical
p ope ies o ma e ials and ci cui s. Since hen, he e has been conside able wo k o ex end
hei measu emen capabili ies such as equency co e age om low RF o hund eds o GHz,
mul i-po de ices cha ac e iza ion, balanced, di e en ial, ha monic, modula ion and pulsed
measu emen s. Nowadays, he e is an u gen need o u he ex end he ne wo k analyze
capabili ies o mee he speci ic needs o cha ac e iza ion ools o impedances clea ly highe
han he 50 Ω e e ence impedance o he VNA. In pa icula , he elec ical cha ac e iza ion
o high impedance nanode ices is a well-known scien i ic challenge. The main measu emen
limi a ion in hese applica ions is he impedance misma ch be ween he e e ence impedance
o he ne wo k analyze close o 50 Ω ha is oo di e en compa ed o he impedance o
nanode ices ha is in he ange o ens o hund eds o kΩ. Indeed, when high impedances
a e conside ed, he VNA is insensi i e o he a ia ions o he e lec ion coe icien .
The issue o dealing wi h ex eme impedance measu emen has yielded a a ie y o mea-
su emen echniques. In 2005, he i s measu emen s o he high equency conduc ance
o a me allic single walled nano ube (SWNT) wi h esis ance below 200 kΩ inse ed in a
coplana wa eguide (CPW) ansmission line we e pe o med up o 10 GHz [51]. In 2010, o
imp o e he VNA sensi i i y, an indi idual SWNT iwas inse ed in a speci ic high impedance
Whea s one b idge ha helps o educe he impedance misma ch be ween he VNA and he
high-impedance nanode ice [52].
Among he al e na i es o hese s udies, he in e e ome ic p inciple commonly used in
op ics h ough Michelson o Mach Zende con igu a ions has gained he in e es om he
mic owa e esea ch communi y o measu e small complex impedance con as s. Basically, a
monoch oma ic signal is spli wi h one pa a eling a ixed pa h and he o he a a iable
one. The wo esul ing signals a e euni ed, ampli ied i necessa y, and p oduce he well-
known in e e ence. In 1949, a Michelson- ype mic owa e in e e ome e was in oduced o
he i s ime a he ee-space wa eleng h o 3.2 cm o ee-space dielec ic cha ac e iza ion
[53]. In 2007, mic owa e in e e ome y was applied o he i s ime o he measu emen o
high impedance de ices a ound 1.8 GHz [54, 55]. In pa icula , he se up included a ec o
ne wo k analyze in e aced wi h an in e e ome ic se up buil up wi h a hyb id couple
associa ed o low noise ampli ie s. In 2011, a mechanically unable in e e ome ic ma ching
ne wo k in he ange 1-18 GHz buil up wi h a powe di ide , a a iable a enua o and
a sliding-sho was applied o high impedance measu emen s [56]. To u he enhance he
sensi i i y in a b oadband equency ange, an in e e ome e buil up wi h a high- esolu ion
p og ammable delay line and a mo o -d i en a iable a enua o has been de eloped [57].
In 2015, an I/Q-mixe -based in e e ome ic echnique is de eloped o speed ope a ion [58].
These s udies ha e p o en ha RF in e e ome ic echniques a e candida es o ackle he
p oblem o impedance misma ch.
The ecommenda ion o high impedance measu emen s is o inse a uning ma ching
ne wo k be ween he measu emen po o he ec o ne wo k analyze and he measu emen
o he po o he de ice unde es . The uning ma ching ne wo k based on mic owa e
in e e ome y emains he mos e icien me hod. This la e can be buil up easily wi h
coaxial o guided comme cial equipmen (couple s, powe di ide s, a iable a enua o s and
phase-shi e s). In addi ion, he me hod o e s b oadband equency measu emen s.
40
po -4. Subsequen ly, he s abili y be ween a1and ain signals in single-sou ce in e e ome e
is e alua ed using po -1 o he VNA o p o ide he a1signal sou ce and o se e as inpu o
he single-sou ce in e e ome e as shown in Fig. 32(b). Again, bo h signals a e subsequen ly
measu ed by he ecei e s o po -2 and po -4.
In bo h expe imen s, he powe le el o each signal sou ce is se o -10 dBm, and subse-
quen ly 20 ·103measu emen alues a e ex ac ed a 3 GHz om bo h ecei e s (po -2 and
po -4). F om hese alues, he a io ain /a1is calcula ed and no malized o demons a e
he s abili y be ween he wo signals.
Figu e 36 Measu emen esul s om [68] showing he cancella ion sensi i i y o he phase-
componen ealized wi h wo ac i e in e e ome e opologies a 3 GHz (dual-sou ce:
blue ci cles; single-sou ce: ed squa es, and inse ). The black line depic s phase-
componen s abili y o b-wa e measu ed using me hod ou lined in (9).
The linea magni ude s abili y o ain /a1 o bo h me hods is ound o be compa able and
smalle han 1 ·10−4. The esul o he ela i e phase s abili y be ween a1and ain signals
is shown in Fig. . As expec ed, hese esul s demons a e he much highe phase s abili y
o he single-sou ce con igu a ion compa ed o he dual-sou ce me hod [64]. Mo eo e , as
shown in Fig. 36, he model p edic ions, plo ed as black dashed line, accu a ely co ela e
wi h he expe imen ally ound phase luc ua ions o he dual-sou ce me hod.
47

5 Unce ain ies in on-wa e measu emen s
5.1 In oduc ion
The e alua ion o unce ain ies in VNA measu emen s is a challenging ask because o
1. he mul i a ia e na u e o he measu and. S-pa ame e s a e wo-dimensional quan i-
ies, exp essed ei he in magni ude and phase o complex- alued wi h eal and imagi-
na y componen s.
2. he mul is ep measu emen p ocess wi h calib a ion and e o co ec ion. This leads
o an elabo a e measu emen model.
3. The ela i ely la ge numbe o da a poin s. I is no unusual o collec da a a se e al
hund ed equency poin s and he unce ain y migh show a p onounced equency
dependence.
The e has been signi ican p og ess in he las yea s o imp o e unce ain y e alua ion in
VNA measu emen s. A supplemen [69] o he GUM [70] has been published, speci ically
dealing wi h mul i a ia e and complex- alued quan i ies. This documen se es as he basic
guideline o de e mine unce ain ies associa ed wi h es ima es o S-pa ame e s. Jus e-
cen ly a e ised e sion o he EURAMET VNA Guide [28] has been published emb acing
he p inciples o he GUM supplemen and p omo ing an unce ain y e alua ion based on a
measu emen model, which ep esen s he en i e measu emen p ocess and akes quan i ies
in luencing he measu emen in o accoun . The EURAMET VNA Guide has been p ima -
ily w i en o coaxial measu emen s, bu i s basic p inciples a e applicable o on-wa e
measu emen s as well.
An essen ial pa o unce ain y e alua ion is he cha ac e isa ion o in luence quan i ies.
This is discussed in some de ail in [28] and he same in luences need o be conside ed in
on-wa e measu emen s oo. The cha ac e isa ion p ocedu es gi en in [28] can gene ally
be applied wi h li le and s aigh o wa d modi ica ions. Unde connec o epea abili y
di e en con ibu ions speci ic o on-wa e posi ioning and alignmen can be summa ized,
by pe o ming he ollowing cha ac e iza ions
1. Repea ed connec ions by keeping p obes a same posi ion and mo ing sample in z.
2. Repea ed posi ioning o p obe s a ion o each measu emen o same s anda d a same
posi ion.
3. Repea ed measu emen o same s anda d a sligh ly di e en con ac poin s.
On-wa e measu emen s a e a ec ed mo e by c oss alk compa ed o coaxial measu emen s.
The e ec is s ongly dependen on he dis ance be ween p obes and he e o e on he de ice
unde es . One way o acknowledge his e ec in he unce ain y e alua ion is o come up
wi h an addi ional DUT unce ain y (as shown in he example in he nex sec ion), which
can be cha ac e ized by he ansmission coe icien as a unc ion o dis ance when measu ing
wo one-po s anda ds. O he app oaches migh be possible.
In he mul i a ia e case he p opaga ion o measu emen unce ain ies is mo e in ol ed,
see [71]. I co ela ions should be aken in o accoun p ope ly i is una oidable o use
specialized so wa e. Sui able so wa e solu ions, which a e able o handle he unce ain y
p opaga ion o complex- alued quan i ies, a e a ailable nowadays [72, 73]. These ools p o-
ide gene al amewo ks o ealize cus om-buil implemen a ions o S-pa ame e unce ain y
e alua ion. Fo so wa e solu ions ha a e speci ically a ge ing S-pa ame e measu emen s
see [12, 74]. These solu ions al eady con ain he VNA measu emen models and suppo
di e en calib a ion algo i hms, i.e. p og amming is no necessa y.
48
Figu e 37 Basic se up o new p ojec .
One o hese solu ions is he so wa e VNA Tools II. O iginally de eloped o coaxial
VNA measu emen s i has been ecen ly ex ended o suppo on-wa e measu emen s as
well. In he nex sec ion he di e en s eps in an on-wa e measu emen wi h VNA Tools
II a e explained. An o e iew o he ea u es o VNA Tools II is gi en in [75]. Fu he
in o ma ion and use guidance can be ound a [12]. Measu emen models, calcula ions and
da a o ma s a e documen ed in publicly a ailable documen s, which can be downloaded
om he websi e as well.
5.2 VNA Tools II on-wa e example
5.2.1 In oduc ion
This example shows he use o he VNA Tools so wa e o pe o m an SOLT on-wa e mea-
su emen . The ollowing ypical s eps a e co e ed:
1. De ini ion o a new p ojec .
2. Collec ion o measu emen da a and eco d o he measu emen p ocess in he Mea-
su emen Jou nal.
3. Con igu a ion o VNA calib a ion and compu a ion o e o coe icien s.
4. E o co ec ion o he aw measu emen da a.
5. Use o da a explo e o isualiza ion.
5.2.2 New p ojec and basic de ini ions
The i s s ep in VNA Tools II is o de ine a new p ojec . This de ines he loca ion, whe e
he da a iles o he p ojec a e s o ed and some basic se ings. I can be speci ied in he
na iga ion ba on he op. By selec ing New P ojec he dialog in Fig. 37 opens. The
en ies unde Name and Loca ion will de ine he global oo pa h. Unde VNA Se up a VNA
49
Figu e 38 VNA Se ings.
de ice, es po cable and p obe can be selec ed. In his example a Tes VNA is selec ed,
which usually se es jus o es pu poses. Clicking OK will s o e hese en ies and close he
dialog.
By selec ing VNA Se ings VNA de ice pa ame e s can be se in a sepa a e dialog, see
Fig. 38. The dialog allows o se some pa ame e s and speci y he sweep mode, which in
his case is a segmen ed sweep. The sweep is de ined by he en ies in he segmen a-
ble, e.g. he maximum equency is se o 50 GHz and he IFBW o 10 Hz. By clicking
Se Segmen Table he alues will be sa ed o he VNA. By clicking OK he VNA Se ings
a e sa ed o he measu emen jou nal.
Selec ing Cus om DUT Unc in New DUT Unc opens he dialog in Fig. 39 o accoun o
c oss alk be ween p obes du ing measu emen s. The alues en e ed as ansmission unce -
ain ies a e dependen on dis ance and p obe ype. In his example all measu emen s a e
done on he same subs a e, wi h he same p obes and he same dis ance be ween p obes.
The size o he unce ain y con ibu ion is he e o e he same o each measu emen , bu
unco ela ed when changing om one s anda d o ano he . When clicking OK he i s wo
en ies, VNA Se ings and Cus om DUT Unc can be seen in he measu emen jou nal.
5.2.3 Measu emen s
Fo he simul aneous measu emen o he opens o bo h po s an unce ain y con ibu ion
due o c oss alk be ween p obes needs o be aken in o accoun . This is gene a ed by clicking
on New DUT Unc and selec ing om he d op-down menu Cus om, see Fig. 40. Inc ease he
numbe in he Index ield when measu ing a new s anda d. Use same index i measu ing he
same s anda d again. This keeps ack o he co ela ion. Click OK o gene a e he unce -
ain y con ibu ion. I will show up in he measu emen jou nal. To s a he measu emen
he boxes unde New Connec ion need o be checked o bo h po s, see Fig. 41. Because
bo h p obes a e kep a a ixed posi ion du ing he measu emen s no unce ain y con ibu-
ions due o cable mo emen need o be accoun ed o . The boxes unde Cable Mo emen
50
Figu e 39 Se ing cus om DUT unce ain y.
Figu e 40 Selec ing cus om DUT unce ain y o c ea e an unce ain y con ibu ion due o c oss
alk.
51
Figu e 41 Cable mo emen s and new connec ions be o e measu emen s a e indica ed by checking
boxes.
Figu e 42 Measu emen dialog box.
he e o e emain unchecked. As soon as one o he p obes is mo ed be o e a measu emen
he co esponding box needs o be checked. Selec ing Open nex o he VNA De ice ield,
see Fig. 41, will open he connec ion o VNA. Selec ing Measu emen opens he dialog in
Fig. 42. In his dialog he se up needs o be speci ied in he d op-down menu Se up, in his
case Sx,x Po s: 1,2. Clicking on Measu e will ini ia e he measu emen and he da a
will be displayed in he g aph. The measu emen o he open in his example is showing
noise con ibu ions o S21 and S12. When sa is ied wi h he measu emen he da a can be
s o ed wi h Sa e Da a. The same p ocedu e will be epea ed o he measu emen o sho ,
load and h ough. In he inal measu emen s ep he DUT, in his case a line, is measu ed,
see Fig. 43. When he measu emen s a e inished he measu emen jou nal can be sa ed by
clicking Sa e Jou nal.
52

Figu e 43 A e inal measu emen o DUT pe o med.
5.2.4 Calib a ion con igu a ion
A e clicking on he abs Calib a ion Con ig and New Con ig we selec SOLT in he d op-
down menu as he calib a ion ype, see Fig. 44 A e clicking on OK he empla e can be illed
in by linking measu emen da a, in column Raw Measu emen , and de ini ions, in column
De ini ion, o he calib a ion s anda ds, see Fig. 45. In he same dialog he measu emen
jou nal needs o be speci ied, in his case Jou nal 01. nalog. Wi h Sa e Con ig he calib a-
ion con igu a ion can be sa ed o a ile SOLT 01.calc g. By clicking on S a Compu a ion
he e o coe icien s a e compu ed and s o ed as SOLT 01.calb.
5.2.5 E o co ec ion
A e selec ing he ab E o Co ec ion he dialog in Fig. 46 opens The ields need o
be popula ed wi h he loca ion o measu emen jou nal, e o coe icien s, aw measu e-
men s and ou pu olde . Wi h Sa e Con ig he con igu a ion will be sa ed o a ile
SOLT 01.co c g. Clicking on S a Compu a ion will ini ia e he e o co ec ion and s o e
e o co ec ed S-pa ame e iles in SOLT 01 ou .
5.2.6 Da a Explo e
By selec ing he ab Da a Explo e he measu emen esul s can be isualized as shown in
Fig. 47. The Da a Explo e has a da a b owse on he le . By clicking on da a iles hey will
be displayed on he igh . The e a e di e en basic display modes, which can be selec ed wi h
G aph,Table,Poin and Co a iance. As o se up and o ma he e a e a ious selec ions
as well. Unce ain ies can be uned on o o . Da a can as well be expo ed o o he ile
o ma s.
53
Figu e 44 Selec ion o calib a ion ype.
Figu e 45 Calib a ion Con igu a ion.
54
Figu e 46 E o Co ec ion.
Figu e 47 Da a Explo e .
55
5.3 Unce ain y budge examples
In he ollowing unce ain y esul s o h ee ypical de ices on a used silica subs a e a e
shown o he case o a mul iline TRL calib a ion ( om [11]), co e ing a la ge po ion o
he impedance ange measu able by a VNA: a nominally 15 dB ma ched a enua o ( e med
‘a enua o ’), a 7065 µm-long misma ched line ( e med ‘misma ch’), and a 2-po open
(high- e lec de ice, e med ‘open’)).
5.3.1 Expanded unce ain ies
10 20 30 40 50 60 70 80 90 100 110
F equency (GHz)
-0.04
-0.02
0
0.02
0.04
|S11| (exp. unc.)
a enua o
misma ched line
open
10 20 30 40 50 60 70 80 90 100 110
F equency (GHz)
-15
-10
-5
0
5
10
15
(S11)/°(exp. unc.)
a enua o
misma ched line
open
10 20 30 40 50 60 70 80 90 100 110
F equency (GHz)
-0.05
0
0.05
|S21| (exp. unc.)
a enua o
misma ched line
open
Figu e 48 Expanded unce ain y in e als a a co e age p obabili y o 95% (k=2).
56
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