Academic Edi o : Yi Xi
Recei ed: 10 July 2025
Re ised: 1 Augus 2025
Accep ed: 13 Augus 2025
Published: 2 Sep embe 2025
Ci a ion: Rom, M.; an den B om,
H.E.; Hou zage , E.; an Leeuwen, R.;
an de Bo n, D.; Rie eld, G.; Muñoz,
F. Measu emen Sys em o Cu en
T ans o me Calib a ion om 50 Hz o
150 kHz Using a Wideband Powe
Analyze . Senso s 2025,25, 5429.
h ps://doi.o g/10.3390/s25175429
Copy igh : © 2025 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license
(h ps://c ea i ecommons.o g/
licenses/by/4.0/).
A icle
Measu emen Sys em o Cu en T ans o me Calib a ion om
50 Hz o 150 kHz Using a Wideband Powe Analyze
Mano Rom 1,2 , Helko E. an den B om 1,* , E nes Hou zage 1, Ronald an Leeuwen 1,
Dennis an de Bo n 2, Ge Rie eld 1,3 and Fabio Muñoz 2
1VSL B.V. (VSL), 2629 JA Del , The Ne he lands
2Elec ical Sus ainable Ene gy Depa men , Del Uni e si y o Technology (TU Del ),
2628 CD Del , The Ne he lands
3Depa men o Elec ical Enginee ing, Ma hema ics and Compu e Science (EEMCS), Uni e si y o Twen e,
7522 NB Enschede, The Ne he lands
*Co espondence: h db [email p o ec ed]
Abs ac
Accu a e and eliable cha ac e iza ion o cu en ans o me (CT) pe o mance is essen ial
o main aining g id s abili y and powe quali y in mode n elec ical ne wo ks. CT mea-
su emen s a e key o e ec i e moni o ing o ha monic dis o ions, suppo ing egula o y
compliance and ensu ing he sa e ope a ion o he g id. This pape add esses a me hod o
he cha ac e iza ion o CTs ac oss an ex ended equency ange om 50
Hz
up o 150
kHz
,
d i en by inc easing powe quali y issues in oduced by enewable ene gy ins alla ions and
non-linea loads. T adi ional CT calib a ion app oaches in ol e measu emen se ups ha
o e ppm-le el unce ain y bu a e complex o ope a e and limi ed in p ac ical equency
ange. To simpli y and expand calib a ion capabili ies, a calib a ion sys em employing a
sampling amme e (powe analyze ) was de eloped, enabling he di ec measu emen o
CT seconda y cu en s o an unknown CT and a e e ence CT wi hou any u he auxilia y
equipmen . The esul ing expanded magni ude a io unce ain ies o he wideband CT
calib a ion sys em a e 10 ppm (
k=
2) up o 10
kHz
and less han 120 ppm om 10
kHz
o
150
kHz
; hese unce ain ies do no include he unce ain y o he e e ence CT. Addi ionally,
he ope a ional condi ions and se up design choices, such as ins umen wa m-up du a-
ion, g ounding me hods, measu emen shun selec ion, and cable ype, we e e alua ed
o hei impac on measu emen unce ain y and epea abili y. The esul s highligh he
signi icance o minimizing pa asi ic impedances a highe equencies and main aining
consis en es ing condi ions. The de eloped calib a ion se up p o ides a obus ounda ion
o u u e s anda diza ion e o s and p ac ical guidance o cha ac e ize CT pe o mance in
he inc easingly impo an sup aha monic equency ange.
Keywo ds: cu en ans o me s; cu en a io; wideband; wide dynamic ange;
calib a ion
;
p ecision powe analyze s; sampling cu en a io b idge; phase e o ; a io e o ;
unce ain y
1. In oduc ion
High- equency dis o ion in elec ici y g ids is gaining scien i ic and echnical in e es
due o i s g owing occu ence and impac . These dis u bances a e mainly injec ed by new
de ices o decen alized enewable gene a ion. Powe con e e s connec ed o he g id
inc ease swi ching equencies, in oducing ha monic componen s in o he g id [
1
,
2
]. These
ha monics, p oduced by non-linea loads and swi ching de ices, deg ade powe quali y
Senso s 2025,25, 5429 h ps://doi.o g/10.3390/s25175429
Senso s 2025,25, 5429 2 o 23
(PQ). Recen s udies epo educ ions in he powe ac o (up o 60%) and inc eases in
line losses exceeding 2% [
3
,
4
]. Al hough in e na ional s anda ds such as IEC 61000-3-2 [
5
]
and IEEE S d 519 [
6
] p o ide ha monic emission limi s, en o cemen emains inconsis en ,
emphasizing he need o enhanced PQ moni o ing.
Measu emen s in medium- ol age (MV, up o 36
kV
) dis ibu ion ne wo ks ypically
ely on ins umen ans o me s (ITs), such as cu en ans o me s (CTs), o scale down
cu en s (up o 2
kA
) o accu a e e alua ion by PQ analyze s and powe analyze s. S an-
da diza ion o PQ analyze s is well-es ablished up o 150kHz and 20A a 230V [7,8]. Ex-
ensi e esea ch has e ined he measu emen me hods aligned wi h hese s anda ds [
9
,
10
].
In con as , he pe o mance o ins umen ans o me s a highe equencies, especially in
he sup aha monic ange ( ha is, in he ange o 2–150 kHz), emains less well de ined [
11
].
Cu en s anda ds like IEC 61869-2 [
12
] and ecen esea ch [
13
,
14
] add ess pe o mance up
o lowe -o de ha monics bu do no co e equencies beyond 10
kHz
, whe e pa icula
dis o ions occu as well [15,16].
Sup aha monic dis o ions pose isks o medium- ol age dis ibu ion g ids [
17
]. High
dV/d
ol age spikes exceeding 100
kV/µs
can lowe pa ial-discha ge incep ion ol ages,
po en ially sho ening insula ion li e imes by as much as an o de o magni ude [
17
–
19
].
Mo eo e , sup aha monics inc ease eddy-cu en and p oximi y losses in ans o me s,
which can aise ho spo empe a u es by up o 10–15
◦
C [
20
]. These dis o ions can igge
unin ended ac i a ion o p o ec i e de ices, posing a isk o g id s abili y, and gene a e audi-
ble noise exceeding 50
dB(A)
in low- ol age swi chgea s [
19
]. Addi ionally, sup aha monic
dis o ion can p opaga e om medium- ol age ne wo ks in o low- ol age ci cui s h ough
ans o me s, causing LED ligh ing licke , in e e ence wi h powe -line communica ion,
and damage o domes ic appliances and sensi i e equipmen [17,21].
To add ess he isks associa ed wi h inc easing ha monic emissions in medium- ol age
g ids, i is essen ial o egula e he gene a ion o hese emissions and ensu e ha sup a-
ha monic ol ages and cu en s can be accu a ely measu ed. Consequen ly, wideband
accu acy classes (WB0–WB4) o CTs ha e been p oposed in IEC 61869-2 [
12
] o equencies
up o 500
kHz
, bu he me ological in as uc u e needed o e i y such pe o mance is
s ill incomple e. In esponse, Na ional Me ology Ins i u es (NMIs) ha e ex ended CT
calib a ion se ices in o he wideband egion. Se e al leading labo a o ies now o e CT
cha ac e iza ions up o 10
kHz
. Fo example, he compa a o sys em desc ibed in [
22
]
achie ed expanded unce ain ies (
k=
2) o a ew hund ed pa s pe million (ppm) o
magni ude a io e o and a ew mic o adians o phase measu emen s up o 9
kHz
. Simi-
la ly, he e e ence se up de eloped in [
23
] demons a ed unce ain ies o
±
20 ppm and
±20 µ ad a he undamen al equency, ising o ±400 ppm and ±800 µ ad a 9kHz.
Despi e he ecen p og ess, se e al impo an limi a ions emain. Mos cu en mea-
su emen sys ems ha e only been alida ed up o 10
kHz
, lea ing he equency ange
be ween 10
kHz
and 150
kHz
la gely uncha ac e ized and unexplo ed [
23
]. In addi ion, he
exis ing wideband calib a ion echniques o en depend on auxilia y equipmen , such as
wideband shun s, cu en ansduce s, and bu e ampli ie s [
24
–
26
], which complica es
he calib a ion p ocess, especially a highe equencies; see also Sec ion 2.2.2.
The sampling amme e app oach in oduced in [
27
] o e s a p omising simpli ica ion
by educing he numbe o equi ed componen s and s eamlining he p ocedu e. Howe e ,
his sys em was only e alua ed up o 10
kHz
and did no p o ide a comple e analysis
o he measu emen chain o assess he impac o p ac ical se up a ia ions. As a esul ,
a comp ehensi e unce ain y budge o he me hod was no es ablished. These limi a ions
highligh he ongoing need o esea ch and de elopmen in wideband CT calib a ion,
pa icula ly in he sup aha monic equency band.
Senso s 2025,25, 5429 3 o 23
This pape add esses hese sho comings by in oducing a b oadband calib a ion se up
capable o cha ac e izing CT a io and phase e o s om 50
Hz
o 150
kHz
. Building on he
sampling amme e concep o [
27
], he p esen wo k uses he same measu emen sys em
and demons a es i s simpli ica ion compa ed o adi ional wideband calib a ion me hods
ha ely on mo e auxilia y equipmen . This pape also analyzes how p ac ical design
choices—including CT p oximi y, conduc o placemen , seconda y-side cabling, g ounding
schemes, shun selec ion, and compensa ion elec onics—in luence o e all measu emen
accu acy. In doing so, his wo k aims o help es ablish a me ological ounda ion o
he u u e implemen a ion o he IEC WB3 class [
12
] and suppo s he measu emen o
sup aha monic powe quali y phenomena.
The emainde o his pape is o ganized as ollows. Sec ion 2p o ides he heo e ical
backg ound ele an o CT a io and phase e o cha ac e iza ion, including he complex
a io e o o mula ion, he a io-based calib a ion app oach, and an o e iew o he ex-
is ing echniques along wi h hei limi a ions. Sec ion 3 hen desc ibes he expe imen al
se up and me hodology, ou lining he measu emen sys em a chi ec u e, ins umen a ion,
and da a p ocessing p ocedu es. Sec ion 4p esen s and analyzes he expe imen al esul s,
co e ing he baseline calib a ion pe o mance and examining he in luence o he key ope -
a ional and se up pa ame e s. This sec ion also discusses he main sou ces o measu emen
unce ain y and p o ides an unce ain y budge . Finally, Sec ion 5discusses he indings
in he con ex o CT calib a ion p ac ices, o e s p ac ical ecommenda ions o wideband
measu emen s, and sugges s di ec ions o u u e esea ch.
2. Backg ound and Theo y
2.1. Complex Ra io E o o a Cu en T ans o me
Cu en ans o me s a e used o scaling high p ima y cu en s in he MV g id o
lowe mo e easily measu able seconda y cu en s. Ideally, a CT p o ides a ep oduc ion
Is
o he p ima y cu en
Ip
a i s seconda y winding wi h a cons an a io
n=Ip/Is
.
Howe e , in eali y, CTs ha e ampli ude and phase e o s ha can be exp essed as a
complex a io e o :
ϵ(ω) = n Is(ω)
Ip(ω)−1. (1)
This a io e o can be measu ed as a unc ion o equency ω=2π .
2.2. Calib a ion Me hods o Cu en T ans o me s
His o ically, ins umen ans o me calib a ion has been pe o med a powe e-
quencies o 50
Hz
o 60
Hz
using b idge o compa a o echniques [
28
–
31
]. In hese con-
igu a ions, a es CT and a mul i-winding e e ence a e ene gized by a common p ima y
conduc o , and hei seconda ies a e connec ed in opposi ion; he esidual cu en p o ides
a di ec measu e o CT e o [
28
]. By nulling his esidual, he sys em de e mines bo h a io
and phase e o . Al hough such app oaches can deli e sub-ppm unce ain ies, hey a e
complex and ypically limi ed o compa ing CTs wi h equal nominal a ios.
The p oli e a ion o ha monics, in e ha monics, and sup aha monics in mode n g ids
has d i en he need o CT calib a ion o e an ex ended equency ange [
25
]. Mul iple
wideband calib a ion s a egies ha e eme ged in esponse.
2.2.1. Shun -Based Me hods
As demons a ed o ins ance by [
25
], CT calib a ion can be achie ed using wideband
shun s [
32
–
34
] o di ec ly measu e he p ima y cu en ha is wound mul iple imes
h ough he CT co e. A composi e signal—con aining he undamen al and ha monics up
o 5
kHz
—is injec ed in o he p ima y windings. Two wideband coaxial shun s measu e
Senso s 2025,25, 5429 4 o 23
p ima y and seconda y cu en s simul aneously, wi h equency-domain analysis p o iding
a io and phase e o o each spec al componen .
Howe e , his app oach aces p ac ical cons ain s a high cu en and equency.
In [26], he use o coaxial manganin shun s demons a es DC unce ain y o 10 ppm up o
10 kA bu is limi ed o ens o kHz. In [
35
], expe imen al esul s a e limi ed o below 100A,
wi h ens o ppm e o a 100 kHz. Simila ly, Re . [
36
] epo s unce ain ies o 200
ppm
o
500
ppm
in ampli ude and below 0.05
m ad
in phase up o 100
kHz
a 100A. As a esul ,
no a ailable shun echnology combines
>
1
kA
a ing, bandwid h o 150
kHz
, and ppm-
le el accu acy. While esea ch con inues, he e e ence CT and DUT CT combina ion o
high-cu en wideband calib a ion emains a p ac ical al e na i e.
2.2.2. Sampling Cu en Techniques
As desc ibed in [
24
,
37
], ano he app oach employs cu en ansduce s, cu en bu e s,
and high-p ecision sampling ol me e s (see Figu e 1 o a schema ic o e iew o he se up
used in [
24
]). Al hough such se ups can achie e unce ain ies a he ppm le el, hey a e
complex o main ain and ope a e due o he numbe o componen s, and he measu emen
bandwid h is ul ima ely limi ed by he pa icula componen s.
Figu e 1. Schema ic o a CT sampling cu en a io measu emen sys em. High p ima y cu en s a e
gene a ed using a powe ampli ie and a s ep-up ans o me . The CT unde es (DUT) is measu ed
agains a e e ence CT whe e bo h seconda y cu en s a e scaled down using s ep-down ans o me s
(SDTs). Ope a ional ampli ie s wi h p ecision AC esis o s ac as cu en bu e s ha con e cu en
o ol age, while digi al sampling ol me e s eco d he bu e ol age signals [24].
An al e na i e simpli ied measu emen sys em in oduced by [
27
] uses a high-
esolu ion sampling amme e (powe analyze ) o measu e seconda y cu en s o bo h
DUT and e e ence CT. I achie ed unce ain ies below 35 ppm up o he 50 h ha monic
(2
kHz
), wi h demons a ed pe o mance o 10
kHz
, all wi h signi ican ly educed sys em
complexi y compa ed o ea lie me hods.
In his s udy, he digi al sampling compa a o measu emen sys em om [
27
] is
ex ended o 150kHz, a comp ehensi e unce ain y budge is p esen ed, and he in luence
o p ac ical es -bench pa ame e s—including g ounding, cabling, conduc o placemen ,
and compensa ion elec onics—is sys ema ically analyzed.
Bo h he DUT and he e e ence CTs a e o he ype desc ibed in [
38
], which employ
elec onic compensa ion o achie e unce ain ies below 1 ppm a 50
Hz
. Mino di e ences
in he componen s o he compensa ion elec onics ha e shown o p o ide negligible impac
a 50 Hz bu migh in oduce di e en equency esponses. While hei high- equency
pe o mance is discussed, he de elopmen o a de ailed unce ain y budge o he CTs
hemsel es—and po en ial imp o emen s o hei design—a e conside ed opics o u u e
wo k. The p ima y ocus o his pape is on he measu emen sys em and me hodology
su ounding hese CTs a he han on he CTs’ in insic p ope ies.
Senso s 2025,25, 5429 5 o 23
2.3. Ra io-Based App oach o CT Cha ac e iza ion
Ins ead o measu ing
Ip
wi h a wideband high-cu en shun , he de ice-unde - es CT
(DUT, subsc ip
X
) is placed in se ies wi h a well-cha ac e ized e e ence CT (subsc ip
R
).
Because bo h CTs measu e he same p ima y cu en , i is possible o elimina e
Ip
om
he equa ions:
IsX =Ip
nX1+ϵX(ω),IsR =Ip
nR1+ϵR(ω); (2)
hei complex a io p o ides
ϵX(ω) = nX
nR
IsX
IsR 1+ϵR(ω)−1. (3)
Hence, he e o
ϵX
o he unknown CT can be exp essed di ec ly in e ms o he measu ed
a io o he seconda y cu en s and he known e o ϵRo he e e ence CT.
3. Measu emen Se up and Me hodology
To accu a ely cha ac e ize cu en ans o me s o e a equency ange om 50
Hz
o 150
kHz
, wo complemen a y measu emen app oaches we e employed. The p ima y
app oach in ol es compa ing he seconda y cu en s o he CT unde es (de ice unde
es , DUT) di ec ly agains hose o a e e ence CT. By compa ing hese wo measu emen s,
he a io be ween he DUT and e e ence CT can be de e mined using Equa ion (3). Changes
made o he measu emen se up—such as di e en cable con igu a ions—will be e lec ed
in a ia ions o his a io, p o iding insigh s in o he speci ic in luence o each change.
The second app oach in ol es di ec ly measu ing he p ima y cu en using an am-
me e and compa ing i o he CT’s seconda y cu en . Al hough his di ec measu emen
p o ides an immedia e indica ion o he absolu e a io e o o he CT, i ca ies g ea e
unce ain y due o calib a ion o he amme e ’s gain. Ne e heless, his me hod emains
aluable as i quan i ies he ue pe o mance and absolu e e o o he CT. Due o di icul-
ies in calib a ing high-cu en high-bandwid h shun , his me hod is p ac ically limi ed o
a ound 20A.
Figu e 2illus a es he simul aneous cha ac e iza ion app oach, whe e a high-
equency high-cu en ampli ie gene a es up o 10A ac oss he speci ied equency ange
h ough se ies-connec ed DUT and e e ence CTs. Seconda y cu en s a e measu ed by
in e nal shun s wi hin he sampling amme e .
Figu e 2. Schema ic o s anda d CT cha ac e iza ion se up. A high- equency high-cu en sou ce si-
mul aneously ene gizes he DUT and e e ence CTs, enabling ela i e seconda y cu en measu emen
and a io compa ison.
3.1. Measu emen Componen s and Condi ions
The measu emen s we e ca ied ou wi hin a empe a u e-con olled labo a o y
(23.0
◦C±
0.5
◦C
, 45%
±
5% RH), enclosed in a Fa aday cage whe e ins umen s use
a 58
Hz
powe supply o minimize mains in e e ence. I should be no ed ha hese con-
Senso s 2025,25, 5429 6 o 23
di ions do no ully mimic eal-wo ld applica ions whe e mul iple in luence ac o s such
as empe a u e, mechanical ib a ion, bu den, adjacen phases, and p oximi y e ec s can
in luence he accu acy o he CT unde es [
39
,
40
]. The se up and expe imen s desc ibed
in his pape a e designed o he calib a ion o CTs ha a e used as e e ence CTs o
u he applica ions.
The measu emen sys em comp ises wo nea ly iden ical NRC elec onically com-
pensa ed cu en ans o me s [
38
], each wi h an accu acy o a ound 1
ppm
a 50
Hz
. One
ans o me se es as he DUT, while he o he ac s as he e e ence. These CTs use in e nal
compensa ion elec onics ha minimize magne iza ion cu en s, imp o ing linea i y. Al-
hough he compensa ion elec onics ensu e low e o s—less han 20
ppm
and 20
µ ad
—up
o app oxima ely 5
kHz
, he pe o mance a highe equencies is less known. In pa icula ,
he bandwid h o he in e nal ampli ie s limi s he e ec i eness o compensa ion beyond
se e al kilohe z. Sub le di e ences in ampli ie design be ween he wo models could also
in luence high- equency pe o mance. Thei pe o mance is examined h oughou his
pape , pa icula ly in Sec ion 4.8. As such, a ques ion add essed in his s udy is up o wha
equency he elec onic compensa ion emains e ec i e.
A bus-ba cable ca ies he p ima y exci a ion cu en , which is ou ed sequen ially
h ough he co es o bo h CTs o ensu e exposu e o iden ical cu en wa e o ms. The p i-
ma y conduc o is ca e ully cen e ed in each CT using non-conduc i e magne ically neu-
al plas ic space s, s anda dizing he geome y and minimizing any possible posi ion-
dependen measu emen e ec s. Al hough subsequen es s e ealed minimal sensi i i y o
conduc o posi ion (see Sec ion 4.9), his a angemen allows o he sepa a ion o a iables.
Cu en and ol age measu emen s a e pe o med using a p ecision powe analyze
(WT5000 om Yokogawa Elec ic Co po a ion, Tokyo, Japan), capable o high-speed sam-
pling up o 2
MS/
s. The analyze con ains in e changeable modules equipped wi h p eci-
sion shun esis o s: 6.5
mΩ
(up o 30A), 110
mΩ
(up o 5A), and 500
mΩ
(up o 500
mA
).
The app op ia e shun selec ion and i s impac on measu emen unce ain y a e de ailed in
Sec ion 4.6. Th oughou his wo k, he e m “sampling amme e ” e e s o his ins umen .
The sampling amme e in eg a ed wi hin he powe analyze was calib a ed o ensu e
accu a e cu en measu emen s. Fi s , calib a ion o he ol age channels was pe o med
using an AC measu emen s anda d (5790B om Fluke Co po a ion, E e e , WA, USA),
which p o ided a e e ence ol age o he powe analyze ol age inpu . Fo cu en
calib a ion, he s anda d measu emen ci cui was used o gene a e ei he 100 mA o 10 A
h ough p ecision shun esis o s ( ype JV; see [
34
]). Bo h he ol age and cu en channels
we e eco ded simul aneously, and he ampli udes we e de e mined using he same signal
p ocessing algo i hm as applied in he main expe imen al measu emen s, minimizing
sys ema ic bias.
This calib a ion p ocedu e esul s in an es ima ed gain unce ain y o app oxima ely
2.5
ppm
a 50
Hz
and up o 50
ppm
a 150
kHz
o he powe analyze . I should be no ed
ha , in he seconda y- o-seconda y cu en compa ison, his unce ain y is e ec i ely
elimina ed due o he in e change o he measu emen channels be ween uns.
Measu emen da a is collec ed, s o ed, and p ocessed on a lap op PC, which in e aces
wi h he sampling amme e ia high-speed USB o ans e o aw measu emen da a.
Twis ed-pai cables a e used o connec he seconda y ou pu s o bo h CTs o he
sampling amme e , minimizing induced elec omagne ic in e e ence, as discussed in
Sec ion 4.11
. Fo diagnos ic and pe o mance e i ica ion, addi ional cables a e connec ed
o di ec ly measu e he seconda y ol age a he CT e minals.
All seconda y ci cui s, he amme e enclosu e, he CT compensa ion elec onics, CT
housings, and he high-cu en gene a ion sys em a e connec ed o a single common g ound
Senso s 2025,25, 5429 7 o 23
poin on he amme e . This single-poin g ounding s a egy is implemen ed o p e en
g ound loops and minimize elec ical noise, as desc ibed in Sec ion 4.5.
3.2. High-Bandwid h Powe Ampli ie Sys em
To gene a e he equi ed p ima y exci a ion cu en o 10A ac oss he ull equency
ange up o 150
kHz
, a dedica ed high-bandwid h ampli ie sys em was employed. The co e
o he se up is an a bi a y wa e o m gene a o , which p o ides a s able sinusoidal ou pu
wi h con ollable equency. This signal is passed in o an adjus able po en iome e , enabling
manual smoo h amp-up o he cu en ampli ude. This allows o consis en p ima y
cu en le els a each equency while also p o iding an addi ional laye o sa e y. This
signal is hen ed o a high-bandwid h ampli ie capable o deli e ing he necessa y powe
o d i e high cu en s h ough he CTs, o e coming he equency-dependen eac ance
wi hin he measu emen ci cui .
To ensu e ha no di ec cu en componen is p esen , which could o he wise lead o
unwan ed magne iza ion o he CT co es, auxilia y LC il e ing is implemen ed. An induc o
se es as a DC bypass, while a se ies-connec ed capaci o compensa es o ci cui eac ance
a highe equencies.
Fo quick e i ica ion o he gene a ed p ima y cu en , a clamp me e is placed
a ound he p ima y cu en ca ying bus-ba h ough he CTs, which is used o con i m he
ampli ude p io o and du ing each es .
3.3. Gain Elimina ion Me hod o Sampling Amme e
When he same p ima y cu en
Ip1
is ed h ough bo h CTs, each CT’s seconda y
cu en is measu ed on a sepa a e cu en amme e channel (o “module”). Le gmod1 and
gmod2
be he gain co ec ion ac o s o hese wo modules (ideally
gmod =
1). The measu ed
seconda y cu en s a e hen
ICTA1=Ip1·nCTA ·gmod1,ICTB1=Ip1·nCTB ·gmod2 . (4)
Because
gmod1
and
gmod2
a e ne e uly uni y and a y wi h ac o s like equency and
amme e con igu a ion, one canno di ec ly in e
nCTA/B
om ei he
nCTA/B1
o
nCTA/B2
alone. A he ppm le el, measu ing and compensa ing o hese gains ac oss he en i e
equency ange would be cumbe some.
A me hod o elimina e module gain e o s is o in e change he measu emen con-
nec ions: a e he ini ial measu emen , CT A is connec ed o he second cu en amme e
module, and CT B is connec ed o he i s module. A second p ima y cu en
Ip2
(which
will be app oxima ely he same as Ip1) is hen applied, yielding he a io measu emen s
nCTA/B1=ICTA 1
ICTB 1=nCTA gmod1
nCTB gmod2 and nCTA/B2=ICTA 2
ICTB 2=nCTA gmod2
nCTB gmod1 , (5)
whe e he second equa ion applies a e in e changing he modules.
The unknown module gains appea in ecip ocal o m ac oss he wo a io measu e-
men s,
nCTA/B1
and
nCTA/B2
. By aking he geome ic mean, he module gains cancel ou :
nCTA/B=√nCTA/B1·nCTA/B2= nCTA gmod1
nCTB gmod2 ×nCTA gmod2
nCTB gmod1 =nCTA
nCTB
. (6)
This simple in e changing app oach he e o e p o ides he ela i e a io
nCTA/B
wi h-
ou indi idually cha ac e izing he module gains. In p ac ice, his echnique simpli ies he
calib a ion o CTs.
Senso s 2025,25, 5429 8 o 23
3.4. Ra io Es ima ion Algo i hm
Accu a e es ima ion o ampli ude and phase o disc e e sinusoidal signals is c ucial
o p ecise CT a io measu emen s. To achie e his, i is impo an o use good measu emen
p ac ices, such as selec ing a sampling equency ha is an exac in ege mul iple o he
signal equency, ho oughly emo ing any DC o se , and acqui ing su icien ly long da a
eco ds. By aking a Fas Fou ie T ans o m (FFT) o he signal and selec ing he highes
bin, he signal ampli ude is es ima ed om he magni ude o his dominan equency bin.
Howe e , when he equency o he signal does no exac ly align wi h disc e e FFT bins,
spec al leakage occu s. This leakage edis ibu es signal ene gy in o adjacen bins, causing
inaccu a e ampli ude es ima es. I is impo an o no e ha , echnically, i one measu es he
a io be ween wo signals wi h small phase di e ences using he highes -bin FFT me hod,
ampli ude biases may pa ially cancel ou . Mo eo e , his app oach does no accu a ely
es ima e he absolu e ampli ude o he sine wa e, p e en ing e i ica ion o he expec ed
measu emen esul s.
A solu ion is he use o a esampling algo i hm [
41
]. This me hod e ec i ely ealigns
signal equencies on o FFT bins, educing leakage and simpli ying analysis. Despi e i s
e ec i eness, esampling is compu a ionally e y in ensi e. As an al e na i e, his pape
uses he in e pola ed Disc e e Fou ie T ans o m (DFT) echnique, speci ically he h ee-
poin in e pola ed Hanning window DFT me hod (
id 3phann
), based on [
42
] and adap ed
om he algo i hm in [43].
Algo i hm S eps
The p ocess o de e mining he a io be ween wo measu emen channels is desc ibed
below and in he lowcha shown in Figu e 3.
S a Di ide da a in o 0.04 s segmen s
Apply Hanning window o each segmen
Compu e DFT
Iden i y peak magni ude bin Es ima e o se om adjacen bins
In e pola e DFTCompu e a io and phase di e ence
F om a ios, ge mean & s d. de . End
Figu e 3. Flowcha o he algo i hm o de e mining he a ios.
1.
Di ide each channel’s da a in o segmen s o du a ion 0.04s, deno ing each segmen
as x[n]. Fo example, a 1s eco ding yields 25 segmen s pe channel.
2.
Apply a Hanning window o each segmen
x[n]
o educe spec al leakage. The Han-
ning window is chosen o i s a o able side-lobe a enua ion (
−
31.5
dB
) and mode a e
main-lobe wid h (app oxima ely wo-FFT-bin inc ease o e non-windowed signal).
3.
Compu e he DFT o each windowed segmen and iden i y he bin wi h he highes
magni ude ( he peak bin).
4.
Examine he magni udes o he bins adjacen o he peak bin o es ima e an o se
pa ame e . This o se quan i ies how a he ue equency lies om he cen e o he
peak disc e e bin using he ela i e heigh s o he side bins.
5.
In e pola e he DFT using he o se pa ame e and side-bin magni udes o es i-
ma e he ue signal cha ac e is ics, including equency, ampli ude, phase, and he
DC componen .
Senso s 2025,25, 5429 9 o 23
6.
Calcula e he a io be ween he wo channels o each segmen using he ampli ude
and phase alues, ollowing he p ocedu e desc ibed in Sec ion 3.3.
7.
A e age he compu ed a ios ac oss all segmen s o ob ain he o e all mean and
s anda d de ia ion o he measu emen .
4. Resul s
4.1. Baseline Measu emen Se up Resul s
This sec ion p esen s he baseline esul s om he measu emen se up, se ing as he
e e ence o all he subsequen con igu a ion changes. To ensu e eliable compa isons,
a new e e ence measu emen was pe o med daily p io o any se up changes, and he
baseline se up emained consis en h oughou .
The measu emen sys em uses wo simul aneous me hods: he p ima y cu en (ap-
p oxima ely 10A) and each CT’s seconda y cu en (100
mA
) a e eco ded. The nominal
CT a io is 100:1, bu p ac ical e ec s, such as losses and in e nal impedance, esul in a
seconda y cu en ha is sligh ly less han he ideal alue. By sys ema ically measu ing
a disc e e equencies be ween 50
Hz
and 150
kHz
, a io e o s can be accu a ely quan-
i ied. The ocus is on de eloping he e e ence measu emen se up, bu he e is always
some in e dependence be ween he CTs used and he measu emen . The indings should
gene alize o o he sys ems, bu he exac de ia ions and unce ain ies a e de e mined by
he exac componen s used.
A di ec compa ison o he seconda y cu en s enables he e alua ion o ela i e
CT pe o mance (see Equa ion (3)). I he CTs ha e iden ical equency esponses and
he e is no capaci i e cu en leakage be o e he p ima y cu en passes h ough bo h CTs,
he seconda y cu en s will be equal. I any pa ame e is changed—such as subs i u ing a
shun esis o in one CT— he esul ing di e ences a e di ec ly a ibu able o ha change.
Addi ionally, his seconda y- o-seconda y me hod is how a DUT CT a highe cu en s
would be cha ac e ized. No e ha , in his expe imen , a DUT o e e ence CT is no
explici ly p esen . Ra he , wo CTs o he same model and manu ac u e a e used. This
helps wi h he de elopmen o he measu emen me hod, and in he u u e can lead o a
se up wi h a e e ence CT and an unknown DUT.
4.1.1. Cu en Ra io Compa ison
Figu e 4shows he di ec seconda y- o-seconda y compa ison using egula (le )
and symme ic loga i hmic scale ( igh ). Below 5
kHz
, he di e ence is less han 7
ppm
,
which is wi hin he s a ed measu emen unce ain y. Abo e 5
kHz
, de ia ions inc ease,
eaching up o 3000
ppm
a 150
kHz
. No e ha he symlog scale combines linea scaling
(be ween
−
10
ppm
and 10
ppm
) wi h loga i hmic scaling elsewhe e, highligh ing small
a ia ions a ound ze o. No e ha isually he e ical jump om 5
kHz
o 10
kHz
may
appea simila o he jump om 10
kHz
o 50
kHz
; howe e , nume ically, he i s is abou
10
ppm
, whe eas he second is nea ly 500
ppm
. Always e e o he egula ly scaled plo o
accu a e in e p e a ion o e la ge equency anges.
P ima y- o-seconda y cu en a io analysis u he cha ac e izes he equency-
dependen beha io o he CTs. We compa ed he measu ed p ima y cu en
Ip
wi h
he seconda y cu en s
Is,CTA
and
Is,CTB
, he measu ed a ios ac oss he ull equency
ange a e shown in Figu e 5. The powe analyze was calib a ed a each disc e e measu e-
men equency o bo h he 100 mA and 10 A cu en anges. Calib a ion was pe o med
p io o he s a o es ing using a e e ence shun and ol age calib a o sys em a 50 Hz,
achie ing an unce ain y o 2.5 ppm [
34
]. A 150 kHz, he calib a ion unce ain y inc eased
o app oxima ely 50 ppm. The unce ain y ba s shown in he p ima y- o-seconda y a io
plo s accoun o hese calib a ion unce ain ies. In he case o seconda y- o-seconda y mea-
Senso s 2025,25, 5429 16 o 23
Vol age-induced leakage cu en s in luence he calib a ion esul s o CTs [
29
,
44
,
45
].
In [
45
], i is shown ha his ol age-induced leakage cu en in he shielded high- ol age
cable equals
Ileak =ωCV
, esul ing in a ol age-dependen complex a io e o o a cu en
ans o me gi en by
ε(V) = ωCV
Ipsin φ. (7)
Al hough in ou expe imen s only low ol ages a e p esen , a highe equencies he
possibili y o capaci i e coupling be ween he p ima y conduc o and he CT seconda y
winding emains, which could in oduce simila e o s [46].
Fo he expe imen al e alua ion, wo con igu a ions we e compa ed: cen e ed and
eccen ic. F om he esul s, no s a is ically signi ican de ia ion is obse ed up o 150
kHz
.
Hence, o cu en s below 10A and wi h he adop ed 110
mΩ
bu den, wi h no addi ional
ol age p esen , conduc o posi ioning does no measu ably a ec he a io o he CTs
used in his expe imen .
Fo he CTs used in his expe imen , ha ing p ecisely spaced seconda y windings o
minimize coupling, an ai -gap ape u e, and ope a ed wi h bu dens below 0.5 V, he mea-
su emen s indica e ha achie ing ppm-le el a io accu acy does no equi e sub-millime e
cen e ing ix u es. Rou ine cen e ing o wi hin a ew millime e s su ices, simpli ying
mechanical design o calib a ion ou ines.
4.10. Mu ual P oximi y o Two CTs
When wo CTs sha e he same p ima y conduc o du ing compa ison, mu ual induc-
ance and s ay capaci i e coupling be ween hei co es and compensa ion ci cui s could,
in p inciple, a ec he measu ed a io. The CTs used in his s udy a e equipped wi h a
g ounded me al shield speci ically designed o supp ess ex e nal lux linkage. Howe e ,
o e i y he e ec i eness o his shielding and o quan i y any po en ial p oximi y e ec s,
he CTs we e es ed a spacings o 3cm and 30cm.
The esul s show ha , up o 10
kHz
, he e is no obse able impac o CT spacing wi hin
he measu emen unce ain y. A equencies abo e 10
kHz
, a dec ease in he measu ed
seconda y cu en was obse ed when he CTs we e closely spaced, sugges ing ha some
coupling o leakage may occu a highe equencies.
In his s udy, a spacing o 30
cm
was used o all he subsequen expe imen s as a
p ac ical p ecau ion. I should be no ed, howe e , ha his guideline may no gene alize
o o he CT designs, pa icula ly hose wi hou dedica ed shielding, which may be mo e
suscep ible o p oximi y e ec s. Addi ionally, spacing CTs oo a apa may in oduce ca-
paci i e leakage cu en s om he p ima y conduc o , causing he CTs o no longe measu e
iden ical p ima y cu en s. The e o e, ca e ul conside a ion o bo h p oximi y and shielding
is ecommended when designing calib a ion se ups, and alida ion measu emen s should
be conduc ed o each new CT ype and a angemen .
4.11. Cable Cha ac e iza ion
This sec ion examines he elec ical p ope ies o cables linking he cu en ans-
o me ’s seconda y side o he cu en measu emen b idge. Seconda y side cable selec ion
could in luence measu emen accu acy, p ima ily due o he inhe en cable impedance.
This impedance includes se ies esis ance (
R
), and, o high- equency measu emen , espe-
cially impo an , induc i e eac ance (
XL
), and po en ially pa allel pa asi ic capaci ance
depending on he cable design. An equi alen ci cui illus a ing he measu emen sys em
is p o ided in Figu e 13.
Senso s 2025,25, 5429 17 o 23
Figu e 13. Simpli ied equi alen ci cui depic ing he cable measu emen se up. The seconda y
winding o he CT (g een) is connec ed ia he es cable (o ange) o he in e nal shun esis o o he
PA ( ed). Seconda y cu en (Is) is de e mined by measu ing he ol age ac oss he PA shun . Cable
cha ac e is ics a e de i ed by measu ing he ol age (
Vs
, blue) a he CT ou pu e minals. In his
model, i is assumed ha he induc ance o he shun esis o inside he powe analyze is negligible
compa ed o ha o he ex e nal cable. This assump ion occu s as he powe analyze employs
in e nal coaxial shun s speci ically enginee ed o minimize induc ance and main ain linea i y a
highe equencies.
Cable impedance (
Zcable
) was de e mined expe imen ally by simul aneously cap u ing
ol age (
Vs
) and cu en (
Is
) ampli ude and phase. These measu emen s spanned equen-
cies om 50Hz o 150kHz. Impedance componen s we e compu ed using phaso no a ion:
Zcable =V
I=⇒R=ℜ(Zcable),XL=ℑ(Zcable)(8)
High- equency ope a ion o cu en ans o me s makes hem pa icula ly sensi i e
o ele a ed seconda y impedance. The CT mus p oduce a su icien seconda y ol age
o achie e he speci ied cu en a io. This e ec is no ably p onounced in elec onically
compensa ed CTs since hei in e nal eedback mechanisms injec compensa o y cu en
o mi iga e leakage. Figu e 13 illus a es how seconda y impedance p omp s he CT
o gene a e ol age ac oss i s magne izing induc ance (
Lm
) and co e losses (
R e
), hus
inc easing leakage cu en h ough hese pa allel componen s.
4.11.1. Twis ed-Pai Cable Pe o mance
Twis ed-pai s anded cables, p e e ed o hei elec omagne ic noise shielding, we e
assessed o induc ance and esis ance. The cables used in his s udy we e banana es leads
wi h a 0.75
mm2
c oss sec ion. A 150
kHz
, induc i e eac ance (
XL
) measu emen s o
leng hs 50, 100, and 190 cm showed an induc ance o app oxima ely 0.78
µH/
m (Table 2).
Linea eg ession con i med cable induc ance linea i y wi h leng h, yielding R2=0.99.
Table 2. Twis ed-pai cable eac ance and esis ance a 150kHz.
Cable Leng h (cm) Reac ance XL(Ω) Measu ed R o al (Ω)Rcable (Ω)
50 0.52 0.14 0.03
100 0.88 0.16 0.05
190 1.56 0.20 0.09
Resis ance measu emen s co ec ed o he in e nal PA shun (0.110
Ω
) indica ed cable
esis ance o abou 0.04
Ω/
m, con i ming negligible addi ional esis ance beyond he known
in e nal shun , as shown in Figu e 14.
Senso s 2025,25, 5429 18 o 23
Figu e 14. Le : Linea co ela ion be ween cable leng h and esis ance a 150
kHz
, indica ing a
esis ance o 0.04
Ω/
m and alida ing ha he o he esis ance is om he in e nal shun o 0.11
Ω
.
Righ : F equency-dependen esis ance highligh ing inc eased esis ance p opo ional o cable leng h.
High- equency e ec s (skin and p oximi y) can inc ease he obse ed
R
compa ed o he 50
Hz
alue).
4.11.2. Coaxial Cable Pe o mance
RG-58 coaxial cables o e shielding and p ecise impedance con ol, displaying sligh ly
lowe induc ance (0.68
µH/
m) bu signi ican ly highe esis ance compa ed o wis ed-pai
cables, as shown in Figu e 15. Addi ionally, inhe en pa allel capaci ance in coaxial cables
isks accu acy a highe equencies by bypassing he measu emen shun .
Figu e 15. Compa ison o coaxial and wis ed-pai cables (100 cm) a a ying equencies.
Le : Highe
coaxial cable esis ance is e iden . Righ : Induc i e eac ance (
XL
), indica ing linea
equency-dependen induc ance.
O e all, wis ed-pai cables balance lowe esis ance and manageable induc ance,
whe eas coaxial cables, al hough lowe in induc ance, in oduce highe esis i e and
capaci i e leakage pa hs. Fo p ima y o seconda y cu en measu emen s, he choice
o cable is dependen on CT seconda y ol age capabili ies and measu emen accu acy
equi emen s. Fo CT o CT a ios, as long as he cables a e easonably iden ical, he e ec s
should la gely cancel ou . Howe e , he signal- o-noise a io dec eases, which can be c i ical
o de ec ing high-o de ha monics wi h e y small ampli udes. The e o e, minimizing
cu en losses helps o imp o e sensi i i y.
4.12. Unce ain y Budge
An unce ain y budge was cons uc ed ollowing he GUM guidelines o quan i y
he unce ain y associa ed wi h he CT a io e o measu emen sys em [
47
]. This budge
consolida es he main con ibu ions iden i ied h oughou he p e ious analyses. Table 3
p esen s he expanded unce ain ies (
k=
2) o he seconda y- o-seconda y cu en com-
pa ison me hod. I is impo an o no e ha he unce ain y o he e e ence CT i sel is no
included; he c ea ion and ull cha ac e iza ion o a b oadband e e ence CT a e iden i ied
as aspec s o u u e wo k.
Senso s 2025,25, 5429 19 o 23
In he seconda y- o-seconda y me hod, many sou ces o unce ain y a e elimina ed
because hey a e common o bo h CTs. Fo example, any gain e o in he amme e
cancels due o he channel in e change echnique. This makes he me hod obus and
pa icula ly sui able o high-accu acy ela i e measu emen s. The cu en se up can
also be adap ed o p ima y- o-seconda y calib a ion, whe e he measu emen o p ima y
cu en in oduces addi ional unce ain y (app oxima ely 2.5
ppm
a 50
Hz
and inc easing
o 50ppm a 150 kHz).
Table 3highligh s he combined expanded unce ain ies in he magni ude a io mea-
su emen o h ee ep esen a i e equencies: 50
Hz
, 10
kHz
, and 150
kHz
. Addi ional
equency poin s ollow simila ends, and hei unce ain ies a e depic ed in he ele an
esul igu es.
Table 3. Magni ude a io unce ain y budge o he seconda y- o-seconda y cu en CT a io mea-
su emen sys em. All en ies a e expanded unce ain ies (k=2) in ppm.
Sou ce o Unce ain y 50 Hz 10 kHz 150 kHz
Same- ype shun empe a u e d i (Sec ion 4.2) 0.5 0.5 1.0
Measu emen noise (Sec ion 4.3) 3.0 3.3 10.8
In a-day epea abili y (Sec ion 4.4) 3.1 3.4 96
G ounding/in e e ence (Sec ion 4.5) 4.0 5.0 10.0
Ins umen esolu ion (Sec ion 4.7)13.8 3.8 3.8
Combined expanded unce ain y U(k=2)7.0 7.9 97
1
Ins umen quan iza ion is modeled as a ec angula dis ibu ion (
k=
1
/√3
). As he e o s a e co ela ed,
he e ec i e e o is u he di ided by 1/√2.
This unce ain y analysis con i ms ha , o he seconda y- o-seconda y compa ison
me hod, he combined expanded unce ain y emains below 10
ppm
up o 10
kHz
, and be-
low 100ppm a 150 kHz.
5. Discussion and Conclusions
This pape p esen s a simpli ied calib a ion me hod o cu en ans o me s (CTs),
u ilizing a sampling amme e (powe analyze ) o di ec ly measu e he a io o seconda y
cu en s, eplacing he mo e complex sys ems p e iously employed in ol ing s anda d
ans o me s, bu e ing ci cui s, and ol age sample s. The measu emen me hod simpli ies
he calib a ion p ocess, educes complexi y, and di ec ly enables up o 150
kHz
bandwid h,
co e ing he IEC WB3 class [12].
The de eloped calib a ion se up achie ed an expanded measu emen unce ain y
(
k=
2) o app oxima ely 10
ppm
up o 10
kHz
, an imp o emen wi h espec o he
p e ious 50
ppm
achie ed wi h he same sys em [
27
]. Beyond 10
kHz
and up o 150
kHz
,
he magni ude a io unce ain ies emained below 120
ppm
, hus ou pe o ming he p esen
s a e-o - he-a app oaches [
22
,
23
] and con i ming he sui abili y o his simpli ied se up
o high- equency cha ac e iza ion. No e ha he e e ence CT i sel will in oduce an
addi ional magni ude a io unce ain y o app oxima ely 2.5
ppm
a 50
Hz
up o 50
ppm
a
150kHz.
Se e al ope a ional pa ame e s and con igu a ion choices a ec ing he measu emen
accu acy and epea abili y we e also in es iga ed. A ypical wa m-up pe iod o app oxi-
ma ely 30 min o he sampling amme e was es ablished, e ec i ely limi ing empe a u e-
induced d i o app oxima ely 1
ppm
. Wi h a measu emen sampling du a ion o 10 s
pe equency se poin , he unce ain y due o sampling was main ained below 5
ppm
o
150
kHz
. To achie e hese unce ain ies, daily e e ence measu emen s o compa ison we e
pe o med o accoun o po en ial empo al o labo a o y-condi ion- ela ed d i s.
Senso s 2025,25, 5429 20 o 23
G ounding he seconda y ci cui s o he CTs esul ed in a measu able di e ence
o abou 4
ppm
in he measu emen a equencies up o 100
Hz
, whe eas no signi ican
impac was obse ed beyond his equency. To imp o e epea abili y, g ounding was
implemen ed o all he subsequen es s.
The choice o he measu emen shun esis o alue plays a signi ican ole in balancing
measu emen accu acy and a e aging ime. In his wo k, a esis ance o app oxima ely
110
mΩ
was e ec i e, al hough he op imal alue may a y depending on he applica ion
and ins umen cha ac e is ics. The selec ed alue is ela i ely high o CT calib a ions as i s
bu den leads he CT o deli e ol age, which inc eases magne iza ion losses. Howe e ,
gi en ha 1m o wis ed pai cable connec ed o he seconda y side adds an impedance o
a ound 1
Ω
a 150
kHz
, i is p obably an accep able comp omise. Al hough he elec onically
compensa ed CTs in his s udy did no exhibi measu able sensi i i y o cable ype, di e en
CT designs may be mo e suscep ible.
The shielded housings o he CTs, when p ope ly g ounded, we e e ec i e in mi iga -
ing in e e ence a close p oximi y up o 10
kHz
; abo e his, some coupling can be obse ed.
Whe eas a spacing o 30
cm
be ween ans o me s was used o hese expe imen s, alida-
ion o di e en CTs and con igu a ions emains impo an . The posi ion o he p ima y
conduc o did no signi ican ly in luence he measu emen esul s o he CTs used in hese
expe imen s ei he .
To demons a e he applicabili y o he new se up, in u u e wo k, he CTs used in his
s udy will be used as a e e ence o calib a e o he ypes o CTs, such as hose de eloped
in [
48
]. The in luence o a high-cu en undamen al one o se e al hund eds o ampe es
a 50
Hz
can be in es iga ed using a sepa a e p ima y winding [
49
]. I may be bene icial o
design highe -bandwid h compensa ion elec onics o he e e ence CTs o la en hei
equency esponse. This way, he bandwid h o he en i e sys em could be ex ended o
500kHz o co e he IEC WB4 class [12] as well.
Fu he imp o emen s may be ealized by op imizing g ounding. Measu ing ea h cu -
en s ac oss a ange o seconda y cu en le els o de e mine scaling beha io o isola ing
he con ibu ion o g ounded in e nal ampli ie s wi hin he CTs by disabling o emo ing
hem could help o cla i y he o igin o obse ed ea h loop cu en s. In addi ion, he e -
ec s o cable geome y and ma e ial could be examined, o ins ance, by using sho Li z
wi es o al e na i e cable con igu a ions o be e unde s and and manage high- equency
impedance and leakage e ec s. Capaci i e coupling be ween he p ima y and seconda y
windings, pa icula ly a highe ol ages a hese ele a ed equencies, emains a opic o
u he explo a ion as i may become mo e signi ican unde di e en ope a ing condi ions.
The impac o elec omagne ic in e e ence, which could be he o igin o day- o-day luc u-
a ions ( he la ges unce ain y con ibu ion a he highes equencies), migh be u he
in es iga ed by changing he inpu il e se ings o he amme e s.
Au ho Con ibu ions: Concep ualiza ion, F.M. and G.R.; me hodology, M.R., E.H. and H.E. .d.B.;
so wa e, M.R.; o mal analysis, M.R. and H.E. .d.B.; in es iga ion, M.R. and R. .L.; w i ing—o iginal
d a p epa a ion, M.R. and F.M.; w i ing— e iew and edi ing, M.R., H.E. .d.B., D. .d.B., F.M., E.H.
and G.R.; supe ision, H.E. .d.B. and F.M.; p ojec adminis a ion, H.E. .d.B.; unding acquisi ion,
F.M., G.R. and H.E. .d.B. All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding: This esea ch is pa o he 22NRM06 ADMIT join esea ch p ojec ha has ecei ed
unding om he Eu opean Pa ne ship on Me ology, co- inanced om he Eu opean Union’s
Ho izon Eu ope Resea ch and Inno a ion P og amme and by he Pa icipa ing S a es.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Senso s 2025,25, 5429 21 o 23
Da a A ailabili y S a emen : Da ase a ailable on eques om he au ho s.
Acknowledgmen s: Comme cial equipmen is only iden i ied in his pape in o de o adequa ely
speci y he expe imen al p ocedu e. This iden i ica ion does no imply a ecommenda ion o endo se-
men by VSL, no does i imply ha he equipmen iden i ied is necessa ily he bes a ailable o he
pu pose. Du ing he p epa a ion o his manusc ip , he au ho used Gi Hub Copilo ( e sion 1.182.0)
o assis ance wi h de eloping and op imizing Py hon 3.11 code used in da a p ocessing and analysis.
The au ho also used Cha GPT (GPT-4.5, OpenAI) o ex e inemen , edi ing, and s uc u ing o
manusc ip sec ions. The au ho s ha e e iewed and edi ed he ou pu and ake ull esponsibili y
o he con en o his publica ion.
Con lic s o In e es : Au ho s M.R., H.E. .d.B., E.H., R. .L., and G.R. we e employed by he company
VSL. The emaining au ho s decla e ha he esea ch was conduc ed in he absence o any comme cial
o inancial ela ionships ha could be cons ued as a po en ial con lic o in e es . The unde s had
no ole in he design o he s udy; in he collec ion, analyses, o in e p e a ion o da a; in he w i ing
o he manusc ip ; o in he decision o publish he esul s.
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Disclaime /Publishe ’s No e: The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual
au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .
