p
tuned to a resonant frequency f0 = 1/ (2p LC). The coupling
between two adjacent resonators occurs through the mutual
Mi,i+ 1 MAGNETICO
= Mi+ 1,i = M, with
(i = 1, ..., n−DA
1), whereas
STUDIOinductance
DEL CAMPO
GENERATO
UN SISTEMA DI
the couplingDI
between
two nonadjacent
resonators
neglected.
TRASMISSIONE
ENERGIA
ELETTRICA
CON is
ACCOPPIAMENTO
INDUTTIVO IN RISONANZA CHE IMPIEGA UN ARRAY DI RISONATORI
L. Sandrolini, J. Alberto, U. Reggiani
Dipartimento di Ingegneria dell’Energia Elettrica e dell’Informazione - DEI
di Bologna
Risorgimento
Bologna
Fig. 1.Università
Equivalent
circuit of - aViale
system
composed of2, n40136
resonators
with a Fig. 3. Resonator array on
termination impedance.
the measurement.
È proseguita l'attività
di ricerca
sulla
trasmissione
energia
elettrica
By applying
MIW
theory,
in [8], di[14]
it was
shownmediante
that sistemi con
accoppiamento induttivo in risonanza (sistemi IPT) che impiegano risonatori intermedi allo scopo di
at the resonance condition w0 = IPT.
2p f0Siand
for an infinite
migliorare l’efficienza di trasmissione del sistema
sono esaminati risonatori intermedi
low-loss
line the
efficiency of
the WPT
throughun the
array
planari rettangolari
accoppiati
induttivamente
in modo
da comporre
metamateriale,
ovvero un
canrisonanti
be maximized
by a termination
equal to avviene quindi
array di circuiti
[1, 2]. L’accoppiamento
tra il approximately
ricevitore e il trasmettitore
mediante l’array
risonatori.
L'efficienza
di trasmissione
dipende
generalmente dal
ẐT =di w
termination
impedance del
maysistema
also take
into
0M. This
fattore di qualità
dei
singoli
induttori
e
dalla
loro
mutua
induttanza,
in
particolare
dal
coefficiente di
account a receiver coil over the last coil of the array.
accoppiamento tra risonatori adiacenti [1, 2]. Per ottimizzare il progetto di questi sistemi occorre
caratterizzare gli induttori dal punto
elettrico,
in [3, 4]. La problematica rappresentata
III. diEvista
X PERI
M ENTAcome
L SETUP
dal fatto che il comportamento del sistema in presenza di risonatori intermedi varia in modo
The experimental
setup used
in the eexperiments
depicted
significativo in termini
di potenza trasmessa,
efficienza
frequenza in is
funzione
dell’impedenza di
terminazione in
della
è già
stata ampiamente
esaminata,
in rectangular
particolare incoils
[5, 6]. Altri aspetti
Fig.linea
2. As
described
in [9], four
2-layered
Fig. 4. Circular
importanti di of
questi
sistemi
quali
la
compatibilità
elettromagnetica
non
sono
stati
dimensions 10 cm x 25 cm are built and arranged in a planetrattati in modo
altrettanto esteso in letteratura, se non per accenni all’esposizione umana o alla schermatura
along a line; the first coil is connected to a power source and
magnetica. L'attività di ricerca è stata quindi rivolta allo studio del campo magnetico vicino
the
last one
termination
impedance
(aalimentato
resistance).
Three
generato da un
sistema
IPT to
cheaimpiega
un array
di risonatori
da un
inverteroscilloscope
a 300 kHz. and the
different
values
of
termination
impedance
are
used:
0.47W,
to 50 M
L’analisi è stata focalizzata all’esame delle differenze tra il campo magnetico vicino,TCP305
generato DC
a
piccola distanza
dal
sistema
IPT,
e
quello
a
distanza
maggiore;
inoltre,
si
è
studiata
la
relazione
tra
3.3W and 10W. For this resonator array, we have a value of complete setup. A ci
l’impedenza w
di0M
terminazione
dell’array
il termination
campo magnetico
generato,
e si è analizzata
la 4396B sp
= 3.2W [9],
and so ethe
impedance
of 3.3W
an Agilent
distribuzione spaziale dell’induzione magnetica.
is the closest one to the matching value.
electromotive force (
produced by the time
by the WPT system w
voltage value, it is po
the magnetic flux den
probe area Bp
where Vp is the measu
Fig. 2. Equivalent circuit of the WPT system using a resonator array used and w0 is the resonan
for the measurements.
Measurements were
Il sistema IPT considerato nella ricerca è composto da un inverter che alimenta un risonatore di
m of diameter (Fig. 3
forma rettangolare (10 cm x 25 cm) accoppiato magneticamente con un array di tre risonatori
the horizontal symme
planari rettangolari identici al primo alimentato e disposti lungo una linea. L’inverter è alimentato
The power source that feeds the resonant coils consists of a 2.75 cm above them,
da un microprocessore Arduino Due funzionante alla frequenza di 300 kHz. La frequenza di
half-bridge inverter. This configuration uses a Fairchild Semi- density at points far
risonanza del sistema, 294.5 kHz, è stata ottenuta inserendo in ogni risonatore un condensatore di
conductor FSB44104A as the inverter, fed by an Elind 3232 above the coils, respe
DC source and controlled by an Arduino Due microprocessor,
IV. SI M UL A
used to set the working frequency at 300 kHz. The coils were
designed to have a value of self-inductance of about 14.6
The phasor current
Fig. 1. Circuito equivalente del sistema IPT sperimentale con array di risonatori.
T HE M AGNI TUDE OF THE
HE PHA SE I N DEGREES.
2◦
2◦
72◦
10W
0.6926 − 2◦
0.2726 − 107◦
0.5826 − 179◦
opportuna capacità. La tensione ai morsetti dell’impedenza di terminazione ZT del sistema è stata
0.1736 90◦
variata in modo da mantenere costante la potenza assorbita dal sistema (pari a 300 mW). La forza
Fig. 7. Plot of the simulated magnitude of the magnetic flux density for a
elettromotrice (e.m.f.)
generata
in una
sonda
campo
vicino di forma circolare dal
termination
impedance
of 10W
in a di
plane
abovemagnetico
the coils.
campo magnetico variabile nel tempo prodotto dal sistema IPT è stata misurata con un analizzatore
di spettro in punti di una semicirconferenza di 1.82 m di diametro al cui centro è stato collocato il
forsithe
magneticilflux
sistema IPT (vedia similar
Fig. 2). difference
Dalla e.m.f.
è calcolato
valordensity
medio magnitude
della componente normale
generated
in
adjacent
coils
(Fig.
7).
dell’induzione magnetica incidente sull’area della sonda, che è stato poi confrontato con quello
In Figs. 8del
andsistema
9 the con
measured
and simulated
values offiniti.
the Il confronto tra
ottenuto da una simulazione
un software
3D agli elementi
magnetic
flux
density
magnitude
at
points
of
the
considered
valori misurati e simulati per l’induzione magnetica lungo la semicirconferenza considerata è
line above the resonators and of the semicircular line around
nella
oss-section andmostrato
plane above
the Fig. 3.
the resonators, respectively, are plotted.
ively.
I risultati di quest’ultima
ricerca sono
stati illustrati
in [7]. is found from the e.m.f.
The measured
magnetic
flux density
p
quency f0 = 1/ (2p LC). The coupling
at the terminals of the probe with (1), i.e., as the average
resonators occurs through the mutual
nce due to manufacturing normal component of the magnetic flux density incident on the
+ 1,i = M, with (i = 1, ..., n− 1), whereas
ng nonadjacent
between nonadjacent
probe area. By aligning the probe axis along the coordinate
wo
resonators is neglected.
ent values, specially when axes (see Fig. 5) we can then obtain the corresponding average
urrents are unbalanced.
normal components of the magnetic flux density, that can be
using a 2D and 3D finite- then compared with the simulated components of the magnetic
the software the current flux density.
urrent in each coil using
Fig. 2. Sistema IPT con array di risonatori e sonda di campo magnetico vicino.
before,
the ofdifferent
of a systemfor
composed
n resonators with a Fig. 3. Resonator array on the circular table and near field probe ready for
the measurement.
ection
at
theory, inand
[8], the
[14] plane
it was shown
that
oils
used
for
the
spatial
dition w0 = 2p f 0 and for an infinite
ciency
the magnetic
WPT through
tude ofof the
fluxthe array
a termination approximately equal to
agnitude of the magnetic
mination impedance may also take into
ection
over thefor
last acoiltermination
of the array.
calculations were carried
EX PERI M ENTA L SETUP
re. Fig. 7 shows a similar
(a)
(b)
etup
in the
cm used
above
theexperiments
coils for isadepicted
Fig. 3.rectangular
Valori misurati
(a) eMeasured
simulati (b)
dell’induzione
magnetica
(µT) (b)
lungo
semicirconferenza
d in [9], four 2-layered
coils8.
Fig.
(a) probe
and used
simulated
values
of la
the
magnetic flux considerata per
Fig. values
4. Circular
for the e.m.f.
measurements.
hese
the 3Din a plane
alcuni valori dell’impedenza di terminazione.
25 cmcalculations,
are built and arranged
density magnitude (values in µT) along the considered line (from 0 to 406
coil is connected to a power sourcemm)
and for different values of the termination impedance.
nation impedance
(a
resistance).
Three
oscilloscope and the currents in the coils with a Tektronix
BIBLIOGRAFIA
mination impedance are used: 0.47W, TCP305 DC to 50 MHz current probe. Fig. 3 shows the
his resonator array, we have a value of complete setup. A circular probe (Fig. 4) was connected to
[1] impedance
C. J. Stevens,
“A magneto-inductive
wavespectrum
wireless power
transfer
device,”
Wireless
so the termination
of 3.3W
an Agilent 4396B
analyzer
(2 Hz-1.8
GHz).
The Power Transfer, vol. 2, no.
he matching value. 01, pp. 51–59, 2015. electromotive force (e.m.f.) at the terminals of the probe
[2] G. Puccetti, U. Reggiani,
L. Sandrolini,
"Experimental
analysis
wireless
power transmission with spiral
produced
by the time-varying
magnetic
nearoffield
generated
resonators," Energies, vol.6,
n.11,
pp.
5887-5896,
2013.
by the WPT system was then measured. Using this measured
[3] L. Sandrolini, U. Reggiani,
and
G. Puccetti,
"Analytical
calculation
of the value
inductance
of planar zig-zag spiral
voltage
value,
it is possible
to determine
the average
of
inductors," Progress In Electromagnetics Research, vol.142, pp. 207-220, 2013.
the magnetic flux density normal component incident on the
[4] G. Puccetti, U. Reggiani, L. Sandrolini, "Inductance characterization of flat spiral inductors with uniform and
probe area Bp
nonuniform zig-zag arms", in Proc.
The 30th International Review of Progress in Applied Computational
Electromagnetics
(ACES), Jacksonville, FL, USA, MarchVp23-27, 2014, pp. 37-42.
he magnetic flux density
for a
Bp =
(1) study on the termination
[5] J. Alberto, G. Puccetti, G. Grandi, U. Reggiani,
andA L.
Sandrolini, “Experimental
al cross-section.
pw0
impedance effects of a resonator array for inductive power transfer in the hundred kHz range,” in Proc. 2015 IEEE
Vp is
measured
voltage,
ApCO,
is the
areaMay
of the
probe
(a)the
(b)
Wireless Power Transferwhere
Conference
(WPTC
2015),
Boulder,
USA,
13-15,
2015, pp. 1-4.
of the WPT system
resonator
used
bservations
can
made.array
andU.
w0Reggiani,
is the resonant
angular frequency.
[6]usingbe
G.a Puccetti,
C.J.Fig.
Stevens,
L.
Sandrolini,
“Experimental
and
numerical
investigation of termination
9. Measured values (a) and simulated values (b) of the magnetic
Measurements
werevia
made
along a semicircular
line
ofpp.
1.82
impedance
in
wireless
power
transfer
metamaterial,”
Energies,
8
(3),
1882-1895,
ux density is higher
neareffects
flux density magnitude (values in nT) along a semicircular line around the 2015.
m L.
of
diameter
(Fig.
3) centred
the resonator
array andimpedance.
on transfer system using an
[7]
J.
Alberto,
U.
Reggiani,
Sandrolini,
“Magnetic
nearon
field
from
inductive
power
◦ ) for
(from
0◦ to 180
different
values
of theantermination
centre of each coil (Fig. resonators
the horizontal
axis ofInternational
the resonators
at a height
of
array of coupled resonators”,
in Proc. symmetry
7th Asia-Pacific
Symposium
on Electromagnetic
Compatibility
m
in(APEMC
Table
I,
hat the
feedsresults
the resonant
coils consists
a 2.75
2016), of
Shenzen,
China,
May 18-21,
pp. to
1-4.
cm above
them, 2016,
in order
measure the magnetic flux
his configuration
usesadjacent
a Fairchild Semiagnitudes
of two
From
Figs.at8points
and 9farwe
canthesee
that,
are difdensity
from
coils
andalthough
at a small there
distance
Amatched,
as the inverter,
fed
by
an Elind 3232
above
the coils,
respectively.
and this causes
ferences
between
the
measured and simulated values, probably
led by an Arduino Due microprocessor,
I V. SI M UL ATI ONS A ND M EA SUREM ENTS
g frequency at 300 kHz. The coils were
alue of self-inductance of about 14.6
The phasor currents measured in each resonator for three
