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Extending the Inductor Operating Frequencyfor Optimally-coupled
Wireless Power Transfer Systems
Fabian L. Cabrera, Renato S. Feitoza and F. Rangel de Sousafabian.l.c@ieee.org, renato.feitoza@grad.ufsc.br, rangel@ieee.org
RFLaboratorio de RadiofrequenciaUniversidade Federal de Santa Catarina
IMOC 2015
RF Introduction
Inductive linksI Used to wireless powering IMD (implanted medical devices) and
RFID tags.
I The secondary inductor must be miniaturized.I The primary size constraints are more relaxed.
Slide 2
RF Introduction
Inductive linksI Used to wireless powering IMD (implanted medical devices) and
RFID tags.
I The secondary inductor must be miniaturized.I The primary size constraints are more relaxed.
Slide 2
RF Introduction
Inductive linksI Used to wireless powering IMD (implanted medical devices) and
RFID tags.I The secondary inductor must be miniaturized.
I The primary size constraints are more relaxed.
Slide 2
RF Introduction
Inductive linksI Used to wireless powering IMD (implanted medical devices) and
RFID tags.I The secondary inductor must be miniaturized.I The primary size constraints are more relaxed.
Slide 2
RF Power transfer efficiency
Efficiency must be maximized
1η
=1k2 .
1Q1
.1
Q2. (p + 2 +
1p
) + p + 1︸ ︷︷ ︸
I Coupling factor squaredI First Inductor quality factorI Second Inductor quality factorI Load matching dependence
Slide 3
RF Power transfer efficiency
Efficiency must be maximized
1η
=1k2 .
1Q1
.1
Q2. (p + 2 +
1p
) + p + 1︸ ︷︷ ︸I Coupling factor squared
I First Inductor quality factorI Second Inductor quality factorI Load matching dependence
Slide 3
RF Power transfer efficiency
Efficiency must be maximized
1η
=1k2 .
1Q1
.1
Q2. (p + 2 +
1p
) + p + 1︸ ︷︷ ︸I Coupling factor squaredI First Inductor quality factor
I Second Inductor quality factorI Load matching dependence
Slide 3
RF Power transfer efficiency
Efficiency must be maximized
1η
=1k2 .
1Q1
.1
Q2. (p + 2 +
1p
) + p + 1︸ ︷︷ ︸I Coupling factor squaredI First Inductor quality factorI Second Inductor quality factor
I Load matching dependence
Slide 3
RF Power transfer efficiency
Efficiency must be maximized
1η
=1k2 .
1Q1
.1
Q2. (p + 2 +
1p
) + p + 1︸ ︷︷ ︸I Coupling factor squaredI First Inductor quality factorI Second Inductor quality factorI Load matching dependence
Slide 3
RF Mutual coupling model
k = M/√
L1L2
M = µ
√davg1davg2
π
[(2γ− γ)
K(γ)− 2γ
E(γ)
](1)
γ =
√4davg1davg2
(davg1 + davg2)2 + πd2 , (2)
1 10 10010
−3
10−2
10−1
davg1
[mm]
k
d=5mm
d=15mm
d=25mm
Magnetic coupling factor when davg2 = 4 mm. Slide 4
RF Quality factor model
L
R(f)C
10M 100M 1G
10−1
100
101
f [Hz]
R [
Ω]
Radiation
R ∝ f 4
Skin effect
R ∝ f 0.5
Loss factor
Λ =1Q
=R
2πf L
0.01 0.1 1
0.01
0.1
f [GHz]
Λ
davg1
=4 mm
davg1
=10 mm
davg1
=22 mm
davg1
=4 mm
davg1
=10 mm
davg1
=22 mm
Sim. Model
Slide 5
RF Quality factor model
L
R(f)C
10M 100M 1G
10−1
100
101
f [Hz]
R [
Ω]
Radiation
R ∝ f 4
Skin effect
R ∝ f 0.5
Loss factor
Λ =1Q
=R
2πf L
0.01 0.1 1
0.01
0.1
f [GHz]
Λ
davg1
=4 mm
davg1
=10 mm
davg1
=22 mm
davg1
=4 mm
davg1
=10 mm
davg1
=22 mm
Sim. Model
Slide 5
RF Quality factor model
L
R(f)C
10M 100M 1G
10−1
100
101
f [Hz]
R [
Ω]
Radiation
R ∝ f 4
Skin effect
R ∝ f 0.5
Loss factor
Λ =1Q
=R
2πf L
0.01 0.1 1
0.01
0.1
f [GHz]
Λ
davg1
=4 mm
davg1
=10 mm
davg1
=22 mm
davg1
=4 mm
davg1
=10 mm
davg1
=22 mm
Sim. Model
Slide 5
RF Trade-off
To maximize efficiency:I k must be maximized, this leads to a primary inductor bigger
than the secondary.
I Operating frequency is then limited by the biggest inductor.I Therefore, the smaller inductor does not operate in its optimal
frequency.I We can extend the operating frequency of the link using a
segmented inductor.
Slide 6
RF Trade-off
To maximize efficiency:I k must be maximized, this leads to a primary inductor bigger
than the secondary.I Operating frequency is then limited by the biggest inductor.
I Therefore, the smaller inductor does not operate in its optimalfrequency.
I We can extend the operating frequency of the link using a
segmented inductor.
Slide 6
RF Trade-off
To maximize efficiency:I k must be maximized, this leads to a primary inductor bigger
than the secondary.I Operating frequency is then limited by the biggest inductor.I Therefore, the smaller inductor does not operate in its optimal
frequency.
I We can extend the operating frequency of the link using a
segmented inductor.
Slide 6
RF Trade-off
To maximize efficiency:I k must be maximized, this leads to a primary inductor bigger
than the secondary.I Operating frequency is then limited by the biggest inductor.I Therefore, the smaller inductor does not operate in its optimal
frequency.I We can extend the operating frequency of the link using a
segmented inductor.
Slide 6
RF Segmented inductor
L
RS (f,CS)C
CS
CS =CG + CD
N − 1
CG Gap capacitanceCD Discrete capacitorN Number of segments
0.1 1
−600
−400
−200
0
200
400
600
f [GHz]
X [
Ω]
N = 1
N = 2
N = 4
N = 8
0.1 1
0.1
1
10
f [GHz]
RS [
Ω]
N=1
N=4, CD
= 0.5 pF
N=4, CD
= 2 pF
N=4, CD
= 8 pF
(a) Equivalent reactance when CD=0. (b) Segmented inductor losses.
Slide 7
RF Segmented inductor
L
RS (f,CS)C
CS
CS =CG + CD
N − 1
CG Gap capacitanceCD Discrete capacitorN Number of segments
0.1 1
−600
−400
−200
0
200
400
600
f [GHz]
X [
Ω]
N = 1
N = 2
N = 4
N = 8
0.1 1
0.1
1
10
f [GHz]
RS [
Ω]
N=1
N=4, CD
= 0.5 pF
N=4, CD
= 2 pF
N=4, CD
= 8 pF
(a) Equivalent reactance when CD=0. (b) Segmented inductor losses.
Slide 7
RF Segmented inductor
L
RS (f,CS)C
CS
CS =CG + CD
N − 1
CG Gap capacitanceCD Discrete capacitorN Number of segments
0.1 1
−600
−400
−200
0
200
400
600
f [GHz]
X [
Ω]
N = 1
N = 2
N = 4
N = 8
0.1 1
0.1
1
10
f [GHz]
RS [
Ω]
N=1
N=4, CD
= 0.5 pF
N=4, CD
= 2 pF
N=4, CD
= 8 pF
(a) Equivalent reactance when CD=0. (b) Segmented inductor losses.Slide 7
RF Segmented inductor quality factor
0.1 1
100
200
300
400
f [GHz]
Q1
1
2 0~16 pF
4 1~16 pF
8 2~32 pF
N
CD
0.1 11
2
3
4
5
6
7
x 10
f [GHz]Q
1Q
2
1
2 0~16 pF
4 1~16 pF
8 2~32 pF
N
CD
x104
Slide 8
RF Effect of the capacitor losses
1 10
0.1
1
C [pF]
ES
R [
Ω]
2 GHz
1 GHz
250 MHz
2 GHz
1 GHz
250 MHz
Data Fitted
0.1 1
1
2
3
f [GHz]
Q1Q
2
1
2 0~16 pF
4 1~16 pF
8 2~32 pF
N
CD
x104
(a) Equivalent series resistance for discrete capacitors. (b) Quality factorsproduct accounting the capacitors ESR.
I Performance is no longer improved for higher values of N because ofthe capacitor losses.
Slide 9
RF Implementation
davg2 [mm] davg1 [mm] N CD [pF] d [mm]4 22 4 3 15
Slide 10
RF Experimental results
N CD [pF] ηmax [%] fηmax [MHz]1 – 30 415 Meas. [3]4 3 38 735 Sim.4 1.5 37 990 Sim.4 1.5 30 980 Meas.
[3] Fabian L. Cabrera and F. Rangel de Sousa, “Optimal Design of Energy Efficient
Inductive Links for Powering Implanted Devices,”in BioWireleSS 2014.Slide 11
RF Conclusions
Conclusions:I The operating frequency of an optimally-coupled inductive link
was extended from 415MHz to 980 MHz.
I The extension of the operating frequency was achieved bydividing the primary inductor into four segments.
I The technique presented offers potential improvements on thelink efficienncy, however that improvements are limited by thecapacitor losses.
I The extension of the primary inductor frequency offers flexibilityto the inductive link design.
Slide 12
RF Conclusions
Conclusions:I The operating frequency of an optimally-coupled inductive link
was extended from 415MHz to 980 MHz.I The extension of the operating frequency was achieved by
dividing the primary inductor into four segments.
I The technique presented offers potential improvements on thelink efficienncy, however that improvements are limited by thecapacitor losses.
I The extension of the primary inductor frequency offers flexibilityto the inductive link design.
Slide 12
RF Conclusions
Conclusions:I The operating frequency of an optimally-coupled inductive link
was extended from 415MHz to 980 MHz.I The extension of the operating frequency was achieved by
dividing the primary inductor into four segments.I The technique presented offers potential improvements on the
link efficienncy, however that improvements are limited by thecapacitor losses.
I The extension of the primary inductor frequency offers flexibilityto the inductive link design.
Slide 12
RF Conclusions
Conclusions:I The operating frequency of an optimally-coupled inductive link
was extended from 415MHz to 980 MHz.I The extension of the operating frequency was achieved by
dividing the primary inductor into four segments.I The technique presented offers potential improvements on the
link efficienncy, however that improvements are limited by thecapacitor losses.
I The extension of the primary inductor frequency offers flexibilityto the inductive link design.
Slide 12
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