University of Southern California Dissertations and Theses

Circuits for Biomedical Telemetry and Stimulation Applications

(USC Thesis Other)

Circuits for Biomedical Telemetry and Stimulation Applications

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Content Circuits for Biomedical Telemetry and
Stimulation Applications
by
Manjunath Machnoor
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
December 2020
Copyright 2020 Manjunath Machnoor
Dedicated to my parents Jayamma and Veeranagowda Machnoor...
ii
Acknowledgements
Numerouspeoplehavemotivated, inspired, andhelpedme, givingmevaluableadvice
on both research and various aspects of my life. I want to thank them all for making this dissertation
possible.
Firstly, I would like to thank my advisor, Prof. Gianluca Lazzi, for offering me the
Ph.D. position and learning experience in wireless power transfer. His rich experience in the field
has helped with exposure to real-world applications of the wireless power transfer. I am also very
grateful for his valuable suggestions and all the thousands of discussions. Without his technical
guidance and financial support, this work would not have been possible.
I would also like to appreciate the support of my graduate committee for all their
insights into the thesis. My committee members Prof. Mark Humayun, Prof. Mahta Moghaddam,
and Prof. Manuel Monge, have helped me understand the concepts better. My thesis work and the
publications would not have been possible without my labmates and co-authors, including Dr. Erik
Saturnino Gamez Rodriguez, Dr. Pragya Kosta, Javad Paknahad, Dr. John Stang, Ege Iseri, Jinze
Du, Arthur Shao. They are researchers, fabulous people, and I enjoyed their company. I would
like to especially thank Dr. Erik Saturnino Gamez Rodriguez for spending so many hours guiding,
correcting my mistakes, and giving me sufficient feedbacks.
I want to acknowledge all my USC collaborators for their support Prof. Mark Hu-
mayun, Dr. Kim Gokofski, Dr. Biju Thomas, Dr. Alejandra Gonzalez-Calle, Sakai Carolina, Doris
Lee, Ellis Troy, and Jennifer Limon. I would also like to thank Prof. Jamesina Simpson and Dr.
Santosh Pokhrel of the University of Utah for all the help and support.
iii
I also extend my sincere thanks to Prof. K J Vinoy, Dr. T. V. Prabhakar, and Prof.
Dipanjan Gope at the Indian Institute of Science, Bangalore, India, for guiding me and teaching
me RF and Electric Field Energy Harvesting.
Lastly and Most importantly, I would like to thank my mother, Jayamma, father
Veeranagowda Machnoor, my brother Arun Kumar, all my extended family members, and Ritesh
Kumar in supporting me throughout my Ph.D. stay in the US. My parents are the sources of all
my inspiration and motivation.
iv
Contents
Acknowledgements iii
List of Figures ix
List of Tables xv
Abstract xvi
1 Introduction 1
2 AnalysisandDesignofa3-CoilWirelessPowerTransmissionSystemforBiomed-
ical Applications 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Brief notes on Conventional 2-coil and 3-coil Wireless Power Transfer systems . . . . 8
2.2.1 Conventional 2-coil WPT system . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 3-coil WPT system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Performance degradation in conventional 2-coil and 3-coil system as the receiver size
reduces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 ENHANCING THE PERFORMANCE OF 3-COIL SYSTEM AS THE RECEIVER
SIZE REDUCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Goal
1
EFFICIENT USE OF WIRE TO ENHANCE THE R
ref2
F SMALLER RE-
CEIVER 3-COIL SYSTEM L
2
=L
3
. . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.1 Circuit Technique Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.2 Testing the technique: Comparison 1 . . . . . . . . . . . . . . . . . . . . . . . 22
2.6 Goal
2
Reducing Power dissipation in the implanted receiver: Second technique to
enhance the R
ref2
of smaller receiver 3-coil system (
1
!C
2
=
1
!C
3
= 0) . . . . . . . . . 23
2.6.1 Circuit Technique Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.6.2 Testing the technique: Comparison 2 . . . . . . . . . . . . . . . . . . . . . . . 24
2.7 Design Procedure and advantages of proposed 3 Coil system over conventional 3 Coil
system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.7.1 Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.7.2 Advantage 1: Tolerance to load changes . . . . . . . . . . . . . . . . . . . . . 28
2.7.3 Advantage 2: Reducing currents in the secondary coil . . . . . . . . . . . . . 29
2.7.4 Load Current I
3
and I
3p
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
v
2.8 Experiments: Measurements and Results . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.9 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.9.1 K
12
and C
m
for optimization of system Performance . . . . . . . . . . . . . . 34
2.9.2 Tissue effects on the system Performance . . . . . . . . . . . . . . . . . . . . 35
2.9.3 Additional Coil at the transmitter and 4-coil system . . . . . . . . . . . . . . 36
2.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3 Quantifying the efficiency maxima of a three coil WPT system using Q
1
+ Q
2
analysis 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 Conventional and Proposed WPT systems . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.1 Conventional 3-Coil system (System 1) . . . . . . . . . . . . . . . . . . . . . . 42
3.2.2 Same Phase 3-Coil system (System 2) . . . . . . . . . . . . . . . . . . . . . . 43
3.2.3 Series connected 3-Coil: Q
1
+ Q
2
effect (System 3) . . . . . . . . . . . . . . 44
3.2.4 Magnetic Energy Efficiency of WPT Systems . . . . . . . . . . . . . . . . . . 45
3.2.5 Other WPT systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3 Proposed layout: Understanding and avoiding Q-factor degradation . . . . . . . . . . 47
3.3.1 Understanding the Q Degradation in Layout design . . . . . . . . . . . . . . . 48
3.3.2 Q Degradation and Proposed Solution . . . . . . . . . . . . . . . . . . . . . . 49
3.4 PTE
max
and Q
1
+ Q
2
effect in 3Coil system. . . . . . . . . . . . . . . . . . . . . . 49
3.4.1 Schematic Update to account for R
S
. . . . . . . . . . . . . . . . . . . . . . . 52
3.5 Measurements Results and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4 Wireless Power Transfer: Types of Reflected Impedances and Maximum Power
Transfer Theorem 55
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2 Reflected Impedance and WPT systems . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.1 Real Reflected Impedance, 2-Coil system and MPT . . . . . . . . . . . . . . . 57
4.2.2 Imaginary Reflected Impedance and 3-Coil system . . . . . . . . . . . . . . . 58
4.2.3 Negative Reflected Impedance and 4-Coil system . . . . . . . . . . . . . . . . 60
4.3 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3.1 Complete Analysis of 4-Coil system . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3.2 Proposed 4-Coil System Design and Simulations . . . . . . . . . . . . . . . . . 65
4.4 Measurements and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5 Reflected Impedance as the Superposition of Power Flow Paths in Multicoil
Wireless Power Transfer 69
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 Analysis of A General Four Coil WPT system . . . . . . . . . . . . . . . . . . . . . . 70
5.2.1 Total Reflected Impedance of a 4-coil system . . . . . . . . . . . . . . . . . . 71
5.2.2 Real Reflected Impedance and Corresponding Paths of Power flow . . . . . . 72
5.2.3 Imaginary Reflected Impedance and Corresponding Paths of Power flow . . . 74
5.2.4 Negative Reflected Impedance and Corresponding Paths of Power flow . . . . 76
5.2.5 Application to the Design of Practical WPT systems . . . . . . . . . . . . . . 77
5.2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
vi
6 Wireless Telemetry System with Independent Power and Data Frequency Reso-
nance 80
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.2 WPT systems and their performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2.1 Layout and schematics of systems under study . . . . . . . . . . . . . . . . . 83
6.2.2 2 Coil and LCC WPT systems . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2.3 LCCC system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2.4 TL4C System: Tuning to fix the f
d
independent of the value of PDL (Re(Z
11
)) 88
6.2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3 Measurements and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7 Circuit Perspective of the Radial Electric Fields of a Low-Frequency Wireless
Power Transfer Coil 93
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.2 Electric Fields due to Line Charge and Charge - Voltage Relationship in R, L and C 95
7.3 Charge distribution and Radial Electric Fields (E
z
) in a 1-turn and 2-turn coil . . . 97
7.4 Self-Resonance Frequency and Radial Electric Fields . . . . . . . . . . . . . . . . . . 99
7.5 Measurements and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
8 Design of Wireless Power Transfer System to Passively power Electrodes to de-
liver Asymmetric Biphasic Stimulating Waveform 102
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
8.2 Goals and Procedures of this Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
8.3 Solution Based on Differentiation property of induction . . . . . . . . . . . . . . . . 105
8.4 System based on Rectification, Modulation and filtering concepts . . . . . . . . . . . 108
8.4.1 Half Wave Rectifier based Passive Wireless Electrodes . . . . . . . . . . . . . 109
8.4.2 Charge Balanced Half Wave Rectifier Based Solutions . . . . . . . . . . . . . 109
8.4.3 Proposed circuit to deliver higher peak to peak load voltage . . . . . . . . . . 111
8.5 Experimental Results and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 112
9 Non Foster Circuits Applied to Electrical Stimulation Systems 115
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
9.2 Goals and Procedures of this work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
9.3 Non Foster Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9.4 Equivalent Circuit of Electrical Stimulation System . . . . . . . . . . . . . . . . . . 118
9.5 Advantages of Electrical Stimulation System with Non Foster Circuit . . . . . . . . 122
9.5.1 Analysis 1: AC response of the gradient . . . . . . . . . . . . . . . . . . . . . 123
9.5.2 Analysis 2: Transient response of the gradient . . . . . . . . . . . . . . . . . 124
9.5.3 Analysis 3: Behaviour of an Ideal Electrode- Electrolyte Interface . . . . . . 127
9.5.4 Analysis 4: Interface Capacitance Increase due to addition of Non-Foster Circuit128
9.6 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
9.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
9.8 Applications and Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
9.9 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
vii
10 External Circuits to achieve a Charge Balanced Unidirectional gradient with
Biphasic Stimulation 136
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
10.2 Problem Statement Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
10.3 Basic Electrochemical System Description, Goals and Procedures of this work . . . . 139
10.4 Basic Techniques used in the literature to achieve charge balance . . . . . . . . . . . 141
10.5 Approach 1: Pushing the anodic gradient to low frequency using the series low fre-
quency system (LFS). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
10.5.1 Notes regarding the Operation of the Proposed System . . . . . . . . . . . . . 143
10.5.2 simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
10.6 Approach 2: Pushing the anodic gradient to high frequency using the series high
frequency system (HFS). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
10.6.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
10.7 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
10.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
11 Conclusions and Future Work 155
Bibliography 157
viii
List of Figures
1.1 General representation of a WPT system for biomedical applications. The perfor-
mance parameters and design variables are listed. . . . . . . . . . . . . . . . . . . . . 2
2.1 Schematic of a traditional 2-coil Wireless Power Transfer (WPT) system. . . . . . . . 8
2.2
2Coil
Vs:K
12
for a 2 coil system withL
1
=L
2
= 2H,R
1
=R
2
= 1
, RL = 100
,
f = 5MHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Schematic of a Conventional 3-coil Wireless Power Transfer (WPT) system(3Coil)[1–4]. 13
2.4 (a). Schematic of the proposed efficient and compact 3-coil system(3Coil
p
). To
maximize the R
ref2
of small receiver size 3-coil system, two techniques are adopted.
1)L
2
=L
3
and 2)
1
!C
2
=
1
!C
3
= 0 along with the appropriate receiver system’s relative
coil polarity required to increase the R
ref2p
. b) RX system’s relative coil polarity
that leads to the reduction of R
ref2p
. . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 (a) The equivalent schematic of the system used in [1](K
23
= 0:62). (b) The proposed
receiver system incorporating the equal split inductance(K
23p
= 0:84) along with
mutualcapacitanceandappropriaterelativepolarity. Thetworeceiversystemsshown
in this figure are compared using the same Tx. system(left). . . . . . . . . . . . . . . 21
2.6 Comparison of PTE and Gain of two systems in Fig. 2:5(Fig. 2:5a, representing [1]
and Fig. 2:5b, representing smaller and equal split inductance). . . . . . . . . . . . . 21
2.7 ComparisonofFrequencyresponseofloadcurrentoftwosystemsinFig. 2:5(Fig. 2:5a,
representing [1] and Fig. 2:5b, representing smaller and equal split inductance). . . . 22
2.8 (a). Equivalent circuit diagram of the system used in [2]. The system is tested for
its losses in the receiver implanted in the body. (b). The schematic of the proposed
receiver system. The two receiver systems shown in this figure are compared using
the same Tx. system(left). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.9 Comparison of PTE and Gain of systems using two different receiver configurations
in Fig. 2:8 (Fig. 2:8.(a) representing [2] and Fig. 2:8.(b) representing C
m
enhanced
system). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.10 (a). Schematic of the implemented conventional 3 Coil system. (b). Schematic of the
implemented proposed 3 Coil system. The two receiver systems shown in this figure
are compared using the same Tx. system(left). . . . . . . . . . . . . . . . . . . . . . 27
2.11 The
I
2p
I
3p
is lesser than
I
2
I
3
of conventional system. It proves that, we can increase the
receiver performance without affecting the transmitter efficiency. At lowerK
12
, PTE
is limited by the transmitter efficiency which is same for both the systems. . . . . . . 28
2.12 Comparison of load sensitivity of the efficiency of implanted systems designed using
conventional and proposed design techniques. . . . . . . . . . . . . . . . . . . . . . . 29
ix
2.13 Comparison of PDL(V
in
= 1) and secondary coil currents of proposed and conven-
tional design of 3 coil system. It can be noticed that, for a given PDL, the required
value of I
2p
is less than I
2
for all K
12
. . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.14 Layout of the Side view and top view of 3 Coil system in CST Design STUDIO. In
the top view, 3Coil
1
highlighted for differentiation. The diameter of the transmit
and receive coils are 70mm and 35mm respectively. . . . . . . . . . . . . . . . . . . . 32
2.15 Photograph of the measurement setup showing TX coil at the left and RX setup
at the right. The diameter of the transmit and receive coils are 70mm and 35mm
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.16 Experimental and simulation results of PTE of three systems under comparison . . 34
2.17 Experimental and simulation results of Gain of three systems under comparison . . 34
2.18 Study of effect of tissue material on the system performance. On the left, proposed 3-
coil WPT system with skin dry(3.75mm thick) and fat(4 mm thick) tissue in between
the transmitter and the receiver. On the right, plot of PDL Vs. frequency for the
system with and without the tissue. It can be noted that, tissue has no effect on the
PDL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.19 Schematic of 3-coil system with additional coil and the mutual capacitor at the trans-
mitter. The driver coil(L
1
) is connected to the transmitter coil(L
2
) using the mutual
capacitance(C
1
). The choice of relative voltage polarity of L
1
& L
2
(dot convention
not shown here) will determine the PTE and PDL. . . . . . . . . . . . . . . . . . . . 37
3.1 System 1 (Conventional 3-Coil): Transmitter schematic is given by Tx. version 1.
System 2 (Same Phase 3-Coil): Transmitter schematic is given by Tx. version 1. Sys-
tem 3 (Series Resonance): Transmitter schematic is given by Tx. version 2. System
1 and 2 have same layout and schematic but the resonance conditions are different.
The common receiver with parallel resonance is used in the measurements for all the
systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2 Comparison 1: Simulation of MEE and PTE of System 2 and System 1 (Conclusion:
System 2 can have better PTE and MEE than system 1 for the same transmitter
coils). Comparison 2: The plot of PTE vs. RL for System 2 and System 3 with two
similar transmit coils (Conclusion: PTE of system 2 and System 3 can be same if
equal coils are used). The system parameters of the two comparisons are given in
Table 3:3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3 Coil layout used to analyze System 1 and 2. System 3 is made of series connection
of two Tx Coil 1 (Table 3:1 and 3:2) . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.4 The schematic updates to make the efficiency of the System 3 insensitive to the R
s
.
Comparison 3: The PTE Vs. R
L
plot proves that it is possible to design a 3-Coil
system to provide performance equivalent to Q
1
+ Q
2
, which is a property of series
resonance. Comparison 4: The plot shows that R
s
effect on PTE can be minimized
by an appropriate schematic update. System parameters are given in Table 3:3. . . . 53
3.5 Experimental and simulation results of PTE of three systems under comparison. The
experimental results prove the Q adding effect of System 2 described in Comparison
3. The System 2 shows higher PTE than the System 1 and 3 for all the load values. 53
x
4.1 a). Power flow path to obtain imaginary reflected impedance at the transmitter in the
3-CoilWPTsystemb). Powerflowpathtoobtainnegativereflectedimpedanceina4-
Coil WPT system. K
12
is the coupling coefficient between Coil1 and Coil2. Similarly,
K
xy
is coupling coefficient between Coilx and Coily, where x; y = 1; 2; 3; 4 and
also K
xy
=K
yx
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Left: Description of the stand alone coil usedin thesystem. Right: The highcoupling
[5]systemismadeof3identicalcoils(L
2
= L
3
= L
4
= 6:3H)ofgivendimension
on the left. The first coil (L
1
= 8:2H) is made of same parameters except that it
has 10 turns. Schematic of the system is shown in Fig. 4:3. . . . . . . . . . . . . . . 65
4.3 Left: The schematic of the implemented system. Right: Simulated (CST STUDIO
SUITE™) coupling coefficients between the coils. . . . . . . . . . . . . . . . . . . . . 66
4.4 Simulated (CST STUDIO SUITE™) plot of real part of reflected impedance and PDL
vs. distance between Tx. and Rx. The maxima of PDL coincides with the minima
of reflected impedance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.5 Measurement results PTE, PDL and PF of the implemented system. . . . . . . . . . 67
5.1 Three power flow paths that result in real reflected impedance at the source coil. . . 74
5.2 Six power flow paths that result in imaginary reflected impedance at the source coil. 75
5.3 Six power flow paths that result in real reflected impedance at the source coil. . . . . 76
6.1 Layout of the transmit (Number of turns = 8, AWG = 24, spacing between the turns
= 0.2 mm) and receive (Number of turns = 3, AWG = 24, spacing between the turns
= 0.5 mm) coils used in the experiment. The parameters of the telemetry system
used as an example are also given in the figure. The transmit coil (Tx) is tapped
to divide it into two series connected coils Tx1 and Tx2. Tapping creates additional
node on the Tx coil. (AWG: American Wire Gauge) . . . . . . . . . . . . . . . . . . 84
6.2 Schematicofthesystemsunderstudya). 2Coilsystemtransmitandreceiveschematic
using series resonance b). The transmitter schematic of the LCC system c). The
transmitter schematic of the LCCC system d). The transmitter schematic of the
proposed system. Note that the coil layout used for 2 coil and TL4C system are
same as highlighted in the dotted box(i.e L
TX
= L
TX1
+ L
TX2
+ 2L
TX1TX2
) . 85
6.3 Simulation 1 results to show the multiple unity PF points in LCC. It also shows
that, for a given input impedance, the LCCC system can achieve asymmetry in the
frequency response of PF. The parameters are in Sim 1 of Table 6:1. . . . . . . . . . 86
6.4 TL4C system: Simulation 2 results to show that the proposed TL4C system can
achieve same f
d
(= 4:2 MHz) for different real value of input impedance. The
parameters are in Sim 2 of Table 6:1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.5 TL4C system: NOTE: Simulation 3 results to show that the proposed TL4C system
can achieve same real value input impedance for different data transmit frequency
(f
d
) conditions. The parameters are in Sim 3 of Table 6:1. At 4.7 MHz, theRe(Z
11
)
of Ex3 and Ex4 overlap, they also exhibit PF=1. The two systems have different f
d
.
The VG shows maxima at f
d
resonances. . . . . . . . . . . . . . . . . . . . . . . . . 89
6.6 Experimental results showing PTE, VG and CG of the two systems under comparison
at power transfer frequency f
p
= 4:7 MHz. . . . . . . . . . . . . . . . . . . . . . . 91
6.7 Experimental results showing frequency response of PF, magnitude of Z
11
, VG and
CG of the two systems under comparison. . . . . . . . . . . . . . . . . . . . . . . . . 91
xi
7.1 (a). The general uniform line charge distribution with ground at1. The potential
at both ends of the line charge is equal. It is a capacitor with respect to infinity. (b).
The charge-voltage relationship in resistor, capacitor and inductor. (c). The linear
line charge distribution with ground at the center of the line. This charge distribution
can result from a true differential input voltage (Only AC, no DC). . . . . . . . . . 96
7.2 (a) The layout of the 1-turn coil in CST STUDIO SUITE™. (b) Distribution of the Ez
component above the 1-turn coil (Z = 2 mm). (c) Distribution of the Ez component
below the 1-turn coil (Z = -3 mm). (d) The layout of the 2-turn coil in CST STUDIO
SUITE™. (e) The Ez component above the 2-turn coil (Z = 2 mm). (f) A straight
line whose length is equal to the length of the 2-turn coil. (g). The Ez component on
the Z = 2 mm plane. These EF simulations are conducted for 1 mA input current at
5 MHz from the Co-Simulation settings. . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.3 (a). The CST STUDIO SUITE™ layout and parameters of the experimentally imple-
mented coil (b). Description of the charge in each branch of the equivalent circuit of
the coil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.4 Experimental measurement results. The probe orientation and S21 (dB) for the
horizontal and vertical measurement of the EF is shown. Vertical measurements
refer to E
z
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8.1 Schematic of the circuit that can deliver a biphasic assymmetric waveform to the load
when triangular waveform is used as input. . . . . . . . . . . . . . . . . . . . . . . . 106
8.2 Simulation 1: Simulation results of the schematic shown in Fig. 8.1. The values used
for the circuit parameters is given in Table 8:1. . . . . . . . . . . . . . . . . . . . . . 107
8.3 A representative layout of the transmitter and receiver coils used to passively power
the circular electrodes in contact with the tissue. . . . . . . . . . . . . . . . . . . . . 108
8.4 Equivalent schematic of an electrochemical system. The parallel R and C are formed
at the interface of the electrode and electrolyte. The electrode-electrolyte interface
is formed both at the source and the ground electrodes. . . . . . . . . . . . . . . . . 108
8.5 Schematic of a typical wireless system which delivers a monophasic waveform to the
electrodes using a half wave rectifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
8.6 Simulation 2: Simulation results of the schematic shown in Fig. 8.5. The values used
for the circuit parameters is given in Table 8:1. a). A modulated pulse as an input
voltage. b). A monophasic voltage waveform across the load resistor. . . . . . . . . . 110
8.7 Schematic of a wireless system which delivers a charge balanced biphasic waveform
to the electrodes using a half wave rectifier and a series capacitor. . . . . . . . . . . . 111
8.8 Simulation 3: Simulation results of the schematic shown in Fig. 8.7. The values used
for the circuit parameters is given in Table 8:1. a). A modulated pulse as an input
voltage. b). A biphasic voltage waveform across the two different values of the load
resistor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
8.9 Schematic of the proposed wireless system which delivers a charge balanced biphasic
waveform to the electrodes. The proposed circuit provides a higher load voltage
compared to the circuit shown in Fig. 8.7. . . . . . . . . . . . . . . . . . . . . . . . . 112
8.10 Simulation 4: Simulation results of the schematic shown in Fig. 8.9. The values used
for the circuit parameters is given in Table 8:1. a). A modulated pulse as an input
voltage. b). A biphasic voltage waveform across the two different values of the load
resistor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
xii
8.11 Photograph of implemented transmitter and receiver coils. The distance between the
coils is maintained at 25 mm for the two experiments. The half wave rectifier and
the proposed charge balanced circuit was implemented. . . . . . . . . . . . . . . . . . 113
8.12 Experimental measurement results for the circuit shown in Fig. 8.9 and half wave
rectifier. The input voltage is the 100 kHz modulated pulse of 1ms width. The input
voltage is 5 Volts peak to peak and input current is about 0.6 A peak to peak. The
proposed circuit gives better load voltage compared to a half wave rectifier across a
10 k
load resistor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
9.1 Schematic of a typical non-foster Circuit. Conditions necessary to achieve negative
input impedance are described. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9.2 Typical circuit representation of an electrochemical system. In this work, this circuit
is referred to as a basic circuit. V(a) and V(b) are the voltages at the approximate
recording points ’a’ and ’b’ to measure the channel gradient. . . . . . . . . . . . . . . 119
9.3 Variables available for electrical stimulation. Different types of stimulation pulses,
bipolar/monopolar connection of stimulation source and V/I sources are shown in
the diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9.4 A conceptual circuit diagram of an electrochemical system in series with negative
resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
9.5 Schematic of the non-foster circuit in series with an equivalent schematic of an elec-
trochemcial system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
9.6 Analysis 1: AC simulation showing the enhancement in the magnitude and phase
response of the gradient (V(a)-V(b)) offered by the negative resistance in series.
Most of the enhancement is observed at high frequency. . . . . . . . . . . . . . . . . 123
9.7 Analysis 2: SPICE simulated V(a) and V(b) for the the two systems under compar-
ison. It can be noted that the V(b) of the circuit with NF changes the shape and
increase the gradient (V(a)-V(b)) as shown in Fig. 9:8. . . . . . . . . . . . . . . . . . 124
9.8 Analysis 2: Gradient of the two systems under comparison. The circuit with NF has
higher gradient at high frequency components. . . . . . . . . . . . . . . . . . . . . . . 125
9.9 Analysis 3: An ideal interface has higher capacitive gradient and lower low-frequency
gradient. The ideal interface refers to the case with R
Source
= 0. . . . . . . . . . . . 126
9.10 Analysis 4: Channel current behaviour under different C
Source
. A higher C
Source
reduces the decay of the current without affecting the peak current and the low
frequency current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
9.11 Equivalent schematic of the measurement system with non-foster circuit in series. . . 129
9.12 (a). Waveform of the input voltage signal. (b). Recorded voltages of V(a) and V(b)
for the basic setup without non-foster circuit in series. . . . . . . . . . . . . . . . . . 130
9.13 The measured waveforms of V(a) and V(b) for a system with non-foster circuit in
series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
9.14 Thefigurecomparesthegradientalongthenerveforthetwocases. Thegradientalong
the nerve is increased when non-foster circuit is in series with the electrochemcial
system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
9.15 Comparison of the current through the nerve. The current is measured as a voltage
across the 1 k
series resistanceR
s
. The current behaviour in presence of non-foster
circuit indicated higher source electrode-electrolyte capacitance as shown in Fig. 9:10
and analysis 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
xiii
9.16 The gradient enhancement offered by the non-foster circuit in PBS water is shown
to be only limited to high frequency. This behaviour is similar to the analysis of the
ideal interface carried out in Analysis 3. The gradient enhancement is comparable to
Fig. 9:9. In this case, we can observe that the interface capacitance did not increase,
but the conduction through the R
Source
reduced. . . . . . . . . . . . . . . . . . . . . 134
10.1 Schematic of the equivalent circuit of an electrochemical system. An asymmetric
biphasic voltage waveform is also shown. . . . . . . . . . . . . . . . . . . . . . . . . . 143
10.2 Schematic of the proposed LFS system. This system can control the anodic conduc-
tion time constants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
10.3 a) A charge balanced input waveform. b) Simulation of V(a) and V(b) for the basic
system with the system parameters given in Table 10.1. . . . . . . . . . . . . . . . . 144
10.4 a) Simulation of V(a) and V(b) for the LFS system with the system parameters given
in Table 10.1. b). Comparison of simulated gradients of the LFS system and basic
system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
10.5 Schematic of the proposed HFS system. This system can control push the part of
anodic gradients to higher frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
10.6 a) Simulation of V(a) and V(b) for the HFS system with the system parameters given
in Table 10.1. b). Comparison of simulated gradients of the HFS system and basic
system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
10.7 a) The charge balanced 1:4 input waveform. b) Measurement of V(a) and V(b) for
the basic system with tungsten electrodes. . . . . . . . . . . . . . . . . . . . . . . . . 149
10.8 a) Measurement of V(a) and V(b) for a LFS system with 1:4 input waveform. b)
Gradient comparison of the LFS system with basic system for the 1:4 input waveform.149
10.9 a) Measurement of V(a) and V(b) for a HFS system with 1:4 input waveform. b)
Gradient comparison of the HFS system with basic system for the 1:4 input waveform.150
10.10a) The charge balanced 1:8 input waveform. b) Measurement of V(a) and V(b) for
the basic system with tungsten electrodes. . . . . . . . . . . . . . . . . . . . . . . . . 150
10.11a) Measurement of V(a) and V(b) for a LFS system with 1:8 input waveform. b)
Gradient comparison of the LFS system with basic system for the 1:8 input waveform.152
10.12a) Measurement of V(a) and V(b) for a HFS system with 1:8 input waveform. b)
Gradient comparison of the HFS system with basic system for the 1:8 input waveform.153
10.13Measurement of voltages across the series capacitor to assess the charge balance in
the system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
xiv
List of Tables
2.1 Table to summarize results of two comparison exercises and the advantages of the
proposed techniques as compared with the systems in [1] and [2]. . . . . . . . . . . . 25
2.2 properties of the coils used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3 circuit parameters of 3 systems under test . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1 Measured properties of the coils (shown in Fig. 3:3) used . . . . . . . . . . . . . . . . 47
3.2 details of the Coils used in the three systems. . . . . . . . . . . . . . . . . . . . . . . 47
3.3 List of Parameters used in each comparison (Comp.). . . . . . . . . . . . . . . . . . . 48
6.1 Parameters used in Simulation (Sim.) & Experiment (EXP). . . . . . . . . . . . . . . 87
8.1 Parameters used in Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
8.2 Electrical and Physical properties of the coils used . . . . . . . . . . . . . . . . . . . 114
9.1 Parameters used in the Four Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
9.2 Details of the Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
10.1 Parameters used in Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
xv
Abstract
Wireless Power Transfer (WPT) techniques are used in biomedical systems to en-
hance the safety and user experience. Analysis and design of high performance inductive WPT
systems is addressed in this work. Efficiency, telemetry over large distance, independent design of
power delivery and efficiency, and safety are some of the performance parameters analyzed. Circuit
design concepts are applied to achieve new high-performance WPT solutions.
The degrees of freedom available to tune the electrochemical properties of a biomed-
ical stimulation system to achieve desired biological response are limited to waveform choice, duty
cycle, amplitude, and type of source. Concepts of negative resistance and frequency translation
are now applied to achieve electrochemical system performance not possible with the conventional
design strategies. These techniques lead to larger channel gradients and selective control over the
anodic current flow. These systems may help increase the stimulation efficiency.
The concepts presented in this thesis are verified using analytical, simulation, and
experimental tools....
xvi
Chapter 1
Introduction
Wireless power transfer (WPT) techniques enhance safety and user experience of the
applications such as biomedical implants, electric vehicles and home automation, adding value to
the product. An active biomedical implant without an accompanying wireless power transfer system
would require a wired connection from inside the body to an external power supply, which makes it
pronetoinfectionandcausesdiscomforttothepatient. AsimpleWPTsystemintegratedbiomedical
implant can address these issues, promote safety and improve the user experience. Examples of
advantages of a WPT system integration are available in other applications such as electric vehicles
and home automation.
Often, the design of the WPT system determines the performance of an application
and may introduce new implementation challenges of its own. A poorly designed WPT system can
result in the underperformance of the biomedical implant. The design of a WPT system begins
by evaluating the performance parameters and the variables to achieve the desired performance.
Fig. 1.1 shows a typical representation of a WPT system for biomedical applications and records
the performance parameters and the design variables. Successful implementation of a WPT system
1
Figure 1.1: General representation of a WPT system for biomedical applications. The perfor-
mance parameters and design variables are listed.
requires an understanding of electromagnetic fields to evaluate possible safety issue for the patient,
as well as of RF and analog circuits to achieve the desired performance by manipulating the design
variables. Thus, the design process of a WPT system provides a great learning opportunity in
several areas and a technically satisfying experience to the designer.
Since there are several performance parameters of a WPT system which can be im-
proved by manipulating the different design variables, there exists a research opportunity. The
different works presented in this thesis either improve a particular performance parameter by vary-
ing a design variable combined with circuit design techniques or explain a previously unexplained
theoretical aspect of the operation of a WPT system. This thesis does not present new performance
parameters but provides new design variables to achieve the required performance criteria efficiently.
The designed systems are verified using analytical, simulation, and experimental tools.
Chapter 2 seeks to improve the power transfer efficiency of the WPT system for fixed
2
physical coil dimensions. It explores the use of a mutual capacitor in between the two coils whose
impedance adds to the mutual coupling. Analytical, simulation and experimental tools are used to
validate the system. The mutual capacitor not only improves the power transfer efficiency but also
can reduce the size of the coils used. Chapter 3 provides an analytical and experimental explanation
for the maximum limit efficiency of a three coil wireless power transfer system. The sum of quality
factors of individual transmitter coils determines the maximum limit on the efficiency of a wireless
power transfer system.
The main objective of Chapter 4 and 5 is to provide a physical interpretation of
the total reflected impedance of the multi-coil systems. Multi-coil systems have complex reflected
impedance terms, which include not only real positive and imaginary terms but also the negative
terms. The concept of the power flow path is introduced to explain all the possible power flow
paths in a system. A negative reflected impedance term is manipulated to design a system with
power delivery not constrained by the maximum power transfer theorem. The concepts presented
in this chapter are derived analytically, and the developed system is validated using simulation and
experimental tools.
Chapter 6 seeks to explore various impedance matching systems for generating inde-
pendent data and power transfer resonance frequencies. A system design complexity reduces with a
tunableindependentresonancesystemcomparedtoasystemwithaseparatecommunicationlinkfor
data transfer. A center-tapped single transmitter coil with a complex arrangement of capacitance
is experimentally found to provide the desired functionality.
Chapter 7 presents literature survey on the electric fields of a coil used in WPT
systems. The work develops a circuital perspective of the fields. The fields are analyzed using the
fundamentals of electromagnetic theory, simulation, and measurement tools. Measurements show
3
the existence of axial fields with magnitudes comparable to parallel fields. Comments are made on
the consequences of ignoring the axial electric fields on the field analysis.
Chapter 8 investigates the passive wireless electrodes design. It pursues the design
of a passive wireless stimulator system that provides a biphasic current waveform for an application
with variable load. A passive wireless stimulator with a half-wave rectifier provides an output
waveform which is monophasic. A system derived from the concepts of modulation, rectification,
andfilteringprovidesaload-independentasymmetricbiphasicwaveformtodeliveracharge-balanced
current pulse to an electrode.
Chapters9and10explorethepossibilityofdesigninganelectricalstimulationsystem
that can manipulate the properties of an electrochemical system. The available design variables for
electrical stimulation, such as different waveforms, sources, and connection types do not alter the
propertiesofanelectrochemicalsystem. Thetwochaptersexplorethepossibilityofmanipulatingthe
capacitive conduction (Chapter 7) using non-foster circuits and monophasic like gradient generation
(Chapter 8) using active components, without compromising the charge balance of the system.
4
Chapter 2
Analysis and Design of a 3-Coil Wireless
Power Transmission System for
Biomedical Applications
Abstract
Wireless power transfer (WPT) is a practical and widely-used method to power various implantable
devices. Commonly the implanted receiver must be small, often on the order of millimeter, which
poses significant design challenges. In this work, a technique to improve the performance of sys-
tems with size(inductance)-limited implanted receiver coil is explored. Conventionally, only mutual
coupling between coils is used to optimize performance, which constrains the layout/geometry and
choice of coils. In the proposed system, mutual coupling, mutual capacitance and relative polarity
can all be used, thereby reducing the constraints on coil layouts. Performance is further enhanced by
5
two additional techniques that maximize the reflected impedance between the receiver coils. Three
designs (2-coil, conventional 3-coil and proposed 3-coil) are implemented with a 35mm-diameter
receiver coil and their performance is measured at 5 MHz with a 1k
load resistance. The efficiency
of these designs is measured at varying distances (20 to 60 mm) between transmitter and receiver.
The efficiency of the proposed 3-coil system at 50 mm separation is 40% while the implemented con-
ventional 3-coil and the 2-coil systems are each less than 10%. Last, the advantage of the proposed
strategy in terms of receiver coil current and load tolerance is discussed.
2.1 Introduction
Progress in biomedical implants has enabled in recent years unprecedented devices
for health monitoring, treatments of diseases and prosthetics. Advances in enabling technology for
implants (semiconductor industry, packaging, bio-compatible materials etc.) have played a signif-
icant role in rapidly expanding the development and adoption of biomedical implantable devices.
With this growth, Wireless Power Transfer (WPT) has become a critical enabling component, since
implants must often be charged from devices outside the human body. WPT removes the need
for implantable batteries or cabling requirements, making biomedical implants more practical[6, 7].
Besides biomedical implants [1–4, 8], WPT has found application in the fields of electric vehicles
battery charging [9–12] and communication [13, 14] to name a few, with more applications rapidly
emerging thanks to the appeal of charging wirelessly and conveniently.
WPT is commonly implemented using two inductively coupled coils/antennas [6].
In WPT systems, a capacitor is generally used to reduce the reactive power stored in the system by
compensating for the inductive coil reactance [15, 16]. The reactance does not contribute to power
transfer and, therefore, reducing it leads to a better power factor in the system [10]. Improved
6
coupling and load tolerance is often achieved using more than two inductive coils/antennas [1–4, 17]
and impedance matching of the load [8, 18–22] is employed extensively. Load matching can be
achieved using additional passive/active components [8, 18–22] or using 3-coil or 4-coil systems [1–
4, 23, 24]. The ultimate goal of the WPT system is to achieve the required power transfer to a given
load with maximum efficiency [25, 26].
WPTsystemsforbiomedicalimplantshaveadditionalconstraints: theymustcomply
with electromagnetic safety standards (such as that of complying with the maximum allowable
Specific Absorption Rate (SAR)[27]); they must be biocompatible; and have often specific longevity
requirements [28–31]. Both the 2-coil[8, 18, 32] and 3-coil[2] designs have been successfully employed
in biomedical applications: the advantages of using a 3-coil system over a 2-coil system are generally
better misalignment insensitivity, coupling enhancement, lower inducedfields in the body andbetter
bandwidth[1, 2, 11, 33, 34].
The size of the WPT system for biomedical implants is a critical design variable,
as the available area is often very limited [35–37]. Additionally, it has been demonstrated that a
larger size increases the risk of tissue inflammation, cell damage [38, 39], and discomfort to the
patient. These challenges associated with the design of WPT systems for biomedical implants are
the primary motivation of this work.
Summarizing, theoveralldesigngoalsforWPTforbiomedicalimplantsandtherefore
the goals considered in this manuscript are: small size(inductance) of the coil implanted in the body
(Goal
1
), low loss in the receiver (Goal
2
) and high efficiency and power delivery. There are several
popular designs of wireless power transfer systems for biomedical implants available in literature
[1, 2, 4]. To effectively achieve the stated goals in a 3-coil WPT system, circuit-theory based design
strategies are discussed in this work. The performance of the designs in [1, 2], which have two coils
7
Figure 2.1: Schematic of a traditional 2-coil Wireless Power Transfer (WPT) system.
implanted in the body, will be compared with the systems devised through the design strategies
outlined here. In order to pursue the best load matching, in this work we employ two additional
degrees of freedom to maximize the reflected impedance for a given receiver coil size (inductance):
1) the relative voltage polarity of the two receiver coils (given by dot convention) and 2) a mutual
capacitor, Cm,(which in addition to improving the system performance by reducing the complex
power, is also used to tune and match the impedance of the receiver for maximum power transfer).
This simplifies the design process of the 3-coil WPT systems significantly since optimizing the
number of turns of the receiving coil is not required.
2.2 Brief notes on Conventional 2-coil and 3-coil Wireless Power
Transfer systems
2.2.1 Conventional 2-coil WPT system
A conventional two-coil(2Coil) WPT system consists of two inductively coupled
coils, one connected to the transmitter and another to the receiver. The coupling coefficient K
12
of the two coils indicates the ratio of magnetic field density in the load (2Coil
2
) and transmit
8
(2Coil
1
) coils; a schematic view of the system with a power source at the transmitter, load at the
receiver and compensating capacitors (in the resonance condition, expressed by Eqn. 2:1), is shown
in Fig. 2:1. The theory of a 2Coil WPT system can be explained using matrix theory and reflected
impedance theory [1–4]. Kirchhoff’s voltage law (KVL) equations for a 2Coil system can be written
in matrix form, as shown in Eqn. 2:2. The determinant of the impedance matrix Z, when expressed
in canonical form, can be used to obtain the reflected impedance from 2Coil
2
to 2Coil
1
, as shown in
Eqn. 2:3. Compared to the explanation offered in [1–4], the various impedances of the system can
be derived from the determinant of the matrix and the system performance is analyzed using matrix
theory. Following the approach in [1–4], we can write Eqn. 2:1 to 2:4, where R
1
is the parasitic
resistance of 2Coil
1
, R
2
is the parasitic resistance of 2Coil
2
, R
ref
is the reflected impedance from
2Coil
2
to 2Coil
1
, L
12
= K
12
p
L
1
L
2
is the mutual inductance between the coils and i
1
;i
2
are the
currents flowing through 2Coil
1
; 2Coil
2
, respectively.
The performance parameters of the design considered in this work are: 1) Power
Delivered to the Load (PDL) and 2) Power Transfer Efficiency (PTE) , which is defined as the
ratio of PDL to input power under resonance condition. The reflected impedance parameters are
used to define PTE and PDL and analyze the effect of the parameters on design goals (Goal
1
,
Goal
2
). For the 2Coil system, is given by Eqn. 2:4 [1–4]:
1
j!C
1
=j!L
1
;
1
j!C
2
=j!L
2
(2.1)
V =ZI
(2.2)
2
6
6
4
V
s
0
3
7
7
5
=
2
6
6
4
R
1
jwL
12
jwL
12
R
2
+R
L
3
7
7
5
2
6
6
4
i
1
i
2
3
7
7
5
9
det(Z) =Z
1
Z
2
; Z
1
=R
1
+R
ref
; Z
2
=R
2
+R
L
R
ref
=
w
2
L
2
12
R
2
+R
L
(2.3)

2coil
=
ji
2
j
2
R
L
V
s
ji
1
j
(2.4)
Cramer’s rule can be applied to solve impedance matrix equation (Eqn. 2:3) to find values ofi
1
and
i
2
. Eqn. 2:4 can be written in terms of reflected impedance R
ref
, as follows:

2coil
=
R
ref
R
1
+R
ref
R
L
R
2
+R
L
(2.5)
The total system PTE of 2Coil can therefore be expressed as a product of two terms: PTE of
2Coil
1
(
2coil
1
) and PTE of 2Coil
2
(
2coil
2
), as given by Eqn. 2:6 [1–4]:

2coil
=
2coil
1

2coil
2
(2.6)
Similarly, the definition of PDL for 2Coil system can be expressed in terms of R
ref
[1–4]:
PDL
2coil
=P
in

2coil
(2.7)
PDL
2coil
=V
2
s
R
ref
(R
1
+R
ref
)
2
R
L
R
2
+R
L
(2.8)
PDLcanalsobecalculatedbymeasuringthegain(
Vout
V
in
)ofthesystemfrom2-portnetworkparameters[1,
4]. Given thatthequalityfactorof thecoilsin Fig. 2:1canbewritten asQ
1
=
!L
1
R
1
andQ
2
=
!L
2
R
2
+R
L
,
substituting Q
1
;Q
2
and L
12
=K
12
p
L
1
L
2
in the
2coil
, Eqn. 2:5 can be rewritten in a form similar
to [1–4]:

2coil
=
K
2
12
Q
1
Q
2
1 +K
2
12
Q
1
Q
2
R
L
R
2
+R
L
(2.9)
10
0 0:1 0:2 0:3
0
0:2
0:4
0:6
0:8
1
Coupling(K
12
)
Efficiency

2Coil

2Coil
=
2CoilRX
large K
12
(Saturated)

2Coil
=
2CoilTX
small K
12
( / K
2
12
)
Figure 2.2:
2Coil
Vs:K
12
for a 2 coil system withL
1
=L
2
= 2H,R
1
=R
2
= 1
, RL = 100
,
f = 5MHz.
The following observations about the 2 coil system can be made with specific con-
sideration to biomedical applications:
1. IfR
L
>>R
2
,
2coil
2
is close to unity and no power is dissipated in the receiver coil of the system.
This ensures that the power loss in the receiver coils implanted in the body is negligible. This
condition also reduces PDL.
2. SinceR
ref
is inversely proportional toR
L
(Eqn. 2:3), a higher value ofR
L
(which ensures higher

2coil
2
) reduces the
2coil
1
. This results in poor
2coil
and increased power loss in the 2Coil
1
. This
issue can be resolved using the three-coil system and is addressed in the next section.
3. The coupling coefficient K
12
is function of the dimensions of 2Coil
2
and 2Coil
1
.
Fig. 2:2showstheplotof
2Coil
asafunctionofK
12
foratypicalembodimentofatwo
coil WPT system characterized by L
1
= L
2
= 2H;R
1
= R
2
= 1
;R
L
= 100
;f = 5MHz. The
PTE() vs. K
12
plot for a typical WPT has the similar trend. Noting 2Coil
1
is the transmitter(TX)
and 2Coil
2
is receiver(RX), we can write that
2Coil
1
=
2Coil
TX
and
2Coil
2
=
2Coil
RX
. In the
design of a 2Coil system,
2Coil
RX
is constant and does not vary with the distance between the
coils and it is
2Coil
TX
which varies with the distance between the coils. From Fig. 2:2, it can be
11
concluded that the receiver efficiency (implanted coil 2Coil
2
) can be thought of as the saturation
efficiency at highK
12
(which is found for small distances between coils). The efficiency of the system
at lowK
12
is limited by the
2Coil
TX
, which has square dependency on the K
12
for lowK
12
values.
The secondary side of the two-coil system can be also connected in parallel. The
efficiency of secondary of the parallel connected coil is given by [40]:

2Coil
2
Parallel
=
R
L
R
L
+R
s
+
RsR
2
L
!
2
L
2
2

2Coil
2
Series
=
R
L
R
L
+R
s
AsL
2
becomes small, which is typical for a biomedical implant, for a given! &R
L
,
2Coil
2
(Parallel)
is severely limited [40]. Parallel resonance secondary has better reflected impedance compared
to the series connected receiver, but its receiver efficiency is limited. For example, for the 2Coil
system design considered in this paper, L
2
= 1H;R
2
= 0:5
;f = 5MHz;
2Coil
2
(Parallel)
= 0:56
whereas
2Coil
2
(Series)
= 0:99. For this reason, in this work, the series resonance configuration of
the secondary for the two-coil system is considered and its overall efficiency improved using the
three-coil system.
2.2.2 3-coil WPT system
A three-coil(3Coil) WPT system consists of three inductively coupled coils; one
coil is connected to the transmitter and two coils are used at the receiver end [2]. The coupling
coefficients (K
12
and K
23
) and the physical layout and schematic are shown in Fig. 2:3. The
additional coil used at the receiver, termed secondary coil(3Coil
2
) is responsible for enhancing the
PTE of the system under high R
L
conditions. The operation of the 3Coil WPT system can be
also understood using matrix theory and reflected impedance theory [1–4]. Kirchhoff’s voltage law
12
Figure 2.3: Schematic of a Conventional 3-coil Wireless Power Transfer (WPT) system(3Coil)[1–
4].
(KVL) equations for the resonant(Eqn. 2.10) 3Coil system, written in matrix form, lead to the Z
matrix whose determinant can be used to obtain the two reflected impedances R
ref1
,R
ref2
of the
3Coil system, which are given in Eqn. 2:11 [11]:
1
j!C
1
=j!L
1
;
1
j!C
2
=j!L
2
;
1
j!C
3
=j!L
3
(2.10)
R
ref1
=
w
2
L
2
12
R
2
+
w
2
L
2
23
R
3
+R
L
; R
ref2
=
w
2
L
2
23
R
3
+R
L
(2.11)
where R
1
is the parasitic resistance of 3Coil
1
, R
2
is the parasitic resistance of 3Coil
2
, R
3
is the
parasitic resistance of 3Coil
3
. R
ref1
is the reflected impedance from 3Coil
2
to 3Coil
1
and R
ref2
is
the reflected impedance from 3Coil
3
to 3Coil
2
. The mutual inductances between the coils L
12
=
K
12
p
L
1
L
2
; L
23
= K
23
p
L
2
L
3
are the result of the coupling K
12
;K
23
between the coils, while
i
1
; i
2
; i
3
are the currents flowing through 3Coil
1
; 3Coil
2
; 3Coil
3
respectively. Following a similar
analysis to that of the 2 coil system, the equation for the PTE can be written in terms of reflected
13
impedances R
ref1
& R
ref2
as follows:

3coil
=
R
ref1
R
1
+R
ref1
R
ref2
R
2
+R
ref2
R
L
R
3
+R
L
(2.12)
The total efficiency of the 3Coil system can be expressed as a product of the efficiencies of 3Coil
1
,
3Coil
2
and 3Coil
3
, as given by Eqn. 2:13:

3coil
=
3Coil
1

3Coil
2

3coil
3
(2.13)
where,
3coil
1
,
3coil
2
and
3coil
3
are the efficiencies of 3Coil
1
, 3Coil
2
and 3Coil
3
respectively. Simi-
larly, the PDL for the 3Coil system can be expressed in terms of R
ref1
, R
ref2
[1–4]:
PDL
3Coil
=V
2
s
R
ref1
(R
1
+R
ref1
)
2
R
ref2
R
2
+R
ref2
R
L
R
3
+R
L
(2.14)
The following observations about the 3 coil system can be made with specific consideration to
biomedical applications: 1. If R
L
>> R
3
,
3coil
3
is close to 1 and no power is dissipated in the
3Coil
3
of the system. However, this does not guarantee that the power loss in the receiver coils
implanted in the body is minimized. Nonetheless, this condition does not imply sufficiently high
PDL
2. R
ref2
is directly proportional to the L
2
& L
3
. High inductance (obtained through the length
of 3Coil
2
+ 3Coil
3
), results in high R
ref2
and high
3coil
2
. Large R
ref2
(>R
2
) and R
L
(>R
3
) are
sufficient condition to reduce the power dissipation in the implanted coils of 3Coil;
3. The main functionality of 3Coil
2
is to invert and scale the contribution of the load coil
(3Coil
3
) on the reflected impedance at 3Coil
1
. Comparing the R
ref
(Eqn. 2:3) of 2Coil system
with R
ref1
(Eqn. 2:11) of 3Coil system, the above mentioned functionality of the 3Coil
2
can be
14
confirmed (i.e. R
L
!
!
2
L
2
23
R
L
+R
3
). This is referred to as the impedance matching capability of 3Coil
system.
4. The general plot of
3Coil
as a function ofK
12
has the trend shown in Fig. 2:2. Noting that 3Coil
1
is the transmitter(TX) and 3Coil
2
& 3Coil
3
form the receiver(RX), we can write
3Coil
1
=
3Coil
TX
and
3Coil
2

3Coil
3
=
3Coil
RX
.
2.3 Performance degradation in conventional 2-coil and 3-coil sys-
tem as the receiver size reduces
The design of the 3 coil wireless power transfer system involves placing the addi-
tional secondary coil closer to the coil with low Q [41]. In biomedical applications [2] of the 3Coil
system, two coils are located at the receiver side and one coil is at the transmitter. As the size of
the two receiver coils reduces (either in terms of diameter or number of turns), L
2
, L
3
and their
mutual inductance L
23
reduces. This results in reduced R
ref2
; as a result,
3coil
2
(Eqn. 2:12 and
Eqn. 2:13) decreases and losses in the implanted coil increase. Further, R
ref1
, which is inversely
proportional to R
ref2
, either increases or saturates depending on the value of R
ref2
. The efficiency
of system
3coil
will be limited by
3coil
2
: since R
ref2
decreases and R
ref1
either increases or satu-
rates, PDL
3coil
(Eqn. 2:14) also decreases as the size reduces. Thus, as the size of the receiver coils
in the 3Coil decreases, PTE and PDL of the entire system decrease and losses in the implanted
coils increase. This provides a challenge to design a system with good PTE and PDL. Similarly,
by referring to Eqn. 2:3 and Eqn. 2:5, PTE and R
ref
of the 2Coil system reduces as the size of
2Coil
2
(L
2
) reduces. It can also be concluded that, for the 3Coil system with small receiver coils
15
(lowL
2
andL
3
), performance degradation can be linked to reduction inR
ref2
. Thus, this work pro-
poses a technique to maximizeR
ref2
for a 3-coil system to achieve good PTE and PDL performance
for a small receiver 3-coil system.
The effects of frequency of operation on the human body is explained in [1]. The
choice of 700kHz in [1] and 13 MHz in [2] is made considering the Q factor of the coils used, following
an optimization process. In this work, we chose the frequency of 5 MHz as the copper wire of AWG
20 exhibited a Q=150 for L=5H. We have also considered a load resistance R
L
= 1k
. In this
work, and unlike [1], no further optimization of coils was undertaken to chose a frequency with
higher Q as high Q is not necessary to obtain higher PTE with the approach presented here.
There is no established standard for the design of WPT systems for biomedical
implants but the general designs in the literature include transmitter coil larger than the implanted
receiver coil with dimensions in tens of millimeter[1–4, 27, 42]. The biomedical implant systems
are generally designed to efficiently deliver power of the order of 100mW(50mW-300mW) to the
receiver[2].
2.4 ENHANCING THE PERFORMANCE OF 3-COIL SYSTEM
AS THE RECEIVER SIZE REDUCES
The resonant condition for the conventional three-coil system[1–4] is provided in
Eqn. 2:10. In this work, we consider a different resonant condition: while the layout of the proposed
3-coil system (3Coil
p
) remains the same as Fig. 2:3, the resonance condition is changed to Eqn. 2:15
instead of Eqn. 2:10. This results in a new schematic equivalent of the 3Coil
p
system shown in
Fig. 2:4 (note that dot convention is used to denote the voltage polarity of the coils).
16
Figure 2.4: (a). Schematic of the proposed efficient and compact 3-coil system(3Coil
p
). To
maximize the R
ref2
of small receiver size 3-coil system, two techniques are adopted. 1)L
2
= L
3
and 2)
1
!C2
=
1
!C3
= 0 along with the appropriate receiver system’s relative coil polarity required
to increase the R
ref2p
. b) RX system’s relative coil polarity that leads to the reduction of R
ref2p
.
Theadvantageofthissystemisunderstoodusingmatrixtheoryandreflectedimpedance
theory [1–4]. The impedance matrix equation for the modified resonant scheme is provided in
Eqn. 2:16: comparedtotheZmatrixoftheconventional 3Coil[1–4],theZmatrixof 3Coil
p
(Eqn. 2:16)
includes the impedance of capacitorC
m
used for creating a resonance condition at the receiver coils.
From the determinant of the resonant Z matrix (impedance matrix) when expressed in the canoni-
cal form, we can obtain the two reflected impedances R
ref1p
;R
ref2p
for the proposed 3-coil system
3Coil
p
(Eqn. 2:18). The main advantage of this system is that it increases the effective mutual
impedance between the 3Coil
2p
and 3Coil
3p
; the equivalent L
23p
of the system increases, as shown
in Eqn. 2:17. Since we have noted in the previous section that, as the size of the receiver in the 3-coil
system reduces,R
ref2
reduces, adopting this new resonant condition helps us maximizeR
ref2
of the
small receiver in the 3-coil system. By increasing the R
ref2p
, the PTE and PDL can be increased
and the losses in the implanted coil can be reduced. Both 3 Coil systems under consideration
(3Coil; 3Coil
p
) have the same set of variables to describe the operation; in order to differentiate
17
the variables of the two systems, the proposed 3 Coil system uses subscript
p
for all the variables
(for example: R
ref2
is for 3Coil system and R
ref2p
is for 3Coil
p
system).
1
j!C
1
=j!L
1
;
1
j!C
m
+
1
j!C
2
=j!L
2
1
j!C
m
+
1
j!C
3
=j!L
3
(2.15)
V =ZI (2.16)
jwL
23
!j(!L
23
+
1
!C
m
) (2.17)
det(Z) =Z
1
Z
2
Z
3
Z
1
=R
1
+R
ref1p
; Z
2
=R
2
+R
ref2p
; Z
3
=R
3
+R
L
R
ref1p
=
!
2
L
2
12
R
2
+
(!L
23
+
1
!Cm
)
2
R
3
+R
L
;R
ref2p
=
(!L
23
+
1
!Cm
)
2
R
3
+R
L
(2.18)
In Eqn. 2:18, R
1
is parasitic resistance of 3Coil
1p
, R
2
is parasitic resistance of 3Coil
2p
and R
3
is
parasitic resistance of 3Coil
3p
. R
ref1p
is reflected impedance from 3Coil
2p
to 3Coil
1p
andR
ref2p
is
reflected impedance from 3Coil
3p
to 3Coil
2p
. R
L
is instead the load resistance. Following the anal-
ysis of
3Coil
system, PTE and PDL for the
3Coilp
system can be defined as in Eqn. 2:12, Eqn. 2:13
and Eqn. 2:14 with updated definition ofR
ref2p
. The notation
p
is adapted for the proposed system;

3coil
1p
,
3coil
2p
and
3coil
3p
are the efficiency of 3Coil
1p
, 3Coil
2p
, 3Coil
2p
respectively.
For the proposed 3 coil (3coil
p
) system, we can make the following observations:
1. If R
L
>> R
3
,
3coil
3p
is close to 1 and no power is dissipated in the load coil of the system. .
However, this does not guarantee that power loss in the secondary (3coil
2p
) coil implanted in the
body is minimized;
2. It is worth noting that R
ref1p
and R
ref2p
of the 3Coil
p
system in Eqn. 2:18 are different from
those in Eqn. 2:11. !C
m
which helps increase the R
ref2p
, results in decrease of R
ref1p
. A decrease
18
of R
ref1p
will result in reduction of
3Coil
1p
. That is, mutual capacitor at the receiver, reduces the
efficiency of 3Coil
1p
which is used at the transmitter. This calls for efficient design of transmit coil.
This issue is addressed in section 6.
3. In the conventional 3-coil (3Coil) system, only the mutual impedance between the two receiver
coils was used for determination ofR
ref2
and the the PTE and PDL of the 3 coil system(Eqn. 2:11).
Intheproposedthree-coil(3Coil
p
)system,alltheimpedancesofthereceivercontributetotheR
ref2p
(Eqn. 2:19), PTE and PDL. This effectively enhances the reflected impedance for a given receiver
system enabling a smaller and more compact design.
R
ref2p
=
!
2
L
2
23
+
1
!
2
C
2
m
+!
2
L
2
L
23
+!
2
L
3
L
23
R
3
+R
L
(2.19)
As can be noted from Eqn. 2:19,L
2
;L
3
;C
m
;L
m
contribute(if
1
Cm
=!
2
L
2
=!
2
L
3
) to theR
ref2p
of
the 3Coil
p
system. This leads to effective utilization of all the impedance sources implanted in the
body.
4. It should be noted that the relative polarity of the proposed 3coil (3Coil
p
) system (that is, the
orderofconnectedendsoftheinductors)nowbecomesmoreimportantcomparedtotheconventional
3Coil system. If the coils are reversed(as indicated by the adjusted dot locations in Fig. 2:4.(b)),
thenR
ref2p
reduces like in Eqn. 2:20 instead of increasing like in Eqn. 2:18. Therefore, coil polarity
should be configured as shown in Fig. 2:4.(a) for maximum reflected impedance.
R
ref2p
=
(!L
23

1
!Cm
)
2
R
3
+R
L
(2.20)
In this paper, two additional circuit techniques are adopted to maximize R
ref2p
for a given values
ofL
2
andL
3
and to meetGoal
1
andGoal
2
of this paper. The first technique is related to splitting
the given length of wire as L
2
and L
3
equally, to achieve efficient usage of cable length implanted
19
in the body(Goal
1
)(covered in section 5). The second circuit technique leads to
1
!C
2
=
1
!C
3
= 0 for
the circuit shown in Fig. 2:4; this also results in higher R
ref2p
and helps us achieve Goal
2
(covered
in Section 6).
2.5 Goal
1
EFFICIENT USE OF WIRE TO ENHANCE THE R
ref2
F
SMALLER RECEIVER 3-COIL SYSTEM L
2
=L
3
2.5.1 Circuit Technique Description
It is noted from Eqn. 2:11-2:13 that, by using higherL
2
andL
3
, we can increase the
PTE of the secondary 3Coil
2
and load coils 3Coil
3
and reduce the power dissipation in the receiver
system. However, it is always convenient to use smaller implant and shorter wire inside the human
body. Although the inductance that can be achieved for a coil depends on the process used to make
the inductor, on a first approximation we can consider the inductance of the coil is proportional to
the length of the wire. The coupling between two implanted coils K
23
of 3-coil system is function
of the diameter of coils: to maximize K
23
, diameters of two coils must be equal. Although, in this
work, a diameter of 35mm has been chosen for the implanted coils to compare with other reported
biomedical WPT systems [1, 2, 4], the proposed technique is independent of the diameter of the
coils used.
Given a chosen length of coil (fixed maximum inductance,L
max
), the procedure can
be summarized as follows:
L
2
+L
3
=L
max
maximize R
ref2
=
w
2
L
2
23
R
3
+R
L
=
w
2
K
2
23
L
2
L
3
R
3
+R
L
20
Figure2.5: (a) The equivalent schematic of the system used in [1](K
23
= 0:62). (b) The proposed
receiver system incorporating the equal split inductance(K
23p
= 0:84) along with mutual capaci-
tance and appropriate relative polarity. The two receiver systems shown in this figure are compared
using the same Tx. system(left).
0 0:1 0:2 0:3
0
0:2
0:4
0:6
0:8
1
Coupling(K
12
)
Efficiency
PTE: Rx.(Fig. 2:5.(a))
PTE: Rx.(Fig. 2:5.(b))
0
2
Gain (
Vout
V
in
)
Gain: Rx.(Fig. 2:5.(a))
Gain: Rx.(Fig. 2:5.(b))
Figure 2.6: Comparison of PTE and Gain of two systems in Fig. 2:5(Fig. 2:5a, representing [1]
and Fig. 2:5b, representing smaller and equal split inductance).
i:e maximize L
2
L
3
; Solution : L
2
=L
3
=
L
max
2
Themaximumreflectedimpedancefromthereceiverisobtainedwhentheinductance
L
2
and L
3
are equal.
21
600 650 700 750 800
0
10
20
30
40
Frequency(KHz)
Load Current I
L
(mA)
Rx.(Fig. 2:5.(a))
Rx.(Fig. 2:5.(b))
Figure2.7: Comparison of Frequency response of load current of two systems in Fig. 2:5(Fig. 2:5a,
representing [1] and Fig. 2:5b, representing smaller and equal split inductance).
2.5.2 Testing the technique: Comparison 1
As a first test, the implanted coils presented in [1] are considered here. In [1], to en-
hance the efficiency of the implanted coils(to increaseR
ref2
), higherL
2
,L
3
,Q
2
at low frequency(700
kHz) are used. An optimization procedure was considered in [1] to find the values of implanted coil
parameters. The equivalent circuit diagram of the two implanted coils in[1] is shown in Fig. 2:5:(a)
(note that Q
2
=
!L
2
R
2
= 273). Reference [1] uses two implanted coils of smaller diameter (and
multilayer) but very high secondary coil inductance(L
2
) and low load coil inductance(L
3
). Since
in this example only the efficiency of the implanted receiver coils(3Coil
p2
; 3Coil
p3
) is compared,
choice of the transmitter coil does not affect the PTE and PDL comparison. Hence, for comparison
purpose, a 20H transmitter used in Fig. 2:5. It should also be noted that, while the efficient use
of wires implanted inside the body was not the design requirement in [1], the resulting system is
characterized by a larger inductance of the implanted coil of 36H, with corresponding longer wire.
The receiver system of [1](reproduced here as Fig. 2:5.(a)) is compared against the smaller receiver
system shown in Fig. 2:5.(b)(note that Q
2p
= 145). The transmitter used in this smaller receiver
22
design is the same; the Q
2
of this system is smaller by 45%, and the values ofL
2
andL
3
are about
10% of the values used in Fig. 2:5(a). Both circuits are compared at the same frequency and load
and transmitter conditions. The PTE, PDL and the frequency response of the two systems under
comparison are shown in Fig. 2:6 and Fig. 2:7 respectively. It can be concluded that, though L
2
,
L
3
and Q
2
of the Fig. 2:5.(b) is smaller than Fig. 2:5.(a), it achieves same PDL, PTE and fre-
quency performances. This is because of maximization ofR
ref2
achieved usingL
2
=L
3
and mutual
coupling capacitor C
m
. This comparison is also summarized in Table 2.1
2.6 Goal
2
Reducing Power dissipation in the implanted receiver:
Second technique to enhance the R
ref2
of smaller receiver 3-coil
system (
1
!C
2
=
1
!C
3
= 0)
2.6.1 Circuit Technique Description
Theimplantcoils(receiversection)ofconventional3-coilsystemshaveefficiencygiven
by Eqn. 2:11-2:13. It can be rewritten as
RX
3coil
as shown in Eqn. 2:21. Similarly,
RX
3coilp
is the
efficiency of the receiver section of the proposed 3-coil system, which is given in Eqn. 2:22

RX
3coil
=
w
2
L
2
23
R
3
+R
L
R
2
+
w
2
L
2
23
R
3
+R
L

R
L
R
3
+R
L
(2.21)

RX
3coilp
=
(!L
23
+
1
!Cm
)
2
R
3
+R
L
R
2
+
(!L
23
+
1
!Cm
)
2
R
3
+R
L

R
L
R
3
+R
L
(2.22)
23
Figure 2.8: (a). Equivalent circuit diagram of the system used in [2]. The system is tested for its
losses in the receiver implanted in the body. (b). The schematic of the proposed receiver system.
The two receiver systems shown in this figure are compared using the same Tx. system(left).
To minimize the losses in the receiver system,
RX
3coilp
has to be maximized. To maximize the

RX
3coilp
,
1
!Cm
has to be maximized. This condition leads to
1
!C
2
=
1
!C
3
= 0 in Eqn. 2:15 of the
proposed 3-coil system.
2.6.2 Testing the technique: Comparison 2
As a second test, implanted coils from [2] are considered for the redesign. In [2](given
asL
3
andL
4
for a 3 coil system in TableI), a conventional 3 coil system is considered for the design.
In [2], to enhance the efficiency of the implanted coils(to increase R
ref2
), higher frequency(13.56
MHz), Q
2
and low L
2
, L
3
are used. The equivalent circuit diagram of the system of[2] is shown in
Fig. 2:8.(a). The approach considers two implanted coils of equal inductance(L
2
) and (L
3
) and the
obtained receiver efficiency is 0.75. The goal of this section is to increase this implanted receiver
efficiency to reduce losses and demonstrate the functionality of mutual capacitance(C
m
) in the
proposed system.
It is to be noted that neither reduction of power dissipation of the coils implanted in
the body nor the efficient usage of coils implanted in the body was the design requirement in [1]. As
24
a result,K
23
= 0:19 is chosen to reduceR
ref
2
. This design choice may increase the
3Coil
1
although
this may come at the expense of higher power dissipation in the body; the resulting system in [2],
albeit an efficient one, has 25% of constant loss in the coils implanted in the body.
The receiver system of Fig. 2:8.(a) is compared against the receiver system shown in
Fig. 2:8.(b). The coils used in this design are same; the only difference is that a resonant scheme
with
1
!C
2
=
1
!C
3
= 0 (Eqn. 2:15) is used to minimize the losses of the implanted system. Both
the circuits are compared at the same frequency, load and transmitter conditions. The PTE and
PDL(Gain) of the two systems are shown in Fig. 2:9.
The plots of PTE (Fig. 2:9) of the two systems (Fig. 2:8.(a), representing [2] and
Fig. 2:8.(b), representing
1
!C
2
=
1
!C
3
= 0) under consideration indicate that, the receiver efficiency
ofthesystem(Fig. 2:8.(b))withmutualcapacitanceis0.95whilethereceiverefficiencyofthesystem
without mutual capacitance is 0.75. The transmitter efficiency of the receiver enhanced system is
reduced (Fig. 2:9), but can be increased by increasing the mutual impedance with the transmitter.
The plots of PDL(Gain) (Fig. 2:9) of the two systems under consideration indicate the advantages
of the system (Fig. 2:8.(b)) with mutual capacitance at the receiver at higherK
12
. This comparison
is also summarized in Table.2.1.
Table 2.1: Table to summarize results of two comparison exercises and the advantages of the
proposed techniques as compared with the systems in [1] and [2].
System
RX
L
2
; L
3
Q
2
Comments
[1](Fig. 2:5(a),
Rx.only)
0.91 33uH,
3uH
273 Lower L
2
; L
3
and
Q
2
for a given PTE,
PDL and frequency
response.
Proposed
(Fig. 2:5(b))
0.91 0.5uH,
0.5uH
145
[2](Fig. 2:8(a)) 0.75 0.4uH,
0.4uH
179
C
m
increases the
receiver efficiency Proposed
(Fig. 2:8(b))
0.96 0.4uH,
0.4uH
179
25
0 0:1 0:2 0:3
0
0:2
0:4
0:6
0:8
1
Coupling(K
12
)
Efficiency
PTE: Rx.(Fig. 2:11.(a))
PTE: Rx.(Fig. 2:11.(b))
0
2
4
6
8
10
Gain (
Vout
V
in
)
Gain: Rx.(Fig. 2:11.(a))
Gain: Rx.(Fig. 2:11.(b))
Figure 2.9: Comparison of PTE and Gain of systems using two different receiver configurations
in Fig. 2:8 (Fig. 2:8.(a) representing [2] and Fig. 2:8.(b) representing C
m
enhanced system).
2.7 Design Procedure and advantages of proposed 3 Coil system
over conventional 3 Coil system.
2.7.1 Design Procedure
The paper introduces two circuit concepts to enhance the system performance in
the proposed three coil system 3Coil
p
. The equal split of two coils at the receiver and common
capacitor enhance the reflected impedance of the receiver which enables an efficient wireless power
transfer for small receivers. This results in efficient use of wires in the body and reduces the power
dissipation of the coils in the receiver.
The proposed design procedure begins with the observation in [41] that, to increase
the efficiency of the 3 coil system, I
1
; I
2
needs to be reduced for a given I
3
. That is, both
I
1
I
3
;
I
2
I
3
should be minimized. The term
I
1
I
3
relates to the efficiency of the transmitter and the term
I
2
I
3
relates
to the efficiency of the receiver. The conventional and proposed 3 coil systems have the following
ratios
26
Figure2.10: (a). Schematic of the implemented conventional 3 Coil system. (b). Schematic of the
implemented proposed 3 Coil system. The two receiver systems shown in this figure are compared
using the same Tx. system(left).
I
1
I
3
=
R
2
(R
3
+R
L
) + (!M
23
)
2
!M
12
(!M
23
)
;
I
2
I
3
=
(R
3
+R
L
)
j!M
23
(2.23)
I
1p
I
3p
=
R
2
(R
3
+R
L
) + (!M
23
+
1
!Cm
)
2
!M
12
(!M
23
+
1
j!Cm
)
I
2p
I
3p
=
(R
3
+R
L
)
j!M
23
+
1
j!Cm
(2.24)
We note that, if the smaller receiver system is designed withR
2
(R
L
+R
3
) = 2!
2
M
2
23
,
then
I
1
I
3
remains unchanged if M
23
is doubled. That is, if the mentioned condition is satisfied,
doubling!M
23
will not effect the efficiency of the transmitter. This approximate doubling of!M
23
is achieved through the added conductive pathway linking the two receiver coils(with the addition
of mutual capacitance, C
m
).
To demonstrate the operation and advantages of the proposed system, a receiver sys-
tem with limited size(smallerM
23
) is designed and then, using the proposed technique, the efficiency
of the receiver is enhanced without compromising the transmitter efficiency. As an example, we have
27
5 10
2
0:1 0:15 0:15
0
5
10
15
20
25
30
35
40
Coupling K
12
Primary Current Ratio
I
1
I
3
I
1
I
3
- Conventional System with
I
2
I
3
= 40
I
1
I
3
- Proposed System with
I
2p
I
3p
= 17:4
0
0:5
1
PTE
PTE-Conventional 3Coil Design
PTE-Proposed 3Coil Design
Figure 2.11: The
I2p
I3p
is lesser than
I2
I3
of conventional system. It proves that, we can increase the
receiver performance without affecting the transmitter efficiency. At lower K
12
, PTE is limited by
the transmitter efficiency which is same for both the systems.
considered, R
L
= 1k
; R
2
=R
3
= 0:5
; R
1
= 1
,L
1
= 5H;L
2
=L
3
= 1H; f = 5MHz. This
accounts for all the conditions proposed in this work, that isL
2
=L
3
; R
L
>> R
3
; R
2
(R
L
+R
3
) =
2!
2
M
2
23
. The conditionR
2
(R
L
+R
3
) = 2!
2
M
2
23
leadsto smallerreceiversystem withpoor efficiency,
which will be enhanced(doubled) using the proposed system with
1
!C
2
=
1
!C
3
= 0 condition. The
system (schematic of the proposed receiver system shown in Fig. 2:10.(b) and schematic of the con-
ventional system shown in Fig. 2:10.(a)) is implemented experimentally and the results are provided
in the measurements section. The simulation results showing the design approach of reducing
I
2
I
3
by
keeping
I
1
I
3
almost fixed is shown in Fig. 2:11(it proves that we can increase the receiver performance
without affecting the transmitter efficiency).
2.7.2 Advantage 1: Tolerance to load changes
One of the main advantages of the conventional 3 coil system over the 2 coil system
(parallel secondary) is that its PTE is less sensitive to variation of load. The efficiency of the receiver
in the proposed 3 coil system is less sensitive to load variations compared to the conventional 3 coil
28
500 1;000 1;500 2;000
0
0:2
0:4
0:6
0:8
1
1:2
R
L
(
)
Efficiency (
RX
)
Conventional 3 coil design
Proposed 3 Coil system design
Figure 2.12: Comparison of load sensitivity of the efficiency of implanted systems designed using
conventional and proposed design techniques.
system. It is to be noted that while the conventional system achieves insensitivity by reducing
the R
2
[1](or higher Q2), the proposed system improves the insensitivity by increasing the mutual
coupling. The receiver efficiency of the conventional and the proposed 3 coil system for the designed
parameters is shown in Fig. 2:12. Following the same analysis, it can be noted that,
3CoilpRX
is
less sensitive to load compared to
3CoilRX
.
@(
RX3Coil
)
@R
L
=
!
2
M
2
23
R
2
(!
2
M
2
23
+R
2
R
L
)
2
(2.25)
@(
RX3Coilp
)
@R
L
=
(!M
23
+
1
!Cm
)
2
R
2
((!M
23
+
1
!Cm
)
2
+R
2
R
L
)
2
(2.26)
2.7.3 Advantage 2: Reducing currents in the secondary coil
The currents through the intermediate secondary coil of the 3 coil system should be
reduced for a given load to decrease the losses in the system [41]. The proposed and the conventional
system, for the given design parameters, are evaluated for the secondary coil current for different
coupling with the transmitter coil. The proposed system reduces the current through the secondary
29
0
5 10
2
0:1 0:15
0
0:1
0:2
0:3
0:4
0:5
Coupling (K
12
)
I
2
(mA)
I
2p
-Proposed 3Coil Design
I
2
-Conventional 3Coil Design
0
0:1
0:2
PDL (W)
PDL-Proposed 3Coil Design
PDL-Conventional 3Coil Design
Figure 2.13: Comparison of PDL(V
in
= 1) and secondary coil currents of proposed and conven-
tional design of 3 coil system. It can be noticed that, for a given PDL, the required value of I
2p
is
less than I
2
for all K
12
.
coil by enhancing the mutual impedance between the implanted coils as shown in Fig. 2:13. The
magnetic field is proportional to the current flowing through the coil and usually, for a single
antenna, electric field is proportional to the magnetic field. In the measurements section, it will
be shown that the proposed system achieves the same power delivery of the tradition 3 coil system
while achieving higher efficiency.
2.7.4 Load Current I
3
and I
3p
The simulated PDL(I
2
3
R
L
; I
2
3p
R
L
, for V
in
= 1) and current in Coil
2
and Coil
2p
for the conventional 3-coil(Fig. 2:10(a)) system and the proposed 3-coil(Fig. 2:10(b)) system, for a
different K
12
are shown in Fig. 2:13. To analyze the effect of mutual capacitance on the receiver
currents (I
3
; I
2
andI
3p
; I
2p
) for the systems under consideration, we solve the matrix in Eqn. 2:16
for I
2p
(similarly for I
2
) and rewrite the Eqn. 2:23 and 2:24 as Eqn. 2:27 (where, R
3t
= R
3
+R
L
).
Thus, it can be noticed in Fig. 2:13 that at highK
12
(the terms with!M
12
dominate inI
2
(andI
2p
)
and consequently, I
2
becomes equal to I
2p
), for a given I
2
(or I
2p
), the proposed 3-coil system has
30
higher load current (I
3p
) compared to the conventional 3-coil system (I
3
).
I
2
=
j!M
12
R
3t
R
1
R
2
R
3t
+!
2
M
2
23
R
1
+!
2
M
2
12
R
3t
I
2p
=
j!M
12
R
3t
R
1
R
2
R
3t
+ (!M
23
+
1
!Cm
)
2
R
1
+!
2
M
2
12
R
3t
I
3
=
I
2
(j!M
23
)
R
3t
; I
3p
=
I
2p
(j!M
23
+
1
j!Cm
)
R
3t
(2.27)
Conversely, for a given load current(fixed I
3
= I
3p
) or PDL, the required value of I
2p
is less than
the required value of I
2
(at lower K
12
, the terms with !M
23
and !M
23
+
1
!Cm
dominate in I
2
and
I
2p
respectively and
I
2p
I
2
=
!M
23
!M
23
+
1
!Cm
). This can be attributed to the increased mutual impedance
between the Coil
2p
and Coil
3p
for the proposed 3-coil system.
The maxima of the PDL in Fig. 2:13 occurs whenR
ref1
=R
1
for 3Coil andR
ref1p
=
R
1
for 3Coil
p
systems as given by Maximum Power Transfer Theorem(MPT). The PDL maxima
for the 3Coil
p
is higher than the PDL maxima of 3Coil and also occurs at slightly higherK
12
. It is
because, the C
m
which increases the R
ref2
, decrease the R
ref1
slightly. It is to be noted that, this
relation is also the consequence of the choice of relative coil polarity.
2.8 Experiments: Measurements and Results
The proposed three coil system 3Coil
p
is compared against a conventional 3 coil
system 3Coil and 2 coil system 2Coil. The measurement results are compared against simulation.
The side view and top view of the layout of the considered 3 coil system is shown in Fig. 2:14, while
the measurement setup is shown in Fig. 2:15. It is to be recalled that the layout of 3Coil & 3Coil
p
are same but the resonance condition is different. Two coil system 2Coil is formed by removing the
31
Figure 2.14: Layout of the Side view and top view of 3 Coil system in CST Design STUDIO. In
the top view, 3Coil
1
highlighted for differentiation. The diameter of the transmit and receive coils
are 70mm and 35mm respectively.
Figure 2.15: Photograph of the measurement setup showing TX coil at the left and RX setup at
the right. The diameter of the transmit and receive coils are 70mm and 35mm respectively.
3Coil
3
of the 3Coil system. The physical and electrical parameters of the coils used in experiments
are shown in Table 2:2 and Table 2:3 respectively.
Table 2.2: properties of the coils used
coil Coil Diameter(mm) No. Turns L(uH) Q AWG
Tx. 70 8 5 150 20
Sec. 35 8 1 70 20
Load 35 8 1 70 20
In the 3Coil
p
& 3Coil systems, L
2
= L
3
is maintained. Further, in the 3Coil
p
systems,
1
!C
2
=
1
!C
3
= 0 is maintained in the implementation. Finally, in the 3Coil
p
system, a
32
Table 2.3: circuit parameters of 3 systems under test
System L1(H) L2(H) L3(H) R
L
(k
) f(MHz)
2Coil 5 1 1 5
3Coil 5 1 1 1 5
3Coil
p
5 1 1 1 5
smaller receiver system is designed with R
2
(R
L
+R
3
) = 2!
2
M
2
23
, so that,
I
1
I
3
remains unchanged
if M
23
is doubled using the proposed design technique. The measurements are performed using
a VNA; S-Parameters from VNA are converted to Z-Parameters. The performance parameters of
interest( PTE (Eqn. 2:28) and PDL) are expressed using Z-Parameters([1–4]). Since it is difficult
to measure the exact source voltage(V
s
) for VNA measurements, measurement is made independent
of V
s
by measuring the gain instead. PDL is related to the voltage gain by Eqn. 2:29.
=
jZ
2
21
j
R
L
jZ
11
jcos(Phase(Z
11
))
; Gain =
jZ
21
j
jZ
11
j
(2.28)
PDL =
jV
2
2
j
2R
L
=
jZ
21
j
2
V
2
1
2R
L
jZ
11
j
2
=
Gain
2
V
2
1
2R
L
(2.29)
The PTE comparison (Fig. 2:16) shows that, for a small receiver system with large
R
L
,
3Coilp
>
3Coil
>
2Coil
for all the distances. Also,
3Coilp
at large distances(small K
12
) does
not fall below 3Coil. The PTE of the 3Coil at 20 cm separation is 0.4 whereas the PTE of the
3Coil
p
at 20 cm is 0.8. It can be concluded that, in the considered case, the 3Coil
p
has double
the PTE of 3Coil. The gain performance(Fig. 2:17) of the three coil system is better than the two
coil system at larger distances for higher loads and smaller coils. The common capacitor circuit
(3Coil
p
) performs better than the conventional three Coil (3Coil) system both in terms of efficiency
and gain for all the distances between transmitter and receiver.
33
0 20 40 60 80
0
0:2
0:4
0:6
0:8
1
Distance(mm)
Efficiency
3CoilExperimental
3CoilSimulation
2CoilExperimental
2CoilSimulation
3Coil
p
Experimental
3Coil
p
Simulation
Figure 2.16: Experimental and simulation results of PTE of three systems under comparison
0 20 40 60 80
0
5
10
15
20
25
Distance(mm)
Gain
3CoilExperimental
3CoilSimulation
2CoilExperimental
2CoilSimulation
3Coil
p
Experimental
3Coil
p
Simulation
Figure 2.17: Experimental and simulation results of Gain of three systems under comparison
2.9 Discussion
2.9.1 K
12
and C
m
for optimization of system Performance
In the conventional 3-coil(3Coil) system, mutual coupling between the two receiver
coilsK
23
isusedtooptimizethereflectedimpedanceR
ref2
toobtainthedesiredsystemperformance[1–
4]. The maximization of K
23
increases the receiver efficiency but decreases transmitter efficiency
34
and vice verse. This dependency of system performance onK
23
puts a constraint on the coil geom-
etry in the conventional 3-coil system. The system in [1] uses a larger(multi-layer) secondary coil
compared to load coil to achieveK
23
of 0.6. In the system in [2], additional spacing is used between
the two receiver coils to achieve a lower K
23
of 0.22. These geometries are difficult to implement
for a real compact implant receiver.
In this proposed 3-coil(3Coil
p
) work, the adopted architectural update leads to new
reflected impedance of the secondary R
ref2p
which not only depends on K
23
but also on mutual
capacitance(C
m
) and appropriate relative polarity. TheC
m
now have the same effect on the system
as the K
23
. This puts less constraints on the K
23
requirements and we can optimize the layout
of the implanted coils to meet additional requirements like smaller size(inductance) or any other
variables, like SAR[27, 42] requirements.
In this work, to demonstrate the advantage of the proposed technique, a receiver
coils with small inductance is considered. WPT System designed with conventional 3-coil system
approach, achieves a receiver efficiency of about 41% (
RX
)(as can be concluded from the Fig. 2:16
for a distance of 10mm). Whereas, for the same receiver coils, system designed with the proposed 3-
coil (3Coil
p
) system approach leads to higher(82%, Fig. 2:16) receiver efficiency as the enhancement
is obtained by appropriate C
m
and relative polarity.
2.9.2 Tissue effects on the system Performance
TheproposedWPTsystemcouldbeusedinacorticalimplantforvisionrestoration[27].
In the model of human head, there is a 4mm of fat and 3.75 mm of dry skin in between the receiver
coil and the air interface. To analyze the effects of the human tissue on the proposed system perfor-
mance, fat and dry skin layers are used in the CST simulation as shown in Fig. 2:18. The material
35
3 4 5 6 7
0
1
2
3
10
2
Frequency(MHz)
PDL ((W ))
PDL without tissue
PDL with tissue
Figure2.18: Studyof effectoftissue materialonthe systemperformance. On theleft, proposed3-
coilWPTsystemwithskindry(3.75mmthick)andfat(4mmthick)tissueinbetweenthetransmitter
and the receiver. On the right, plot of PDL Vs. frequency for the system with and without the
tissue. It can be noted that, tissue has no effect on the PDL.
density, electrical conductivity and relative permittivity of the materials is presented in Table I of
[27]. The K
12
, PTE of the system are not affected by the tissue and as a result, the PDL of the
system also remains unchanged as shown in Fig. 2:18. The PDL of the proposed system for a sep-
aration of 20mm between transmitter and the receiver, at 5 MHz is 18 mW(Gain=4.25(Fig. 2:17),
PDL=
(V
in
Gain)
2
R
L
=
(14:25)
2
1000
).
2.9.3 Additional Coil at the transmitter and 4-coil system
PTE =
(!M
12

1
!C
1
)
2
!
2
M
2
23
R
3
+R
L
+R
2
(!M
12

1
!C
1
)
2
!
2
M
2
23
R
3
+R
L
+R
2
+R
1
!
2
M
2
23
R
3
+R
L
!
2
M
2
23
R
3
+R
L
+R
2
R
L
R
L
+R
3
PDL =
V
2
in
(!M
12

1
!C
1
)
2
!
2
M
2
23
R
3
+R
L
+R
2
(
(!M
12

1
!C
1
)
2
!
2
M
2
23
R
3
+R
L
+R
2
+R
1
)
2
!
2
M
2
23
R
3
+R
L
!
2
M
2
23
R
3
+R
L
+R
2
R
L
R
L
+R
3
(2.30)
36
Figure 2.19: Schematic of 3-coil system with additional coil and the mutual capacitor at
the transmitter. The driver coil(L
1
) is connected to the transmitter coil(L
2
) using the mutual
capacitance(C
1
). The choice of relative voltage polarity of L
1
& L
2
(dot convention not shown
here) will determine the PTE and PDL.
In this work, a 3-coil system wth additional coil at the receiver is analyzed. The additional coil
of the 3-coil system can also be placed at the transmitter[4]. The schematic of 3-coil system with
additional coil at the transmitter side is shown in the Fig. 2.19. The effect of the mutual capacitance
on the performance parameters PTE (PDL can be analyzed similar to Eqn. 2:14) is analyzed in the
Eqn. 2.30. The
1
!Cm
can add or subtract to the !M
12
depending on the relative polarity between
the transmitter and the driver coil. It can be noticed from the and Eqn. 2.30 that, depending on the
polarity employed, PDL of the system in Fig. 2.19 can be enhanced without compromising the PTE
(if (
(!M
12

1
!Cm
)
2
!
2
M
2
23
R
3
+R
L
+R
2
>> R
1
) or PTE of the system can be enhanced. Similarly, a 4-coil[4] system with
additional coil and mutual capacitance at transmitter and receiver can use C
m
at the transmitter
to enhance PDL(Eqn. 2.30) and C
m
at the receiver to enhance the receiver efficiency(Eqn. 2:22).
2.10 Conclusion
In this work, a modified 3 coil system configuration is proposed that introduces
additional degrees of freedom in the design process. The appropriate relative voltage polarity
37
between coils and the mutual capacitance can now be used in addition to the K
23
in conventional
3-coil systems to control the reflected impedance and hence system performance . In this design,
these additional variables are used to improve systems with low receiver inductance and receiver
efficiency. Two techniques are considered: 1) equal split of two receiver coils in a 3 coil wireless
power transfer system(L
2
= L
3
) and 2)
1
!C
2
=
1
!C
3
= 0. The combined effect of these concepts
leads to a system with high R
ref2p
. Experiments verify the assertions, with results demonstrating
a proposed 3 coil system with twice the efficiency of a conventional system for small receiver coils.
The proposed system design results in PTE and Gain of 0.45 and 15 at 60 mm separation between
the transmitter and receiver at resonance frequency of 5 MHz andR
L
= 1k
. In comparison, under
the same operating conditions, the conventional 3-coil system and 2-coil system result in PTE of
less than 0.1 and Gain of less than 5. The proposed system also achieves receiver designs with better
insensitivity to load variation while also reducing the fields induced in the body due to secondary
coil current. Lastly, we show that, at the considered frequency, system performance is robust to the
presence of human tissue.
38
Chapter 3
Quantifying the efficiency maxima of a
three coil WPT system using Q
1
+ Q
2
analysis
Abstract
Ideally, series-connected coupled identical coils can exhibit quality factor (Q) doubling property.
This ideal property is not observed in conventional 3-coil wireless power transfer (WPT) systems
with two coupled resonant coils at the transmitter, in which the maximum efficiency is solely de-
termined by theQ
2
of the intermediate resonator and not theQ
1
+Q
2
of the two transmitter coils.
Series connected identical coils are not commonly used because two identical coils in proximity don’t
achieve ideal unity coupling factor, and also the Q of individual coil reduces. In this work, a new
resonance condition is proposed to prove that the maximum efficiency of the WPT system with two
39
non-identical transmit coils(Q
1
, Q
2
) is proportional to Q
1
+Q
2
. This increase in equivalent Q of
the system leads to load independent efficiency improvement of the WPT system. Three different
systems are implemented at 5 MHz to show that the conventional 3-coil system (System 1) can be
redesigned(System 2) to satisfy the conditionsthat lead to load-independent efficiencyimprovement
compared to a series resonance system (System 3). The measured maximum efficiencies are 24%,
34.5%, and 30% for Systems 1, 2, and 3 respectively, at 27 mm separation and a load of 600
.
3.1 Introduction
Wireless Power Transfer (WPT) makes biomedical implants more practical as it
removes the need for implantable batteries or cabling requirements [6]. The efficient design of the
WPT system ensures the safe and reliable operation of the implant. One of the simplest forms of a
WPT system is a two inductive coil (2-coil) system [43] delivering power from a transmit coil to a
receive coil. The performance of a simple 2-coil WPT system can be improved by adding additional
coils [11]. In the literature, multi-coil WPT systems are of two kinds: i) systems that utilize
magnetic resonance to improve performance [17] (e.g. [17] uses two self-resonant intermediate coils)
and ii) multi-coil systems that improve performance by impedance transformation [43]. The latter
method requires additional compensating capacitors and typically invert and scale the reflected
impedance [43]. In this work, a low coupling 3-coil WPT system, not operating at self-resonance,
is considered. Techniques are developed to enable the 3-coil system to operate at an equivalent
quality factor given by the sum of quality factors of individual coils. The two transmitter coils of
3- or 4-coil WPT systems may also be connected in series to take advantage of series resonance
properties. The benefits offered by series resonance strictly depend on the type of individual coils
used. The performance of the biomedical WPT system mainly depends on the coil properties such
40
as mutual coupling (K) between the transmit-receive coils and the quality factor (Q). The maximum
power transfer efficiency (PTE
max
) that a system can achieve depends on the load resistance (R
L
=
R
L;max
), coupling (K) and Q [1]. This dependence of thePTE
max
on a specific load (R
L
=R
L;max
,
ordistancebetweenthecoils)requiresoptimizationinthedesignofaWPTsystem. Thisobservation
applies to both the 2-coil and 3-coil systems. Ideally, we would like load-independent performance
improvement of a WPT system (K and Q provide load-independent improvement). The load-
independent improvement is an essential requirement in real-life applications as any power delivery
systemexperiencesarangeofloadvaluesinitsoperatingcycle. Thisusuallyrequirescompletelynew
coils as the K and Q are the intrinsic properties of coils used. In this work, the maximum efficiency
of 3-coil systems and the practical difficulties of using series resonance systems are discussed. A
3-coil WPT system is designed to offer the advantages of a series resonance system without suffering
these difficulties. The series equivalent performance of the multi-coil system is not covered in the
literature [44]. This proposal leads to improved load-independent efficiency in the 3-coil WPT
system as it increases the effective Q at the transmitter. In this work, the Q
1
+Q
2
analysis refers
to the following: the PTE maxima of a 3-coil system (two unequal transmitter coils with quality
factors given byQ
1
&Q
2
and under appropriate circuit and layout conditions) can be equal to PTE
maxima of a 2-coil system whose transmitter coil has quality factorQ
TX
=Q
1
+Q
2
. The proposed
3-coil system is also compared to the conventional 3-coil system [43].
41
Figure 3.1: System 1 (Conventional 3-Coil): Transmitter schematic is given by Tx. version 1.
System 2 (Same Phase 3-Coil): Transmitter schematic is given by Tx. version 1. System 3 (Series
Resonance): Transmitter schematic is given by Tx. version 2. System 1 and 2 have same layout and
schematic but the resonance conditions are different. The common receiver with parallel resonance
is used in the measurements for all the systems.
3.2 Conventional and Proposed WPT systems
3.2.1 Conventional 3-Coil system (System 1)
The 3-coil WPT system with the schematic shown in Fig. 3:1 (formed by Tx: Ver-
sion 1) is referred to as System 1 in this work. The Z-matrix, resonance condition and reflected
impedances are given in [43]. In this work, L
1
and L
2
refer to two coils at the transmitter. L
3
is
the receiver coil. R
1
; R
2
andR
3
are the parasitic resistances of the three coils. R
L
andR
s
are load
and source resistance respectively. C
1
; C
2
and C
3
are the resonance determining capacitors. The
coupling between the coils is given by K
12
; K
23
and K
13
. In order to get proper functionality of
the system, M
13
= K
13
p
(L
1
L
2
) should be negligible. The main advantage of this system is that
the PTE is immune to source resistance Rs as the frequency response of the current in L
1
(I
1
) has
a minima at the resonance. I
1
is 90
0
out of phase with I
2
and does not contribute to the power
42
transfer. The system will be analyzed for its magnetic efficiency in the later sections. System 1 is
implemented in this work only as a reference to compare the performance of System 2.
3.2.2 Same Phase 3-Coil system (System 2)
2
6
6
6
6
6
6
6
4
V
s
0
0
3
7
7
7
7
7
7
7
5
=
2
6
6
6
6
6
6
6
4
R
1
jX1 j!L
12
j!L
13
j!L
12
R
2
jX
2
j!L
23
j!L
13
j!L
23
R
3
+R
L
3
7
7
7
7
7
7
7
5
2
6
6
6
6
6
6
6
4
i
1
i
2
i
3
3
7
7
7
7
7
7
7
5
(3.1)
R
2
+R
ref2
=
V
2
I
2
=
j!M
12
I
1
I
2
= (
!
2
M
2
23
R
3
+R
L
+R
2
)Gain
Gain =
(!M
12
)
2
(R
3
+R
L
) +jM
12
M
23
M
13
!
3
(!M
12
)
2
(R
3
+R
L
) +j
(M
13
M
23
!
2
)
2
(R
3
+R
L
)
(3.2)
The resonance condition of the proposed 3-coil WPT system (System 2) is defined in Section IV.
The schematic and layout of System 2 remain the same as that of System 1, the only difference
being resonance condition (choice ofC
1
&C
2
). The Z-matrix of the system is given by Eqn. 3:1, for
a series resonance at the receiver. The value of X
1
is chosen to achieve resonance (Power Factor =
1) after the appropriate X
2
is chosen. The resonance condition hence depends on X
2
(Section IV).
The performance of System 2 differs from System 1 because of the different phase relations of I
1
and I
2
. The performance of System 2 is more sensitive to Rs compared to System 1. I
1
of System
2 (unlike System 1) induces a current in the receiver coil. System 1 assumes and ensures M
13
= 0.
This assumption results in a reduction of gain (Eqn. 3:2) in the reflected impedanceR
ref2
of 3-coil
43
systems. Reflected impedance derivation of the 3-coil system is described in [43]. The gain offered
by M
13
in R
ref2
is not discussed in the literature [45]. The System 2 takes advantage of the gain,
which is equal to unity in the System 1 i.e. Gain = 1 if M
13
= 0.
3.2.3 Series connected 3-Coil: Q
1
+ Q
2
effect (System 3)
The 3-coil WPT system with series-connected coils (The schematic shown in Fig.
3:1, formed by Tx: Version 2) exhibits Q
1
+ Q
2
effect in an ideal scenario. That is, if two similar
coilsL
1
andL
2
ofQ
1
andQ
2
are connected in series, then the equivalent Q of the system is given by
2Q
1
. This system is referred to as System 3. This system has the Z-matrix and reflected impedance
the same as the 2-coil system [43]; resonance condition is given by Eqn. 3:3.
1
j!C
series
=j!(L
1
+L
2
+ 2L
12
);
1
j!C
3
=j!L
3
(3.3)
2
6
6
6
4
V
s
0
3
7
7
7
5
=
2
6
6
6
4
R
1
+ R
2
j!(L
23
+ L
13
)
j!(L
23
+ L
13
) R
3
+R
L
3
7
7
7
5
2
6
6
6
4
i
1
(= i
2
)
i
3
3
7
7
7
5
(3.4)
The Q adding effect is only possible if both the coils are equal. However, if the two
similar coils are brought closer to each other, the quality factor of individual coils decreases. This
Q degradation effect is due to proximity effect. Also, an ideal mutual coupling of unity is needed
between the two closely placed coils to obtain the Q doubling effect. In practice, we can achieve a
maximum mutual coupling of about 0.9. These are the two reasons for not achieving the Q doubling
effect when two similar coils are placed in series. The layout design technique is discussed in Section
III to address the Q degradation.
44
3.2.4 Magnetic Energy Efficiency of WPT Systems
The currentsi
2
andi
3
in the System 1 are shifted by 90
0
and 180
0
respectively w.r.t.
I
1
. The currents in the two transmitter coils in System 2 are in phase, and I
3
is 90
0
out of phase.
The phase relations of the coils determine the magnetic energy efficiency (MEE). The MEE can be
defined (similar to PTE [23] and [46]) for a 2-Coil and 3-Coil system as follows
MEE =
M:E stored in the receiver coil
RX
Total M:E of the system
(3.5)
MEE
2Coil
=
I
2
2
L
2

RX
I
2
1
L
1
+ I
2
2
L
2
(3.6)
MEE
3Coil
=
I
2
3
L
3

RX
I
2
1
L
1
+ I
2
2
L
2
+L
12
i
1
i
2
+I
2
3
L
3
(3.7)
The fraction of the energy (or power) received by the receiver coil that is delivered
to R
L
is given by
RX
=
R
L
R
L
+R
3
for series resonance[43]. The simulation results shown in Fig. 3:2
(Comparison 1) indicate the following, 1). The PTE and MEE of the same phase system (System
2) is greater than that of the System 1 for all the loading conditions and 2). the load value for
maximum MEE (R
L;maxMEE
) is different from load value for maximum PTE (R
L;maxPTE
). The
System 2 has 35% more MEE at R
L;maxMEE
compared to R
L;maxPTE
. The higher the MEE,
lower the transmitted magnetic field needed for a given energy/power transfer. This also leads to
a lower electric field (comparatively safer) of the transmitter system. Thus, with this approach,
safety aspect (if the amount of magnetic field is increased by additional input current, then the
electric field and hence the SAR increases[43]) of the biomedical WPT system can be made part of
the circuit design process. The transmitter side power source creates the magnetic energy (using
transmitter coils) which results in power transfer. This analysis is possible because a WPT system
45
0 0:5 1 1:5 2
0
0:13
0:25
0:38
0:5
0:6
R
L
(k
)
MEE
Comparison 1: MEE (System 2)
Comparison 1: MEE (System 1)
0
0:13
0:25
0:38
0:5
0:6
PTE
Comparison 1: PTE (System 2)
Comparison 1: PTE (System 1)
Comparison 2: PTE (System 2)
Comparison 2: PTE (System 3)
Figure 3.2: Comparison 1: Simulation of MEE and PTE of System 2 and System 1 (Conclusion:
System 2 can have better PTE and MEE than system 1 for the same transmitter coils). Comparison
2: The plot of PTE vs. RL for System 2 and System 3 with two similar transmit coils (Conclusion:
PTE of system 2 and System 3 can be same if equal coils are used). The system parameters of the
two comparisons are given in Table 3:3.
can be analyzed for a fixed input power (PTE) or for a fixed transmitter magnetic field (MEE). It
can be understood that both MEE and PTE give the same result if the energy stored in the input
power source can be completely converted to magnetic energy at the transmitter.
3.2.5 Other WPT systems
It is a well-recognized effect that two similar coils placed very close to each other
experience a high mutual coupling and resonance mode splitting. Specifically, Ahn [45] presents
a technique at 13.5 MHz to increase the efficiency of a WPT link exploiting such strong coupling
between the coils. In other works [47], two closely placed coils are used to enhance effective perme-
ability. Their systems use equal AWG coils (diameter > 14 cm) at higher frequency (13.5 MHz) and
don’t deal with Q reduction phenomenon or series resonance equivalency, which are the focus of our
work. Although theoretically correct, placing coils very close to each other dramatically worsens
46
Figure 3.3: Coil layout used to analyze System 1 and 2. System 3 is made of series connection of
two Tx Coil 1 (Table 3:1 and 3:2)
their Q-factors. Thus, such systems need careful analysis presented in this work for biomedical
WPT applications[27].
Table 3.1: Measured properties of the coils (shown in Fig. 3:3) used
coil Coil Dia(mm) No. Turns L(uH) Q
i
AWG
Tx Coil 1 35 5 1.77 108 24
Tx Coil 2 35 12 12.8 78 36
Rx Coil 15 9 0.82 70 28
Table 3.2: details of the Coils used in the three systems.
Tx. Q
1i
Q
2i
Q
1s
Q
2s
Coil
1
Coil
2
Syst. 1 108 78 101 60 Tx Coil 1 Tx Coil 2
Syst. 2 108 78 101 60 Tx Coil 1 Tx Coil 2
Syst. 3 108 108 61 61 Tx Coil 1 Tx Coil 1
3.3 Proposed layout: Understanding and avoiding Q-factor degra-
dation
In this work, we are looking for an efficiency enhancement technique that is inde-
pendent of the load applied to the receiver. The layout design (Fig. 3:3) is a crucial step in the two
47
Table 3.3: List of Parameters used in each comparison (Comp.).
Comp. 1 Syst. 1:L
1
, L
2
, Q
1
, Q
2
given
in Table 3:2. C
1
, C
2
given by
Eqn. 3:1
Syst. 2:L
1
,L
2
,Q
1
,Q
2
given in
Table 3:2. C
1
= 420pF, C
2
=
30pF
Comp. 2 Syst. 2: L
1
= L
2
= 1H,
R
1
= R
2
= 1
, C
1
= C
2
=
570pF
Syst. 3:L
1
=L
2
= 1H, R
1
=
R
2
= 1
, C
s
= 285pF
Comp. 3 Syst. 2: same as given in
Comp. 1, System 2
2-Coil:L
TX
= 1:78H, R
TX
=
0:352
, Q
TX
= 160
Comp. 4 Tx schematic of Comp. 1, System 2 is modified as shown in
Fig. 3:4. C
s
= 2pF; C
1
= 530pF. R
s
= 0 Vs: 10

Common Parameters: f = 5 MHz; K
12
= 0:78, L
3
= 0:82 H
K
13
= K
23
= 0:02, C
3
= 1240pF; R
3
= :505

transmitter coil WPT system. The choice of two individual coils of the transmitter determines the
maximum efficiency that a system can achieve.
3.3.1 Understanding the Q Degradation in Layout design
Now, to better understand the strong relationship between series (System 3) and
3-Coil (System 2) configurations, it is useful to analyze the case in which the two coils at the
transmitting side are identical. The resonance values for equal transmitter coils case are calculated
for System 2[45] and System 3 as shown in Table 3:3 (Comparison 2). Under such conditions, the
two WPT systems have the same PTE performance (Fig. 3:2, Comparison 2).
In a practical WPT system (System 2 or 3), the two coils at the transmitter side are
placedclosetoeachothertoachievedesiredcoupling. Weobservedfromexperimentalmeasurements
that, when two identical coils are placed close to each other, their intrinsic Q-factors(Q
i
) worsen
significantly. Thus, even in a series configuration, we cannot claim to obtain an equivalent Q-factor
given by the sum of the individual intrinsic quality factor of the coils. The WPT layout for the
three systems is shown in Fig. 3:3 and Tables 3:1 and 3:2. The PTE performance of the system is
affected due to the in-system Q(Q
s
) degradation effect. The three types of coils (and their intrinsic
48
Q
i
) used in this experiment are described in Table 3:1. When these coils are placed close to one
another to form various systems, their in-system quality factor(Q
s
) reduces as shown in Table 3:2.
3.3.2 Q Degradation and Proposed Solution
A more robust layout to avoid Q-degradation is proposed for the design of System
2. Our design consists of a high-Q Tx coil 1 (i.e., the coil directly connected to the power source)
mutually coupled with a high-inductance, but lower-Q, Tx coil 2 shown in Fig. 3:3 and tabulated
in Table 3.2. This configuration is completely opposite to a typical 3-coil system, in which the
low-Q driver is coupled with a high-Q primary coil [1]. This particular configuration, although not
usually treated in common WPT systems, exhibits a very important property; once the two coils
are placed very close each other, the respective intrinsic Q values are minimally affected (compare
the Q
i
and Q
s
of System 2 and System 3 in Table 3:2). Thus we have realized a robust system in
terms of Q degradation. This effect was demonstrated with experimental measurements carried out
on fabricated prototypes. Systems 1 and 2 have the same layout. Systems 2 and 3 are Q
1
+ Q
2
systems and System 3 has a larger copper surface area and thicker layout than System 2. However,
System 2 achieves higher efficiency maxima as it incorporates layout and circuit (Section IV) design
techniques described in this work. It is to be noted that the similar coils of System 3 exhibit
dependency of Q
s
on the separation between the coils. In this work, the coils are placed very close
to each other with their insulated surfaces in contact with each other.
3.4 PTE
max
and Q
1
+ Q
2
effect in 3Coil system.
We have seen in Section III. A and Eqn. 3:4 that, using two equal transmitter coils
(equal Q) in a System 3 is mathematically equivalent to a single transmitter of 2Q. The goal of
49
this section is to prove that, under low coupling conditions (biomedical) in System 2 (Fig. 3:3), the
maximum PTE performance is proportional to Q
1
+Q
2
. We begin to analyze the maximum PTE
of the 3-Coil system by writing its PTE in a form similar to the PTE of a 2-Coil WPT system[43]
shown in Eqn. 3:8.
PTE
2Coil
=
R
L
R
L
+R
2
+R
1
j
I
1
I
2
j
2
PTE
2Coil
=
1
1 +R
1
R
L
+R
2
!
2
M
2
12
R
L
R
L
+R
2
(3.8)
The matrix for a general 3-Coil system can be written as shown in Eqn. 3:1. The choice ofjX1
only determines the power delivery (achieves maximum power delivery at resonance) and has no
effect on the efficiency. The choice ofjX2 determines the maximum efficiency that the system
can achieve. Hence, we first design forjX2 and then choosejX1. Moreover, the equation of
efficiency is independent ofjX1. The efficiency of the 3-Coil system[47] is given by Eqn. 3:9.
PTE
3Coil
=
R
L
R
L
+R
3
+R
2
j
I
2
I
3
j
2
+R
1
j
I
1
I
3
j
2
PTE
3Coil
=
1
1 +
R
2
R
L
+R
3
j
I
2
I
3
j
2
+
R
1
R
L
+R
3
j
I
1
I
3
j
2

RX
(3.9)
We now write the PTE
3Coil
of Eqn. 3:9 in a form similar to PTE
2Coil
of Eqn. 3:8 and solve for
the currents
PTE
3Coil
=
1
1 +af(X
2
)

RX
; where
a =
R
1
(R
3
+R
L
)
!
2
M
2
13
and f(X
2
) =A(X
2
) +B(X
2
)
A(X
2
) =
(1 +K
2
23
Q
2
Q
3
)
2
+
X
2
R
2
2
1 + (K
12
Q
2
+
X
2
R
2
)
2
B(X
2
) =
R
1
R
2
((K
12
Q
1
g)
2
+ (K
13
K
23
Q
1
Q
3
g)
2
)
1 + (K
12
Q
2
+
X
2
R
2
)
2
(3.10)
50
In order to solve for the PTE
3Coil
, the following assumptions are made. 1). Assume K
13
= K
23
as both the transmitter coils have same outer diameter and closely placed. 2). Define Q1 =
!L
1
R
1
,
Q2 =
!L
2
R
2
, Q3 =
!L
3
R
3
+R
L
, g
2
=
L
2
L
1
,
RX
=
R
L
R
L
+R
3
. Also, to prove the equivalent performance of the
System 2 in the low coupling case, we maintain
X
2
R
2
>> 1, K
2
23
Q
2
Q
3
1 and K
12
> K
23
Q
3
(indicating low coupling case) to get:
f(X
2
) =
X
2
R
2
2
+
R
1
R
2
(K
12
Q
1
g)
2
(K
12
Q
2
+
X
2
R
2
)
2
(3.11)
From Eqn. 3:11, it follows that we need to find the minimum of f(X
2
) in order to obtain the
maximum of the PTE. Thus, it can be recognized that Eqn. 3:11 is described by the following
general function (treating X
2
as a variable x):
h(x) =
x
2
+a
(x +b)
2
; with x
min
=
a
b
(3.12)
Hence, the minimum of f(X
2
) can be achieved when X
2
(and corresponding f(X
2
) andPTE
max
)
is equal to:
X
2
(for minimum f(X
2
)) =
R
1
K
12
Q
2
1
g
2
Q
2
f(X
2
)
min
=
(
Q
1
Q
2
)
2
+
Q
1
Q
2
(1 +
Q
1
Q
2
)
2
PTE
max
=
1
1 +
1
K
2
13
Q
1
Q
3
f(X
2
)
min
PTE
max
=
K
2
13
Q
3
(Q
2
+Q
1
)
1 +K
2
13
Q
3
(Q
2
+Q
1
)
(3.13)
Thus, we have demonstrated analytically that the maximum PTE of System 2 (with two unequal
coils at the transmitter havingQ
1
andQ
2
) is equal to a 2-Coil system with transmitter coil quality
51
factor of Q
1
+Q
2
. The value of capacitor C
2
is extracted from the value of X
2
as follows
C
2
=
1
X
2
(@f(X
2
)
min
) + (2f
resonance
)L
2
(3.14)
Substituting the values of the System 2 from Table 3:3 (Comp. 1), we getX
2
(@f(X
2
)
min
) = 515

and C
2
= 34 pF. The system parameters satisfy the condition
X
2
R
2
>> 1 but the condition
K
12
>> K
23
Q
3
depends on the load value and not always properly satisfied. Hence, a tuned value
ofC
2
= 29 (or 30)pF is found to provide the maxima of PTE. Simulations are conducted to prove
the analytical result for PTE
max
in Eqn. 3:13. System 2 is designed to provide performance equal
toQ
1
+ Q
2
. System 2 is compared against a two coil system[23] whoseQ
TX
= Q
1
+ Q
2
= 160.
System 2 and the equivalent 2-Coil system are compared (Comparison 3) and the results are plotted
in Fig. 3:4. The maxima of PTE(and also the PTE at all load values) of the two systems under
comparison is the same.
3.4.1 Schematic Update to account for R
S
It can be easily shown that the double-sided LCC WPT system [10] has the same
equations for efficiency and reflected impedance as the 4-Coil WPT system with no cross-coupling.
One of the main objectives of the multi-coil system is to avoid the degradation of efficiency due to
source resistance (R
s
). Since the performance degradation due to the R
s
can be avoided by the
passive LCC impedance matching structure, we don’t need to design the coils for this purpose. In
this work, the system design procedure does not consider the source resistance effects for simplicity.
Since the schematic update without an additional coil antenna can accommodate R
s
sensitivity,
a schematic update (Fig. 3:4) to the transmitter of System 2 is proposed that can reduce the
sensitivity of PTE performance to R
s
. The simulation results of Comparison 4 (Fig. 3:4) discuss
52
100 500 900 1;300 1;700 2;000
0
0:1
0:2
0:3
0:4
0:5
R
L
(
)
PTE
Comparison 4:R
s
= 0

Comparison 4: R
s
= 10

Comparison 3: Syst. 2
Comparison 3: 2 Coil
Figure 3.4: The schematic updates to make the efficiency of the System 3 insensitive to the R
s
.
Comparison 3: The PTE Vs. R
L
plot proves that it is possible to design a 3-Coil system to provide
performance equivalent to Q
1
+ Q
2
, which is a property of series resonance. Comparison 4: The
plot shows that R
s
effect on PTE can be minimized by an appropriate schematic update. System
parameters are given in Table 3:3.
0 500 1;000 1;500 2;000
0:1
0:2
0:3
0:4
0:5
0:6
Load, R
L
(
)
Efficiency (PTE)
System1Experimental
System1Simulation
System2Experimental
System2Simulation
System3Experimental
System3Simulation
Figure 3.5: Experimental and simulation results of PTE of three systems under comparison. The
experimental results prove theQ adding effect of System 2 described in Comparison 3. The System
2 shows higher PTE than the System 1 and 3 for all the load values.
a way to make the PTE independent of R
s
. The system parameters for comparison 4 are given in
Table 3:3.
53
3.5 Measurements Results and Conclusions
Three systems (System 1, 2 and 3) were experimentally implemented to show that
the PTE maxima of a 3-coil system with dissimilar coils, can be designed to give a Q
1
+ Q
2
performance which is practically not possible in series resonance. The coil parameters of the three
systems and the layout are discussed in Section II. The observed Q degradation (i.e. intrinsic
and in-system quality factors of the coils used in each system) is tabulated in Table 3:2. No source
resistancewasexplicitlyaddedtotheexperimentalsystems, aresistanceof0.1-0.3
canbeexpected
from the routing and soldering. The capacitor values of System 1 and 3 are determined by their
fixed resonance condition discussed in Section II. The capacitor values of System 2 (discussed in
Section IV) are the same as in Comparison 1. The PTE measurement process is described in [43].
In this work, a distance between the coils is fixed at 25 mm and the load values are changed from
50 to 2000
. The measurement results in Fig. 3:5 prove the load-independent PTE enhancement
due to Q
1
+ Q
2
performance of System 2. In this work, Q degradation is avoided by using two
dissimilar coils in the 3-coil system configuration (System 2). The current work also compares the
performance of the series resonance connected System 3 that has higher Q coils compared to the
3-coil (dissimilar coils with one coil of lower Q) configuration. The equivalent transmitter Q of
series resonant System 3 is reduced because of the Q degradation. System 2 suffers relatively less
Q degradation and hence performs better than System 3. It is derived analytically and verified by
simulation and experiment that the maximum efficiency a 3-coil system can achieve is proportional
to Q
1
+ Q
2
of the two coils at the transmitter.
54
Chapter 4
Wireless Power Transfer: Types of
Reflected Impedances and Maximum
Power Transfer Theorem
Abstract
In this work, different types of resonant reflected impedances (real, imaginary and negative) and
conditions for their existence are introduced using power flow paths. The condition necessary to
achieve maxima of power delivery at a high (>0.5) system efficiency is derived while maintaining
a power factor of 0.85 or above. A 4-Coil WPT system operating at 4.7 MHz is implemented, to
demonstrate that by controlling the different types of reflected impedances it is possible to overcome
MPT induced constraints. The implemented example utilizes four non-overlapping coils of 35 mm
55
radius; a maxima in power delivery is experimentally obtained while maintaining the efficiency and
power factor above 0.5 and 0.85, respectively.
4.1 Introduction
Wireless Power Transfer (WPT) is an integral part of power and data transmission
in applications such as biomedical implants [43], electric vehicles [10] and etc. [48]. In WPT, the
power at the receiver decreases with distance from the source because the magnetic fields decay as
1
distance
2
or
1
distance
3
[43]. The dependency of the system performance on the distance is addressed
using several techniques: arrays of coils [49], ferrite supported systems [50], combined electric and
magnetic power transfer [51], negative resistance generation using parity time electronic circuits
[52], and frequency tuning techniques [53] have been used previously to mitigate the sensitivity to
the distance between transmitter and receiver. Several adaptive electronic tuning/feedback/mod-
ulation/switching techniques [54] are adopted with the goal of dynamically updating the system
parameters for efficient system operation and regulated power delivery.
Power Transmission Efficiency (PTE), Power Delivered to Load (PDL) and Power
Factor (PF) are important performance parameters of a WPT system [43] and [10]. The near field
power delivery can be complex due to input impedances ; however, the imaginary part of the input
power does not result in power transfer to the real load. The resonance phenomenon ensures that
imaginary parts of the input impedances are minimized, thus enabling efficient system operation
with maximum power delivery capability [17]. This leads to lower reflection and desirable PF;
resonance can be achieved using passive and active electronic components or multicoil systems.
56
The multicoil WPT system operation can be explained using the reflected impedance
theory [3]. The reflected impedance of a multi-coil system designed at resonance is a real, positive
quantity. In general, the reflected impedance in the multi coil WPT system can be a real positive,
real negative or complex quantity. The origins (and conditions necessary for existence) of different
types of reflected impedances, which are covered in depth in this work, are not thoroughly covered
in the literature to the best of the authors knowledge [3].
WPT systems, like any electrical power delivery network, follow the maximum power
transfer theorem (MPT). The MPT for an N port system is analyzed in [55]. In this work, a 4-Coil
WPT system designed such that the reflected impedance is not a decreasing monotonic function
of the distance. Thus, the origins of different types of reflected impedances in 2-, 3- and 4-Coil
systems are described (Section II). Further, for the first time, the knowledge of the different types
of reflected impedances is used to design a high coupling 4-Coil WPT system whose PTE and PDL
relationship is shown in Section III not to be dictated by the MPT condition in Section III. The
measurement results of the implemented system topology are presented in Section IV.
4.2 Reflected Impedance and WPT systems
4.2.1 Real Reflected Impedance, 2-Coil system and MPT
The real reflected impedance can be understood by analyzing a resonant 2-Coil
system[43]. A resonant 2-Coil system has two coils with inductances L
1
(transmitter or Coil1) and
L
2
(receiver or Coil2) and their parasitic resistances R
1
and R
2
with receiver coil terminated in
a series load R
L
. The term M
12
= K
12
p
L
1
L
2
is the mutual inductance between the coils that
results in real reflected impedance at Coil1 due to Coil2, given by R
ref2C1;2
(Eqn. 4:1). The
57
reflected impedance is the representation of the induced back voltage (Eqn. 4:1) on the transmitter
coil given by Lenz’s Law [3]. It should be noted that the real reflected impedance results in real
power delivery to the load resistance R
2
+ R
L
. The term ! = 2f is the angular frequency and
j =
p
1. The voltage V
b
opposes the source voltage V
s
in Coil1, hence it has a negative sign. The
resonant 2-Coil (subscript 2C in Eqn. 4:2) system has reflected impedance R
ref2C1;2
[43] which
is in series with the transmit coil parasitic resistance R
1
. The maxima of PDL in the 2-Coil system
is located at the root R
ref2C1;2
= R
1
. The PTE() at this value of PDL is less than or equal
to 0.5. As the distance between the coils increases, R
ref2C1;2
only decreases as a result of the
reduction in mutual couplingM
12
. Thus, the MPT condition (Eqn. 4:2) is a result of the monotonic
nature of R
ref2C1;2
.
V
b
=j!M
12
i
2
=
!
2
M
2
12
R
2
+R
L
i
1
= (R
ref2C1;2
)i
1
(4.1)

2C
j @(PDL
2C
)
@(Z
11
(R
1
+R
ref2C
))
=0
<= 0:5 (4.2)
4.2.2 Imaginary Reflected Impedance and 3-Coil system
A resonant 3-Coil system has three coils as shown in Fig 1.a. The additional coil can
be at the transmitter or at the receiver [43]. The parameters L
1
, L
2
and L
3
are the inductances of
the three coils. R
1
; R
2
and R
3
are the parasitic resistances of the coils. The mutual inductance is
related to the coupling coefficient byM
xy
= K
xy
p
L
x
L
y
, where x, y = 1, 2, 3. In a 2-Coil system,
the voltage in the secondary coil is 90
0
out of phase with the transmit coil current i
1
. If V
2
is
180
0
out of phase with i
1
, then the reflected impedance will be imaginary: in this case, the system
will not be at resonance. However, the resonant imaginary reflected impedance can be achieved
with a 3-Coil system (Fig. 4:1.(a)). The conditions necessary to achieve the imaginary reflected
58
Figure 4.1: a). Power flow path to obtain imaginary reflected impedance at the transmitter in
the 3-Coil WPT system b). Power flow path to obtain negative reflected impedance in a 4-Coil
WPT system. K
12
is the coupling coefficient between Coil1 and Coil2. Similarly, K
xy
is coupling
coefficient between Coilx and Coily, where x; y = 1; 2; 3; 4 and also K
xy
=K
yx
.
impedance (or the necessary power flow path) can be described as follows. The current i
1
through
Coil1 induces voltageV
2
=j!M
12
i
1
in Coil2; when the loop of Coil2 is closed,i
2
=
V
2
R
2
+R
ref2C2;3
(if the Coil2 is resonant at !) flowing in Coil2 induces V
3
=j!M
23
i
2
in Coil3. The real reflected
impedance from Coil3 to Coil2, given by R
ref2C2;3
includes the loading effect of Coil3 on Coil2.
The resulting currenti
3
=
V
3
R
3
induces a back emfV
b
= j!M
13
i
3
in Coil1 which can be represented
by an imaginary reflected impedance on Coil1 due to Coil2 and Coil3 given by R
ref3C1;23
(Eqn.
4:3).
V
b
=j!M
13
i
3
=j!M
13
j!M
23
i
2
R
3
=j!M
13

j!M
23
R
3

j!M
12
i
1
R
2
+
!
2
M
2
12
R
3
=j!M
13

j!M
23
R
3

j!M
12
i
1
R
2
+R
ref2C2;3
=j
w
2
L
12
L
23
!L
13
(R
3
)(R
2
+R
ref2C2;3
)
i
1
=jR
ref3C1;23
i
1
(4.3)
59
TheimaginaryreflectedimpedancetermjR
ref3C1;23
isduetooneparticularpower
flow path in the 3-Coil system described above. However, there are four terms in the total reflected
impedance of the 3-Coil system at Coil1 due to Coil2 and Coil3 given by R
ref3Ctotal12;3
(Eqn.
4:4). These four terms are indicative of four possible power flow paths in a 3-Coil system. It should
be noted thatR
L
is connected to Coil3; hence, the equivalent definition ofR
3
will includeR
L
. The
first two terms are real reflected impedance terms. Term 1 and 2 indicate the real power delivered
to R
3
(via Coil2 and R
2
) and R
2
(via Coil3 and R
3
) respectively. If the system is designed such
that (R
L
+R
3
>> R
2
) and/or M
13
= 0, then the total reflected impedance of a 3-Coil system
is given by first term as all other terms vanish. This design assumption is also innately present in
[43] and [56]. The termR
ref3Ctotal12;3
also exhibits similar monotonicity as the 2-Coil system;
therefore, the system designed with theM
13
= 0 assumption exhibits PTE and PDL relationships
governed by MPT (Fig.10 of [2]).
R
ref3Ctotal12;3
=
w
2
L
2
12
R
2
+
w
2
L
2
23
R
3
+R
L
+
w
2
L
2
13
R
3
+R
L
+
w
2
L
2
23
R
2
j
!L
13
!L
23
!L
12
R
2
(R
3
+R
L
) +
w
2
L
2
23
R
2
j
w
2
L
12
L
23
!L
13
R
3
+R
L
R
2
+
w
2
L
2
23
R
3
+R
L
(4.4)
R
ref3Ctotal12;3
=Real power to Coil3 via Coil2
(i:e: M
13
= 0) + Real power to Coil2 via Coil3
(i:e: M
23
= 0)jR
ref3C1;23
jR
ref3C1;32
4.2.3 Negative Reflected Impedance and 4-Coil system
Following the analysis presented for imaginary reflected impedance, a resonance
negative reflected impedance can only be obtained when there are four coils to achieve the required
60
phase relationship between V
b
and the i
1
. One of the power flow path necessary to obtain negative
reflected impedance (Eqn. 4:5) is shown in Fig.4:1:(b). Note that the sourceV
s
is on Coil1 and load
R
L
is part of Coil4. The Eqn. 4:5 (written similar to Eqn. 4:3) describes the negative reflected
impedanceR
ref4C12;3;4
of a 4-Coil system at Coil1 due to the power flow path Coil1 to Coil2 to
Coil3 to Coil4 shown in Fig. 4:1:(b).
V
b
=
!
4
M
12
M
23
M
34
M
14
i
1
(R
2
+R
ref3Ctotal23;4
)(R
3
+R
ref2C3;4
)(R
4
)
=
!
4
M
12
M
23
M
34
M
14
i
1
(R
2effective
)(R
3effective
)(R
4
)
=R
ref4C12;3;4
i
1
(4.5)
Also, therecanbeotherpowerflowpathsthatresultinnegativereflectedimpedance.
For example, power from Coil1 to Coil3 to Coil2 to Coil4 also results in negative reflected impedance
at Coil1 which can be given byR
ref4C13;2;4
. These terms will be obtained from the matrix
evaluationofreflectedimpedanceofthe4-Coilsystem. ThetotalreflectedimpedanceatCoil1dueto
Coils2, 3and4(R
ref4Ctotal12;3;4
)isthesuperpositionofallthereflectedimpedances, indicative
of respective power flow paths (real, imaginary and negative included). The R
ref4Ctotal12;3;4
term with no cross coupling ( i.eM
13
=M
14
=M
24
= 0) condition is given by Eqn. 4:6 and exhibits
monotonicity and MPT dependency like 2-Coil system as in Eqn. 4:2. This is how conventional
4-Coil systems are designed [4].
R
ref4Ctotal12;3;4
=
w
2
M
2
12
R
2
+
w
2
M
2
12
R
3
+
w
2
M
2
34
R
4
+R
L
(4.6)
61
4.3 System Design
Our goal in this work is to design the system to achieve the maxima of PDL in the
high efficiency (>0.5) region of operation so that we can overcome the MPT and introduce some
degree of insensitivity of PDL w.r.t. distance (d). Systems with such capabilities can help transfer
power to electric vehicles and implanted biomedical coils uniformly at high efficiency. The condition
necessary to obtain the maxima of PDL at higher efficiency is analyzed as follows:
PDL =
V
2
s
R
ref
(R
1
+R
ref
)
2
;
@(PDL)
@(d)
=
@(PDL)
@(R
ref
)
@(R
ref
)
@(d)
@(PDL)
@(d)
=
(R
1
R
ref
)
(R
1
+R
ref
)
3
@(R
ref
)
@(d)
for high efficiency scenario, reflected impedanceR
ref
is far greater than the parasitic
resistance R
1
. Simplifying the expression, we have
@(PDL)
@(d)
=
(1)
(R
ref
)
2
@(R
ref
)
@(d)
(4.7)
Real positiveR
ref
at the input port is needed to deliver real power to the load. The
slope of the PDL curve w.r.t. d is opposite of the slope of R
ref
w.r.t. d (Eqn. 4:7). It can be
concluded that, to obtain the maxima of PDL at high efficiency, the system should create a minima
ofR
ref
and the magnitude ofR
ref
should also be sufficiently larger than parasitic resistance of the
coil.
62
4.3.1 Complete Analysis of 4-Coil system
The complete matrix equation for a 4-Coil system [43] is solved in Mathematica
®
to find the expression for (R
ref4Ctotal12;3;4
=
Vs
i
1
R
1
) (Eqn. 4:8).
R
ref4Ctotal12;3;4
=
AjB
CjD
A =!
2
M
2
13
R
2
R
4
+!
4
M
2
13
M
2
24
+!
2
M
2
12
R
3
R
4
+!
2
M
2
12
!
2
M
2
34
2!
4
M
12
M
13
M
24
M
34
+!
2
M
2
14
R
2
R
3
+!
4
M
2
14
M
2
23
2!
4
M
13
M
14
M
23
M
24
2!
4
M
12
M
14
M
23
M
34
B = +2!
3
M
13
M
12
M
23
R
4
+ 2!
3
M
13
M
14
M
34
R
2
+2!
3
M
12
M
14
M
24
R
3
C =R
2
R
3
R
4
+!
2
M
2
34
R
2
+!
2
M
2
24
R
3
+!
2
M
2
23
R
4
D = +2!
3
M
23
M
24
M
34
(4.8)
R
ref4Ctotal12;3;4
=
(AC +BD) +j(ADBC)
C
2
+D
2
(4.9)
This system is difficult to work with as there are a significant number of reflected impedance terms
resulting in degradation of PF and PDL. InR
ref4Ctotal12;3;4
,M
14
contributes to two out of four
imaginary reflected impedance terms. It also appears in two out of ten positive and two negative
reflected impedance terms, effectively contributing more to degradation of PF and PDL compared
to any other mutual inductance terms. It should be noted that M
14
is not the only cross coupling
term responsible for negative reflected impedance (term2!
4
M
12
M
13
M
24
M
34
in A).
63
Since M
14
is designed to be small (discussed in next subsection) compared to other
mutual coupling terms, the terms in A with M
2
14
can be ignored. The term A in Eqn. 4:8 will
increase if theM
14
is reduced as the two negative terms with M
14
dominate the two positive terms
withM
2
14
. Also, reducingM
14
will reduce the termB. Since denominator of the Eqn. 4:8 (C + jD)
is unaffected by theM
14
, we can conclude that reducingM
14
increases the real part of Eqn. 4:8 and
decreases the imaginary part of Eqn. 4:8, thus increasing the PF. This is the reason for selecting the
non-overlapping layout in this work. The layout is chosen to reduce the M
14
but the measurement
and simulation results presented in the next section do not ignore the M
14
offered by the layout.
Eqn. 4:8 can be rewritten as Eqn. 4:9 to observe that the form of the denominator
(C + jD) can be used to reduce the imaginary part of the reflected impedance. This combined with
low M
14
layout choice can help achieve good PF. The maxima of the real power delivery depends
only on the minima of the real reflected impedance (Eqn. 4:7). The minima of real part of Eqn.
4:9 is possible only because of the term A as terms B ;C and D are monotonic in nature.
The term A of Eqn. 4:8 is of the form ax
2
bx +c (where x is M
13
or M
23
or
M
24
indicating distance), which has a real root. The resulting root is the point of minima which
can be verified by the second derivative test. It should be noted that the minima is possible only
because of the negative reflected impedance term in A. The negative reflected impedance term
2!
4
M
12
M
13
M
24
M
34
C+jD
is similar to Eqn. 4:5 but is due to power flow path from Coil1 to Coil2 to Coil4
to Coil3 (R
ref4C12;4;3
) or from Coil1 to Coil3 to Coil4 to Coil2 (R
ref4C13;4;2
). Since both
the paths are possible, we have multiplicity of 2 similar to Eqn. 4:4. The denominator of Eqn. 4:5
can be shown to be same as C +jD. A form of reflected impedance for a 4-Coil system similar
to Eqn. 4:8 is reported in [57] (with additional adaptive matching networks) and [57] (with coil
switching) to achieve uniformity in power delivery. Differently from our analysis, the system in Fig.
64
Figure4.2: Left: Description of the stand alone coil used in the system. Right: The high coupling
[5] system is made of 3 identical coils (L
2
= L
3
= L
4
= 6:3H) of given dimension on the left.
The first coil (L
1
= 8:2 H) is made of same parameters except that it has 10 turns. Schematic
of the system is shown in Fig. 4:3.
4 of [57] exhibits maxima of the real part of reflected impedance. The implementations of [57] do
not cover the origin of negative/imaginary reflected impedance in the WPT systems.
4.3.2 Proposed 4-Coil System Design and Simulations
Since the problem statement requires us to test for efficiency higher than 0.5, the
operation is limited to the high coupling zone of the WPT system (distance between Tx and Rx
less than the diameter of the coils). The design goal includes achieving the minima of the real part
of reflected impedance (at Coil1) at a particular distance between Tx and Rx in the high coupling
zone [5] of WPT system and verifying the maxima of PDL at this location. To reduceM
14
, the four
coils are arranged in a non-overlapping manner as shown in Fig. 4:2. The Coil1 and Coil2 form the
transmitter and Coil3 and Coil4 form the receiver. The distance between the Tx and Rx is varied in
CST STUDIO SUITE™ simulation and it results in different coupling coefficients of the system as
given in Fig. 4:3. It can be noted that,K
12
andK
34
are independent of the distance,K
13
; K
23
and
K
24
are identical and K
14
is reduced compared to other coupling coefficients for all the distances.
65
Figure 4.3: Left: The schematic of the implemented system. Right: Simulated (CST STUDIO
SUITE™) coupling coefficients between the coils.
The frequency of operation is chosen as 4.7 MHz. The coupling coefficient K
14
is not a resonant
property and hence remains low for a good frequency, for example from 4 MHz to 5.5 MHz to allow
for any resonance frequency tuning. The maxima of PDL coincides with minima of the real part of
reflected impedance at Coil1 as demonstrated in Fig. 4:4. The real part of reflected impedance is
calculated by plotting the ratio of input voltage to current through the Coil1 and plotting only the
real part of it.
4.4 Measurements and Conclusion
The proposed 4-Coil system was designed and the orientation of the coils was chosen
such that PTE (given by Eqn. 32 of [43]), PDL (given by Eqn. 33 of [43]) and PF requirements are
satisfied. The implemented system is tested for its PTE, PDL and PF using a Network Analyzer.
PDL is analyzed by measuring the voltage gainj
V
2
V
1
j as described in [43]. Our system is designed
for 50
load resistor and hence S
21
=
V
2
V
1
[58] is used as the measure of voltage gain (or PDL). The
measurement results (Fig. 4:5) indicate that it is possible to implement a system with a maxima of
66
Figure 4.4: Simulated (CST STUDIO SUITE™) plot of real part of reflected impedance and PDL
vs. distance between Tx. and Rx. The maxima of PDL coincides with the minima of reflected
impedance.
Figure 4.5: Measurement results PTE, PDL and PF of the implemented system.
67
PDL (S
21
) at high efficiency (>0.5) with a good control over PF. The system exhibited a maxima of
PDL at 20 mm separation with an efficiency greater than MPT limit(0.5) and good PF(>0.85). It
can be concluded that the PDL(S
21
) response (Fig. 4:5) is not monotonic at high efficiency (>0.5),
which is not observed in conventional multi-coil WPT systems.
The coils of inductive wireless power transfer system can be arranged to obtain real,
imaginary and negative reflected impedances. Under resonance conditions, an imaginary reflected
impedance is not possible in a 2-Coil system and negative reflected impedance is not possible in a
3-Coil system. A system can benefit from the negative reflected impedance and deliver power in
a manner that overcomes the MPT. This can also be used to design PTE independent of PDL. In
this work, a condition necessary to obtain the maxima of PDL at higher efficiency levels is derived.
A 4-Coil system is implemented to meet the derived conditions (minima of real part of reflected
impedance to get maxima of PDL) and is experimentally verified to exhibit a maxima at efficiency
higher than MPT limit (0.5).
68
Chapter 5
Reflected Impedance as the
Superposition of Power Flow Paths in
Multicoil Wireless Power Transfer
Abstract
In this work, it is shown analytically that the total reflected impedance of a four-coil system con-
figuration for Wireless Power Transfer (WPT) can be derived from the superposition of all power
flow paths. Each power flow path in a multi-coil system can, in fact, be associated to a unique
reflected impedance. This understanding underscores the importance of the reflected impedance in
describing the operation and design of a wireless power transfer system. In-depth derivation of real,
imaginary, and reflected impedance in a four-coil system is also carried out.
69
5.1 Introduction
WirelessPowerTransfer(WPT)systemsfindnumerousapplications,includingbiomed-
ical devices, electric vehicle charging, and wireless communications. The interest in WPT systems
was recently renewed due to the necessity of the dependent applications [59]. Coupled Mode Theory
(CMT) [17] and Reflected Impedance (Load) Theory[3] have been used to explain the operation of
two-coil and multi-coil WPT systems. The simplified form of multi-coil WPT systems, and its re-
flected impedance, is described in the literature [60]. However, the significance of the total reflected
impedance of a multi-coil system is seldom analyzed. The power flow from the source coil to the
load coil in a multi-coil system, which is termed in this work ’power flow path,’ occurs via interme-
diate coils. In this work we mathematically show that the total reflected impedance of a multi-coil
system is indicative of all the possible independent power flow paths. This insight may thus help
choose the most efficient path(s) from source (single or multiple) to load (single or multiple) for
a given coil configuration and the application environment during the design of a multicoil WPT
system. Some of the power flow paths result in imaginary reflected impedance that can affect the
Power Factor and some paths result in negative reflected impedance that can be used to achieve
efficiency-independent power delivery to the load [61]. The in-depth analysis of the power flow paths
and their relation to different types of reflected impedances presented in this work is not covered in
the literature per authors knowledge.
5.2 Analysis of A General Four Coil WPT system
The complete reflected impedance analysis of a 3-Coil system was carried out in [61].
The 3-Coil system is a subset of the 4-Coil system analyzed here in detail. First, the total reflected
70
impedance of a 3-Coil system (formed by three coils C1, C2 and C3.) at source coil C1
s
can be
derived analytically, and it is given byZ
3CC1;2;3
(Eqn. 5:1). The complete analysis a 3-Coil system
considers the three coils and all of their mutual impedances[61].
Z
3CC1;2;3
=
w
2
L
2
12
R
3
+w
2
L
2
13
R
2
j2!
3
L
12
L
23
L
13
R
2
R
3
+w
2
L
2
23
(5.1)
Similarly, the total resonance reflected impedance of a 2-Coil system (formed by coils
C1 and C2) at source coil C1 is given by [61]:
Z
2CC1;2
=
!
2
M
2
12
R
2
5.2.1 Total Reflected Impedance of a 4-coil system
The complete matrix equation for a 4-Coil system [62] is solved in Mathematica
®
to find the expression for the reflected impedance Z
4CC1;2;3;4
=
Vs
i
1
R
1
at C1 due to C2, C3 and
C4 (Eqn. 5:2).
71
Z
4CC12;3;4
=
N
D
N = [!
2
M
2
12
(R
3
R
4
+!
2
M
2
34
) +!
2
M
2
13
(R
2
R
4
+!
2
M
2
24
)+
!
2
M
2
14
(R
2
R
3
+!
2
M
2
23
)] + [j2!
3
M
12
M
14
M
24
R
3
j2!
3
M
13
M
14
M
34
R
2
j2!
3
M
13
M
12
M
23
R
4
]+
[2!
4
M
12
M
14
M
23
M
34
2!
4
M
12
M
13
M
24
M
34
2!
4
M
13
M
14
M
23
M
24
]
D =R
2
R
3
R
4
+!
2
M
2
34
R
2
+!
2
M
2
24
R
3
+!
2
M
2
23
R
4
j2!
3
M
23
M
24
M
34
Z
4CC1;2;3;4
=T
1r
+T
2r
+T
3r
+T
1i
+
+T
2i
+T
3i
+T
1n
+T
2n
+T
3n
(5.2)
The analysis of reflected impedance of the 4-Coil system needs a fixed source coil
because it is the source coil that experiences the reflected impedance. In this work, Coil 1 (C1) is
fixed as a source coil (noted as C1
s
).
5.2.2 Real Reflected Impedance and Corresponding Paths of Power flow
The real reflected impedance terms in a 4-coil system are due to three power flow
paths shown in Fig. 5:1. The mathematical analysis of the power flow path shown in Fig. 5:1(a)
that results in the term T
1r
is carried out in detail. The study of other real impedance terms T
2r
and T
3r
can be performed similarly.
72
The power flow from the source coil (C1
s
) in Fig. 5:1(a) is shown through a dotted
single-ended arrow to the second coil (C2). The reflected impedance to the source coil is shown in
single-ended solid arrow (from C2 in Fig. 5:1(a)). These conventions are followed throughout the
work. The effect of C3 and C4 are accounted for by their effect on the C2 (dashed doubles headed
arrows). Coil C2 delivers the power to C3 and C4 and is loaded by them. The effect of C3 and C4
on C2 can be accounted for by treating the C2, C3 and C4 as a subset 3-Coil system. This results
in effective impedance at C2 given by R
2
+Z
3CC2;3;4
.
The real reflected impedance term T
1r
can be analyzed as follows. Current i
1
flow-
ing in C1
s
induces voltage V
2
= j!M
12
i
1
across C2. The voltage V
2
across C2 results in
i
2
=
V
2
R
2
+Z
3CC2;3;4
. Current i
2
induces a back electro motive force (e.m.f) on the C1
s
given by
V
b
= j!M
12
i
2
, which results in the first real reflected impedance term T
1r
=
v
b
i
1
. Thus, the term
T
1r
can be calculated as follows:
T
1r
=
j!M
12
i
2
i
1
=
!
2
M
2
12
i
1
i
1
R
2eff
=
!
2
M
2
12
R
2
+Z
3C(C2;3;4)
T
1r
=
!
2
M
2
12
(R
3
R
4
+!
2
M
2
34
)
D
(5.3)
The termZ
3CC2;3;4
is the 3-Coil impedance given by Eqn. 5:1 formed by Coils C2,
C3 and C4. The D in Eqn. 5:2 is the denominator in Eqn. 5:2. Thus, the real reflected impedance
term T
1r
is derived using the power flow path of Fig. 5:1(a). It is noted that the three power flow
paths result in real reflected impedance terms. In order to result in a real reflected impedance,
there must be only one coil in the forward and reverse power flow paths originating from source
73
Figure 5.1: Three power flow paths that result in real reflected impedance at the source coil.
coil. In Fig. 5:1(a), the source coil C1
s
delivers power the power to C2 and C2 is the only coil in
the forward and reverse power flow path originating from source coil C1
s
.
5.2.3 Imaginary Reflected Impedance and Corresponding Paths of Power flow
The six power flow paths that result in the imaginary reflected impedance are shown
in Fig. 5:2. The power flow path shown in Fig. 5:2(a) that results in the imaginary reflected
impedance term T
1i
is explained in detail. Other imaginary reflected impedance terms T
2i
and T
3i
can be described similarly. The description of dotted and solid single-headed arrow remains the
same as that of Fig. 5:1. The dashed single-headed arrow is used here to show the additional power
flow path. The additional power flow paths are needed because the source has different coils in the
forward and reverse direction of the power flow paths originating from it. The source coil (C1s) has
Coil C2 in its forward path and coil C4 in the reverse power flow path. The power flow path in Fig.
5:2(a) on the left shows the power flow from C1s to C2 to C4, and C4 results in reflected impedance
on C1s. The power flow path in Fig. 5:2(a) on the right shows the power flow from C1s to C4 to
74
Figure 5.2: Six power flow paths that result in imaginary reflected impedance at the source coil.
C2, and C2 results in reflected impedance on C1s. Both paths result in the same equation, hence
the multiplier 2 in T
1i
.
The left side path of Fig. 5:2(a) can be analyzed as follows. Current i
1
flowing in
C1
s
induces V
2
= j!M
12
i
1
in C2. The voltage V
2
in C2 results in i
2
=
V
2
R
2
+R
3CC2;3;4
. The
current i
2
induces a voltage V
4
= j!M
24
i
2
in C4 which results in current i
4
=
V
4
R
4
+R
2CC3;4
.
The i
4
induces a back e.m.f on the C1
s
given by V
b
= j!M
14
i
4
, resulting in the imaginary
reflected impedance term T
1i
=
v
b
i
1
. Thus, the term T
1i
can be calculated as shown in Eqn. 5:4.
The effect of C3 and C4 on C2 are included in theZ
3CC2;3;4
as explained before. The effect of C3
on C4 is included in the Z
2CC4;3
.
T
1ileft
=
j!M
14
i
4
i
1
=
!
2
M
14
M
24
i
2
i
1
(R
4
+Z
2CC4;3
)
=
j!
3
M
14
M
24
M
12
i
1
i
1
(R
4
+Z
2CC4;3
)(R
2
+Z
3CC2;3;4
)
T
1i
=T
1ileft
+T
1iright
=
j2!
3
M
12
M
14
M
24
R
3
D
(5.4)
75
Figure 5.3: Six power flow paths that result in real reflected impedance at the source coil.
It is to be noted that imaginary reflected impedance arises when is the coil resulting
in the reverse power flow path on the source coil is immediate neighbor of the coil receiving a direct
power from the source. In the left side power flow path of the term T
1i
in Fig. 5:2(a), C4 generates
the reflected impedance and is the immediate neighbor of C2 that directly receives power from the
source coil.
5.2.4 Negative Reflected Impedance and Corresponding Paths of Power flow
T
1nleft
=
j!M
14
i
4
i
1
=
!
2
M
14
M
34
i
3
i
1
(R
4
)
=
j!
3
M
14
M
34
M
32
i
2
i
1
R
4
(R
3
+R
ref2CC3;4
)
=
!
4
M
14
M
34
M
23
M
12
i
1
i
1
R
4
(R
3
+R
2CC3;4
)(R
2
+R
3CC2;3;4
)
=
!
4
M
14
M
34
M
23
M
12
D
76
T
1n
=T
1nleft
+T
1nright
=
j2!
4
M
12
M
13
M
23
D
(5.5)
The six power flow paths that result in the negative reflected impedance in a general
4-Coil system is shown in Fig. 5:3. The definition of different types of arrows remains the same as
described in the previous section. The only difference between the power flow paths of the negative
and imaginary reflected impedance is that the coil responsible for the reflected impedance on the
source coil is not the immediate neighbor of the coil that receives the power directly from the source
coil. In Fig. 5:3(a), for the power flow path given on the left, C4 results in the reflected impedance
onC1
s
and is not the immediate neighbor of C2 that receives the power from the source coil directly.
The left side path of Fig. 5:3(a) can be analyzed as follows. Current i
1
flowing in
C1
s
induces V
2
= j!M
1
2i
1
in C2. The voltage V
2
in C2 results in i
2
=
V
2
R
2
+R
3CC2;3;4
. The
currenti
2
induces a voltageV
3
= j!M
23
i
2
in C3 which results in current i
3
=
V
3
R
3
+R
2CC3;4
. The
i
3
induces a V
4
on the C4 given by V
4
= j!M
34
i
3
, which results in i
4
=
V
4
R
4
. The i
4
induces
a back e. m. f on C1
s
given by V
b
= j!M
14
i
4
. Thus, the term T
1n
can be calculated as shown
in Eqn. 5:5. The effect of C3 and C4 are considered on the effective 3-coil reflected impedance at
C2 given by R
3CC2;3;4
as given by Eqn. 5:1. The effect of C4 on C3 is considered in the effective
2-Coil reflected impedance at C3 given by R
2CC3;4
.
5.2.5 Application to the Design of Practical WPT systems
In a multi-coil system, the power from a source coil is delivered to all the coils in
the system. The current analysis also holds for a multi-coil WPT system with single/multiple
source coils or single/multiple load coils [63]. Understanding of the concepts of this work may help
designers select/avoid specific power flow paths to achieve desired performance parameters such as
77
Power Transfer Efficiency (PTE), Power Delivered to Load (PDL) and Power Factor [43] for a given
source and load arrangements. For example, to deliver power from a source coil C1 to load coil C4
via C2 and C3, we can choose any one of the paths shown in Fig. 5:1 that result in higher real
reflected impedance at C1. The higher reflected impedance at the source can increase the PTE [43].
The paths are selected as per the equivalent value of the load resistor R4 connected to C4. If R4 is
large, we can select preferential paths of T1r and T2r as the reflected impedance of these paths are
proportional to R4. If the values of the load R4 is small, we can select the path that maximizes T3r
with appropriate coupling parameters. Thus, power flow paths can be used as part of impedance
matching to maximize PTE. In order to reduce the power delivery to C2 and C3, R3 and R4 must
be minimized (high Q). Further, coupling from C1 to C4 and C1 to C3 must be small to reduce
the imaginary reflected impedance and achieve good PF. The negative reflected impedance can be
exploited to achieve desired power delivery without compromising the PTE and PF as presented by
authors in [61]. The coupling between C1 and C4 or C1 and C3 can be tuned to achieve a negative
reflected impedance (T1n, T2n, or T3n) to avoid the monotonic nature of reflected impedance (
w.r.t distance ) and achieve the desired PDL profile ( w.r.t distance ), without compromising the
PTE and PF [61]. Thus, power flow path helps the designer choose the appropriate layout ( dictated
by the coupling relations between the coils ) to meet the performance requirements.
5.2.6 Conclusion
In this work, a total reflected impedance of a general 4-Coil system is shown to be
the superposition of the reflected impedances due to 15 power flow paths. The power flow paths that
result in real, imaginary, and negative reflected impedances were studied in detail. The differences
between the power flow paths that result in different types of reflected impedance are identified.
78
The conventional 4-coil WPT systems often presented in the literature [60] consider only single path
shown in Fig. 5:1(a) ( along with the assumption M
24
= 0 ).
79
Chapter 6
Wireless Telemetry System with
Independent Power and Data Frequency
Resonance
Abstract
Wireless power and data transmission systems are important components in bio-electronics. Achiev-
ing resonance at the data transmission frequency without negatively impacting the efficiency at the
power transmission frequency may enhance data transmission capability. In this work, a new system
referred to as Tuned Inductor Four Capacitor (TL4C) is proposed to achieve resonance at the data
transmission frequency of a wireless telemetry system without significantly affecting the efficiency
at the power transmit frequency; as a result, this leads to increased voltage and current gains and
reduced reflections at the data transmit frequency when compared to an equivalent, traditional,
80
two-coil system. The performance of the proposed design is demonstrated through a system imple-
mentation characterized by a transmit coil of 40 mm diameter and receive coil of 15 mm diameter,
with a distance between them varied from 17 mm to 40 mm. This system is experimentally com-
pared with the equivalent two-coil system that has the same transmit and receive coil footprint and
layout but conventional transmitter matching circuitry: results show that, at the data telemetry
frequency, there is no reflection, the voltage gain is 60% higher than that of the traditional two coil
system, while the current gain is 250% higher.
6.1 Introduction
Transmission of wireless power and data using inductive coupling is widely used
in biomedical electronic systems (such as cochlear implants and visual prostheses) and electrical
vehicles. In biomedical implants, a good power and data link provides support to patients carrying
out critical functions. There are several techniques to achieve wireless power and data transfer[64].
One of the simplest ways is to use separate links (different coils for data and power) [65]; however,
the usage of independent power and data coil links reduces communication quality [66]. Several
coding techniques have been explored to achieve quality communication, such as Amplitude Shift
Keying (ASK) [67], Frequency Shift Keying (FSK) [68], Cyclic ON-OFF Keying (COOK) [69], Load
Shift Keying schemes [70] and others [71]. The ASK and FSK techniques use simpler circuits at the
receiver and, therefore, are commonly used [66].
A typical WPT system performance is characterized by power transfer efficiency
(PTE), power delivery to load (PDL) [43], voltage gain (VG), current gain (CG), and power factor
(PF). In order to achieve favorable system frequency response for both wireless power and data
transfer performance, several designs have been explored: multicoil [33], frequency splitting [72],
81
multicoil systems with several resonators [73], dual band systems with series and parallel resonator
circuits (SPRC) [74]. Frequency splitting is a high coupling phenomenon [75] and is a promising
technique for electric vehicle applications; however, the coupling factors practically observed in
biomedical applications do not result in the frequency splitting. The multi-band and SPCR systems
use multiple resonators at both transmitters and receivers to achieve two or more bands with good
efficiency. Dual band systems suffer from efficiency reduction and minimum separation requirements
between the bands [74].
WPT systems for biomedical applications use a single frequency for power transmis-
sion and efficient system operation is crucial for safety and longevity [33]. It is not desirable to
have multiple bands for the power transfer because it can lead to reduced efficiency maxima [74].
The receiver coil (15-20 mm in diameter, and often much smaller than this) is usually smaller than
the transmitter coil (30-40 mm diameter) [27] and coupling factors are in the range of 0.5-1.5%.
Since it is desirable for the system to be operating at the maximum possible efficiency at the power
transfer frequency (f
p
), no circuit design changes are usually carried out at the transmitter coil to
improve the system performance at the data transmitting frequency (f
d
) [2]. The reported biomed-
ical telemetry systems show maxima in the PTE, PDL, PF frequency response at f
p
but there is
no resonance performance observed at f
d
. In this work, PDL refers to power delivery at f = f
p
unless otherwise specified.
In this work, system design concepts validated by simulation and experiment de-
scribe a technique to achieve a resonance performance at f
d
(to enhance the PDL at f
d
) without
compromising the PTE at f
p
. The proposed technique also maintains the PF = 1 at f = f
d
irrespective of the value of real(Z
11
) at f = f
p
(which changes as per the PDL requirements
of the system). This makes resonances at f
p
and f
d
less dependent on each other in biomedical
82
telemetry. The condition PF = 1 at f
d
ensures that the power at f
d
does not suffer reflections
at the transmitter input and also increases the voltage/current gain of the system. Therefore, the
PDL at f
d
compared to conventional two-coil system is improved. The addition of these features
to a biomedical telemetry system may enhance data transmission capability without impacting the
power delivery performance.
The conventional two-coil [76] and LCC [10] systems do not have enough degrees
of freedom to achieve independent resonances at f
p
and f
d
. The proposed system, that we term
as “tuned inductor four capacitor (TL4C)” system, has sufficient degrees of freedom to achieve
independent resonances at f
p
and f
d
. The TL4C system has the same layout as the two-coil (also
LCC) system but additional node is created on the transmit coil by tapping as shown in Fig. 1.
The description of different types of systems and the achieved performance along with the layout is
discussed in section 2. Measurement results and conclusions are presented in section 3.
6.2 WPT systems and their performance
6.2.1 Layout and schematics of systems under study
In this work, four types of transmitter side impedance matching networks are studied
for their capacity to achieve independent resonance at f
p
and f
d
. The four systems use the same
layout of transmit and receive coils shown in Fig. 6.1, which also reports dimensions of a sample
system considered in this paper to illustrate the design procedure. The only difference is that the
proposed TL4C system makes an additional connection on the transmit coil by tapping (that is, by
loading the transmit coil to separate loads at a specific point on it).
83
Figure 6.1: Layout of the transmit (Number of turns = 8, AWG = 24, spacing between the turns
= 0.2 mm) and receive (Number of turns = 3, AWG = 24, spacing between the turns = 0.5 mm)
coils used in the experiment. The parameters of the telemetry system used as an example are also
given in the figure. The transmit coil (Tx) is tapped to divide it into two series connected coils Tx1
and Tx2. Tapping creates additional node on the Tx coil. (AWG: American Wire Gauge)
The schematics of four types of systems under study are shown in Fig. 6.2. Fig.
6.2.(a) shows the transmitter and receiver schematic of the conventional two-coil system. Fig.
6.2.(b) is the schematic of the transmitter section of the LCC system. Fig. 6.2.(c) is the schematic
of the transmitter section of the LCCC system; the LCCC system will enable us to understand
the proposed TL4C system. Finally, the schematic of the proposed TL4C system is shown in Fig.
6.2.(d). Note that, because of tapping an additional connection on the transmit coil, L
TX
(layout
in Fig. 6.1 and schematic in Fig. 6.2(a)) is split into L
TX1
and L
TX2
(of Fig. 6.2(d)). The mutual
inductance between the coils is given by L
TX1TX2
. The tapping allows for use of two capacitors
C
3
and C
4
that have opposite effect on im(Z
11
), thus resulting in an additional degree of freedom.
All the systems use the same receiver circuit in this work as shown in Fig. 6.2.(a). It can have
either series or parallel resonance.
84
Figure6.2: Schematicofthesystemsunderstudya). 2Coil systemtransmitandreceiveschematic
using series resonance b). The transmitter schematic of the LCC system c). The transmitter
schematic of the LCCC system d). The transmitter schematic of the proposed system. Note that
the coil layout used for 2 coil and TL4C system are same as highlighted in the dotted box(i.e
L
TX
= L
TX1
+ L
TX2
+ 2L
TX1TX2
)
6.2.2 2 Coil and LCC WPT systems
The main advantage of 2Coil system shown in Fig. 6.2.(a) (with series resonance
at transmitter) is that, under resonance condition (f
p
=
1
p
L
TX
C
1
), the maxima in the frequency
response of the system’s PTE, PDL and PF, VG and CG all coincide to the resonance frequency
[76]. The main disadvantage of such a simple system is that the current to the input coil (or the
PDL) is fixed and cannot be uniquely determined independent of PTE. One technique followed in
the literature to control the power delivery is given by the LCC system [10] shown in Fig. 6.2.(b).
The LCC connected system offers two equations to design for specific value of the PDL without
compromising PTE. In this way it operates similarly to conventional multicoil systems [33]. The
PF = 1 (imaginary component of Z
11
goes to zero i.e im(Z
11
= 0)) is observed at power transfer
frequency (f
p
) for both the systems (2Coil and LCC) under resonance conditions.
85
3 3.5 4 4.5 5 5.5 6
(a) Frequency (MHz)
0
0.5
1
PF
Sim1:LCCC
Sim1:LCC
3 3.5 4 4.5 5 5.5 6
(b) Frequency (MHz)
0
50
100
Re(Z11) ( )
Sim1:LCCC
Sim1:LCC
Figure 6.3: Simulation 1 results to show the multiple unity PF points in LCC. It also shows that,
for a given input impedance, the LCCC system can achieve asymmetry in the frequency response
of PF. The parameters are in Sim 1 of Table 6:1.
The PF frequency response of an example LCC (unlike 2Coil) system shown in Fig.
6.3 has three unity PF points at 3.95 MHz, 4.7 MHz (f
p
) and 5.45 MHz for the system parameters
given in Table 6:1 (Sim 1, LCC). The PF = 1 points at 3.95 MHz and 5.45 MHz are explored for
their use as f
d
. The resonant PDL of the system is a function of the real value of input impedance
Re(Z
11
) at f
p
and this value can be controlled by the appropriate choice of C
1
. To utilize the
additional unity PF points in the LCC for the information transmission purposes, it is desirable
to have the data frequency points (f
d
) independent of the value of PDL (Re(Z
11
)). That is, we
are able to maintain the fixed data transfer frequency (f
d
) resonance (Im(Z
11
) = 0) points
independent of power delivery (or Re(Z
11
)) atf
p
. The PF frequency response of the example LCC
system demonstrates three points of unity PF, but it is not possible to achieve the same unity PF
frequency points (f
d
) for different power delivery levels in LCC. A technique to obtain fixed values
of f
d
independent of the Re(Z
11
) at f
p
is the topic of discussion in this work.
86
Table 6.1: Parameters used in Simulation (Sim.) & Experiment (EXP).
Sim.
1
LCC:
L
1
=358nH,
C
1
=3200pF,
C
2
=320pF
LCCC:
L
1
=5uH,
C
1
=250pF,
C
2
=25pF,
C
3
=260pF
Sim.
2
TL4C (Ex1):
L
1
=5uH,
C
1
=240pF,
C
2
=32pF,
C
3
=750pF,
C
4
=460pF
TL4C (Ex2):
L
1
=3:3uH,
C
1
=390pF,
C
2
=30pF,
C
3
=750pF,
C
4
=460pF
Sim.
3
TL4C (Ex3):
L
1
=5uH,
C
1
=240pF,
C
2
=32pF,
C
3
=750pF,
C
4
=460pF
TL4C (Ex4):
L
1
=5uH,
C
1
=320pF,
C
2
=42pF,
C
3
=600pF,
C
4
=500pF
Exp. TL4C
:L
1
=3:3uH,
C
1
=330pF,
C
2
=42pF,
C
3
=680pF,
C
4
=470pF
2Coil: Trans-
mitter coil series
resonant at 4.7
MHz
Common (also measured) Parameters: L
TX
=3:97uH,R
TX
=1:08
,
L
RX
=210nH, parallel capacitor C
RX
=5460pF, R
RX
=0:2

K
TxRx
=0:013, L
TX1
= 880nH,L
TX2
= 1655nH
K
Tx1Tx2
= 0:478, R
L
=50
, R
s
=3

6.2.3 LCCC system
The schematic of the LCCC in Fig. 6.2.(c) has one additional capacitor in parallel
to the transmit coil compared to LCC system in Fig. 6.2.(b). The LCCC system is designed in
SPICE simulator to have the sameRe(Z
11
) atf
p
as the LCC and the plots of PF are shown in Fig.
6.3. Compared to the LCC, the LCCC system offers more control over the PF frequency response.
The PF frequency response of LCCC can be designed to be asymmetric and the second additional
unity PF point (off
d
) can be designed to be very close tof
p
. This asymmetry is important because
it increases the bandwidth of the PF at f
p
. This can offset the PF bandwidth reduction due to the
87
large Re(Z
11
) at f
p
observed in LCC systems. Nevertheless, the LCCC system does not solve the
issue of making the value of f
d
independent of the value of Re(Z
11
) at f
p
.
6.2.4 TL4C System: Tuning to fix the f
d
independent of the value of PDL
(Re(Z
11
))
The proposed TL4C system (Fig. 6.2.(d)) is similar to a 2Coil system in layout
but it has different schematic because an additional connection is tapped on the transmit coil to
connect additional capacitor C
4
as indicated in Fig. 6.2.(d). The proposed system requires us to
re-tune the values of capacitors C
2
; C
3
and C
4
to obtain a fixed f
d
for different values of Re(Z
11
)
at f
p
. The simulation results shown in Fig. 6.4 demonstrate the ability of the system to provide
fixed f
d
for different transmit power levels (Re(Z
11
)). Also, we can design the proposed system to
offer different values off
d
for a fixed value of power delivery (Re(Z
11
)) as shown in Fig. 6.5. These
features of TL4C make the design of power delivery and data transmission in a telemetry system
independent of each other.
6.2.5 Discussion
The main advantage of the Im(Z
11
) of the proposed TL4C system (Eqn. 6.3) com-
pared to the LCC and LCCC systems given by Eqn. 6.1 and 6.2 respectively is the presence of the
negative component (in the expression for T as shown in Eqn. 6.4). The negative sign allows for
the tuning of f
d
using C
3
and C
4
. The frequency response of Im(Z
11
) of the proposed system can
be tuned by adjusting the values of C
3
; C
4
; L
TX1
; L
TX2
; L
TX1Tx2
. This allows us to design f
d
88
3 3.5 4 4.5 5 5.5 6
(a) Frequency (MHz)
0
0.5
1
PF
Sim2:TL4C(Ex1)
Sim2:TL4C(Ex2)
3 3.5 4 4.5 5 5.5 6
(b) Frequency (MHz)
0
50
100
Re(Z11) ( )
Sim2:TL4C(Ex1)
Sim2:TL4C(Ex2)
Figure 6.4: TL4C system: Simulation 2 results to show that the proposed TL4C system can
achieve same f
d
(= 4:2 MHz) for different real value of input impedance. The parameters are in
Sim 2 of Table 6:1.
3 3.5 4 4.5 5 5.5 6
(a) Frequency (MHz)
0
0.5
1
PF
Sim3:TL4C(Ex3)
Sim3:TL4C(Ex4)
3 3.5 4 4.5 5 5.5 6
(b) Frequency (MHz)
0
0.2
0.4
0.6
Voltage Gain
0
50
100
Re(Z11) ( )
Sim3:Ex3 VG
Sim3:Ex4 VG
Sim3:Ex3 Re(Z11)
Sim3:Ex4 Re(Z11)
Figure 6.5: TL4C system: NOTE: Simulation 3 results to show that the proposed TL4C system
can achieve same real value input impedance for different data transmit frequency (f
d
) conditions.
The parameters are in Sim 3 of Table 6:1. At 4.7 MHz, the Re(Z
11
) of Ex3 and Ex4 overlap, they
also exhibit PF=1. The two systems have different f
d
. The VG shows maxima at f
d
resonances.
89
of the system independent of the Re(Z
11
) at f
p
.
Im(Z
11
)
LCC
=j!L
1
+
L
TX
C
2

1
!
2
C
1
C
2
j!L
TX
+
1
j!
(
1
C
1
+
1
C
2
)
(6.1)
Im(Z
11
)
LCCC
=j!L
1
+
1
j!C
1
(
1
j!C
2
+
L
TX
C
3
j!L
TX
+
1
j!C
3
)
L
TX
C
3
j!L
TX
+
1
j!C
3
+
1
j!
(
1
C
1
+
1
C
2
)
(6.2)
Im(Z
11
)
TL4C
=j!L
1
+
1
j!C
1
(
1
j!C
2
+T )
T +
1
j!
(
1
C
1
+
1
C
2
)
(6.3)
T =
1
j!
(
1
C
3
+
1
C
4
) +
1
!
2
C
2
4
j!L
TX2
+
1
j!C
4

(
L
TX1TX2
C
4
j!L
TX2
+
1
j!C
4

1
j!C
3
)
2
j!L
TX1
+
1
j!C
3
+
!
2
L
2
TX1TX2
j!L
TX2
+
1
j!C
4
(6.4)
6.3 Measurements and Conclusion
The layout of the implemented transmit and receive coil is shown in Fig. 1 (param-
eters in Table 6:1 (Exp.)). Experiments are performed using a vector network analyzer [15]: the
proposed TL4C system with resonance at data transfer frequency (f
d
= 4:2 MHz) is compared
with the 2Coil system (parameters in Table 6:1). The proposed system is tuned using varactors to
achieve the appropriate power transfer frequency f
p
= 4:77 MHz. The experimental results in
Fig. 6.6.(a) show that the PTE of the two systems atf
p
is the same. If the PTE of the two systems
is the same (at PF = 1) atf
p
, then the product of voltage gain (VG) and current gain (CG) remains
the same. The results in Fig. 6.6(b) show that the plots of VG and CG of the two systems at f
p
maintain a constant product as the efficiency of the two systems is same atf
p
. This proves that the
two systems have same efficiency at f
p
; we will now demonstrate the performance improvement at
90
20 25 30 35 40
(a) Distance (mm)
0
50
100
PTE (x10
-3
)
Exp: 2 Coil
Exp: TL4C
20 25 30 35 40
(b) Distance (mm)
0
500
1000
VG (x10
-3
)
0
200
400
CG (x10
-3
)
Exp: VG, 2 Coil
Exp:VG, TL4C
Exp: CG, 2 Coil
Exp:CG, TL4C
Figure6.6: Experimental results showing PTE, VG and CG of the two systems under comparison
at power transfer frequency f
p
= 4:7 MHz.
3 4 5 6 7 8 9
Frequency (MHz)
0
0.5
1
PF
0
50
100
|Z11|
Exp:TL4C, PF
Exp:2-Coil, PF
Exp:TL4C, |Z11|
Exp:2-Coil, |Z11|
3 4 5 6 7 8 9
Frequency (MHz)
0
0.2
0.4
0.6
Voltage Gain (VG)
0
0.1
0.2
Current Gain (CG)
f
d
f
p
Exp:TL4C, VG
Exp:2-Coil, VG
Exp:TL4C, CG
Exp:2-Coil, CG
Figure 6.7: Experimental results showing frequency response of PF, magnitude of Z
11
, VG and
CG of the two systems under comparison.
91
f
d
. The measured frequency response (at transmit and receive coil separation of 27 mm) of the PF,
magnitude of Z
11
, VG and CG of the two systems is plotted in Fig. 6.7. The CG of the 2Coil and
proposed TL4C system atf
d
= 4:2MHz is 5.94 m and 14.9 m respectively, showing improvement
by a factor of 2.5. The VG of the 2Coil and proposed TL4C system at f
d
= 4:2 MHz is 53 m
and 85 m respectively showing improvement by a factor of 1.6.
The 2Coil and LCC systems lack sufficient degrees of freedom to achieve resonance
at both data and power transmission frequencies independent of the required power delivery. The
resonanceatthedatatransmissionfrequencynotonlyreducesreflections(PF=1),butalsoincreases
thepowerdeliveryatf
d
byincreasingthevoltagegainandcurrentgain. TheproposedTL4Csystem
achieves resonance at both power and data transmission frequencies. The dimensions of the coils
used, distance between the coils (small receiver and low PTE) and frequency choice are suitable for
biomedical applications[27]. The system can now be designed to achieve data frequency resonance
independent of power delivery at f
p
. The designed TL4C system has higher Re(Z
11
) of 40
at f
p
(more tolerant to source resistance R
s
[16]) compared to 2Coil system (Re(Z
11
) is 7
, relatively
wideband). Still, the designed TL4C system improves voltage gain and current gain by a factor of
2.5 and 1.6 respectively compared to a 2Coil system at f
d
, while keeping efficiency the same at f
p
.
92
Chapter 7
Circuit Perspective of the Radial Electric
Fields of a Low-Frequency Wireless
Power Transfer Coil
Abstract
This chapter is a brief introduction to the analysis of the radial electric fields of a coil used in
low-frequency wireless power transfer applications. The linear line charge distribution of a straight
wire resulting from the differential input voltage at its ends displays a distributed ideal capacitance
behavior. Even when the straight wire is turned into a coil, the line charge distribution remains the
samefortheconsidereddimensionofthecoilandfrequencies. Thischargedistributionisrepresented
by the coil’s distributed capacitance, leading to the self-resonance frequency (SRF) and the radial
electric field of the coil. We conclude that on a planar (on XY-plane) spiral coil, an assumption of
93
E
z
= 0 equates to the impractical infinite SRF. If the material properties of the coil’s medium do
not change with the frequency (below SRF),
L
C
or
E
H
ratios also remain constant with the frequency.
However, the energy density stored in L or C may vary with the frequency for a given source.
7.1 Introduction
Coils are widely used for Wireless Power Transfer (WPT) applications[43, 60, 61] in
biomedical systems, electric vehicles[77, 78], and for magnetic neural stimulation[79]. These coils
are often analyzed for their electric fields (EF) to evaluate their safety and performance. The early
derivation[79–81] of EF of a solenoid coil supported the application of helical/spiral inductors for
hypothermal treatment of tumour [82, 83], and planar spiral inductors for biomedical WPT and
magnetic neural stimulation[27, 79, 84, 85]. Early works [80, 81] explain that the axial fields of the
helical coils exist to cancel out the circumferential EF generated by the magnetic fields to satisfy
the zero EF parallel to the PEC surface. However, the relationship between the charge distribution
of a coil and its EF remains unexplained. Further, as the general circuit model of a coil/inductor
includes parasitics (such as capacitor and resistor [86, 87]), a self-resonance frequency (SRF) of
the coil exists that needs to be considered while evaluating EFs. The self-capacitance of the coil,
resulting in self-resonance, also finds application in magnetic resonance WPT due to its unique
power transmission properties[17, 88, 89].
The quasi-static approximation for modelling and evaluation [90] of EF of a coil
often ignores either the charge distribution [27, 84–86, 91] or the self-capacitance [81]. Moreover,
several works in the literature [27, 79, 84, 85, 91] ignore the charge distribution and radial EF
(for convenience) without discussing the SRFs of the considered coils. Therefore, in this study, we
explain how the charge distribution, EF, and SRF of a planar spiral coil are related. To perform the
94
simulation and experimental analyses, we used core electromagnetic, RF, and circuit concepts. The
results and the concise explanation provided in this study would benefit the engineers in designing
and analyzing the coil antennas for electrical stimulation and wireless power transfer applications.
7.2 Electric Fields due to Line Charge and Charge - Voltage Rela-
tionship in R, L and C
According to Maxwell’s equations, EFs can arise from the charge (point, line, and
volume) distribution and the time-varying magnetic field (Faraday’s law of induction). Under
quasi-static assumptions of coil modeling, though EF induced by time-varying magnetic fields is
considered, EF due to charge distribution is often ignored. Therefore, in this study, we briefly
describe the EF components arising due to charge distribution in the planar spiral coils.
First, we considered a simple finite-length fictitious uniform line charge distribution
(k
0 C
m
), as shown in Fig. 7:1(a). The potential at the two ends (x = +b; x = b) of the line
charge distribution is given by:
V (x) =
1
4
0
Z
b
a
k
0
jrj
dr (7.1)
Although the potential at the two ends is non-zero, the potential difference between the ends is
zero. A linear potential difference can exist across a linear line charge distribution, as shown in Fig.
7:1(c).
The Voltage-Charge relationship for basic linear circuit elements resistor (R), induc-
tor (L), and capacitor (C) are shown in Fig. 7:1(b). We can conclude from these relations that an
equivalent line charge can represent a capacitor, and the line charge problem can be thought of as
a distributed capacitive media. Inductors and resistors do not have a line charge. For the linear
95
Figure 7.1: (a). The general uniform line charge distribution with ground at1. The potential
at both ends of the line charge is equal. It is a capacitor with respect to infinity. (b). The charge-
voltage relationship in resistor, capacitor and inductor. (c). The linear line charge distribution
with ground at the center of the line. This charge distribution can result from a true differential
input voltage (Only AC, no DC).
charge distribution shown in Fig. 7:1(c), as per the Gauss’s law, there will be more EF lines originat-
ing/leaving from the extreme ends compared to the center region as the charge distribution reaches
a zero at the center. Thus, the existence of a distributed capacitance can lead to radial conservative
fields. The capacitor stores the charge by separating the charge (equal and opposite charge on two
ends) in linear charge distribution. Note that several line charge distribution solutions (not just
linear) are possible based on medium properties. The only criterion for charge distribution is that
the charge and potential distribution should satisfy the Poisson’s equation. The charge distribution
on the coil generates radial fields (Ex, Ey, and Ez components). The Ex and Ey fields for a coil in
XY-plane can arise from the time-varying magnetic field and line charge distribution. In contrast,
the Ez field can only arise due to line charge distribution. Thus, we concentrate more on the Ez
component as an example of the radial field.
96
7.3 Charge distribution and Radial Electric Fields (E
z
) in a 1-turn
and 2-turn coil
The existence of the coil’s self-capacitance and applying a differential voltage across
the coil leads to a line charge along the surface. In order to show this linear distribution and charge
separation on a coil, 1-turn and 2-turn coils are simulated in CST STUDIO SUITE™, as shown in
Fig. 7:2.
Fig. 7:2(a) shows the orientation of a 1-turn (20 AWG, 70 mm diameter) coil on
an XY-plane. The Port 1 is located sufficiently far from the coil surface to avoid any port induced
asymmetries in the EF distribution. The Ez component measured at 2 mm above the surface and
3 mm below the surface indicates that the charge distribution is the same on the coil’s top and
bottom side. The charge distribution and Ez component is higher at the edges of the coil length
and is minimum at the center of the coil length. This kind of charge distribution also makes the
Ez component positive for one half of the coil and negative for the other half of the coil, as shown
in Fig. 7:2(b) and (c). Conversely, the linear charge distribution on a 2-turn coil (shown in Fig.
7:2(d)) result in positive charge distribution on the outer turn and negative charge distribution on
the inner turn. The zero-crossing of the charge occurs at the junction of two turns, as shown in
Fig. 7:2(e). The plots of the Fig. 7:2 prove that for both coils, the radial EF is minimum at the
center of the coil length and the charge distribution is either linear (or other function that satisfies
Poisson’s equation) with the maximum at the two ends and zero-crossing in the middle of the coil
length. The Ez component in a planar spiral coil is produced due to spatial separation (and resulting
distributed capacitance) of the positive and negative charges along the length of the coil wire. In
other words, the Ez component at any location is a result of unequal cancellation of the fields due
97
Figure 7.2: (a) The layout of the 1-turn coil in CST STUDIO SUITE™. (b) Distribution of the
Ez component above the 1-turn coil (Z = 2 mm). (c) Distribution of the Ez component below the
1-turn coil (Z = -3 mm). (d) The layout of the 2-turn coil in CST STUDIO SUITE™. (e) The
Ez component above the 2-turn coil (Z = 2 mm). (f) A straight line whose length is equal to the
length of the 2-turn coil. (g). The Ez component on the Z = 2 mm plane. These EF simulations
are conducted for 1 mA input current at 5 MHz from the Co-Simulation settings.
to distributed charges on the coil surface. Therefore, an increase in the number of turns increases
the charge separation, which finally increases the Ez component.
The Ez component of a straight line charge carrying the same current is shown in
Fig. 7:2(g). The fields of the straight line are greater than the 2-turn coil at the same observation
plane because the fields of the 2-turn coil are reduced due to the field cancellation by adjacent turn.
The Fig. 7:2 proves that the Ez component of a coil comes from the charge distribution of the
straight line, which itself is a capacitor, as shown in Fig. 7:1.
98
7.4 Self-Resonance Frequency and Radial Electric Fields
The layout of the coil used in the experiment section to measure the Ez component
is shown in Fig. 7:3(a). The equivalent circuit of the coil shown in Fig. 7:3(b) has R, L and
C. The L can be found from the low frequency (such that
1
j!C
contribution is less. However, this
doesn’t mean that C doesn’t exist.
L
C
ratio is fixed for a linear, homogeneous and isotropic material)
measurement of the input impedance im(Z
11
) = j!L and the capacitance can be calculated by
measuring the SRF. One can deduce a very simplistic view of the different sources of EF in the coil
by analyzing the type of charge flowing through the R, L and C. The net charge through the R leads
to heat loss and hence can be assumed to not contribute to the EFs. The charge through L can not
be individually separated because the inductor stores energy in terms of magnetic moment which
cannot be divided into individual charges. Thus, L can only produce the magnetic fields whose
variation in turn can produce EF (non-conservative, non-radial Ex and Ey). The charge storage in
the capacitor can lead to radial EF as described before. Thus, EF due to line charge and magnetic
field from Biot-Savart Laws are dual of each other as capacitor stores electric energy (charge) and
inductor stores magnetic energy (current).
7.5 Measurements and Conclusion
The coil shown in Fig. 7:3(a) is fabricated and its SRF and EF are analyzed as
shown in Fig. 7:4. The SRF of the coil is measured to be 32 MHz. The EF probe is fabricated to
measure the EF along its length as an induced voltageV =
R
b
a
Edl across its terminals. The probe
is shielded along the lengths that don’t receive the Electric Field. The shield voltage is fixed as it
is connected to the Port 2 ground of the VNA. The current drawn from the probe is kept (Port 2
99
Figure 7.3: (a). The CST STUDIO SUITE™ layout and parameters of the experimentally imple-
mented coil (b). Description of the charge in each branch of the equivalent circuit of the coil.
of the VNA as its 50
load) minimum because the source impedance of the probe when it senses
the induced voltage, owing to it’s small length ( compared to ) is very high (open on VNA). The
measurement results show that the Ez component due to a 40 mm probe placed along axis of the
coil from the origin is comparable to horizontal EF measured 10 mm above the coil on a xy plane.
The Ez component and line charge distribution in a spiral coil located on a xy plane
can be ignored only ifSRF =1Hz. Since the L, C and material constants of the coil don’t change
with frequency, the ratios
L
C
and
E
H
don’t change with the frequency as per the Transmission Lines
Theory. Thus, error in estimation of SRF by 10 times can lead to 10 times error in the
Ez
H
ratio.
The relationship Q(w) / V (w) indicates that the line charge distribution is always proportional
to the potential difference across the coil irrespective of the frequency.
100
Figure 7.4: Experimental measurement results. The probe orientation and S21 (dB) for the
horizontal and vertical measurement of the EF is shown. Vertical measurements refer to E
z
.
101
Chapter 8
Design of Wireless Power Transfer
System to Passively power Electrodes to
deliver Asymmetric Biphasic Stimulating
Waveform
Abstract
In this chapter, wireless power delivery to passive electrode systems is presented. Solutions based
on the differentiation property of the induction phenomenon and half wave rectifiers are imple-
mented. A new circuit design methodology is presented for the design of an efficient system to
wirelessly deliver a power to passive electrodes and generate charge balanced biphsic waveforms at
the stimulation site.
102
8.1 Introduction
The scientific innovations behind the retinal prosthetics[92–94], spinal cord pain
management [95] and Deep Brain Stimulation for Parkinson’s disease[96] can be supported by the
wireless power transfer (WPT) techniques. The WPT can help achieve wireless powering of the
implanted electrode system[97–99], enhance user experience, and safety. There are several solutions
to wireless powering of the implanted electrodes based on the source of power used. Ultrasonic,
IR and microwave sources of power can be utilized to meet the power demands of the implanted
systems[100–102]. Inductive power transfer is also a possible solution to the power delivery problems
as it is safe[27] and easy to design.
Inductive power delivery system consists of a transmitting coil and receiving coil.
The transmitting coil is connected to a voltage/current source and the receiving coil is implanted
inside the body to deliver power to specific tissue sites or an implanted energy storage device. Hence
in the literature, there are two types of inductive wireless power delivery systems for the biomedical
electrical stimulation applications. The active power delivery systems[103–108] utilize an implanted
battery/capacitor that stores the energy received from the receiving coil, often to drive a CMOS
chip that delivers the regulated current/voltage waveforms to stimulate a tissue using electrodes. A
passive wireless power delivery to an implanted electrodes[100–102, 109–111] is also possible where
the storage system is avoided and the stimulating waveforms are either transmitted directly from
the transmit coil or an additional simple circuitry at the receiver converts the received signal into a
stimulating voltage/current waveform. This technique simplifies the design process by avoiding the
use of complex CMOS ICs for the purpose of generating stimulation waveforms inside the body. In
this work, passive wireless electrode power delivery systems to deliver a charge balanced assymetric
biphasic waveform to electrodes is discussed.
103
The receiver coil of a passive wireless power delivery system is in direct contact
with the electrochemical system formed by the electrode and tisssue. Hence, the receiver coil
must be carefully designed to receive the appropriate waveforms. The typical design and safety
parameters of a electrochemical system such as charge balance[112–114], waveform characteristics
(pulse-width/amplitude/duty cycle) [115–117] and charge/charge-density per phase[118–123] need
to be controlled by the transmit/receive coil layouts. Though the efficiency of the system is brought
down by the low frequency of the transmitted stimulation waveforms, several techniques such as
modulation, rectification and filtering can be used to improve the performance.
8.2 Goals and Procedures of this Work
Thisworkaimstodiscussandcomparetwodifferentsolutionstothedesignofpassive
wirelesselectrodestodeliverchargebalancedassymetricbiphasicwaveform. Firstly, asolutionbased
onthedifferentiationpropertyofinductivepowertransferisdiscussed. Itssimplicityofconstruction,
necessary conditions for the maintainance of the waveform shape and charge balance properties are
discussed. Secondly, a solution that takes advantage of the rectification, modulation and filtering
principles to deliver power to loads of larger resistance is discussed. A new circuit is presented that
can convert the monophasic output of the half wave rectifier based passive wireless electrode into
a high performance charge balanced assymetric biphasic waveform. Thus, the goal of this work is
to compare the two commonly used techniques for passive wireless electrode design and present a
new high efficiency circuit that can deliver an assymetric biphasic charge balanced waveform to the
load. Measurement results are presented to provide a proof of concept implementation of the two
techniques.
104
8.3 Solution Based on Differentiation property of induction
A charge balanced assymetric biphasic waveform can be delivered to an implanted
receiver coil without using any additional matching components on the load side. It can be achieved
usingaWirelessPowerTransfer(WPT)circuitshowninFig.8.1. Asuitabletriangularinputvoltage
waveform with a different rising and falling edge shown in Fig. 8:2can deliver an assymetric biphasic
waveform to a load connected to the receiver. The receiver coil current, delivered to the load can
be related to input voltage by a differentiation operation as evident from the simulated waveforms
shown in Fig. 8.2.(b).
Thereareseveralassumptionsthatdeterminetheaccuratewaveformdelivery. Firstly,
we would like to ensure that the current in the transmitter coil is also a triangular waveforom similar
to (scaled version) of the input voltage. In order to achieve this, following conditions have to be
satisfied.
I
TX
=
V
in
R
TX
+R
Source
+j!L
TX
must havejR
TX
+R
Source
j > j!L
TX
j
(8.1)
The condition in Eqn. 8.1 would ensure that the transmitter coil current and input voltage are the
scaled versions of each other, maintaining the triangular shape of the transmitter coil current I
TX
.
If either the frequency content(!) or the transmitter inductance (L
TX
) are large, then the current
waveform will be integrated form of the input voltage.
Secondly, we need to ensure that the shape of the secondary/ receiver coil current
is same as the induced voltage waveform. Induced secondary voltage is the differentiation of the
primary current waveform given byV
RX
= j!L
TxRX
I
TX
. SImilar to Eqn. 8.1, a condition shown
in Eqn. 8.2 must be ensured to achieve the desired secondary current waveform shape. The term
105
Figure 8.1: Schematic of the circuit that can deliver a biphasic assymmetric waveform to the load
when triangular waveform is used as input.
L
TxRX
I
TX
is the mutual coupling inductance between the transmit and receive coil antennas.
I
RX
=
j!L
TxRX
I
TX
R
RX
+R
Load
+j!L
RX
must havejR
RX
+R
Load
j > j!L
RX
j
(8.2)
That is, we need to choose the load resistor to be larger than the receiver coil inductive impedance
to maintain the waveform shape and small enough that the desired current is delivered to the load.
It is to be noted that the load resistance shown in Fig. 8:1is the simplified form of the complex
electrochemical impedance of the stimulation system formed by the two circular disc electrodes at-
tached to the surface of the eye ball as shown in the conceptual diagram Fig. 8.3. In this system area
of the electrodes can be optimized to achieve desired equivalent load impedance. The equivalent
load to this stimulation system is the electrochemical system shown in Fig. 8.4. The R
Source
and
theC
Source
are the impedances at the interface formed between the source electrode and the tissue
electrolyte. The R
Ground
and the C
Ground
are the impedances at the interface formed between the
ground electrode and the tissue electrolyte. In this passive stimulation electrode design, we don’t
have a source and ground electrode as the coil delivering voltage to the stimulation system provides
106
Figure 8.2: Simulation 1: Simulation results of the schematic shown in Fig. 8.1. The values used
for the circuit parameters is given in Table 8:1.
differential voltage. Thus, the terms source and ground in the literature refer to V
+
and V

in this
work.
In order to maintain the shape of the current flowing through the tissue, we need
the combination of impedances offered by L
TX
and equivalent capacitance of the electrochemical
system to be less than the total resistance (channel resistance +R
Rx
) in the secondary receiver coil
loop.
The Power Transfer Efficiency (PTE) of this system will be less due to lower operat-
ing frequency (for 1 ms cathodic pulse of Fig. 8:2and requirement to maintain dominating resistance
contribution in both the receiver and transmitter coils. Also, this system cannot deliver higher cur-
rent to larger load resistance system. We would need a wide-band impedance matching circuit to
convert higher load system into an equivalent lower load system in order to maintain the shape of
the biphasic pulse over entire frequency band of the pulse.
107
Figure 8.3: A representative layout of the transmitter and receiver coils used to passively power
the circular electrodes in contact with the tissue.
Figure 8.4: Equivalent schematic of an electrochemical system. The parallel R and C are formed
at the interface of the electrode and electrolyte. The electrode-electrolyte interface is formed both
at the source and the ground electrodes.
8.4 System based on Rectification, Modulation and filtering con-
cepts
The technique based on the differentiation property of the induced voltage presented
in the previous section is not suitable for high performance applications and higher load scenarios.
In order to increase the induced voltage, a common practice is to transmit a pulse modulated with
the high frequency at the transmitter coil. This waveform will induce more voltage at the receiver
due to its high frequency contents. The received voltage is then rectified and filtered to deliver the
low frequency pulse to the load. The rectification is necessary because the induced voltage is a pure
differential signal devoid of any DC component. Filtering is necessary to remove the high frequency
signals used for pulse modulation. Since this circuit is non-linear, its performance depends on the
108
frequency contents of the pulse, amplitude of the transmitted/received signals and etc. In this
section several circuits are analyzed for their performance at the receiver side.
Table 8.1: Parameters used in Simulations
Simulation and System Parameters and Values
Simulation 1: Schematic shown in
Fig. 8:1and results shown in Fig. 8.2.
These parameters and values are
common to all other simulations.
L
Tx
= 10 H;L
Rx
= 10 H;R
Tx
= 4
,
R
Rx
= 1
, ,K
TxRx
= 0:1, All Diodes:
1N5819
Simulation 2: Schematic shown in
Fig. 8:5and results shown in Fig. 8:6
C
L
=0.1 F
Simulation 3: Schematic shown in
Fig. 8:7and results shown in Fig. 8:8
C
L
=0.02 F, C
Series
=0.0.02 F
Simulation 4: Schematic shown in
Fig. 8:9andresultsshowninFig. 8:10
C
L1
= C
L2
= C
S1
= C
S2
= 0.02 F
8.4.1 Half Wave Rectifier based Passive Wireless Electrodes
A wireless system to deliver a monophasic stimulation waveform is shown in Fig. 8.5.
The transmitter coil transmits a modulated pulse shown in Fig. 8.6(a). The received pulse voltage
across the load resistor is as shown in Fig. 8.6(b). The received pulse is monophasic in nature as
the diode conducts for only half of the cycle. Use of schottky diodes improves the performance
due to its reduced threshold[110]. The half wave rectifier solutions can be used to deliver small
charges of stimulation without creating any safety concerns[110]. In order to meet the goals of this
work, we need to convert the monophasic output of the half wave rectifier based system to a charge
balanced output. This can be done using a series capacitor [116, 117, 124, 125] as discussed in the
next section.
8.4.2 Charge Balanced Half Wave Rectifier Based Solutions
In this subsection, we discuss the circuit of Fig. 8:7and its simulation results shown
in Fig. 8.8. The charge balances in a half wave rectifier based circuit can be achieved by a series
109
Figure 8.5: Schematic of a typical wireless system which delivers a monophasic waveform to the
electrodes using a half wave rectifier.
Figure 8.6: Simulation 2: Simulation results of the schematic shown in Fig. 8.5. The values used
for the circuit parameters is given in Table 8:1. a). A modulated pulse as an input voltage. b). A
monophasic voltage waveform across the load resistor.
capacitor. The capacitor provides a reverse conduction path for the current (modifies the biasing
of the schottky diode accordingly) after a monophasic pulse and thus provides a charge balanced
performance. The output voltage across the load for same input voltage as in the Fig. 8.6(a) is
shown in Fig. 8.8(b). It can be noticed that the pulse shape is dependent on the load resistor value.
Also, the value of the peak to peak voltage of this circuit is reduced compared to the peak to peak
voltage of the monophasic output shown in Fig. 8.6(b). Thus, placement of a series capacitor may
provide charge balance at the cost of power delivery to the load. Also, unlike the solution based on
the differentiation property of the induction, the shape of the output voltage waveform delivered
110
Figure 8.7: Schematic of a wireless system which delivers a charge balanced biphasic waveform
to the electrodes using a half wave rectifier and a series capacitor.
Figure 8.8: Simulation 3: Simulation results of the schematic shown in Fig. 8.7. The values used
for the circuit parameters is given in Table 8:1. a). A modulated pulse as an input voltage. b). A
biphasic voltage waveform across the two different values of the load resistor.
to load is dependent on the load. The amplitude of the output voltage for such systems can be
improved by adopting circuit shown in Fig. 8.9.
8.4.3 Proposed circuit to deliver higher peak to peak load voltage
In this subsection, we discuss the circuit of Fig. 8:9and its simulation results shown
in Fig. 8.10. The output load resistor is connected between the two nodes names outn and outp.
The output voltage is the voltage difference between the two nodes. In this circuit, additional load
111
Figure 8.9: Schematic of the proposed wireless system which delivers a charge balanced biphasic
waveform to the electrodes. The proposed circuit provides a higher load voltage compared to the
circuit shown in Fig. 8.7.
capacitors C
L1
and C
L2
are used to increase the output load voltage. The working principle of
the circuit can be explained as follows: when the voltage at the p-end of the schottky diode D
1
is
positive, D
1
is foreward biased and D
2
is reverse biased. A high frequency current can flow from
D
1
to C
L1
via C
S1
and enter the C
L2
via it’s ground. The current can then complete the closed
loop by flowing through C
S2
and D
2
in a reverse direction. This will position the node outn at a
negative potential compared to the nodeoutp. Thus, the circuit provides a higher negative reference
to acquire the output load voltage compared to the circuit in Fig. 8.7. This circuit can increase the
load voltage as long as the load resistor is large enough to not to load the load capacitors and the
voltage at the p-end of the diode D
1
is large enough to support the described direction of current
flow.
8.5 Experimental Results and Conclusions
The proposed charge balanced circuit of Fig. Fig. 8.9 was experimentally imple-
mented to provide proof of the concept. The photograph of the transmitter and receiver coil used
in the experiment is shown in Fig. 8.11. The values of the physical and electrical properties of the
coils is given in Table 8:2. The waveforms of the the load voltages are shown in Fig. 8.12. The load
112
Figure8.10: Simulation 4: Simulation results of the schematic shown in Fig. 8.9. The values used
for the circuit parameters is given in Table 8:1. a). A modulated pulse as an input voltage. b). A
biphasic voltage waveform across the two different values of the load resistor.
Figure 8.11: Photograph of implemented transmitter and receiver coils. The distance between
the coils is maintained at 25 mm for the two experiments. The half wave rectifier and the proposed
charge balanced circuit was implemented.
113
Figure 8.12: Experimental measurement results for the circuit shown in Fig. 8.9 and half wave
rectifier. The input voltage is the 100 kHz modulated pulse of 1ms width. The input voltage is
5 Volts peak to peak and input current is about 0.6 A peak to peak. The proposed circuit gives
better load voltage compared to a half wave rectifier across a 10 k
load resistor.
Table 8.2: Electrical and Physical properties of the coils used
Parameters Tx. Coil Rx. Coil
Outer Diameter (mm) 70 26
Inner Diameter (mm) 68 14
AWG 20 32
Number of Turns 3 40
Inductance (uH) 1 22
Resistance (
) 0.9 2
resistor value used for this system is shown in the Fig. 8.12. The input voltage amplitude of the
modulated pulse was sufficient to operate the diodes of the receiver circuit in completely forward
bias. The output voltage at the output of the receiver coils was about 800 mV and 1N5819 schottky
diodes used were operating in the forward bias. The load output voltage is shown in Fig. 8.12.
114
Chapter 9
Non Foster Circuits Applied to Electrical
Stimulation Systems
Abstract
The charge conduction at the interface of an electrochemical system via double layer capacitance
is unconditionally stable compared to the conduction via parallel faradaic resistance. The chemical
reactions indicative of the double-layer capacitance charge conduction and faradaic charge conduc-
tion are coupled. Thus, in the electrode-electrolyte interface, it is difficult to control the current
flow in the capacitor independent of the resistor. In this work, an equivalent circuit of a general
electrochemical system is considered. It is shown using SPICE simulations that the use of non-foster
circuits in series with the electrochemical system results in enhanced capacitive charge conduction
over resistive charge conduction in the electrode-electrolyte interface. This system increases the
voltage gradient along the channel, improving the stimulation targeting efficiency. Measurements
115
are carried out on a in-vitro nerve tissue to demonstrate the two above mentioned advantages of
the non-foster circuit. We have verified that the non-foster circuit can increase the high-frequency
conduction and voltage gradient along the channel.
9.1 Introduction
Developments in the field of electrical engineering and electrochemistry have enabled
the use of electrical stimulation systems for wide range of applications such as retinal prosthetic for
artificial vision [93], spinal cord stimulator for pain management [95] and deep brain stimulation
for Parkinson’s disease [96]. Some of the systems are under development while few are available
commercially.
Circuit techniques find applications in multi-channel recording and stimulation[94,
97, 98], offset control using feedback[124–127] and real time waveform optimization[99, 128]. In
this work, we would like to selectively enhance the capacitive performance by utilizing an external
circuit to the electrochemical system. This is because, most electrical stimulation systems use wave-
forms that target the high frequency/capacitive conduction over low frequency/resistive conduction
through the interface. Capacitive conduction is important in stimulation applications where fast
recovery is important and directly linked to stability of an electrochemical system.
9.2 Goals and Procedures of this work
The goal of this work is to increase the capacitive conduction in an electrochemical
system by adding a non-foster circuit in series. The increase in capacitive conduction will lead
to improved stability and increased voltage gradient along the channel, thereby improving the
116
Figure 9.1: Schematic of a typical non-foster Circuit. Conditions necessary to achieve negative
input impedance are described.
stimulation targeting efficiency. We propose that the capacitive conduction of the electrochemical
systemcanbeselectivelyenhancedbyanexternalcircuitthatmimicsanequivalentnegativeresistor.
The negative resistance is obtained by the non-foster circuits, as shown in Fig. 9:1.
First, the circuit theory behind the generation of the negative resistance is pre-
sented, followed by the description of the equivalent circuit of the electrochemical system to lay the
groundwork for our proposal. Second, the advantages of adding a negative resistor in series with an
electrochemical system are explained both using frequency domain and time domain simulations.
Finally, in-vitro experimental results are provided as a proof of concept for our proposal.
9.3 Non Foster Circuits
Non-foster circuits are used in RF and antenna fields to generate negative resistance,
negative capacitance or negative inductance. Non-foster circuit usage in the system gives more
degrees of freedom compared to using linear impedance matching elements such as resistor (R),
capacitor(C)orinductor(L).PassiveimpedancematchingcircuitsusingR,LandCelementscannot
provide power gain or negative impedances. The non-foster circuits contain active elements such
117
as an op-amp or a transistor to generate negative impedance. Hence, these circuits can be used to
enhance the bandwidth[129–131], improve the SNR[132] or improve the Q factor[133]. Conceptually,
non-foster circuits are analogous to metamaterials[25, 134, 135]. Metamaterials generate negative
permittivity and permeability, which can be thought of as distributed negative capacitance and
negative inductance. From an implementation perspective, metamaterials are composed of 10-20
repeated unit cells (a type of resonator) per wavelength, whereas non-foster circuits are mostly
constructed using active or passive elements (op-Amp, transistor, R, L, C and diode). Due to
presence of active elements, stability is an important implementation issue in non-foster circuits[132,
136–140] unlike in metamaterials.
Asimpleformofnon-fostercircuitisshowninFig. 9.1. TheimpedancesZ
1
; Z
2
Z
3
; Z
4
can be any combination of R, L and C. The values must be chosen to satisfy the stability criteria and
achieve negative input impedance[139]. It is noted that the impedance Z
4
can be tuned by keeping
all the other impedances fixed to achieve negative impedance. In this work, Z
4
tuning is used to
achieve desired performance and avoid instability. Increase in Z
4
increases the positive feedback
(for a fixed Z
1
; Z
2
; Z
3
) and pushes the circuit towards instability as V
out
is common between V
+
and V

. Thus, there exist a maximum value of Z
4
that makes the positive feedback greater than
the negative feedback.
9.4 Equivalent Circuit of Electrical Stimulation System
An electrical stimulation system can be represented by an equivalent electrochemical
circuit[141]. The system consists of an electrode, electrolyte and the stimulation source. The elec-
trode and electrolyte are made of different materials and conduct electricity differently; an interface
118
Figure 9.2: Typical circuit representation of an electrochemical system. In this work, this circuit
is referred to as a basic circuit. V(a) and V(b) are the voltages at the approximate recording points
’a’ and ’b’ to measure the channel gradient.
Figure 9.3: Variables available for electrical stimulation. Different types of stimulation pulses,
bipolar/monopolar connection of stimulation source and V/I sources are shown in the diagram.
is formed between them to convert the electron current in the electrode to ionic current in the elec-
trolyte. The equivalent circuit representation of an electrochemical system involves the impedance
of the source electrode-electrolyte interface and the ground electrode-electrolyte interface[112]. The
channel resistance represents the electrolyte between the source and the ground. Thus, the equiva-
lent circuit representation can be given by Fig. 9:2.
TheR
source
andC
source
represent the source electrode - electrolyte impedance. The
R
Ground
and C
Ground
represent the ground electrode - electrolyte impedance. The C
source
is due
to the double layer capacitance between the source electrode and electrolyte. Current conduction
via double layer capacitance occurs via charge induction. This method of charge conduction is
119
very stable and does not result in any damage to the electrode or the electrolyte. The R
Source
is due to the faradaic current conduction between the source electrode and the electrolyte. The
faradaic reaction can be reversible or non-reversible depending on how far the reactants diffuse in
the electrolyte. The reversible faradaic reactions are considered stable and non-reversible reactions
are considered unstable and must be avoided.
It is desirable to have all the current conduction through the double layer capacitor
as it is unconditionally stable. Ideally, for a given electrochemical system design, we would like to
study all the possible reactions that can occur and classify the reactions according to safety[118–
123]. We would like to determine the safe stimulation criteria (charge per phase or charge density
per phase) to avoid unwanted irreversible chemical reactions. However, it is difficult to study all the
possiblereactionsinelectricalstimulationapplications. Acommonpracticeistocomparethecharge
per phase or charge density per phase of the system against Shannon’s curves[113]. Lower charge
per phase and charge density per phase guarantee the chemical stability of an electrical stimulation
system[114]. Another design choice to guarantee the stability is to use a charge balanced waveform.
A charge balanced waveform can ensure that the cathodic and anodic reactions can be perfectly
reversible and reduce the product formation from irreversible chemical reactions.
It is difficult to avoid a faradaic current in the electrochemical system. The faradaic
current and the double layer current are coupled to each other. The polarization of the interface
couples the faradaic and double layer currents. A higher polarization voltage leads to a higher
faradaic current. Faradaic current also prevents polarization voltage from increasing indefinitely.
Thus, the electrodes can be classified by their polarization property. A platinum (Pt) electrode is
more polarizable than tungsten (W). Number of available valence electrons and half-cell reaction
potentials influence the polarization property. Higher the polarization, stronger is the coupling
120
Figure 9.4: A conceptual circuit diagram of an electrochemical system in series with negative
resistance.
between faradaic current and the double layer current.
There are many degrees of freedom available for the designer to achieve desirable
stimulation results. Different waveform choices such as monophasic/ symmetric biphasic/ asym-
metric biphasic are available to get the desired stimulation response[115–117]. The amplitude and
pulse widths of these waveforms can also be tuned. Electrochemical systems can be connected in
either a monopolar or bipolar manner. Also, a waveform source can either be a constant current
or a constant voltage. Each of these choices affects system design and response. The three design
choices are shown in Fig. 9:3. Irrespective of the electrode-type, waveform used or the source, we
want the electrochemical system to be stable. Hence, we want a greater current to flow through the
double layer capacitor and smaller current to flow through the faradaic resistor.
Inthiswork, voltagegradientalongachannelismeasuredusingarecordingelectrode
close to the source V (a) and another electrode close to the ground V (b) as shown in Fig. 9:2. The
resistor R
sp1
is the channel resistance between the source electrode and the recording electrode
closest to the source electrode measuringV (a). The resistorR
sp2
is the channel resistance between
the ground electrode and the recording electrode closest to the ground electrode measuring V (b).
A series capacitor C
s
in Fig. 9:2 was used to avoid formation of an offset voltage[124]. The series
capacitor can also reduce the offset formation in a monophasic input current pulse and this property
is referred to as ’Voltage Slide Back’[116, 117].
121
Figure 9.5: Schematic of the non-foster circuit in series with an equivalent schematic of an
electrochemcial system.
Table 9.1: Parameters used in the Four Analysis
1. AC Anal-
ysis: Schematics
of Fig. 9:2 and
Fig. 9:4 are con-
sidered.
Basic (Fig. 9:2): R
s
= 5
,
R
Source
= 5k
, C
Source
= 40nF,
R
Ground
= 5k
,C
Ground
= 40nF,
R
Sp1
= R
Sp2
= 100
,
R
Channel
= 1000
, C
S
= short
Negative Resis-
tance (Fig. 9:4):
R
Negative
= -1
k
. Other Pa-
rameters remain
same.
2. Transient
Analysis:
Schematics of
Fig. 9:2 and
Fig. 9:5 are
considered.
Basic (Fig. 9:2): R
s
= 5
,
R
Source
= 5k
, C
Source
= 40nF,
R
Ground
= 12k
,
C
Ground
= 100nF, R
Sp1
=
R
Sp2
= 100
,R
Channel
= 1000
,
C
S
= 100nF
Negative Resis-
tance (Fig. 9:5):
AD711 op-amp,
L
nf
= 20 uH,
R
nf
= 10
,
R
pf
= 10
,
R
p
= 400

3. Ideal Inter-
face Analysis:
Schematic of
Fig. 9:2 is consid-
ered.
Non Ideal (Fig. 9:2): R
s
= 5
,
R
Source
= 2k
, C
Source
= 40nF,
R
Ground
= 12k
,
C
Ground
= 100nF, R
Sp1
=
R
Sp2
= 100
,R
Channel
= 2000
,
C
S
= Short;
Ideal Inter-
face (Fig. 9:2):
R
Ground
= 0,
R
Source
= 0
4. Interface Ca-
pacitance Analy-
sis: Schematic of
Fig. 9:2 is consid-
ered.
Basic (Fig. 9:2): R
s
= 5
,
R
Source
= 2k
, C
Source
= 40nF,
R
Ground
= 12k
,
C
Ground
= 400nF, R
Sp1
=
R
Sp2
= 100
,R
Channel
= 1000
,
C
S
= short
Higher Source
interface capaci-
tance (Fig. 9:2):
C
Source
=
100 nF
9.5 Advantages of Electrical Stimulation System with Non Foster
Circuit
The advantages offered by the non-foster circuit can be analyzed by SPICE simu-
lations on the equivalent circuit of an electrochemcial system. In this section, the values for the
122
Figure 9.6: Analysis 1: AC simulation showing the enhancement in the magnitude and phase
response of the gradient (V(a)-V(b)) offered by the negative resistance in series. Most of the
enhancement is observed at high frequency.
parameters (such asR
source
,C
source
,C
Ground
,R
Ground
andR
Channel
) of a basic electrical equivalent
circuit of an electrochemical system are chosen to be in the range of the measured values presented
in the literature[142–144]. Four simulations (analysis) are performed to highlight the advantages
offered by the non-foster circuit.
9.5.1 Analysis 1: AC response of the gradient
The basic electrochemical system is shown in Fig. 9:2. The goal is to enhance the
system gradient along the channel in a stable manner using a non-foster circuit, which results in a
negative impedance at ground. The equivalent circuit of an electrochemical system in series with
the non-foster circuit is shown in Fig. 9:4. The goal of increasing the gradient along the channel in a
stable manner requires us to increase the gradient at high frequencies where the current through the
capacitor is greater than the current through the resistor. This can be obtained by using a negative
resistor in series as shown in Fig. 9:4. The frequency response of the gradientV (a)V (b) is plotted
123
Figure9.7: Analysis2: SPICEsimulatedV(a)andV(b)forthethetwosystemsundercomparison.
It can be noted that the V(b) of the circuit with NF changes the shape and increase the gradient
(V(a)-V(b)) as shown in Fig. 9:8.
in Fig. 9:6. The magnitude response is plotted on the left vertical axis and the phase response is
plotted on the right side vertical axis. Fig. 9:6 compares the basic circuit shown in Fig. 9:2 and the
circuit with series negative resistance shown in Fig. 9:4. The values of the parameters is provided
in the first row of the Table 1. It can be noticed from Fig. 9:6 that the high frequency magnitude
response of theV (a)V (b) gradient is enhanced without affecting the low frequency response. Also,
phase response of the V (a)V (b) is enhanced across all the frequencies. Thus, we conclude that
using a negative resistance in series with the electrochemical system enhances the high frequency
(double layer capacitor) conduction.
9.5.2 Analysis 2: Transient response of the gradient
The transient analysis of the circuit with R
Negative
(R
Neg
) is carried out in this
section. Previously, the effect of a negative resistance (R
Neg
=-1000 Ohms) was evaluated in the
124
Figure 9.8: Analysis 2: Gradient of the two systems under comparison. The circuit with NF has
higher gradient at high frequency components.
frequencydomain. Frequencydomainsimulationassumeslinearitywhichisnotpracticalforthenon-
foster circuits which are composed of non-linear components. Frequency simulation of the previous
section establishes the working principle and influence of a negative resistor on the equivalent circuit
of the electrochemical system. In this subsection, transient analysis is carried out using the non-
foster circuit as shown in Fig. 9:5. The circuits parameters are given in the second row of the Table
1. The transient response observed at points ’a’ and ’b’ on the circuit is shown in Fig. 9:7. The
input waveform is the charge balanced 1:4 asymmetric voltage waveform with the cathodic pulse
width of 0.1 mS (-4V) and anodic pulse width of 0.4 mS (1V). The gradient V (a)V (b) for the
two circuits is shown in Fig. 9:8.
It can be noticed that the gradient for the circuit with non-foster is larger in the
high frequency region of the pulse and smaller at the low frequency region of the pulse. It is because
the non-foster circuit provides negative resistance at certain high frequencies that we observe this
phenomenon. It doesn’t provide equal negative resistance at all frequencies unlike the ideal case
125
Figure 9.9: Analysis 3: An ideal interface has higher capacitive gradient and lower low-frequency
gradient. The ideal interface refers to the case with R
Source
= 0.
presented in the frequency simulation in Fig. 9:6. Since the current in the circuit is fixed, an
increase in the current through the capacitor must result in the reduction of the current through
the resistor. Thus, we can see from Fig. 9:8 that the low frequency current in the circuit with
non-foster is reduced.
The plot ofV (b) for a circuit with non-foster in Fig. 9:7 shows a distinct behaviour.
The value of V (b) at high frequency changes the phase to increase the gradient. It is an indication
of negative resistance in series with the system. It can be thought of as the ground of the system is
moving inside the electrolyte at high frequencies. The analysis in this subsection assumes that the
interface impedance values remain the same when a series non-foster circuit is used. The interface
parameters may change as a result of series non-foster circuit.
126
Figure 9.10: Analysis 4: Channel current behaviour under different C
Source
. A higher C
Source
reduces the decay of the current without affecting the peak current and the low frequency current.
9.5.3 Analysis 3: Behaviour of an Ideal Electrode- Electrolyte Interface
In this subsection, the behaviour of an ideal interface is analyzed, to prove that
non-foster circuit in series with the electrochemical system enhances the conduction through the
capacitor and reduces the conduction through the resistor. An ideal interface is characterized by
the absence of the faradaic resistor. The details of the schematics, figures and the parameter values
are given in the third row of the Table 1.
The simulated gradient plots of the two circuits under comparison is shown in
Fig. 9:9. It is seen that the voltage gradient increases for high frequencies and decreases for low
frequencies. This behaviour is observed for both positive and negative half cycles. Thus, we can
conclude that the performance obtained by a practical non-foster circuit in series with the system is
identical to the behaviour of an ideal electrode-electrolyte interface. The improvement in the capac-
itive behaviour is higher when the system has higher faradaic current and higher channel resistance.
In the third row of Table 1,R
Source
is decreased andR
Channel
is increased compared to Analysis 1.
The values of R
Ground
and C
Ground
are kept larger to represent a larger ground area. Thus, if the
127
interface parameters don’t change with the addition of the non-foster circuit, then the behaviour of
the interface becomes ideal.
9.5.4 Analysis 4: Interface Capacitance Increase due to addition of Non-Foster
Circuit
The conclusions in the previous two subsections (Analysis 2 and 3) assume that the
interface properties do not change with the addition of the non-foster circuit. In this subsection,
the variation of the interface capacitance at the source electrode on the current through the system
is analyzed. The circuits and the parameter details of this analysis is given in the fourth row of the
Table 1. In this analysis, only the source interface capacitance of the basic system shown in Fig. 9:2
is varied and all other parameters are kept fixed. The higher capacitance results in slower decay of
the current through the system as shown in Fig. 9:10. The peak values of the currents of the two
cases under comparison in Fig. 9:10 remain the same as the impedance offered by the capacitance is
negligible at higher frequency regions of the pulse. At the transients of the pulse, only the channel
resistance dominates and the impedance offered by the interfaces maybe less significant. Hence,
the increment in the source capacitance can decrease the decay of the current without affecting the
currents at the high and low frequency regions of the anodic pulse. The reduced decay of the current
increases the current at the middle region of the anodic pulse and can increase the channel gradient
without affecting the maximum current, which maybe limited by the tolerances of the animal under
test.
128
Figure 9.11: Equivalent schematic of the measurement system with non-foster circuit in series.
Table 9.2: Details of the Measurement Setup
System Parameters Values
Input Pulse width (Cathode : An-
ode)
0.1 mS : 0.4 mS
Input Pulse Voltage (Cathode : An-
ode)
0.8 V : 0.2 V
Total Pulse Duration (T) 0.5 mS
Gap between two Input Pulses (G) 10 mS
Duty Cycle (
T
G+T
) 0.01
Source and Ground Electrodes (Pt)
(PlasticsOne.Inc)
E363/6/SPC ELEC .010/.25MM PT
Recording Electrodes (W) (Plastic-
sOne.Inc)
E363T/2/SPC ELEC .008"/.2MM
Op-Amp TL081
R
fn
, R
p
and R
pf
10
, 2000
and 10

Series Resistance (R
s
) 1 k

Series Capacitance (C
s
) 100 nF
L
fn
6 uH
+VCC and -VCC +10V and -10V
Pulse Generator 33250A
Oscilloscope (4-Channel) DSOX2014A
Acquisition Mode Averaging Mode: 4
9.6 Measurements
Our goal is to increase the gradient along the channel by enhancing the conduction
via interface capacitance. The use of non-foster circuit in series with an electrochemical system may
lead to one of the two situations at the source interface. First, it can make the interface more ideal
by increasing the conduction at high frequencies (via capacitance) and decreasing the conduction at
129
Figure 9.12: (a). Waveform of the input voltage signal. (b). Recorded voltages of V(a) and V(b)
for the basic setup without non-foster circuit in series.
low frequencies (via resistance) without changing the source interface capacitance value as shown
in Analysis 2 and 3. Second, the source capacitance could be increased without affecting any other
parameters as shown in Analysis 4. We expect that the results may vary based on the pulse widths
(frequency content), electrode type, tissue (channel) type, design of the non-foster and amplitude
of the input pulse as a practical electrochemical system is non-linear.
The equivalent schematic of the measurement system is shown in Fig. 9:11. The
details of the values of the parameters, electrodes, measurement conditions and input waveform are
given in Table. 2. The ground electrode (250 um diameter) is scrapped by 5mm and the source
electrode (250 um diameter) is scrapped by 1mm. The larger ground area is maintained to ensure
that the majority of the capacitance effect is due to the source electrode-electrolyte interface. The
input voltages and series resistance are chosen to ensure that the current amplitude is below 100 uA
to limit any non-linearities. The source and ground electrodes are separated by 5 cm. The distance
between the V(a) recording electrode and source is about 3 mm. The distance between the V(b)
130
Figure 9.13: The measured waveforms of V(a) and V(b) for a system with non-foster circuit in
series.
recording electrode and ground is about 3 mm.
The proposed system is tested in-vitro on a nerve tissue. In this section, the experi-
mental results of the non-foster circuit implemented on the nerve of the rat is presented. The input
waveform and the measured V(a) and V(b) on the nerve of the rat is shown in Fig. 9:12 for a basic
system. In this work, basic system refers to an electrochemical system without the series non-foster.
The V(a) and V(b) of the nerve tissue with non-foster circuit in series is shown in Fig. 9:13. The
gradients of the basic system and the system with non-foster circuit in series is shown in Fig. 9:14.
The measured current waveforms of the basic system and system with non-foster (with NF) is shown
in Fig. 9:15. The non-foster circuit resulted in higher gradient along the channel compared to the
basic system. The plots of current through the nerve given in Fig. 9:15 are similar to the plots of
Fig. 9:10. We can conclude for the nerve that the effect of non-foster circuit is similar to increasing
the C
Source
of the source electrode-electrolyte interface.
131
Figure 9.14: The figure compares the gradient along the nerve for the two cases. The gradient
along the nerve is increased when non-foster circuit is in series with the electrochemcial system.
Figure 9.15: Comparison of the current through the nerve. The current is measured as a voltage
acrossthe1k
seriesresistanceR
s
. Thecurrentbehaviourinpresenceofnon-fostercircuitindicated
higher source electrode-electrolyte capacitance as shown in Fig. 9:10 and analysis 4.
132
9.7 Conclusion
The non-foster circuit can increase the gradient along the channel without increasing
the peak current through the system. The equivalent effect of the non-foster circuit on the source
electrode-electrolyte interface is analyzed. The effect on the source electrode-electrolyte interface
is studied in Analysis 3 and 4. We can have a response where the decay in current waveform is
reduced (Analysis 4), which is indicative of the increased source capacitanceC
source
. We can also see
a response where the gradient at high frequency increases and gradient at low frequency decreases,
which is indicative of the reduced faradaic conduction without changing the source capacitance
C
Source
. However, in both the cases, the non-foster circuit in series with an electrochemical system
provides higher capacitive conduction compared to a basic system.
9.8 Applications and Future Directions
Limitations of electrical stimulation in biological systems includes poor targeting
and unwanted activation of surrounding tissue due to the highly inhomogeneous medium and the
large spread of the applied fields. This is particularly a concern if it is desirable to have maximum
power transfer to the center of the neuronal receptive field and minimum power transfer to the pe-
riphery, such as the case in cortical brain stimulation. The increased efficiency in the directionality
of power flow pathways proposed by the non-foster circuits can be applied towards neural stim-
ulation techniques for improved results. This approach can potentially find a niche in implanted
electrode systems such as retinal prosthetics where it could be desirable to have a focused area of
stimulation for functional targeting [145] or inducing nerve growth along a narrow pathway by ap-
plying an electric field gradient [146]. As demonstrated in this work, implementation of a non-foster
133
Figure 9.16: The gradient enhancement offered by the non-foster circuit in PBS water is shown
to be only limited to high frequency. This behaviour is similar to the analysis of the ideal interface
carried out in Analysis 3. The gradient enhancement is comparable to Fig. 9:9. In this case, we can
observe that the interface capacitance did not increase, but the conduction through the R
Source
reduced.
circuit with the electrode system can increase the ratio of power flow along the central conduction
path and reduce the ratio of power flow along the peripheral paths. Increasing the spatiotemporal
targeting efficiency of implantable neurostimulators is highly valuable for neuroscience research for
monitoring and controlling neuronal activity. One such neuromodulation technique that has gained
attention is optogenetics. Various system designs that incorporate precise optical stimulation with
electrode sensor arrays were proposed, which claim a high spatiotemporal accuracy compared to
conventional electrical stimulation methods [147]. The main limitation involved with optogenetic
methods however, is the requirement of genetic modification, which makes it complicated to begin
testing on humans. Thus, it is important to consider possible improvements to widely used electrical
stimulation systems, such as the non-foster circuits proposed in this work.
134
9.9 Discussion
The experiment on a nerve tissue resulted in a current behaviour consistent with
Analysis 4. It is argued that if the source capacitance does not change, then the behaviour will
be similar to the ideal interface in Analysis 3. The gradient will increase only at high frequency
and decrease slightly at the low frequency as shown in Fig. 9:9. This is explained in Analysis 3.
This kind of behaviour was observed in the PBS water with W electrodes used as source/ground/
recording electrodes. The measured results are shown in Fig. 9:16.
135
Chapter 10
External Circuits to achieve a Charge
Balanced Unidirectional gradient with
Biphasic Stimulation
Abstract
Some cellular activities in biological systems such as growth guidance and migration are driven by
time-varying electric fields(EF). Because EF in biological systems is unidirectional, we can only
apply direct current(DC) or monophasic current to generate unidirectional EF with implantable
electrical circuits. Since direct and monophasic currents will induce greater damage to the tissue
than alternating currents, it is essential to use a biphasic stimulation waveform to maintain charge
136
balance. In this experiment, we designed two circuits that may generate a charge balanced, unidi-
rectional electrical field using biphasic stimulation. This is achieved by shifting the anodic gradient
along the channel to either low frequency or high frequency.
10.1 Introduction
Developments in the field of electrical engineering and electrochemistry have enabled
theelectricalstimulationsystemsforwiderangeofapplicationssuchasretinalprostheticforartificial
vision [92, 93, 148], spinal cord stimulator for pain management [95], deep brain stimulation for
Parkinson’sdisease[95,96]andmemoryprosthesis[149]. Someofthesystemsareunderdevelopment
while few are already available commercially. The electronic circuits can not only support new
applications of an electrochemical systems but also provide new functionality such as adoptive
waveform generation to guarantee charge balance[99, 115] and operation range adjustment[128],
adaptive offset correction [125] and easy neural recording interfaces[126, 127, 150].
Electric Field (EF) caused by voltage gradient in a biological system is intrinsically
unidirectional for the purpose of promoting cells growth guidance in wound healing [24, 151] and
nerve growth [152] due to ion distribution. Moreover, many types of the cell growth can be guided
through application of direct current (DC) [153–156]. However, when symmetric alternating current
(AC) is applied, EF becomes bidirectional and will lose the ability of growth guidance[157, 158].
In some previous studies, researchers used biphasic monopolar alternating current to reduce the
opposite gradient and succeeded to induce directed neuron migration [158].
137
10.2 Problem Statement Description
In an electrochemical system designed to elicit the electric field directed axonal
growth, unidirectional field is desired to achieve a net unidirectional growth. The presence of
alternating electric field may not be efficient for this application. In-vitro experiments show that a
DC voltage is more efficient for the axonal growth compared to an alternating voltage[146, 156, 157].
An electrical stimulation system design and analysis is governed by the electrochem-
istry of the underlying electrodes and the electrolytes. The safety of an electrochemical system is
an important aspect of the system. The easiest way to achieve safety is to target the charge balance
of the electrochemical reactions[113, 116, 117]. Electrically, the charge balance can be ensured if a
biphasic balanced voltage/current waveform is used as a stimulus and the charge/ charge density
per phase of the waveform are kept below certain maximum limit[118–123]. These aspects of the
design not only put a limit on the usable waveforms but also govern the electrode design.
The safety requirement of an electrochemical system prevents us from using a DC
voltage or unidirectional electric field for the axonal growth application. Thus, the designer has
a challenge to achieve a charge balance without generating similar net electric fields on both the
cathodic and anodic phase.
The first obvious solution to the above described problem is to use a charge balanced
asymmetric biphasic waveform which has the short duration cathodic pulse of large amplitude
compared to longer anodic pulse of lower amplitude. The pulse must have equal cathodic and
anodic area and must adhere to the limits on charge/charge density per phase restrictions[112, 114].
This waveform can be used for the unidirectional axonal growth application but may still offer a
huge anodic gradient at the cathode-to-anode transition region due to higher and sudden change
138
in the applied input voltage. This high gradient at the cathode-to-anode transition area may be
desired to support quick recovery at the source electrode region of the electrochemical system. The
system stimulated with such a pulse may still exhibit comparable net cathodic and anodic gradients
which is not an ideal solution to the axonal growth applications. Thus we need a solution that
can support a quick recovery of the voltage at the source, exhibit charge balance, and also provide
greater difference between the net anodic and cathodic gradients along the channel to support
unidirectional electric field.
10.3 Basic Electrochemical System Description, Goals and Proce-
dures of this work
Theelectricalequivalentschematic[112]ofalinearelectrochemcialsystemisshownin
Fig.10.1. ThestimulatingvoltagesourceV
Waveform
generatesachargebalancedassymmetricbipha-
sic waveform (also shown inside the figure). The voltage source is in series with a capacitor C
Series
that ensures charge balance[116, 117, 124] and prevents build up of the unwanted offset voltage after
the electrochemical reactions. In the equivalent schematic of an electrochemical system shown in
Fig. 10.1, R
source
and C
source
represent the source electrode - electrolyte interface impedance. The
R
Ground
andC
Ground
represent the ground electrode - electrolyte interface impedance. The interface
capacitance C
source
or C
Ground
is due to the double layer capacitance between the electrode and
electrolyte. The interface resistanceR
source
orR
Ground
is due to the Faradaic conductance between
the electrode and electrolyte. Current conduction via double layer capacitance is stable, while the
Faradaic conductance can become unstable[112]. The resistor R
Channel
is the channel resistance of
the electrochemical system.
139
In this work, voltage gradient along the channel is measured using two simultaneous
recording electrodes. One of the recording electrode close to the source measures V (a) and another
recording electrode, close to the ground measuresV (b). The gradient along the channel is calculated
byV (a)V (b). It is assumed that the gradient along the channel is the representation of the electric
field along the channel. The usage of the term electric field in this work refers to the gradient. The
gradient along the channel can be different during the anodic and the cathodic part of the input
waveform. The resistor R
sp1
is the channel resistance between the source electrode and the first
recording electrode measuringV (a). The resistorR
sp2
is the channel resistance between the ground
electrode and the second recording electrode measuring V (b).
The goal of this work is to design a system that results in an increased unidirectional
electric field along the channel of a charge balanced electrochemical system without compromising
the quick recovery property near the source electrode. The gradient along the channel of an elec-
trochemical system during the cathodic pulse is unchanged. The gradient along the channel of
the implemented system, during the anodic pulse, is either pushed to lower frequency or higher
frequency compared to a conventional electrochemical system setup. This functionality is achieved
without compromising on the quick recovery of the voltage waveform at the source electrode which
maybe crucial to the operation of an electrical stimulation system.
The above goal is achieved by using additional electrical/electronic components in
series with the electrochemical system. The additional components are placed after the ground
electrode and outside the body. Thus, the proposed series systems do not result in any additional
implants.
The additional system placed in series with the electrochemical system achieve the
140
stated goals by modulating the voltage near the ground electrode-electrolyte interface without af-
fecting the source electrode-electrolyte interface. The modulation of the voltage near the ground
can allow us to push the gradient along the channel to either low frequency or high frequency.
10.4 Basic Techniques used in the literature to achieve charge bal-
ance
In this section, we analyze two techniques used to maintain the charge balance in
the literature. There can be other techniques based on the electronic feedback techniques, but
they are not discussed here as our work is not focused on the control system analysis to achieve
charge balance. First technique is to use a charge balanced waveform as shown in Fig. 10.1. In
this scenario, the voltage/current source provides the positive and negative charges for foreword
and reverse half cell reactions of an electrochemical system. The electrochemical system acts as a
load for the voltage/current source in both the half cycles and achieves a charge balance by proper
design of the waveform. Thus, in this case the properties of the waveforms such as amplitude (of the
positive and negative half cycles), pulse width (of the positive and negative half cycles) and duty
cycle of application of the stimulus can be seen as available degrees of freedom for the designer to
analyze the response using the electrical stimulation system. Addition of a series capacitor C
Series
can be viewed either as an additional load to the voltage/current source or as a component that
modifies the effective applied voltage/current waveform to the electrochemical system. The voltage
drops across the capacitor and the capacitor modifies the current with its differentiation property.
Thus, we can see the combination of the capacitor and the voltage source as effectively a new
source of different waveform. Here, the series capacitor provides an additional degree of freedom
to control the applied stimulus. The series capacitor also provides an additional functionality. In
141
the absence of any applied stimulus, if there is a charge imbalance in the electrochemical system, it
can establish the charge balance in the system by encouraging reverse current flow from the source
electrode side to the ground electrode side [116, 117, 124]. The charge imbalance creates an offset
voltage in the system and capacitor provides an instantaneous short circuit between the source and
ground electrodes. This instantaneous short circuit establishes the reverse current and achieves
charge balance. The principle of charge balance based on a monophasic input waveform and series
capacitor is well established in the literature as voltage slide back effect [116, 117]. Thus, series
capacitor assisted charge balance operation where the electrochemical system acts as a source or a
battery is treated as a second technique to achieve charge balance in this work.
In the first technique of achieving a charge balance (only using a balanced waveform)
withoutusingtheexternalcapacitor, thetimeconstantsofthecurrentsinthesystemaredetermined
by thecombination of theinterface capacitance andresistance, andchannel. In thesecondtechnique
of achieving a charge balance (monophasic waveform + series capacitor), the combination of the
internal impedance of the source, series capacitor, equivalent time constants of the electrochemical
systemdeterminetheoveralltimeconstantsofthecurrentconduction. Theseparametersinfluencing
the time constants or the degrees of freedom are the same for both the anodic and cathodic pulse.
10.5 Approach 1: Pushing the anodic gradient to low frequency
using the series low frequency system (LFS).
In this section, an external circuit is used in series with an electrochemical system
to push the frequency contents of the anodic gradient along the channel to lower frequency com-
pared to a basic electrochemical system without external system. The anodic gradient of the basic
142
Figure 10.1: Schematic of the equivalent circuit of an electrochemical system. An asymmetric
biphasic voltage waveform is also shown.
Figure 10.2: Schematic of the proposed LFS system. This system can control the anodic conduc-
tion time constants.
electrochemical system shown in Fig. 10.1 can be selectively moved to low frequency by using an
external circuit in Fig. 10.2. The additional circuit components shown in Fig. 10.2 are composed of
two diodes (D
neg
andD
pos
), two resistances (R
neg
andR
pos
) and a capacitor (C
pos
). The subscripts
indicate the half cycles (negative or positive) of the input waveform during which the respective
components conduct.
10.5.1 Notes regarding the Operation of the Proposed System
TheoperationofthesystemshowninFig.10.2isgovernedbythetwodiodes. During
the cathodic pulse, diode D
neg
conducts and the gradient along the channel is unaffected as the
143
Figure 10.3: a) A charge balanced input waveform. b) Simulation of V(a) and V(b) for the basic
system with the system parameters given in Table 10.1.
impedance offered by the foreward biased diode is insignificant compared to the total impedance
of the electrochemical system. The resistance R
neg
is an internal resistance of the diode during
conduction. It is not a physical resistor in the system. During the anodic pulse, D
neg
is turned
off and D
pos
is foreward biased. The combination of the physically placed R
pos
and C
pos
is now in
series with the electrochemical system.
In the proposed system, we use the combination of the two charge balancing tech-
niques presented above. We use a charge balanced waveform source with a series capacitance along
with capability to tune the time constants differently in the positive and negative half cycles. The
system remains unchanged during the cathodic region of operation. During the anodic region of op-
eration, we encourage the charge balance by current flow from source to the electrochemical system
and also capacitor assisted flow of current out of the electrochemical system.
The presence of C
pos
ensures that the source side fast recovery is maintained. The
effect of R
pos
on the gradient is seen only after the transients. It can decrease the current flow
144
Figure 10.4: a) Simulation of V(a) and V(b) for the LFS system with the system parameters
given in Table 10.1. b). Comparison of simulated gradients of the LFS system and basic system.
and decrease the gradient in the low frequency parts of the anodic pulse. Thus, this circuit is more
effective if the system has significant anodic gradient due to faradaic conduction. The effect of the
additional R
pos
and C
pos
can be seen on a linear equivalent circuit in the next simulation section.
10.5.2 simulation results
In this section values for the parameters of a basic electrical equivalent circuit of
an electrochemical system is assumed. The values are chosen to be in the range of the measured
values presented in the literature[142–144]. To this system, an external LFS circuit is added and
the SPICE simulation results are compared. This analysis assumes linearity of the system, which
may not be practical. Nonetheless the analysis helps compare the gradients and sets expectations
for the experimental results on an electrochemical system. The values assumed for the basic and
the LFS system are provided in the Table 10.1. The simulation results are provided in Fig. 10.3
and 10.4.
145
Table 10.1: Parameters used in Simulations
System Parameters and Values
Basic System (Parameters and val-
ues are common to other two sys-
tems), Schematic shown in Fig. 10:1.
R
int
= 5
, R
Source
= 1k
,
C
Source
= 40nF, R
Ground
= 2k
,
C
Ground
= 80nF,R
Sp1
=R
Sp2
= 100
,
R
Channel
= 1000
, C
Series
= 100nF,
LFS System shown in Fig. 10.2: D
pos
: 1N4148, D
neg
: 1N914, M
1
:
AO6407, M
2
: BSB012N03MX3
HFS System shown in Fig. 10.5: D
pos
, D
neg
: 1N5818, R
pos
= 9:1k
,
C
pos
= 20 nF
Figure 10.5: Schematic of the proposed HFS system. This system can control push the part of
anodic gradients to higher frequency.
The input waveform to the two system under comparison is shown in Fig. 10.3(a).
The simulated voltages at V(a) and V(b) for the basic and LFS systems are shown in Fig. 10.3(b)
and Fig. 10.4(a) respectively. The gradients V (a)V (b) of the two systems is plotted on the
same graph in Fig. 10.4(b) for comparison. The peak gradient for the cathodic pulse of the LFS
system is reduced because the impedance of the electrochemical system at this higher frequency
region of operation of the pulse may become comparable to the foreward biased diode D
neg
. The
channel gradient during the anodic pulse exhibit different properties. The effect of control of the
time constants of the current flow can be observed in the reduced gradient at the low frequency
region of operation of the pulse. The gradient at the transient region of the anodic pulse may remain
unchanged due to additional series capacitance C
pos
. Thus the proposed LFS system can be used
to control the gradient along the channel selectively during the anodic pulse operation. The two
systems under comparison here are charge balanced.
146
Figure 10.6: a) Simulation of V(a) and V(b) for the HFS system with the system parameters
given in Table 10.1. b). Comparison of simulated gradients of the HFS system and basic system.
10.6 Approach 2: Pushing the anodic gradient to high frequency
using the series high frequency system (HFS).
The system to push the anodic gradient to high frequency is shown in Fig. 10.5. The
system consists of two diodes (D
pos
and D
neg
) and two transistors (M
1
and M
2
). The system also
has an additional high frequency pulse generator which is ideally turned on only during the anodic
region. The transistor M
1
prevents any high frequency pulses from reaching the ground electrode
during the cathodic pulse. The transistor M
1
turns on during the cathodic pulse and conducts all
of the current from M
2
to ground and maintains the cathodic voltage of D
pos
close to 0V. It thus
provides a high frequency pulse free cathodic gradient. The transistor M
2
is controlled by the high
frequency pulse generator. It does not controls the turn on/off of theD
pos
. The current through the
diodeD
pos
has high frequency components without changing its DC bias. This allows us to control
the voltage at the ground electrode and change the gradient along the channel. The high frequency
current pulses from D
pos
flows though the channel. The capacitance of the D
neg
act as low pass
147
filter on the current flowing into the channel from D
pos
and smooths the pulse. The voltage at the
junction of the the D
pos
, M
1
andM
2
is controlled by the turn on/off of the M
1
which is controlled
by the input waveform.
The voltage at V(a) is less affected by the high frequency current because the
impedance offered by the comparatively large C
series
and the C
Source
is small at high frequency.
That is we assume that the capacitors act as short at the frequency of the pulse and the node V(a)
act as a ground to the high frequency pulse. All of the high frequency pulse voltage is dropped
across the resistive channel resistor. Thus, modelling of the channel as a resistor helps in this system
operation. The current flowing through the channel does not reverse the direction in the anodic
pulse. The high frequency current only modulates the current from the main biphasic waveform
input of the source. Thus the gradient along the channel is determined by the low frequency current
from the biphasic source and the high frequency pulsed monophasic currents. We can increase the
high frequency share of the current (and thus the gradient encoded in the high frequency pulses)
by controlling M
2
, M
1
and amplitude of the V
HighFrequencyPulse
source.
10.6.1 Simulation Results
The values of the parameters used in the simulation of HFS circuit is shown in Table
10.1. The simulation results of voltages at V(a) and V(b) are plotted in Fig. 10.6 (a). The V(a)
is largely free of high frequency pulses wherease V(b) is mmodulated by high frequency pulses
significantly. This ensures that part of the anodic gradient is now encoded in the higher frequency
pulses compared to a basic system as plotted in Fig.10.6(b).
148
Figure 10.7: a) The charge balanced 1:4 input waveform. b) Measurement of V(a) and V(b) for
the basic system with tungsten electrodes.
Figure 10.8: a) Measurement of V(a) and V(b) for a LFS system with 1:4 input waveform. b)
Gradient comparison of the LFS system with basic system for the 1:4 input waveform.
149
Figure 10.9: a) Measurement of V(a) and V(b) for a HFS system with 1:4 input waveform. b)
Gradient comparison of the HFS system with basic system for the 1:4 input waveform.
Figure 10.10: a) The charge balanced 1:8 input waveform. b) Measurement of V(a) and V(b) for
the basic system with tungsten electrodes.
150
10.7 Experimental Results
TheexperimentsareconductedonastandardPBSliquid. Intheexperiment,weused
two different biphasic waveforms with different anodic duration and amplitude. Both waveforms
have a cathodic duration of 0.1ms and -4V amplitude. The first waveform has an anodic duration
of 0.4ms (1:4 asymmetric biphasic waveform) with amplitude of 1V and the second waveform has
an anodic duration of 0.8ms (1:8 asymmetric biphasic waveform) with amplitude of 0.5V. The
stimulation electrode, counter electrode and recording electrodes were implemented using Tungsten
electrodes inserted into PBS media.
The experimental results on a PBS water using 1:4 waveforms for basic, LFS and
HFS systems are shown in Fig. 10.7, 10.8 and 10.9. The comparison of gradients of basic system
and LFS system is shown in Fig. 10.8(b) and The comparison of gradients of basic system and HFS
system is shown in Fig. 10.9(b). No significant unidirectional gradient improvement was noticed in
the 1:4 waveform. Hence, the experiment was repeated with the 1:8 waveform. The experimental
results using 1:8 waveforms for basic, LFS and HFS systems are shown in Fig. 10.10, 10.11 and
10.12. The comparison of gradients of basic system and LFS system is shown in Fig. 10.11(b) and
The comparison of gradients of basic system and HFS system is shown in Fig. 10.12(b). Significant
improvement in the anodic gradient was observed for a 1:8 input waveform using the HFS external
system as shown in Fig. 10.12 (b).
It can be noted that not 1:4 waveform didn’t provide the expected results for the
external system. The success of the experiment depends on the channel resistance. Higher the
channel resistance, more control we can exert on the channel gradient. In all the cases, including
the HFS with 1:8 waveform case, we can see that the V(a) indicates quick recovery on the source
side.
151
Figure 10.11: a) Measurement of V(a) and V(b) for a LFS system with 1:8 input waveform. b)
Gradient comparison of the LFS system with basic system for the 1:8 input waveform.
The offset voltage existence and nullification depends on external capacitor (fixed at
100nF for all the cases here), duty cycle and charge imbalance. Different offset levels are measured
for different cases. The charge balance in the system is measured by analyzing the voltage waveform
across theC
series
capacitor. For the HFS system measured with 1:8 waveform, which exhibits higher
control over anodic gradient, the voltage waveform across the series capacitor is given in Fig. 10.13.
It is assumed that if the voltage across the capacitor at the end of the pulse goes to zero, then there
is no charge imbalance between the positive and negative charge conduction (Q = CV). This
technique of charge balance measurement was adopted to avoid integration of the voltage across a
series resistance which will be corrupted by an oscilloscope noise.
10.8 Conclusions
In this work, two new systems were tested on PBS using W electrodes with a goal
of achieving control over the anodic gradient. After experimenting with 1:4 and 1:8 waveforms, it
152
Figure 10.12: a) Measurement of V(a) and V(b) for a HFS system with 1:8 input waveform. b)
Gradient comparison of the HFS system with basic system for the 1:8 input waveform.
Figure 10.13: Measurement of voltages across the series capacitor to assess the charge balance in
the system.
153
is observed that the HFS system can reduce the anodic gradient without compromising on the fast
recovery at the source voltage. The HFS system is more useful compared to LFS system in reducing
the anodic gradient of a charge balanced system. More testing in different tissues and media could
be conducted to draw better conclusions on the performance of the two systems.
154
Chapter 11
Conclusions and Future Work
The work presents a collection of circuit techniques to increase the performance of
a WPT system. The addition of a mutual capacitor in between the two receiver coils of a three-coil
system not only doubles the efficiency but also increases the power delivery, reduces inductor coil
sizes and currents. Analytical and experimental results also show that the maximum efficiency
that could be achieved in a two-transmitter coil system is shown to be limited by the summation
of the individual quality factor of the coils. The TL4C impedance matching achieves independent
resonances for efficient power and data delivery. A four-coil system designed to take advantage of a
negative reflected impedance makes the power delivery response of a WPT system independent of
its efficiency. This technique helps the designer achieve a power delivery profile not dictated by the
Maximum Power Transfer Theorem.
A complete understanding of different types of reflected impedances is presented in
this work. It is accompanied by the derivation of real, imaginary, and negative reflected impedance.
The power delivery in a four-coil system is explained using all the possible power flow paths. The
155
total reflected impedance of a WPT system is shown to be the superposition of all the power flow
paths.
Negative resistance is generated using the Non-Foster circuit and is used to increase
the high-frequency gradient along the channel in an electrochemical system. The external circuit
comprised of a Non-Foster circuit is shown not only to increase the channel gradient but also focuses
the current along the least resistance path between the source and ground. Selective control over
an anodic gradient in an electrochemical system can be exercised by using the external circuits.
These external circuits translate the anodic gradient to either lower frequency or higher frequency
and can decrease the gradient along the channel. The additional performance observed using these
externalcircuitscannotbeachievedbytuningthetraditionaldegreesoffreedom, suchasstimulation
waveforms, amplitudes, pulse widths, or voltage/current sources.
The Non-Foster and Frequency Translation techniques applied to electrical stimula-
tion needs to be verified by exhaustive in-vivo and in-vitro testing.
156
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Abstract (if available)

Abstract Wireless Power Transfer (WPT) techniques are used in biomedical systems to enhance the safety and user experience. Analysis and design of high performance inductive WPT systems is addressed in this work. Efficiency, telemetry over large distance, independent design of power delivery and efficiency, and safety are some of the performance parameters analyzed. Circuit design concepts are applied to achieve new high-performance WPT solutions. The degrees of freedom available to tune the electrochemical properties of a biomedical stimulation system to achieve desired biological response are limited to waveform choice, duty cycle, amplitude, and type of source. Concepts of negative resistance and frequency translation are now applied to achieve electrochemical system performance not possible with the conventional design strategies. These techniques lead to larger channel gradients and selective control over the anodic current flow. These systems may help increase the stimulation efficiency. The concepts presented in this thesis are verified using analytical, simulation, and experimental tools.

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Asset Metadata

Creator Machnoor, Manjunath (author)

Core Title Circuits for Biomedical Telemetry and Stimulation Applications

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2020-12

Publication Date 11/09/2022

Defense Date 09/08/2020

Publisher University of Southern California Libraries (digital)

Tag biomedical stimulation systems,OAI-PMH Harvest,wireless power transfer systems

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Humayun, Mark (committee member), Moghaddam, Mahta (committee member), Monge, Manuel (committee member), Lazzi, Gianluca (dissertation committee chair)

Creator Email machnoor@usc.edu

Unique identifier UC11666281

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Document Type Dissertation

Format theses (aat)

Rights Machnoor, Manjunath

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Type texts

Source batch-786-metadata (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, Carol Little Building, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu