# A Literature Survey on Wireless Power Transfer for Biomedical Devices

Authors: Reem Shadid; Sima Noghanian
Journal: International Journal of Antennas and Propagation
 (2018)

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## Abstract

This paper provides a review and survey of research on power transfer for biomedical applications based on inductive coupling. There is interest in wireless power transfer (WPT) for implantable and wearable biomedical devices, for example, heart pacemaker or implantable electrocardiogram (ECG) recorders. This paper concentrates on the applications based on near-field power transfer methods, summarizes the main design features in the recent literature, and provides some information about the system model and coil optimization.


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## Body

## 1. Introduction

Implantable medical devices such as cochlear implants, cardiac defibrillators, electrocardiogram (ECG) implanted recorders, and pacemakers play an important role in monitoring treatment of various diseases. These devices interact with physiological processes including sensing, drug delivery, and stimulation, to monitor or influence their progression. However, minimizing the size of implanted devices makes them less invasive to human body and decreases the surgical complexity in order to install them easily inside the body. While recent progress in microfabrication has dramatically minimized the size of electronic and mechanical components, electrochemical energy storage has been much slower to miniaturize. In most existing devices, the battery constitutes the bulk of the implant [1]. In addition, surgical procedures for replacing the batteries and the risk of leakage are the major disadvantages of using them [2]. Wireless power transfer (WPT) is used to transmit power to help avoid these problems.In WPT, an external power source will transmit energy to the implanted power receivers. Although many techniques, such as optical and ultrasound methods, have been launched to transfer power wirelessly, wireless powering through radio-frequency (RF) electromagnetic waves is the most established one.Section2 of this paper gives a general overview of the WPT methods based on induction methods. Section 3 presents the concept of inductive coupling and illustrates the circuit models for biomedical WPT applications. Section 4 provides the comparison list of the research works that are summarized in a tabular format in the Appendix. Power efficiency (η) and optimization methods that are achieved in researcher publications are summarized too. Section 5 provides the conclusions.


## 2. A General Review on Wireless Power Transfer

Nikola Tesla was the leader of WPT. In 1891, he successfully performed an experiment to energize a lamp using a pair of coils. Later, he successfully performed similar experiments on two hundred lamps and transmitted power to them over a 25-mile distance [3].WPT can be categorized into two methods: near-field and far-field transmission. Table1 shows a comparison between these two methods. In general, near-field power transfer methods have higher η in comparison to the far-field ones. Most of the WPT applications are using the near-field method. In order to consider any region to be near-field, two conditions should be considered: first, the distance between the transmitter and receiver coil (r) should be less than one wavelength (λ) at the operating frequency (r<λ), and secondly, the largest dimension of the transmitter coil should be less than λ/2. For implantable biomedical device applications based on far-field transfer, a good review may be found in [4]. The far-field methods are based on delivering power to a device using antennas. In this paper, the focus is on the applications of near-field power transfer methods.Table 1
Comparison of WPT methods.
Method of WPT
Frequency
Directivity
Range
Penetration
η
Near field
Low Hz to MHz
Weak
Short
Strong
High
Far field
Medium MHz to THz
Medium to strong
Long
Medium to weak
Medium to lowMost biomedical near-field WPT methods use operating frequencies within the range of 100 kHz to 50 MHz. Comparing the wavelength at this range with the typical transmission, which is between 1 cm and 11 cm, the correspondingλ of the electromagnetic field is relatively long. Therefore, the transfer can be viewed as a near-field progress [5]. There are three major ways to accomplish a near-field WPT: (1) capacitive coupling based on electric fields, (2) inductive coupling based on magnetic fields, and (3) magnetic resonant inductive coupling.WPT by inductive coupling and resonant coupling is the main alternative to power implantable devices [6]. The survey provided in this paper is mainly focused on the studies that considered an inductive method to deliver power wirelessly to biomedical devices.The first reported use of inductive power transfer (IPT) was in the 1960s [7]. This paper introduced IPT to transfer power to an artificial heart. Since then, many implantable devices have used similar methods for power transfer. In the 1970s, IPT was used in other biomedical applications [2, 8–16].In the late 1970s, IPT was used to transfer high levels of power. Some projects were launched in the 1980s, but they were unsuccessful due to the rating of semiconductor devices used in the power supply that limited the use of high frequencies andη [17]. In the mid-1990s, IPT was successfully commercialized in many applications [18]. Nowadays, the WPT based on IPT is still developing in many areas. This paper concentrates on biomedical applications.


## 3. Inductive Coupling Concept and Wireless Power Transfer Models for Biomedical Devices

An IPT system consists of two coils referred to as the “primary” and “secondary” coils. Figure1 shows the system model. Power transfer occurs when a primary source generates magnetic and electric fields, H→ and E→, respectively, that induce voltage V at the secondary receiver
(1)V=jωμ∫H→⋅ds→,where ω is the operating angular frequency and μ is the permeability of transfer medium. According to (1), coupling between coils mainly depends on the amount of magnetic flux linkage between the primary and secondary coils. Decreasing the distance between the primary transmitter and secondary receiver while increasing the length of the coils helps to increase the amount of magnetic flux. If the primary and secondary coils are not well aligned, efficiency (η) will drop down causing more power loss.Figure 1
Inductive coupling principle.A power transfer system block diagram for biomedical systems is shown in Figure2. This system has three components; the first component is the power transmitter. The power transmitter is located outside the body. It may also be worn or placed in a distant location, for example, in a room under the floor, chair, or bed. The power transmitter circuit consists of DC source, a DC-AC converter (which enables transfer of power at the proposed operating frequency), a tuning circuit, a power antenna which allows the data connectivity to send data to the receiver and also as a feedback to receive information sending by the implanted device, and a primary power coil (which allows the power transfer). The second component is the power receiver which is implanted inside the body below the tissue or even patched on human skin. The receiver receives the wireless power and provides a stable energy to the load or use the energy to charge a battery. The receiver circuit consists of a secondary power antenna, a tuning circuit, an AC-DC converter, a DC-DC converter (regulator), and a power management unit to interact with the transmitter through the implanted antenna. The third component is the middle power resonator. This component is used as a third part to resonate at the operating frequency and to help deliver power to farther distance places. It could also be worn or located at the receiver circuit under the human body. This component is not mandatory for all WPT system design.Figure 2
Model of WPT system for a biomedical device.The main goal to be achieved by any WPT design is to transfer power with high efficiency and power stability. There are five main challenges facing that. The first challenge is the transmitter’s and receiver’s size; as the receiver will be located inside the human body, its size will be limited. This small size will affect the quality factor and will decrease the coupling coefficient andη accordingly. The second challenge is the operating frequency; as the operating frequency increases, η will increase, but that will increase the energy loss in human tissue, which is causing increased heat that can be a safety issue. The third challenge is the ratio between the transfer distance and the antennas size. As the distance increases, η decreases. The fourth factor is the lateral and angular misalignments between the transmitter and the receiver antennas, which cause degradation of the coupling factor and as a result, η will decrease too. The fifth challenge is the required power level by the receiver. For low power level application, the main issue is how to transfer power with high η, since efficiency decreases as the power level decreases. On the other hand, the challenges for high power applications are to avoid the thermal issue at the transmitter coil side and how to keep the electromagnetic energy absorbed by the body tissues as low as possible.


## 4. Prior Art

Tables2–4 present the collection of papers on this topic. These papers are focused on the research topics of wireless power transfer for biomedical applications. The papers are sorted in a descending order based on the year they were published. If two papers have the same year of publication, they are sorted based on operating frequency used in the methodology. The design criteria of these papers are as follows.Table 2
Implantable power device modeled in tissue.
Ref
Journal
Year
Frequency
Output power (mW)
Optimization method for inductor dimension
Transmitter dimension (mm)
Receiver dimension [mm]
Gap (mm)
η (%)
Simulation model
[29]
IEEE Antennas and Wireless Propagation Letters
2017
13.56 MHz (power) and 910 MHz (data)
Frequency domain solver in CST MWS
doutT = 83.2dinT = 59.6Circular (CST MWS)
doutT = 24.2dinT = 19.2Circular (CST MWS)
16
17% for power link
2 mm skin, 2 mm fat, 7 mm bone, 50 mm tissue
[30]
IEEE Transactions on Power Electronics
2015
800 KHz
30e3
Based on the method in [31]
doutT = 70dinT = 34Circular litz wireFinite element (FE)
doutR = 70dinR = 34Circular litz wire (FE)
20
95
One layer of skin (performed its effect on simulation)
[32]
IEEE Transactions on Biomedical Circuits and Systems
2015
200 MHz
0.224
Follow flow chart in the paper
doutT = 24Printed hexagon (HFSS)
doutR = 1Wire wound (HFSS)
12
0.56
Design was wrapped with a 10 mm thick layer of beef
[23]
Sensors
2014
13.56 MHz
150
Based on the method in [24]
doutT = 56dinT = 10Printed spiral (Matlab, HFSS, FE & SEMCAD)
doutR = 11.6dinR = 0.5Printed spiral (Matlab, HFSS, FE & SEMCAD)
6
32 to 80
Three layers of 70 × 60 × 6 mm3, 1 mm skin, 2 mm fat, 3 mm muscle
[33]
IEEE Transactions on Industrial Electronics
2014
8.1 MHz
29.8 ~ 93.3
Optimization has been done only for frequency
doutT = 30Printed square (HFSS)
doutR = 20Printed square (HFSS)
12 ~ 20
47.6 to 65.4
Various types of tissue including blood
[34]
“European Solid State Circuit Conference (ESSCIRC)”
2013
160 MHz
>183
Based on the method in [35, 36]
doutT = 14.5Printed square (Momentum EM & HFSS)
doutT = 2.2Printed square (Momentum EM & HFSS)
10
0.8
7.5 mm of muscle layer, 2.5 mm air
[21]
IEEE Transactions on Circuits and Systems
2013
13.56 MHz
10
Based on the method in [19]
60 × 25Printed rectangle (HFSS & CST EM)
25 × 10Printed rectangle (HFSS & CST EM)
10 ~ 50
0.16 to 58.2
Receiver sandwiched between two layers of pork tissues
[36]
IEEE Electron Device Letters
2013
6.78 MHz
10
Based on the method in [37]
doutT = 20Printed square (HFSS)
doutT = 4.5Printed square (HFSS)
5 and 12
30 and 4.3
One layer of muscle tissue
[38]
IEEE Transactions on Biomedical Circuit and Systems
2009
13.56 MHz
Based on the method in [19]
doutT = 24dinT = 9.4Printed square (HFSS)
doutR = 10dinR = 7.2Printed square (HFSS)
10
30.84
Receiver sandwiched between two layers of muscle
[39]
IEEE Transactions on Biomedical Circuits and Systems
2007
6.785 MHz
1 ~ 10
Follow flow chart in the paper
doutT = 30Circular litz wire
doutR = 30Circular litz wire
1 ~ 10
51 to 74
One layer of skin
[40]
IEEE Transactions on Circuits and Systems
2005
1 MHz
250
Coil effective series resistance (ESR) formulations
doutT = 40Circular litz wire
doutT = 22Circular litz wire
7
67
A tissue through retinal prosthesis
[41]
IEEE Transactions on Circuits and Systems
2005
1 MHz
>250
doutT = 40dinT = 32Disk
doutR = 22dinR = 18Disk
7 and 15
33.3 to 65.8
A tissue through retinal prosthesis
[42]
ELSEVIER Sensors and Actuators
2004
700 KHz
50
Using a self-developed design tool and equations
doutT = 60Pancake/disk (FastHenry and Matlab)
doutR = 20Solenoid (FastHenry and Matlab)
30
36
One layer of skinTable 3
Implantable power device modeled in air.
Ref
Journal
Year
Frequency
Output power (mW)
Optimization method for the inductor dimension
Transmitter dimension (mm)
Receiver dimension (mm)
Gap (mm)
η (%)
Simulation model
[32]
IEEE Transactions on Biomedical Circuits and Systems
2015
200 MHz
0.224
Follow flow chart in the paper
doutT = 24Printed hexagonal (HFSS)
doutR = 1Wire wound (HFSS)
12
1.02
Air
[34]
“European Solid State Circuit Conference (ESSCIRC)”
2013
160 MHz
>183
Based on the method in [35, 36]
doutT = 14.5Printed square (Momentum EM & HFSS)
doutT = 2.2Printed square (Momentum EM & HFSS)
10
1.5
Air
[43]
Hindawi: Active and Passive Electronic Components
2012
211.9 KHz
125
Based on the method in [42]
10
12.5
Air
[44]
“Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS”
2011
13.56 MHz
27
Based on the method in [19]
doutT = 27dinT = 11Printed spiral
12 × 10RectangleWire wound litz
7
Air, worn as a jacket on back of a rat
[45]
IEEE Transactions on Biomedical Circuits and Systems
2011
13.56 MHz
49.5
Follow flow chart in the paper
2 coildoutT = 37Printed spiral (HFSS)
2 coildoutR = 10Printed spiral (HFSS)
10
75.7
Air
43.4
3 coildoutT = 43Printed spiral (HFSS)
3 coildoutR = 10Printed spiral (HFSS)
78.63 coil
3.9
4 coildoutT = 36.5Printed spiral (HFSS)
4 coildoutR = 10Printed spiral (HFSS)
83.54 coil
[25]
ELSEVIER: Procedia Engineering
2011
1 MHz
380
Area = 1000 mm2Spiral litz wire
Area = 520 mm2Spiral litz wire
10
50
Air
[20]
IEEE Transactions on Bio Circuits and Systems
2011
700 KHz
100
Follow flow chart in the paper
doutT = 64Spiral litz wire (Spice)
doutR = 22Spiral litz wire (Spice)
20
82
Air
[46]
“2010 3rd International Symposium on Applied Science in Biomedical and Communication Technology”
2010
27 MHz
794
Coil built based on [47], no optimization used
doutR = 15Square (CST MWS)
15
80
Air
[48]
IEEE Transactions on Circuits and Systems
2010
13.56 MHz
11.2
Based on the method in [19]
doutT = 20dinT = 10Printed square
doutR = 10dinR = 6Printed square
5 ~ 20
1 to 14.1
Air
[49]
IEEE Transactions on Biomedical Circuits and Systems
2010
13.56 MHz
Based on the method in [19]
doutT = 79dinT = 11.2Printed square (HFSS)
doutR = 10dinR = 2.96Printed spiral (HFSS)
10
56.65
Air
[22]
“IEEE International Solid-StateCircuits Conference”
2009
13.56 MHz
7.05
Based on the method in [19]
doutT = 168Printed hexagon (HFSS)
doutR = 30Wire wound solenoid (HFSS)
70
80.2
Air
[38]
IEEE Transaction Biomedical Circuit System
2009
13.56 MHz
Based on the method in [19]
doutT = 38dinT = 14.9Printed square (HFSS)
doutR = 10dinR = 5.8Printed square (HFSS)
10
72.22
Air
[24]
“2007 IEEE International Symposium on Circuits and Systems”
2007
6.78 MHz
<100
dinT ≈ 0.18doutTdinR ≈ 0.75doutR
doutT = 52dinT = 10Printed spiral
doutR = 10dinR = 5Printed spiral
15
10 to 20
Air
[19]
IEEE Transactions on Circuits and Systems
2007
1 MHz
Follow flow chart in the paper
doutT = 69dinT = 8Printed square (HFSS)
doutR = 20dinR = 8Printed square (HFSS)
10
41.2
Air
5 MHz
doutT = 70dinT = 8Printed square (HFSS)
doutR = 20dinR = 8Printed square (HFSS)
85.8
[50]
IEEE Transactions on Circuits and Systems
2007
125 KHz
125
Based on the method in [51]
doutT = 36dinT = 13Spiral litz wire (FastHenry-2)
doutR = 26dinR = 12Spiral litz wire (FastHenry-2)
10
50
Air
125 KHz
doutT = 64dinT = 14Spiral litz wire (FastHenry-2)
doutR = 22dinR = 6Spiral litz wire (FastHenry-2)
18
50
500 KHz
doutT = 44dinT = 14Spiral litz wire (FastHenry-2)
doutR = 22dinR = 7Spiral litz wire (FastHenry-2)
10
29.9
[51]
IEEE Transactions on Biomedical Engineering
1996
2 MHz
dinT ≈ 0.4doutT
doutT = 24dinT = 22.5Spiral
doutR = 24dinR = 22.5Spiral
1 ~ 25
5 to 90
Air
doutT = 15.86dinT = 13.58Spiral
doutR = 15.86dinR = 13.58Spiral
doutT = 24With 3.55 turn spiral
doutR = 24With 3.55 turn spiral
[52, 53]
IEEE Transactions on Power Electronics
1992
53 ~123 KHz
48e3
Based on the method in [54, 55]
Area = 37 mm2
Area = 37 mm2
10 ~ 20
72 to 76
AirTable 4
Other model of implantable power device.
Ref
Journal
Year
Frequency
Output power (mW)
Optimization method for inductor dimensions
Transmitter dimension (mm2)
Receiver dimension (mm2)
Gap (mm)
η (%)
Simulation model
[34]
“European Solid State Circuit Conference (ESSCIRC)”
2013
160 MHz
>183
Based on the method in [35, 36]
doutT = 14.5Printed square (Momentum EM & HFSS)
doutT = 2.2Printed square (Momentum EM & HFSS)
10
1
7 mm of 0.2 molar NaCl layer and 3 mm air
[56]
IEEE Transactions on Biomedical Engineering
2012
13.56 MHz
24
Based on the method in [57, 58]
doutT = 480CircularBuilt under floor
Capsule13 × 27
1000
3.04
Endoscopic capsule
[26]
ELSEVIER: Procedia Engineering
2010
300
Capsule16 × 28
Free move
Endoscopic capsule
[38]
IEEE Transaction Biomedical Circuit System
2009
13.56 MHz
Based on the method in [19]
doutT = 30dinT = 11.1Printed square (HFSS)
doutR = 10dinR = 5.5Printed square (HFSS)
10
51.8
Receiver placed between two layers of saline in


### 4.1. Size Optimization Method for Transmitter and Receiver

Optimization methods to determine the transmitter and receiver coil dimensions are used to increase the coupling coefficient and to determine the optimal frequency to improveη. Probably, one of the major challenges with biomedical wireless power transfer is the restrictions on the size of devices. The devices are implanted in layers of body tissue. The maximum size may lay between a few to tens of millimeters. The receiver is usually in a small packaging. As an example, capsule endoscopy is taken orally. The size of this capsule is between 11 mm to 27 mm in general applications [5]. The optimum antenna shape and dimensions for both the transmitter and receiver should be predicted based on optimum operating frequency and the gap range that is needed to power it.Basic optimization for transmitter coil could be performed in two ways which most of the collected paper started with. The first one considers that the transfer distance is known (x is fixed and constant). This method is suitable for medical applications where the device is implanted in a certain place under the skin and within tissue layers. Based on that, the optimum transmitter coil radius (a) is calculated using (2). This equation is derived by calculating the maximum generated H→ field by the transmitter coil at certain distance [5].
(2)a=2x.The second optimization method is presented for those applications having portable or nonfixed receivers, with predicted range such as capsule endoscopy. Transmitter coil radius is optimized by calculating the integration ofH→ (Ψ) within the transfer range (x) [5], based on the following:
(3)Ψ=∫x1x2H→⋅dx→=∫x1x2INa22a2+x23dx,where I is the coil current in ampere and N is the number of coil turns. One example of the capsule endoscope is modeled on Matlab® to determine the optimum coil radius for a range of distance between the centers of transmitter coil and the capsule endoscope (x1–x2) that varies within 0–10 cm, in steps of 1 cm. Figure 3 shows the results. For example, the optimized transmitter radius for the transfer range from 2 cm to10 cm is 7 cm.Figure 3
Magnetic field integration for specified transfer range.The sixth columns of Tables2–4 indicate the optimization method that each paper performed. The methods presented in [19, 20] use custom-made methods for geometry optimization. Methods presented in [21, 22] are based on the optimization method described in [19]. This optimization method is used when the operating frequency of the design is known. This method applies five steps for optimizing the dimensions of the transmitter and receiver antenna. The first step is to apply the design constraints for the receiver. The second step is to set the initial values for coil dimensions based on manufacturing limitation and optimum transmitter coil dimension described at the beginning of this section. The third step is to optimize the size and fill factor for the transmitter coil. The fourth step is to set the line width and fill factor for the receiver coil side. The fifth step is to return back and reset the size and line width of the transmitter side. After that, iterations are going until the value of the required tolerance of the η value is achieved.The work in [23] follows Harrison’s method to optimize the coil size [24]. Harrison’s method is used for designing planar spiral pancake-shape coils. He concluded that the maximum η could be achieved by considering dinT=0.18doutT and dinR=0.75doutR, where dinT is the inner transmitter diameter, doutT is the outer transmitter diameter, dinR is the inner receiver diameter, and doutR is the outer receiver diameter. The paper results are based on derived equations and an experimental study, which was conducted using multiple coils and their dimensions at maximum achieved η.Reported research in [25, 26] did not include any optimization process to calculate the geometries of coils.


### 4.2. Circuit Model and Efficiency Calculation

The simplified schematic model circuit of the resonant coupling inductive link is shown in Figure4. L1, R1, and Cp1 are the self-inductance, resistance, and capacitance of the transmitter coil, respectively. L2, R2, and Cp2 are the self-inductance, resistance, and capacitance of the receiver coil, respectively. RL is the load resistance. CS1 and CS2 are the added capacitance on the transmitter and receiver part, respectively. The highest voltage gain and efficiency (η) could be achieved when both inductors (L1 and L2) and total equivalent capacitors (C1 and C2) from the transmitter and receiver are tuned at the operating frequency according to the following:
(4)ω0=1L1C1=1L2C2,where C1≈CS1 and C2≈CS2+Cp2; the delivered power to primary LC tank is divided between the transmitter coil resistance R1, and the secondary load RL. The primary resistance converts the power to heat, and the power is transferred into the secondary coil through their mutual inductance (M). M is related to the coupling coefficient k according to the following:
(5)k=ML1L2.Figure 4
Circuit model of inductive coupling.The quality factors for the transmitter (Q1), receiver (Q2), and load (QL) circuit are calculated as follows:
(6)Q1=ω0L1R1,Q2=ω0L2R2,QL=RLω0L2.The total AC-AC efficiency (η) is calculated according to the following:
(7)η=k2Q1Q21+k2Q1Q2+Q2/QL×11+QL/Q2.Consequently, maximum achievable efficiency (ηmax) is given by
(8)ηmax=k2Q1Q21+1+k2Q1Q22.Details of derivation of (7) and (8) can be found in [27]. The efficiency of DC-DC depends mostly on the efficiency of converters and is calculated as the product of η and the converter efficiency.


### 4.3. Summary of Achieved Performances

Figure5 shows the efficiency versus the output or delivered power that the receiver collects from the transmitter for the papers listed in Tables 2, 3, and 4. It should be noted that the efficiency increases at high delivered power. However, various efficiencies may have been achieved for the same delivered power depending on the system design.Figure 5
Efficiency versus delivered power.Figure6 presents the graph of efficiency versus frequency. It is clear that the frequency for most of the biomedical devices in the papers reviewed in this survey is below 50 MHz.Figure 6
Efficiency versus frequency.


### 4.4. Future Directions

Nowadays, the focus is on miniaturizing implantable devices to reduce surgical complexity and infection risk. Electromagnetic energy transfer enables transcutaneous communication and powering with fully implantable wireless biomedical devices [28]. The main goal of WPT is to provide sufficient power to the implanted device while minimizing tissue heating due to the absorbed energy. This has led to an extensive research toward maximizing efficiency, through optimizing operating frequency, coils geometries, impedance matching, and power delivery.The last columns of Tables2–4 summarize the models that were considered as a medium surrounding the implanted device. Future directions for research also include addressing the effects of expected variations in the tissue medium and monitoring absorption in tissue to inform adjustments to transmit power, frequency, and impedance matching.


## 4.1. Size Optimization Method for Transmitter and Receiver

Optimization methods to determine the transmitter and receiver coil dimensions are used to increase the coupling coefficient and to determine the optimal frequency to improveη. Probably, one of the major challenges with biomedical wireless power transfer is the restrictions on the size of devices. The devices are implanted in layers of body tissue. The maximum size may lay between a few to tens of millimeters. The receiver is usually in a small packaging. As an example, capsule endoscopy is taken orally. The size of this capsule is between 11 mm to 27 mm in general applications [5]. The optimum antenna shape and dimensions for both the transmitter and receiver should be predicted based on optimum operating frequency and the gap range that is needed to power it.Basic optimization for transmitter coil could be performed in two ways which most of the collected paper started with. The first one considers that the transfer distance is known (x is fixed and constant). This method is suitable for medical applications where the device is implanted in a certain place under the skin and within tissue layers. Based on that, the optimum transmitter coil radius (a) is calculated using (2). This equation is derived by calculating the maximum generated H→ field by the transmitter coil at certain distance [5].
(2)a=2x.The second optimization method is presented for those applications having portable or nonfixed receivers, with predicted range such as capsule endoscopy. Transmitter coil radius is optimized by calculating the integration ofH→ (Ψ) within the transfer range (x) [5], based on the following:
(3)Ψ=∫x1x2H→⋅dx→=∫x1x2INa22a2+x23dx,where I is the coil current in ampere and N is the number of coil turns. One example of the capsule endoscope is modeled on Matlab® to determine the optimum coil radius for a range of distance between the centers of transmitter coil and the capsule endoscope (x1–x2) that varies within 0–10 cm, in steps of 1 cm. Figure 3 shows the results. For example, the optimized transmitter radius for the transfer range from 2 cm to10 cm is 7 cm.Figure 3
Magnetic field integration for specified transfer range.The sixth columns of Tables2–4 indicate the optimization method that each paper performed. The methods presented in [19, 20] use custom-made methods for geometry optimization. Methods presented in [21, 22] are based on the optimization method described in [19]. This optimization method is used when the operating frequency of the design is known. This method applies five steps for optimizing the dimensions of the transmitter and receiver antenna. The first step is to apply the design constraints for the receiver. The second step is to set the initial values for coil dimensions based on manufacturing limitation and optimum transmitter coil dimension described at the beginning of this section. The third step is to optimize the size and fill factor for the transmitter coil. The fourth step is to set the line width and fill factor for the receiver coil side. The fifth step is to return back and reset the size and line width of the transmitter side. After that, iterations are going until the value of the required tolerance of the η value is achieved.The work in [23] follows Harrison’s method to optimize the coil size [24]. Harrison’s method is used for designing planar spiral pancake-shape coils. He concluded that the maximum η could be achieved by considering dinT=0.18doutT and dinR=0.75doutR, where dinT is the inner transmitter diameter, doutT is the outer transmitter diameter, dinR is the inner receiver diameter, and doutR is the outer receiver diameter. The paper results are based on derived equations and an experimental study, which was conducted using multiple coils and their dimensions at maximum achieved η.Reported research in [25, 26] did not include any optimization process to calculate the geometries of coils.


## 4.2. Circuit Model and Efficiency Calculation

The simplified schematic model circuit of the resonant coupling inductive link is shown in Figure4. L1, R1, and Cp1 are the self-inductance, resistance, and capacitance of the transmitter coil, respectively. L2, R2, and Cp2 are the self-inductance, resistance, and capacitance of the receiver coil, respectively. RL is the load resistance. CS1 and CS2 are the added capacitance on the transmitter and receiver part, respectively. The highest voltage gain and efficiency (η) could be achieved when both inductors (L1 and L2) and total equivalent capacitors (C1 and C2) from the transmitter and receiver are tuned at the operating frequency according to the following:
(4)ω0=1L1C1=1L2C2,where C1≈CS1 and C2≈CS2+Cp2; the delivered power to primary LC tank is divided between the transmitter coil resistance R1, and the secondary load RL. The primary resistance converts the power to heat, and the power is transferred into the secondary coil through their mutual inductance (M). M is related to the coupling coefficient k according to the following:
(5)k=ML1L2.Figure 4
Circuit model of inductive coupling.The quality factors for the transmitter (Q1), receiver (Q2), and load (QL) circuit are calculated as follows:
(6)Q1=ω0L1R1,Q2=ω0L2R2,QL=RLω0L2.The total AC-AC efficiency (η) is calculated according to the following:
(7)η=k2Q1Q21+k2Q1Q2+Q2/QL×11+QL/Q2.Consequently, maximum achievable efficiency (ηmax) is given by
(8)ηmax=k2Q1Q21+1+k2Q1Q22.Details of derivation of (7) and (8) can be found in [27]. The efficiency of DC-DC depends mostly on the efficiency of converters and is calculated as the product of η and the converter efficiency.


## 4.3. Summary of Achieved Performances

Figure5 shows the efficiency versus the output or delivered power that the receiver collects from the transmitter for the papers listed in Tables 2, 3, and 4. It should be noted that the efficiency increases at high delivered power. However, various efficiencies may have been achieved for the same delivered power depending on the system design.Figure 5
Efficiency versus delivered power.Figure6 presents the graph of efficiency versus frequency. It is clear that the frequency for most of the biomedical devices in the papers reviewed in this survey is below 50 MHz.Figure 6
Efficiency versus frequency.


## 4.4. Future Directions

Nowadays, the focus is on miniaturizing implantable devices to reduce surgical complexity and infection risk. Electromagnetic energy transfer enables transcutaneous communication and powering with fully implantable wireless biomedical devices [28]. The main goal of WPT is to provide sufficient power to the implanted device while minimizing tissue heating due to the absorbed energy. This has led to an extensive research toward maximizing efficiency, through optimizing operating frequency, coils geometries, impedance matching, and power delivery.The last columns of Tables2–4 summarize the models that were considered as a medium surrounding the implanted device. Future directions for research also include addressing the effects of expected variations in the tissue medium and monitoring absorption in tissue to inform adjustments to transmit power, frequency, and impedance matching.


## 5. Conclusion

This paper presents a short survey of WPT based on IPT concept for biomedical applications. The delivered power to biomedical devices reported in the collected papers ranges from few mW to 48 W, with maximum efficiency of up to 95% for 20 mm range.



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*Source: 4382841-2018-04-12.xml*