Wireless Power Transmission on Biomedical Applications

Abstract

Wireless power transmission (WPT) can provide an alternative for wireless power in implantable medical devices (IMDs). The WPT in implantable medical devices will involve many emerging biomedical topics, such as implantable pacemakers, optogenetic devices, and bio-impedance sensors. To this end, this chapter comprehensively reviews the recent WPT studies for those mentioned above emerging biomedical applications. The specific key components are carried out for those applications. Besides, the operation principle and system design are presented. In conclusion, this chapter’s significance can help evolve reliable implantable device development in the future.

1. Introduction

Wireless power transmission (WPT) is an emerging technology to transmit power without wires [1, 2]. It is widely studied in various applications such as consumer electronics charging [3], radio-frequency identification (RFID) system [4], electric vehicle charging [5], biomedical applications [6], etc. Especially in implantable devices, the market benefit of global implantable medical devices achieved a value of US$ 120.5 billion in 2021 by IMARC Group. The market can be expected to reach US$ 168.3 billion by 2027, exhibiting at a compound annual growth rate (CAGR) of 5.54% during 2022–2027. In practice, implantable devices solve today’s problems using advanced medical technologies such as a well-known pacemaker and capsule endoscopy [7, 8]. The pacemaker and capsule endoscopy invention brings new perspectives for cardiovascular disease therapy and direct health diagnosis of the whole small bowel. Although several miniatured battery systems have been developed to provide several years of power supply for implantable devices, a battery replacement would induce patients’ inconvenient and unexpected surgery risks [9, 10]. Recently, the WPT technique has been widely applied in implantable medical devices that are expected to power supply issues in the future [11, 12].

WPT technique can be mainly divided into the coupling and radiative approaches [13, 14], as shown in Figure 1. The WPT coupling can be categorized into magnetic and electric field methods. The radiative approach can be categorized into electromagnetic waves and optical power transmission. In the radiative method (far-field), power is transferred by electromagnetic radiation in terms of microwave, laser, and light. Although radiative techniques can transfer power over longer distances, the large environmental loss-induced transfer efficiency is considerable due to poor air medium. The nonradiative method (near field) utilizes magnetic field and electric field coupling to approach wireless power transfer. The main advantage of nonradiative techniques is high transfer efficiency; however, its technical limitation is that the transfer distance is limited.

Figure 1.

WPT classification, including nonradiative and radiative methods.

The nonradiative method is also called coupling-based WPT, which can be described as the power-transmitting side (primary side) and power-receiving side (secondary side). The coupling type can be classified as a magnetic field (Figure 2a) and electrical field coupling (Figure 2b). Both magnetic and electric field coupling methods can be further categorized as resonance mode, based on LC resonance (Figure 2c and d).

Figure 2.

Magnetic and electric field coupling with and without resonant circuit.

2. Magnetic field coupling without resonance

The magnetic field coupling without resonance type utilizes the principle of electromagnetic induction, as shown in Figure 3. According to Ampere’s law as Eq. (1), the magnetic pulsing (dB/dt) of the primary coil can be generated by time-varying driving current (dI/dt). Where B, μ₀, J are magnetic field, permeability, and current density. The electric field E can be induced on the secondary coil, according to Faraday’s law as Eq. (2) [9, 15]. Thus, the charge can be stored via a secondary coil.

Figure 3.

Circuit topology of electromagnetic induction.

$$▽\times \mathbf{B}={\mathrm{\mu }}_0\mathbf{J}$$E1

$$\mathbf{E}=-\frac{\partial \mathbf{B}}{\mathrm{\partial t}}$$E2

To understand the principle of magnetic field coupling without resonance, Figure 3 shows the topology of the circuit analysis. The mutual inductance, ${\mathrm{L}}_{\mathrm{m}}=\mathrm{k}\sqrt{{\mathrm{L}}_1{\mathrm{L}}_2}$, depends on the distance x between the two coils, where k is the coupling factor (0 < k < 1) between the primary and the secondary coil. Based on Kirchhoff’s voltage law, Eqs. (3) and (4) can be obtained as below [16]:

$$\mathrm{j\omega }{\mathrm{L}}_1{\mathrm{I}}_1+{\mathrm{I}}_1{\mathrm{R}}_1+\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}{\mathrm{I}}_2={\mathrm{U}}_1$$E3

$$\mathrm{j\omega }{\mathrm{L}}_2{\mathrm{I}}_2+{\mathrm{I}}_2{\mathrm{R}}_2+{\mathrm{I}}_2{\mathrm{R}}_{\mathrm{L}}+\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}{\mathrm{I}}_1=0$$E4

I₂ can be expressed as Eq. (5), according to Eq. (4).

$${\mathrm{I}}_2=-{\mathrm{I}}_1\left[\frac{\mathrm{\omega }{\mathrm{L}}_{\mathrm{m}}}{\mathrm{\omega }{\mathrm{L}}_2-\mathrm{j}\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}\right]$$E5

The relation between I₁ and U₁ can be obtained as Eq. (6), according to Eqs. (3) and (5).

$${\mathrm{I}}_1=\left[\frac{{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}+\mathrm{j\omega }{\mathrm{L}}_2}{\left({\mathrm{R}}_1+\mathrm{j\omega }{\mathrm{L}}_1\right)\left(\mathrm{j\omega }{\mathrm{L}}_2+{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}\right]{\mathrm{U}}_1$$E6

The relation between I₁ and I₂ can be expressed as Eq. (7), according to Eqs. (5) and (6).

$${\mathrm{I}}_2=-\left[\frac{\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}}{\left({\mathrm{R}}_1+\mathrm{j\omega }{\mathrm{L}}_1\right)\left(\mathrm{j\omega }{\mathrm{L}}_2+{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}\right]{\mathrm{U}}_1$$E7

The ratio of I₁ and I₂ can be expressed as Eq. (8), according to Eqs. (6) and (7).

$$\frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}=-\frac{{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}+\mathrm{j\omega }{\mathrm{L}}_2}{\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}}$$E8

To better understand the input impedance and power efficiency of the circuit, a T-type equivalent circuit is used in Figure 4.

Figure 4.

T-type equivalent circuit for electromagnetic induction.

$${\mathrm{V}}_{\mathrm{Lm}2}=\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}{\mathrm{I}}_1$$E9

$${\mathrm{V}}_{\mathrm{Lm}2}=\frac{\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}+\mathrm{j\omega }{\mathrm{L}}_2\right)}{\left({\mathrm{R}}_1+\mathrm{j\omega }{\mathrm{L}}_1\right)\left(\mathrm{j\omega }{\mathrm{L}}_2+{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}{\mathrm{U}}_1$$E10

According to Eq. (11), Z_in2 can be obtained from Eqs. (8) and (9).

$${\mathrm{Z}}_{\text{in}2}=\frac{{\mathrm{V}}_{\mathrm{Lm}2}}{-{\mathrm{I}}_2}=\frac{\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}{\mathrm{I}}_1}{-{\mathrm{I}}_2}={\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}+\mathrm{j\omega }{\mathrm{L}}_2$$E11

Then, Z₂ can be further obtained, according to Eq. (12).

$${\mathrm{Z}}_2=\frac{{\mathrm{V}}_{\mathrm{Lm}1}}{{\mathrm{I}}_1}=\frac{\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}{\mathrm{I}}_2}{{\mathrm{I}}_1}=\frac{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}{{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}+\mathrm{j\omega }{\mathrm{L}}_2}$$E12

Finally, the Z_in1 can be acquired, according to Eq. (13).

$${\mathrm{Z}}_{\text{in}1}={\mathrm{R}}_1+\mathrm{j\omega }{\mathrm{L}}_1+{\mathrm{Z}}_2={\mathrm{R}}_1+\mathrm{j\omega }{\mathrm{L}}_1+\frac{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}{{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}+\mathrm{j\omega }{\mathrm{L}}_2}$$E13

To understand the power efficiency, the energy loss ratio for the primary-side internal resistance, secondary resistance, and load can be denoted by P_R1, P_R2, and P_RL as Eq. (14).

$${\mathrm{P}}_{{\mathrm{R}}_1}:{\mathrm{P}}_{{\mathrm{R}}_2}:{\mathrm{P}}_{\mathrm{L}}={\left|{\mathrm{I}}_1\right|}^2{\mathrm{R}}_1:{\left|{\mathrm{I}}_2\right|}^2{\mathrm{R}}_2:{\left|{\mathrm{I}}_2\right|}^2{\mathrm{R}}_{\mathrm{L}}$$E14

The square ratio of I₂ and I₁ can be expressed as Eq. (15), according to Eq. (8)

$${\left|\frac{{\mathrm{I}}_2}{{\mathrm{I}}_1}\right|}^2=\frac{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}{{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}$$E15

The power ratio can be rewritten as Eq. (16), according to Eqs. (14) and (15).

$${\mathrm{P}}_{{\mathrm{R}}_1}:{\mathrm{P}}_{{\mathrm{R}}_2}:{\mathrm{P}}_{\mathrm{L}}=\left\{{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_1:\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_2:\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_{\mathrm{L}}$$E16

Finally, the power efficiency can be obtained, according to Eq. (17).

$$\mathrm{\eta }=\frac{{\mathrm{P}}_{\mathrm{L}}}{{\mathrm{P}}_{\text{in}}}=\frac{{\mathrm{P}}_{\mathrm{L}}}{{\mathrm{P}}_{{\mathrm{R}}_1}+{\mathrm{P}}_{{\mathrm{R}}_2}+{\mathrm{P}}_{\mathrm{L}}}=\frac{\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_{\mathrm{L}}}{\left\{{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_1+\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_2+\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_{\mathrm{L}}}$$E17

3. Magnetic field coupling with resonance

Compared with electromagnetic induction, magnetic resonance coupling utilizes resonance with the series capacitor in primary and secondary sides to approach high efficiency and high power (Figure 5). Based on Kirchhoff’s voltage law, Eqs. (18) and (19) can be obtained as below [16]:

Figure 5.

Circuit topology of magnetic field coupling with resonance.

$$\frac{1}{\mathrm{j\omega }{\mathrm{C}}_1}{\mathrm{I}}_1+{\mathrm{R}}_1{\mathrm{I}}_1+\mathrm{j\omega }{\mathrm{L}}_1{\mathrm{I}}_1+\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}{\mathrm{I}}_2={\mathrm{U}}_1$$E18

$$\mathrm{j\omega }{\mathrm{L}}_2{\mathrm{I}}_2+{\mathrm{R}}_2{\mathrm{I}}_2+\frac{1}{\mathrm{j\omega }{\mathrm{C}}_2}{\mathrm{I}}_2+{\mathrm{R}}_{\mathrm{L}}{\mathrm{I}}_2+\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}{\mathrm{I}}_1=0$$E19

I₂ can be expressed as Eq. (20), according to Eq. (18).

$${\mathrm{I}}_2=\frac{-\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}}{\mathrm{j\omega }{\mathrm{L}}_2+\frac{1}{\mathrm{j\omega }{\mathrm{C}}_2}+{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}}{\mathrm{I}}_1$$E20

The relation between I₁ and U₁ can be expressed as Eq. (21), according to Eqs. (18) and (20).

$${\mathrm{I}}_1=\left\{\left.\frac{{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}+\mathrm{j}\left(\mathrm{\omega }{\mathrm{L}}_2-\frac{1}{\mathrm{\omega }{\mathrm{C}}_2}\right)}{\left[({\mathrm{R}}_1+\mathrm{j}\left(\mathrm{\omega }{\mathrm{L}}_1-\frac{1}{\mathrm{\omega }{\mathrm{C}}_1}\right)\right]\left[{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}+\mathrm{j}\left(\mathrm{\omega }{\mathrm{L}}_2-\frac{1}{\mathrm{\omega }{\mathrm{C}}_2}\right)\right]+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}\right\}\right.{\mathrm{U}}_1$$E21

The relation between I₂ and U₁ can be expressed as Eq. (22), according to Eqs. (20) and (21).

$${\mathrm{I}}_2=-\left\{\left.\frac{\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}}{\left[({\mathrm{R}}_1+\mathrm{j}\left(\mathrm{\omega }{\mathrm{L}}_1-\frac{1}{\mathrm{\omega }{\mathrm{C}}_1}\right)\right]\left[{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}+\mathrm{j}\left(\mathrm{\omega }{\mathrm{L}}_2-\frac{1}{\mathrm{\omega }{\mathrm{C}}_2}\right)\right]+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}\right\}\right.{\mathrm{U}}_1$$E22

The relation between I₁ and U₁ can be expressed as Eq. (23), according to Eqs. (21) and (22).

$$\frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}=-\frac{{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}+\mathrm{j\omega }\left(\mathrm{\omega }{\mathrm{L}}_2-\frac{1}{\mathrm{\omega }{\mathrm{C}}_2}\right)}{\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}}$$E23

When the operating and resonant frequencies are equal on primary and secondary sides, I₁ and I₂ can be expressed as (25) and (26), according to Eqs. (21), (22), and (24).

$${\mathrm{\omega }}_0={\mathrm{\omega }}_1={\mathrm{\omega }}_2=\frac{1}{\sqrt{{\mathrm{L}}_1{\mathrm{C}}_1}}=\frac{1}{\sqrt{{\mathrm{L}}_2{\mathrm{C}}_2}}$$E24

$${\mathrm{I}}_1=\frac{{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}}{{\mathrm{R}}_1\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}{\mathrm{U}}_1$$E25

$${\mathrm{I}}_2=-\frac{\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}}{{\mathrm{R}}_1\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}{\mathrm{U}}_1$$E26

The ratio of I₁ and I₂ can be rewritten as Eq. (27), according to Eqs. (25) and (26).

$$\frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}=-\frac{{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}}{\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}}$$E27

To further understand the input impedance and power efficiency of the magnetic field coupling with the resonance circuit, a T-type equivalent circuit is used as Figure 6.

Figure 6.

T-type equivalent circuit for magnetic field coupling with resonance.

$${\mathrm{V}}_{\mathrm{Lm}2}=\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}{\mathrm{I}}_1$$E28

$${\mathrm{V}}_{\mathrm{Lm}2}=\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}\frac{{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}}{{\mathrm{R}}_1\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}{\mathrm{U}}_1$$E29

Z_in2 can be obtained as Eq. (30), according to Eqs. (26) and (29).

$${\mathrm{Z}}_{\text{in}2}=\frac{{\mathrm{V}}_{\mathrm{Lm}2}}{-{\mathrm{I}}_2}=\frac{\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}{\mathrm{I}}_1}{-{\mathrm{I}}_2}={\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}$$E30

Then, Z₂ can be further obtained as Eq. (31).

$${\mathrm{Z}}_2=\frac{{\mathrm{V}}_{\mathrm{Lm}1}}{{\mathrm{I}}_1}=\frac{\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}{\mathrm{I}}_2}{{\mathrm{I}}_1}=\frac{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}{{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}}$$E31

Finally, the Z_in1 can be acquired, according to Eq. (32).

$${\mathrm{Z}}_{\text{in}1}={\mathrm{R}}_1+\frac{1}{\mathrm{j\omega }{\mathrm{C}}_1}+\mathrm{j\omega }{\mathrm{L}}_1+{\mathrm{Z}}_2={\mathrm{R}}_1+\frac{1}{\mathrm{j\omega }{\mathrm{C}}_1}+\mathrm{j\omega }{\mathrm{L}}_1+\frac{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}{{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}}$$E32

To understand the power efficiency, the ratio of energy loss for the primary-side internal resistance, secondary resistance, and load can be denoted by P_R1, P_R2, and P_RL as Eq. (14).

$${\mathrm{P}}_{{\mathrm{R}}_1}:{\mathrm{P}}_{{\mathrm{R}}_2}:{\mathrm{P}}_{\mathrm{L}}={\left|{\mathrm{I}}_1\right|}^2{\mathrm{R}}_1:{\left|{\mathrm{I}}_2\right|}^2{\mathrm{R}}_2:{\left|{\mathrm{I}}_2\right|}^2{\mathrm{R}}_{\mathrm{L}}$$E33

The square ratio of I₂ and I₁ can be expressed as Eq. (34), according to Eq. (27).

$${\left|\frac{{\mathrm{I}}_2}{{\mathrm{I}}_1}\right|}^2=\frac{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}{{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2}$$E34

The power ratio can be rewritten as Eq. (35), according to Eqs. (33) and (34).

$${\mathrm{P}}_{{\mathrm{R}}_1}:{\mathrm{P}}_{{\mathrm{R}}_2}:{\mathrm{P}}_{\mathrm{L}}=\left\{{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2\right\}{\mathrm{R}}_1:\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_2:\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_{\mathrm{L}}$$E35

Finally, the power efficiency can be obtained, according to Eq. (36).

$$\mathrm{\eta }=\frac{{\mathrm{P}}_{\mathrm{L}}}{{\mathrm{P}}_{\text{in}}}=\frac{{\mathrm{P}}_{\mathrm{L}}}{{\mathrm{P}}_{{\mathrm{R}}_1}+{\mathrm{P}}_{{\mathrm{R}}_2}+{\mathrm{P}}_{\mathrm{L}}}=\frac{\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_{\mathrm{L}}}{\left\{{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2\right\}{\mathrm{R}}_1+\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_2+\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_{\mathrm{L}}}$$E36

Table 1 summarizes the results from the previous derivation in terms of the efficiency and power of the two types of magnetic field coupling circuits. With C₁ and C₂ inserted on the primary and secondary sides, the power efficiency and power at R_load will increase, which is why resonance is important.

	Efficiency	Power at Rload
Magnetic field coupling without resonance	$\frac{\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_{\mathrm{L}}}{\left\{{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_1+\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_2+\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_{\mathrm{L}}}$	${\left|\frac{\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}}{\left({\mathrm{R}}_1+\mathrm{j\omega }{\mathrm{L}}_1\right)\left(\mathrm{j\omega }{\mathrm{L}}_2+{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}\right|}^2{{\mathrm{U}}_1}^2{\mathrm{R}}_{\mathrm{L}}$
Magnetic field coupling With resonance	$\frac{\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_{\mathrm{L}}}{\left\{{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2\right\}{\mathrm{R}}_1+\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_2+\left\{{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2\right\}{\mathrm{R}}_{\mathrm{L}}}$	${\left|\frac{\mathrm{j\omega }{\mathrm{L}}_{\mathrm{m}}}{{\mathrm{R}}_1\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)+{\mathrm{\omega }}^2{{\mathrm{L}}_{\mathrm{m}}}^2}\right|}^2{{\mathrm{U}}_1}^2{\mathrm{R}}_{\mathrm{L}}$

Table 1.

Comparison between magnetic field coupling under either no or with resonance.

4. Electric field coupling

Compared with magnetic field coupling, the electric field coupling without resonance uses a displacement current instead of an electromagnetic induction (Figure 7), as Eq. (37). Where ε, E, and D are permittivity, electric field intensity, electric flux density, respectively [17, 18, 19].

Figure 7.

Diagram of displacement current.

$$\mathrm{I}=\frac{\partial \mathbf{D}}{\mathrm{\partial t}}\bullet \mathrm{S}=\mathrm{\epsilon }\frac{\partial \mathbf{E}}{\mathrm{\partial t}}\bullet \mathrm{S}$$E37

In Figure 8, the mutual inductance of C_m between two capacitances on the distance x between the two coils can be written as ${\mathrm{C}}_{\mathrm{m}}=\mathrm{k}\sqrt{{\mathrm{C}}_1{\mathrm{C}}_2}$.

Figure 8.

Circuit topology of electric field coupling with resonance.

The electrical field coupling schematic diagram can be equivalent to π-type coupling, as shown in Figure 9. Based on the mesh-analysis method, the basic mathematical expression can be described as a matrix, according to Eq. (38).

Figure 9.

π-type equivalent circuit for electric field coupling with resonance.

$$\left[\begin{array}{c}\mathrm{U}\\ 0\\ 0\end{array}\right]=\left[\begin{array}{ccc}{\mathrm{R}}_1+{\mathrm{j\omega L}}_1+\frac{1}{\mathrm{j\omega }\left({\mathrm{C}}_1-{\mathrm{C}}_{\mathrm{m}}\right)}& -\frac{1}{\mathrm{j\omega }\left({\mathrm{C}}_1-{\mathrm{C}}_{\mathrm{m}}\right)}& 0\\ -\frac{1}{\mathrm{j\omega }\left({\mathrm{C}}_1-{\mathrm{C}}_{\mathrm{m}}\right)}& \frac{1}{\mathrm{j\omega }\left({\mathrm{C}}_1-{\mathrm{C}}_{\mathrm{m}}\right)}+\frac{1}{\mathrm{j\omega }{\mathrm{C}}_{\mathrm{m}}}+\frac{1}{\mathrm{j\omega }\left({\mathrm{C}}_2-{\mathrm{C}}_{\mathrm{m}}\right)}& -\frac{1}{\mathrm{j\omega }\left({\mathrm{C}}_2-{\mathrm{C}}_{\mathrm{m}}\right)}\\ 0& -\frac{1}{\mathrm{j\omega }\left({\mathrm{C}}_2-{\mathrm{C}}_{\mathrm{m}}\right)}& {\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}+{\mathrm{j\omega L}}_2+\frac{1}{\mathrm{j\omega }\left({\mathrm{C}}_2-{\mathrm{C}}_{\mathrm{m}}\right)}\end{array}\right]\left[\begin{array}{c}{\mathrm{I}}_{\mathrm{l}1}\\ {\mathrm{I}}_{\mathrm{m}}\\ {\mathrm{I}}_{\mathrm{l}2}\end{array}\right]$$E38

$${\mathrm{Z}}_{\text{in}2}=\frac{1}{\mathrm{j\omega }{\mathrm{C}}_2+\frac{1}{{\mathrm{R}}_2+\mathrm{j\omega }{\mathrm{L}}_2+{\mathrm{R}}_{\mathrm{L}}}}$$E39

$${\mathrm{Z}}_2=\frac{1}{{\mathrm{\omega }}^2{\mathrm{C}}_{\mathrm{m}}^2{\mathrm{Z}}_{\text{in}2}}$$E40

$${\mathrm{Z}}_{\text{in}1}=\frac{1}{\mathrm{j\omega }{\mathrm{C}}_1+\frac{1}{{\mathrm{Z}}_2}}+\mathrm{j\omega }{\mathrm{L}}_1+{\mathrm{R}}_1$$E41

To analyze the input impedance, the extended π-type circuit with a separate capacitance is shown in Figure 10. The input impedance of each stage can be expressed as Eqs. (38), (39), and (40).

Figure 10.

π-type circuit with a separate capacitance for electric field coupling with resonance.

When operating frequency is equal to the resonant frequency on the secondary side, the imaginary part of the Z_in2 becomes zero. Then, the resonant frequency can be acquired as Eq. (42).

$${\mathrm{\omega }}_2=\sqrt{\frac{1}{{\mathrm{L}}_2{\mathrm{C}}_2}-{\left(\frac{{\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}}{{\mathrm{L}}_2}\right)}^2}$$E42

In the same way, when the operating frequency is equal to the resonant frequency on the primary side, the imaginary part of the Z_in1 becomes zero. The L₁ can be obtained as Eq. (43).

$$\begin{array}{rcl}{\mathrm{L}}_1& =& \frac{{\mathrm{C}}_1{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2-{\mathrm{\omega }}_1^2\left\{{\mathrm{C}}_2\left[{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2+{\left({\mathrm{\omega L}}_2\right)}^2\right]-{\mathrm{L}}_2\right\}\left\{{\mathrm{L}}_2{\mathrm{C}}_1-\left({\mathrm{C}}_1{\mathrm{C}}_2-{\mathrm{C}}_{\mathrm{m}}^2\right)\left[{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2+{\left({\mathrm{\omega L}}_2\right)}^2\right]\right\}}{{\mathrm{\omega }}_1^4{\left\{{\mathrm{L}}_2{\mathrm{C}}_1-\left({\mathrm{C}}_1{\mathrm{C}}_2-{\mathrm{C}}_{\mathrm{m}}^2\right)\left[{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2+{\left({\mathrm{\omega L}}_2\right)}^2\right]\right\}}^2+{\mathrm{\omega }}_1^2{\mathrm{C}}_1^2{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2}\end{array}$$E43

To understand the power efficiency, the ratio of energy loss for the primary-side internal resistance, secondary-side internal resistance, and load can be denoted by P_R1, P_R2, and P_RL as Eq. (44).

$${\mathrm{P}}_{{\mathrm{R}}_1}:{\mathrm{P}}_{{\mathrm{R}}_2}:{\mathrm{P}}_{{\mathrm{R}}_{\mathrm{L}}}={\left|{\mathrm{I}}_1\right|}^2{\mathrm{R}}_1:{\left|{\mathrm{I}}_2\right|}^2{\mathrm{R}}_2:{\left|{\mathrm{I}}_2\right|}^2{\mathrm{R}}_{\mathrm{L}}$$E44

The square ratio of I₂ and I₁ can be calculated as Eq. (45), according to Eq. (38) [16].

$${\left|\frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}\right|}^2=\frac{{\mathrm{\omega }}^2{\mathrm{C}}_1{\mathrm{C}}_2\left[{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2+{\left({\mathrm{\omega L}}_2\right)}^2\right]+{\mathbf{C}}_1^2\left(1-{\mathrm{\omega }}^2{\mathrm{L}}_2{\mathrm{C}}_2\right)}{{\mathbf{C}}_{\mathrm{m}}^2}$$E45

The power ratio can be rewritten as Eq. (46), according to Eqs. (44) and (45).

$${\mathrm{P}}_{{\mathrm{R}}_1}:{\mathrm{P}}_{{\mathrm{R}}_2}:{\mathrm{P}}_{\mathrm{L}}=\left\{{\mathrm{\omega }}^2{\mathrm{C}}_1{\mathrm{C}}_2\left[{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2+{\left({\mathrm{\omega L}}_2\right)}^2\right]+{\mathbf{C}}_1^2\left(1-{\mathrm{\omega }}^2{\mathrm{L}}_2{\mathrm{C}}_2\right)\right\}{\mathrm{R}}_1:\left\{{\mathbf{C}}_{\mathrm{m}}^2\right.\}{\mathrm{R}}_2:\left\{{\mathbf{C}}_{\mathrm{m}}^2\right\}{\mathrm{R}}_{\mathrm{L}}$$E46

Finally, the power efficiency can be expressed as Eq. (47).

$$\begin{array}{rcl}\mathrm{\eta }\left(\mathrm{\omega }\right)& =& \frac{{\mathrm{P}}_{\mathrm{L}}}{{\mathrm{P}}_{\text{in}}}=\frac{{\mathrm{P}}_{\mathrm{L}}}{{\mathrm{P}}_{{\mathrm{R}}_1}+{\mathrm{P}}_{{\mathrm{R}}_2}+{\mathrm{P}}_{\mathrm{L}}}\\ & =& \frac{\left\{{\mathbf{C}}_{\mathrm{m}}^2\right\}{\mathrm{R}}_{\mathrm{L}}}{\left\{{\mathrm{\omega }}^2{\mathrm{C}}_1{\mathrm{C}}_2\left[{\left({\mathrm{R}}_2+{\mathrm{R}}_{\mathrm{L}}\right)}^2+{\left({\mathrm{\omega L}}_2\right)}^2\right]+{\mathbf{C}}_1^2\left(1-{\mathrm{\omega }}^2{\mathrm{L}}_2{\mathrm{C}}_2\right)\right\}{\mathrm{R}}_1+\left\{{\mathbf{C}}_{\mathrm{m}}^2\right\}{\mathrm{R}}_2+\left\{{\mathbf{C}}_{\mathrm{m}}^2\right\}{\mathrm{R}}_{\mathrm{L}}}\end{array}$$E47

5. WPT system overview

The basic topology of magnetic field resonant coupling is shown in Figure 11 [16, 20, 21]. The transmitter and receiver sides are coupled through the magnetic field (Figure 11a) and electric field (Figure 11b). The DC power supply generates the source power. The inverter is responsible for DC/AC conversion to produce the high-frequency AC power. The AC power is transferred to the receiver side and converted from AC to DC power by a rectifier. Then, the power is transferred to the load. In the WPT operating frequency for implantable devices, the common frequency is a at low frequency because of the reduction of tissue heating effect [22]. The typical frequency is 13.56 MHz within the license-free industrial, scientific, and medical (ISM) band [23].

Figure 11.

System overview for (a) magnetic field coupling and (b) electric field coupling methods.

The class E power amplifier is commonly applied in MHz-range WPT applications because of its excellent power efficiency from the properties of zero voltage switching and zero voltage derivative switching [24]. The class-E power amplifier can be depicted in Figure 12. In theory, it has a maximum efficiency of 100% [25], according to Eq. (48). The overall circuit consists of the power supply V_dc, RF-chuck, and passive load network. The RF-chuck with high reactance ensures DC voltage pass through the system. The passive load network is responsible for minimizing the overlap between drain voltage and drain current and further reducing the output power loss [26].

Figure 12.

Circuit diagram of a class E power amplifier.

$${\mathrm{P}}_{\text{dissipation}}=\frac{1}{{\mathrm{T}}_0}{\int }_{{\mathrm{T}}_0}{\mathrm{I}}_{\mathrm{DS}}\ast {\mathrm{V}}_{\mathrm{DS}}\mathrm{dt}=0$$E48

Some group has proposed a class E power amplifier-based WPT system for implantable biomedical in practical applications. Mutashar et al. [27] designed a wireless magnetic resonant coupling system using a class-E power amplifier and inductive power links via two spiral transmitters and receiver coils (Figure 13a). The 13.56 MHz carrier frequency within the ISM band range was selected to avoid tissue damage. The proposed class-E power amplifier can reach up to 87.2% power efficiency. The overall inductive coupling system achieves a power transmission efficiency of 73%. The compact structure could be implemented in bio-implants in the future. In practical applications for the electrical field coupling method, Narayanamoorthi et al. [24] developed a class-E-based capacitive coupled wireless power transfer system for biomedical implants (Figure 13b). They optimize the class E-based capacitive coupling WPT systems at an operating frequency of 13.56 MHz. Moreover, the matching circuit consisted of inductive-capacitive-inductive (LCL) impedance was used to improve the power efficiency of the power amplifier up to 96.34%.

Figure 13.

WPT system by (a) magnetic field coupling [27] and (b) electric field coupling for implantable applications [24].

6. WPT in emerging biomedical topics

WPT systems are rapidly evolving for biomedical implants, including emerging topics of implantable pacemaker devices, implantable optogenetic devices, and implantable impedance plethysmography (IPG).

6.1 Wireless charge-based implantable pacemaker

Heart failure is one of the most killers worldwide. It occupies one-third of all global death. Nowadays, the implantable cardioverter pacemaker is a common approach to directly suppress heart failure [28, 29]. However, the battery life could cause health risks and patient inconvenience. Parinaz Abiri et al. [30] developed an inductively powered wireless pacing device to realize remote cardiac stimulation. They designed a Class E-based magnetic field resonant coupling system with a resonant frequency of 13.56 MHz to pace rhythm on Yucatan miniature pig.

6.2 WPT-based implantable optogenetic device

Optogenetics is an emerging field that provides an alternative for direct electrical stimulation to modulate membrane voltage. By genetic modification, the ion channels in the cell can be sensitive to certain wavelengths of light [31]. Nowadays, several advanced biomedical topics have involved the optogenetic topic in different applications, including neuroscience to control animal behavior [32, 33] and cardiology to find out a solution for cardiovascular disease [34, 35]. Yu et al. [36] implement an implantable optogenetic device implanted into the dog’s chest. WPT-based optogenetic modulation of cardiac sympathetic nerve activity can prevent ventricular arrhythmias.

6.3 WPT-based implantable bio-impedance sensor

Bio-impedance sensing is a noninvasive sensing technology based on Ohm’s law. It was commonly applied to cell structural depiction, human composition, and physiological measurement [37, 38, 39, 40]. The main advantage of bio-impedance sensing is providing wearable and low-cost applications in biomedical engineering. The bio-impedance technique commonly uses the two-pair electrodes to detect arterial pulsation by Ohm’s law. One pair of electrodes is responsible for current excitation in our body. Furthermore, the other pair electrodes are responsible for sensing voltage signals. Theodor et al. [41] developed an implantable bio-impedance sensor to measure the artery activity from the domestic pig for additional cardiovascular parameters extraction such as pulse rate and blood pressure [42].

7. Conclusion

This chapter has presented the WPT methodology for implantable medical devices. The common configuration of WPT and its principle were demonstrated, including magnetic field coupling and electric field coupling. Most of all, the recent emerging biomedical topics such as wireless-charging pacemakers, implantable optogenetic devices, and implantable bio-impedance sensors were demonstrated. Overall, this chapter thoroughly presented the electric principle of WPT and extended it to emerging biomedical applications.