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.

▽×B=μ0JE1

E=−∂B∂tE2

To understand the principle of magnetic field coupling without resonance, Figure 3 shows the topology of the circuit analysis. The mutual inductance, Lm=kL1L2, 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]:

jωL1I1+I1R1+jωLmI2=U1E3

jωL2I2+I2R2+I2RL+jωLmI1=0E4

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

I2=−I1ωLmωL2−jR2+RLE5

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

I1=R2+RL+jωL2R1+jωL1jωL2+R2+RL+ω2Lm2U1E6

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

I2=−jωLmR1+jωL1jωL2+R2+RL+ω2Lm2U1E7

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

I1I2=−R2+RL+jωL2jωLmE8

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.

VLm2=jωLmI1E9

VLm2=jωLmR2+RL+jωL2R1+jωL1jωL2+R2+RL+ω2Lm2U1E10

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

Zin2=VLm2−I2=jωLmI1−I2=R2+RL+jωL2E11

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

Z2=VLm1I1=jωLmI2I1=ω2Lm2R2+RL+jωL2E12

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

Zin1=R1+jωL1+Z2=R1+jωL1+ω2Lm2R2+RL+jωL2E13

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).

PR1:PR2:PL=I12R1:I22R2:I22RLE14

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

I2I12=ω2Lm2R2+RL2+ω2Lm2E15

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

PR1:PR2:PL=R2+RL2+ω2Lm2R1:ω2Lm2R2:ω2Lm2RLE16

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

η=PLPin=PLPR1+PR2+PL=ω2Lm2RLR2+RL2+ω2Lm2R1+ω2Lm2R2+ω2Lm2RLE17

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.

1jωC1I1+R1I1+jωL1I1+jωLmI2=U1E18

jωL2I2+R2I2+1jωC2I2+RLI2+jωLmI1=0E19

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

I2=−jωLmjωL2+1jωC2+R2+RLI1E20

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

I1=R2+RL+jωL2−1ωC2(R1+jωL1−1ωC1R2+RL+jωL2−1ωC2+ω2Lm2U1E21

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

I2=−jωLm(R1+jωL1−1ωC1R2+RL+jωL2−1ωC2+ω2Lm2U1E22

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

I1I2=−R2+RL+jωωL2−1ωC2jωLmE23

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).

ω0=ω1=ω2=1L1C1=1L2C2E24

I1=R2+RLR1R2+RL+ω2Lm2U1E25

I2=−jωLmR1R2+RL+ω2Lm2U1E26

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

I1I2=−R2+RLjωLmE27

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.

VLm2=jωLmI1E28

VLm2=jωLmR2+RLR1R2+RL+ω2Lm2U1E29

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

Zin2=VLm2−I2=jωLmI1−I2=R2+RLE30

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

Z2=VLm1I1=jωLmI2I1=ω2Lm2R2+RLE31

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

Zin1=R1+1jωC1+jωL1+Z2=R1+1jωC1+jωL1+ω2Lm2R2+RLE32

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).

PR1:PR2:PL=I12R1:I22R2:I22RLE33

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

I2I12=ω2Lm2R2+RL2E34

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

PR1:PR2:PL=R2+RL2R1:ω2Lm2R2:ω2Lm2RLE35

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

η=PLPin=PLPR1+PR2+PL=ω2Lm2RLR2+RL2R1+ω2Lm2R2+ω2Lm2RLE36

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 R_load
Magnetic field coupling without resonance	ω2Lm2RLR2+RL2+ω2Lm2R1+ω2Lm2R2+ω2Lm2RL	jωLmR1+jωL1jωL2+R2+RL+ω2Lm22U12RL
Magnetic field coupling With resonance	ω2Lm2RLR2+RL2R1+ω2Lm2R2+ω2Lm2RL	jωLmR1R2+RL+ω2Lm22U12RL

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.

I=∂D∂t∙S=ε∂E∂t∙SE37

In Figure 8, the mutual inductance of C_m between two capacitances on the distance x between the two coils can be written as Cm=kC1C2.

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.

U00=R1+jωL1+1jωC1−Cm−1jωC1−Cm0−1jωC1−Cm1jωC1−Cm+1jωCm+1jωC2−Cm−1jωC2−Cm0−1jωC2−CmR2+RL+jωL2+1jωC2−CmIl1ImIl2E38

Zin2=1jωC2+1R2+jωL2+RLE39

Z2=1ω2Cm2Zin2E40

Zin1=1jωC1+1Z2+jωL1+R1E41

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).

ω2=1L2C2−R2+RLL22E42

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).

L1=C1R2+RL2−ω12C2R2+RL2+ωL22−L2L2C1−C1C2−Cm2R2+RL2+ωL22ω14L2C1−C1C2−Cm2R2+RL2+ωL222+ω12C12R2+RL2E43

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).

PR1:PR2:PRL=I12R1:I22R2:I22RLE44

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

I1I22=ω2C1C2R2+RL2+ωL22+C121−ω2L2C2Cm2E45

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

PR1:PR2:PL=ω2C1C2R2+RL2+ωL22+C121−ω2L2C2R1:Cm2}R2:Cm2RLE46

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

ηω=PLPin=PLPR1+PR2+PL=Cm2RLω2C1C2R2+RL2+ωL22+C121−ω2L2C2R1+Cm2R2+Cm2RLE47

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.

Pdissipation=1T0∫T0IDS∗VDSdt=0E48

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.

Jose Augusto Bragatti

Chapters authored

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