# Wireless Power Transfer Approaches for Medical Implants: A Review
## 2 Different Approaches for a Wireless Power Transfer System
### Inductive-Based Wireless Power Transfer  
Inductive coupling is the process of transferring power by connecting a source that is generating a varying magnetic field to a primary coil which is usually located outside the body tissue. Then, based on [PERSON]'s law, the voltage is induced across the receiver secondary coil, which is usually implanted inside the body tissues. Figure 2 below illustrates this principle. The amount of induced voltage in implanted coils (\(V_{is}\)) is given by the following equation  
\[V_{is}=\ -N\frac{d\Phi}{dt}=jN\omega\Phi\ =\ jN\omega\mu\int\overset{\rightarrow}{H} \overset{\rightarrow}{ds} \tag{1}\]  
where \(N\) is the number of turns, \(\omega\) is the operating angular frequency, \(\Phi\) is the magnetic flux linkage, and \(\mu\) is the permeability of transfer medium. According to Equation (1), coupling between coils depends mainly on the amount of \(\Phi\) between the primary (transmitter) and secondary (implanted) coils. Thus, when the distance between the transmitter and the implanted receiver is decreased the amount of coupled magnetic flux will increase. Furthermore, the amount of transferred power using inductive coupling could be increased by adding a capacitor for resonance. The simplified diagram of the resonant inductive WPT circuit is shown in Figure 3. \(L_{1}\) is the transmitter coil inductor that is located outside the body tissues, and \(L_{2}\) is the implanted receiver coil inductor, often with the rest of the implant electronics. Coil windings have parasitic capacitance and resistance associated with them, which are shown as symmetric elements (\(R_{s1}\), \(R_{s2}\)), and (\(C_{s1}\), \(C_{s2}\)). Capacitors \(C_{T}\) and \(C_{R}\) are added to the circuit to form an LC resonance with \(L_{1}\) and \(L_{2}\), respectively. \(R_{L}\) is the load resistance. Figure 3: Circuit model of magnetic resonant inductive coupling. Figure 2: Inductive coupling principle. The highest efficiency and voltage gain are achieved when both LC tanks are tuned at the operating frequency of the link \(\omega_{o}=1/\sqrt{L_{1}C_{1}}\ =1/\sqrt{L_{2}C_{2}}\), where \(C_{1}\) and \(C_{2}\) are a combination of the lumped capacitor and the parasitic capacitance of the transmitter and implanted coils, respectively. The delivered power is transferred between the transmitter and the implanted coils through mutual inductance (\(M\)). \(M\) is related to the coupling coefficient (\(k\)) according to  
\[k=\ \frac{M}{\sqrt{L_{1}L_{2}}} \tag{2}\]  
The quality factors for the transmitter (\(Q_{1}\)), receiver (\(Q_{2}\)), and load (\(Q_{L}\)) circuits are calculated as follows:  
\[Q_{1}=\ \frac{\omega_{o}L_{1}}{R_{S1}},\ \ Q_{2}=\ \frac{\omega_{o}L_{2}}{R_{S2}}, \ \ Q_{L}=\ \frac{R_{L}}{\omega_{o}L_{2}} \tag{3}\]  
The total efficiency, \(\eta_{ind}\), is calculated according to Equation (4), as derived in [3]:  
\[\eta_{ind}\ =\ \frac{k^{2}Q_{1}Q_{2}}{1+k^{2}Q_{1}Q_{2}+\frac{Q_{2}}{Q_{L}}} \times\frac{1}{1+\frac{Q_{L}}{Q_{2}}} \tag{4}\]  
More details on how to derive the efficiency of inductive links can be found in [68]. In general, the efficiency increases at high delivered power. However, different efficiencies have been achieved for the same transmitted power depending on the system design. Inductive coupling is a common and efficient way to transfer data and power into implantable medical instruments, including cardiac pacemakers, implantable cardioverter defibrillators, recording devices, neuromuscular stimulators, and cochlear and retinal implants. When the development of an inductive link using a power amplifier is applied, the output power depends on the operating frequency and the distance range. The bandwidth to support data communication and reasonable efficacy for power transfer, insensitivity to misalignments, and biocompatibility are needed for a robust inductive link for medical implants [69]. In general, hundreds of kilohertz to a few megahertz is the operating frequency, and the size of the implanted coil is between several millimeters and a few centimeters.