**3. Basic principle of NFC**

NFC works based on the principle of near field magnetic communication. This principle of inductive coupling is applied to all communications based on near field magnetism between transmitting and receiving devices. **Figure 3** shows the

**Figure 3.**

*Inductive coupling between transmitter and receiver coils [9].*

simplified concept of inductive coupling. When a primary coil generates alternating magnetic field, secondary coil which is placed in the vicinity of the primary coil inductively coupled with the primary coil and generates induced alternating magnetic field according to the Faraday's law. This is the basic principle in transferring power wirelessly between the devices in near field region. The above stated principle also applied on RFID systems that are based on inductive coupling. Even though, there are some differences in other components such as network system and protocols between NFC and general RFID systems.

#### **3.1 Inductive coiled system**

The inductive coupled NFC system can be modeled by using expressions of selfinductance, mutual inductance and resistances [19]. A generalized analytical expression for calculation of self-inductance of circular or rectangular shaped coil is explained below. **Figure 4** shows a representation of single turn circular coil while illustrating the magnetic field pattern surrounding two circular coils [20].

The inductance, *L*0, for a single turn circular coil can be given by Eq. (1) as seen below [21]:

$$L\_0 = \mu\_0 r l n \left(\frac{2r}{d}\right) \tag{1}$$

Where *μ*<sup>0</sup> is permeability of free space, *r* is radius of the coil and *d* is the diameter of the wire. The single turn coil inductance can be utilized to calculate

*Near-Field Communications (NFC) for Wireless Power Transfer (WPT): An Overview*

*<sup>L</sup>* <sup>¼</sup> *<sup>N</sup>*<sup>2</sup>

where *N* is number of turns in a coil. This equation provides appropriate approximation for a cylindrical inductor, but for the case of spiral inductor this equation provides general parameter studies. A detailed study for calculation of inductance of spiral inductors is provided by S. Alturi et al.

Another important figure of merit is mutual inductance of two coupled coils.

*<sup>M</sup>* <sup>¼</sup> *μπN*1*N*2*r*<sup>2</sup>

2

Also, the coupling factor between 2 coils can be expressed in Eq. (5).

*<sup>k</sup>* <sup>¼</sup> *<sup>M</sup>*ffiffiffiffiffiffiffiffiffiffi *L*1*L*<sup>2</sup>

Where *k* is coupling factor and lies between 0 and 1, *L*<sup>1</sup> and *L*<sup>2</sup> are inductance of

Power transfer efficiency between loop antennas for NFC system is expressed as the figure of merit that depends on inductive coupling. As NFC operates at small distance range between transmitter and receiver antennas, its efficiency depends on coupling between the antennas for wireless power transfer [25]. **Figure 5** shows schematic of two mutual magnetic coupled coil antennas for the WPT system [27]. To improve the power efficiency, an impedance matching on both coil antennas (receiver and transmitter) is required. In case of magnetic coupling between receiver and transmitter coil antennas, eddy currents are generated due to alternating magnetic field. This cause a shift of resonant peaks of the input impedance, which shifts resonance frequency of maximum power transfer. Insertion of a high permeability soft magnetic ferrite sheet between coil antenna and metal conductor shifts the frequency back to original resonance frequency [26]. When both circuits resonate at peak frequency, maximum transfer of power is achieved. **Figure 6** depicts the simplified equivalent circuit model of wireless power transfer

In case of complex geometries, numerical methods can be applied to calculate

1*r*2 2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *r*2

where, *N*<sup>1</sup> and *N*<sup>2</sup> are the number of turns in first and second coil, respectively, *r*<sup>1</sup> and *r*<sup>2</sup> are the radius of first and second coil, respectively, *x* is the axial separation and *μ* is the permeability. Eq. (4) is valid only for *r*<sup>2</sup> < *r*<sup>1</sup> ≪ *x*, i.e., the magnetic field generated by current *I1* in first coil should be homogeneous in the mutually bounded area of the 2nd coil. Detailed calculation for mutual inductance for

*<sup>μ</sup>*0*rln* <sup>2</sup>*<sup>r</sup> d*

*<sup>L</sup>* <sup>¼</sup> *<sup>N</sup>*<sup>2</sup>

The mutual inductance between the two coils can be expressed in Eq. (4).

*L*<sup>0</sup> (2)

� � (3)

<sup>1</sup> <sup>þ</sup> *<sup>x</sup>*<sup>2</sup> � �<sup>3</sup> <sup>q</sup> (4)

p (5)

inductance of multiturn coil, *L* and is given by Eq. (2).

*DOI: http://dx.doi.org/10.5772/intechopen.96345*

(2004) [22].

cylindrical coils is presented in [23].

first and second coil, respectively.

systems [26].

**99**

inductances of complex coil systems [24].

**3.2 Wireless power transfer (WPT) efficiency**

**Figure 4.** *Depiction of two magnetic inductive coil system (primary and secondary) [20].*

*Near-Field Communications (NFC) for Wireless Power Transfer (WPT): An Overview DOI: http://dx.doi.org/10.5772/intechopen.96345*

Where *μ*<sup>0</sup> is permeability of free space, *r* is radius of the coil and *d* is the diameter of the wire. The single turn coil inductance can be utilized to calculate inductance of multiturn coil, *L* and is given by Eq. (2).

$$L = N^2 L\_0 \tag{2}$$

$$L = N^2 \mu\_0 r l n \left(\frac{2r}{d}\right) \tag{3}$$

where *N* is number of turns in a coil. This equation provides appropriate approximation for a cylindrical inductor, but for the case of spiral inductor this equation provides general parameter studies. A detailed study for calculation of inductance of spiral inductors is provided by S. Alturi et al. (2004) [22].

Another important figure of merit is mutual inductance of two coupled coils. The mutual inductance between the two coils can be expressed in Eq. (4).

$$M = \frac{\mu \pi N\_1 N\_2 r\_1^2 r\_2^2}{2\sqrt{\left(r\_1^2 + \varkappa^2\right)^3}}\tag{4}$$

where, *N*<sup>1</sup> and *N*<sup>2</sup> are the number of turns in first and second coil, respectively, *r*<sup>1</sup> and *r*<sup>2</sup> are the radius of first and second coil, respectively, *x* is the axial separation and *μ* is the permeability. Eq. (4) is valid only for *r*<sup>2</sup> < *r*<sup>1</sup> ≪ *x*, i.e., the magnetic field generated by current *I1* in first coil should be homogeneous in the mutually bounded area of the 2nd coil. Detailed calculation for mutual inductance for cylindrical coils is presented in [23].

Also, the coupling factor between 2 coils can be expressed in Eq. (5).

$$k = \frac{M}{\sqrt{L\_1 L\_2}}\tag{5}$$

Where *k* is coupling factor and lies between 0 and 1, *L*<sup>1</sup> and *L*<sup>2</sup> are inductance of first and second coil, respectively.

In case of complex geometries, numerical methods can be applied to calculate inductances of complex coil systems [24].

#### **3.2 Wireless power transfer (WPT) efficiency**

Power transfer efficiency between loop antennas for NFC system is expressed as the figure of merit that depends on inductive coupling. As NFC operates at small distance range between transmitter and receiver antennas, its efficiency depends on coupling between the antennas for wireless power transfer [25]. **Figure 5** shows schematic of two mutual magnetic coupled coil antennas for the WPT system [27]. To improve the power efficiency, an impedance matching on both coil antennas (receiver and transmitter) is required. In case of magnetic coupling between receiver and transmitter coil antennas, eddy currents are generated due to alternating magnetic field. This cause a shift of resonant peaks of the input impedance, which shifts resonance frequency of maximum power transfer. Insertion of a high permeability soft magnetic ferrite sheet between coil antenna and metal conductor shifts the frequency back to original resonance frequency [26]. When both circuits resonate at peak frequency, maximum transfer of power is achieved. **Figure 6** depicts the simplified equivalent circuit model of wireless power transfer systems [26].

Using Eq. (8) and (9):

Substituting Eq. (10) into Eq. (8):

*DOI: http://dx.doi.org/10.5772/intechopen.96345*

*Vs* ¼ *Is Rs* þ *jωLs* þ

*Zs* <sup>¼</sup> *Vs Is*

calculated as:

0 @

**101**

*<sup>η</sup>* <sup>¼</sup> *<sup>j</sup>ω<sup>M</sup> <sup>j</sup>ωLL* <sup>þ</sup> <sup>1</sup>

power:

*IL* ¼ *Is*

1 *jωCs*

� � � �

model. The input impedance is given by [26]:

*<sup>j</sup>ωCL* þ *RL* � � 0 @

*Near-Field Communications (NFC) for Wireless Power Transfer (WPT): An Overview*

*jωM*

*<sup>j</sup>ωCL* þ *RL* � �

*<sup>j</sup>ωLL* <sup>þ</sup> <sup>1</sup>

*jωM*

*RL*

� � <sup>þ</sup> *<sup>ω</sup>*2*M*<sup>2</sup>

0 @

*<sup>j</sup>ωLL*<sup>þ</sup> <sup>1</sup> *jωCL* þ*RL* � �

*jωCs*

*<sup>j</sup>ωCL* þ *RL* � �

1

A (10)

Að Þ *jωM* (11)

*CsCL*

1 A

1 A (12)

(13)

(14)

(15)

1

*<sup>j</sup>ωLL* <sup>þ</sup> <sup>1</sup>

0 @

The input impedance is calculated based on the simplified equivalent circuit

<sup>¼</sup> ð Þ *<sup>j</sup>ωCs Rs* <sup>þ</sup> <sup>1</sup> � *<sup>ω</sup>*<sup>2</sup> ð Þ *LsCs* ð Þ *<sup>j</sup>ωCL RL* <sup>þ</sup> <sup>1</sup> � *<sup>ω</sup>*<sup>2</sup> <sup>ð</sup> *LLCL*Þ � *<sup>ω</sup>*<sup>4</sup>*M*<sup>2</sup>

The power transfer efficiency is given by ratio of output power to the input

*<sup>η</sup>* <sup>¼</sup> *POut Pin*

By substituting Eq. (10)–(12) in Eq. (13), the effective power efficiency is

*Rs* <sup>þ</sup> *<sup>j</sup>ωLs* <sup>þ</sup> <sup>1</sup>

where, *M* is Mutual inductance between the coil antennas, *Ls* and *LL* are the inductance of transmitter and receiver coils, *Cs* and *CL* are matching capacitor for transmitter and receiver coils, *Rs* and *RL* are internal resistance and load resistance

The transferred power is maximum at resonance frequency when load current in the circuit becomes maximum, at a given resonance frequency, Eq. (15) describes

> *<sup>M</sup>*<sup>2</sup> <sup>¼</sup> *<sup>R</sup>*<sup>2</sup> *L ω*2 0

The wireless power transfer efficiency using inductive coupling can be greater than 90% within a limited transmission range. During the last decade, methods such as magnetic resonance coupling for WPT have been widely studied by researchers to increase the efficiency of power transmission with greater distance range. Twoloop and four-loop coil systems were studied for magnetic resonance coupling based WPT system [30]. In order to achieve maximum power transfer efficiency, several studies have been done such as loop to coil coupling manipulation [29], automated impedance matching [31], adaptive frequency tuning [32], circuit structure

For resonance coupling system, assuming *C* ¼ *Cs* ¼ *CL:*

1 A

of the coils and *Vs* and *VL* are source and load voltages.

the condition for maximum power transfer efficiency [29]:

2

0 @

0 @

*jωCs*ð Þ ð Þ *jωCL RL* þ 1 � *ω*<sup>2</sup>*LLCL*

¼ *I* 2 *LRL I* 2 *<sup>s</sup> Zs*

� *Is*

#### **Figure 5.**

*Schematic drawing of mutual magnetic coupled coils for wireless power transfer systems [26].*

**Figure 6.** *A simplified equivalent circuit model of wireless power transfer systems [27].*

The resonance frequency *ω* for coil antenna is given by,

$$\rho = \frac{1}{\sqrt{L\_s C\_s}} = \frac{1}{\sqrt{L\_L C\_L}}\tag{6}$$

Base on Kirchhoff voltage law and above circuit diagram, *Vs* can be calculated as [28]:

$$
\begin{bmatrix}
joL\_s + \frac{\mathbf{1}}{jwC\_s} + R\_s & jo\mathbf{M} \\\\jo\mathbf{M} & joL\_L + \frac{\mathbf{1}}{joC\_L} + R\_L
\end{bmatrix}
\begin{bmatrix}
I\_s \\ I\_L
\end{bmatrix} = \begin{bmatrix}
V\_s \\ \mathbf{0}
\end{bmatrix} \tag{7}
$$

From Eq. (7), *Vs* can be calculated [29]:

$$W\_s = I\_s \left( R\_s + j\alpha L\_s + \left(\frac{1}{j\alpha C\_s}\right) - I\_L(j\alpha \mathbf{M}) \right) \tag{8}$$

$$\mathbf{O} = I\_L \left( j a L\_L + \left( \frac{\mathbf{1}}{j a \mathbf{C}\_L} \right) + R\_L \right) - I\_s (j a \mathbf{M}) \tag{9}$$

*Near-Field Communications (NFC) for Wireless Power Transfer (WPT): An Overview DOI: http://dx.doi.org/10.5772/intechopen.96345*

Using Eq. (8) and (9):

$$I\_L = I\_s \left(\frac{j\alpha\mathcal{M}}{j\alpha L\_L + \left(\frac{1}{j\alpha C\_L} + R\_L\right)}\right) \tag{10}$$

Substituting Eq. (10) into Eq. (8):

$$W\_s = I\_s \left( R\_s + joL\_s + \left(\frac{1}{joC\_s}\right)\right) - I\_s \left(\frac{joM}{joL\_L + \left(\frac{1}{joC\_L} + R\_L\right)}\right) (joM) \tag{11}$$

The input impedance is calculated based on the simplified equivalent circuit model. The input impedance is given by [26]:

$$Z\_t = \frac{V\_s}{I\_s} = \frac{((j\rho C\_t)R\_t + \mathbf{1} - \rho^2 L\_t C\_t)((j\rho C\_L)R\_L + \mathbf{1} - \rho^2 L\_L C\_L) - \rho^4 \mathbf{M}^2 C\_t C\_L}{j\rho C\_t((j\rho C\_L)R\_L + \mathbf{1} - \rho^2 L\_L C\_L)} \tag{12}$$

The power transfer efficiency is given by ratio of output power to the input power:

$$\eta = \frac{P\_{\text{Out}}}{P\_{\text{in}}} = \frac{I\_L^2 R\_L}{I\_s^2 Z\_s} \tag{13}$$

For resonance coupling system, assuming *C* ¼ *Cs* ¼ *CL:*

By substituting Eq. (10)–(12) in Eq. (13), the effective power efficiency is calculated as:

$$\eta = \left(\frac{j\alpha\mathcal{M}}{j\alpha L\_L + \left(\frac{1}{j\alpha C\_L} + R\_L\right)}\right)^2 \frac{R\_L}{\left(\left(R\_s + j\alpha L\_s + \left(\frac{1}{j\alpha C\_s}\right) + \left(\frac{1}{j\alpha L\_L + \left(\frac{1}{j\alpha C\_L} + R\_L\right)}\right)\right)\right)} \tag{14}$$

where, *M* is Mutual inductance between the coil antennas, *Ls* and *LL* are the inductance of transmitter and receiver coils, *Cs* and *CL* are matching capacitor for transmitter and receiver coils, *Rs* and *RL* are internal resistance and load resistance of the coils and *Vs* and *VL* are source and load voltages.

The transferred power is maximum at resonance frequency when load current in the circuit becomes maximum, at a given resonance frequency, Eq. (15) describes the condition for maximum power transfer efficiency [29]:

$$M^2 = \frac{R\_L^2}{a\_0^2} \tag{15}$$

The wireless power transfer efficiency using inductive coupling can be greater than 90% within a limited transmission range. During the last decade, methods such as magnetic resonance coupling for WPT have been widely studied by researchers to increase the efficiency of power transmission with greater distance range. Twoloop and four-loop coil systems were studied for magnetic resonance coupling based WPT system [30]. In order to achieve maximum power transfer efficiency, several studies have been done such as loop to coil coupling manipulation [29], automated impedance matching [31], adaptive frequency tuning [32], circuit structure

manipulation [33], improving WPT for future portable consumer electronics using large transmitter coil system [34] and improving efficiency by four-coil system for deep brain simulation [35]. There are studies, which focused on misalignment between receiver and transmitter coil for applications such as wireless EV charging system [36] and wireless mobile phone charging system [37, 38]. With the rapid development in consumer electronics, there is a substantial increase in applications of NFC based wireless power transfer technology.
