**3. Results and discussion**

To compare the transfer efficiency (η) of all configurations, we use the magnitude of |S21|, which can be easily measured using a vector network analyzer (VNA) in experiments. By using the |S21| and |S11|, the function of the transfer efficiency on η = |S21| 2 /(1-|S11| 2 ), however, when the network is matching at both ports, the transfer efficiency equals |S21| 2 . A comparison of simulated |S21| for the four reference cases and the LTLR with the defected MTS (**Figure 2(a)**) is shown in **Figure 4**. Compared with the free space, the magnitude of S21 is increased when a uniform or a defected MTS is used. At 13.56 MHz, the uniform MTS case has a maximum power transfer. It can be observed that a case of free-space case (without MTS) and the uniform MTS have only a single peak. The magnitude of S21 for the free-space case (|S21| = 0.24) is remarkable to lower compared with the case of the uniform MTS (|S21| = 0.69). When the defected unit cell is placed in each position, the magnitudes of |S21| are separated into two or more peaks, called *frequency splitting*, which its mechanism is totally different from the two-coil system as a function of separation distance between coils. In a two-coil system, generally, when the distance between transmitting and receiving coils is closer and smaller than a threshold value, it creates two frequency splitting due to the magnetic over-couplings. Hence, many research efforts have been developed the system performance against frequency splitting using optimizing and compensation methods such as non-identical resonant coil [34]. The frequency splitting phenomenon of the defected MTS occurs when non-identical resonant unit cells. It can be explained in terms of Fano

**Figure 4.** *Comparison of simulated |S21| for LTLR depending on the frequency.*

interference [30, 35], which is much more sensitive to the defected position in its periodicity. It is observed that there are two peaks and the first one is smaller than the second one except two positions of No. 5 and No. 6. The first peak of the separating frequency is shifted to close the resonant frequency (13.56 MHz) when the defected position moves away from the center. As the defected position moves outward to the center of the MTS, the |S21| and the frequency of the first peak also slowly increased accordingly. At the defected position of No. 4, the magnitude of |S21| gets the minimum of 0.106 at 13.56 MHz. From the results, thus, the defected MTS for the cases of the large transmitting and receiving coils has not improved the efficiency due to the magnetic field confinement on the defected cell, as shown in **Figure 5(c)**.

In practice, a transmitting side with a larger coil size than a receiving side for charging portable and implantable devices is used. The typical relative size ratio between transmitting and receiving coils is large, so the efficiency results low. The configurations for a large transmitting side and a small receiving side with uniform and defected MTSs are shown in **Figure 1(d)** and **Figure 2(b)**, respectively. A comparison of the |S21| at six positions for uniform and defected MTSs is shown in **Figure 6**. It can be seen in **Figure 6(a)** for uniform MTS that the |S21| has a significant deterioration when the receiving coil move outward from the center. The difference |S21| at 13.56 MHz between position No. 1 (center) and No. 6 is about 0.42 or 10 dB down, when the maximum is 0.61 at the receiving position in the center. **Figure 6(c)** shows the |S21| of both uniform and defected MTSs at each receiving position. For the uniform MTS, the magnitude gradually decreases from 0.61 to 0.19 when the receiving coil moves from the center (No. 1) to the edge (No. 6) of the MTS.

Meanwhile, the defected MTS shows a |S21| from 0.64 to 0.57. This is confirmed that the proposed defected MTS provides a relatively constant transfer efficiency in all the areas of the MTS. In addition, the defected MTS provides increased transfer efficiency compared with the cases of the free space and uniform one. This proposed configuration is in contrast of the [20, 24], which is constructed in the

**155**

**Figure 6.**

**Figure 5.**

*defected MTSs.*

is confined only specific position.

*A Defected Metasurface for Field-Localizing Wireless Power Transfer*

cavity using an array of the defected unit cells. So, the proposed defected MTS can

*Comparison of the |S21| for LTSR with different positions of the receiving coil on (a) the uniform MTS, (b) the defected MTS when the defected unit cell is the same position with the receiving coil and (c) both uniform and* 

*Magnetic field intensity distribution for LTLR (a) free space, (b) uniform MTS when the receiver at the center* 

The magnitudes of the magnetic field distribution are also used to compare between the WPT systems as shown in **Figure 5**. When whether the uniform or defected MTSs are inserted in the system, strong surface waves existing on both sides of the MTS are observed, which are responsible for the increased magnetic coupling. Obviously, the magnetic field intensity of free space is relatively weak in comparison with the metasurface cases. In case of free-space and the uniform MTS with the LTLR, the receiving coil is placed at the center. The intensity for both cases at the center is more concentrated than at the edge and the uniform MTS has a higher since the magnetic field is enhanced and focused by the negative permeability of the uniform MTS. In the case of the uniform MTS in **Figure 5(b)**, it is showed that the focusing effect of the magnetic field is present due to the negative refractive lens, which the field gradually decays from the center to the edge so, lead to better efficiencies. When the defected unit cell is selected at No. 4 as shown in **Figure 5(c)**, the focusing effect of the magnetic field is presented at position No. 4. However, For the other unit cell of the defected metasurface, the magnetic field intensity is significantly dropped compared with the case of the uniform MTS. According to the magnetic field distribution, the magnitude S21 value of the case of the defected metasurface is not too high, as the case of the uniform metasurface at a frequency of 13.56 MHz, as shown in **Figure 4** because the magnetic field intensity

enhance the transfer efficiency, even with its own loss.

*DOI: http://dx.doi.org/10.5772/intechopen.95812*

*and (c) defected MTS when the receiver located at No. 4.*

*A Defected Metasurface for Field-Localizing Wireless Power Transfer DOI: http://dx.doi.org/10.5772/intechopen.95812*

#### **Figure 5.**

*Wireless Power Transfer – Recent Development, Applications and New Perspectives*

interference [30, 35], which is much more sensitive to the defected position in its periodicity. It is observed that there are two peaks and the first one is smaller than the second one except two positions of No. 5 and No. 6. The first peak of the separating frequency is shifted to close the resonant frequency (13.56 MHz) when the defected position moves away from the center. As the defected position moves outward to the center of the MTS, the |S21| and the frequency of the first peak also slowly increased accordingly. At the defected position of No. 4, the magnitude of |S21| gets the minimum of 0.106 at 13.56 MHz. From the results, thus, the defected MTS for the cases of the large transmitting and receiving coils has not improved the efficiency due to the magnetic field confinement on the defected cell, as shown in

*Comparison of simulated |S21| for LTLR depending on the frequency.*

In practice, a transmitting side with a larger coil size than a receiving side for charging portable and implantable devices is used. The typical relative size ratio between transmitting and receiving coils is large, so the efficiency results low. The configurations for a large transmitting side and a small receiving side with uniform and defected MTSs are shown in **Figure 1(d)** and **Figure 2(b)**, respectively. A comparison of the |S21| at six positions for uniform and defected MTSs is shown in **Figure 6**. It can be seen in **Figure 6(a)** for uniform MTS that the |S21| has a significant deterioration when the receiving coil move outward from the center. The difference |S21| at 13.56 MHz between position No. 1 (center) and No. 6 is about 0.42 or 10 dB down, when the maximum is 0.61 at the receiving position in the center. **Figure 6(c)** shows the |S21| of both uniform and defected MTSs at each receiving position. For the uniform MTS, the magnitude gradually decreases from 0.61 to 0.19 when the receiving coil moves from the center (No. 1) to the edge (No. 6) of

Meanwhile, the defected MTS shows a |S21| from 0.64 to 0.57. This is confirmed that the proposed defected MTS provides a relatively constant transfer efficiency in all the areas of the MTS. In addition, the defected MTS provides increased transfer efficiency compared with the cases of the free space and uniform one. This proposed configuration is in contrast of the [20, 24], which is constructed in the

**154**

the MTS.

**Figure 5(c)**.

**Figure 4.**

*Magnetic field intensity distribution for LTLR (a) free space, (b) uniform MTS when the receiver at the center and (c) defected MTS when the receiver located at No. 4.*

#### **Figure 6.**

*Comparison of the |S21| for LTSR with different positions of the receiving coil on (a) the uniform MTS, (b) the defected MTS when the defected unit cell is the same position with the receiving coil and (c) both uniform and defected MTSs.*

cavity using an array of the defected unit cells. So, the proposed defected MTS can enhance the transfer efficiency, even with its own loss.

The magnitudes of the magnetic field distribution are also used to compare between the WPT systems as shown in **Figure 5**. When whether the uniform or defected MTSs are inserted in the system, strong surface waves existing on both sides of the MTS are observed, which are responsible for the increased magnetic coupling. Obviously, the magnetic field intensity of free space is relatively weak in comparison with the metasurface cases. In case of free-space and the uniform MTS with the LTLR, the receiving coil is placed at the center. The intensity for both cases at the center is more concentrated than at the edge and the uniform MTS has a higher since the magnetic field is enhanced and focused by the negative permeability of the uniform MTS. In the case of the uniform MTS in **Figure 5(b)**, it is showed that the focusing effect of the magnetic field is present due to the negative refractive lens, which the field gradually decays from the center to the edge so, lead to better efficiencies. When the defected unit cell is selected at No. 4 as shown in **Figure 5(c)**, the focusing effect of the magnetic field is presented at position No. 4. However, For the other unit cell of the defected metasurface, the magnetic field intensity is significantly dropped compared with the case of the uniform MTS. According to the magnetic field distribution, the magnitude S21 value of the case of the defected metasurface is not too high, as the case of the uniform metasurface at a frequency of 13.56 MHz, as shown in **Figure 4** because the magnetic field intensity is confined only specific position.

**Figure 7** shows the magnetic field intensity distributions of LTSR with the uniform and defected MTSs at 13.56 MHz, respectively. On the uniform MTS in **Figure 7(a)**, the magnetic field spreads over a relative area, while the defected MTS shows that the focusing effect of the magnetic field from the cavity is presented, which can suppress the filed elsewhere. It is observed in **Figure 7(b)** that the strong magnetic field confinement is realized on the defected MTS at the receiving position and the field is relatively low with uniform outside the cavity. It means that the defected MTS creates the field localization, hence, it can enhance transfer efficiency for a small receiver and reduce leakage EMF. It is because the unit cell forming the cavity resonance while the surrounding cells resonance at lower frequency. When the resonant frequency of surrounding cells falls into the hybridization bandgap, the negative permeability of metasurface forms a stopband for the cavity. Thus, the magnetic fields are prohibited from propagation in an outside area than the cavity. For the uniform MTS, the magnitude of the magnetic field is distributed relatively evenly about 14–22 dB along the surface of the MTS whereas the defected MTS is below 6 dB. Therefore, the defected MTS can enhance not only the field at the receiving coil, but also suppress the field elsewhere without additional shielding box or ferrite.

To experimentally validate the performance of the uniform and defected MTSs, several experimental studies are conducted. **Figure 8** shows the prototype of the proposed metasurface and experimental setup by using the VNA (Rohde & Schwarz model ZVB20). The fabricated MTS consists of 5 × 5 arrays of unit cells that are

**Figure 7.**

*Magnetic field intensity distribution for LTSR when the receiver located at No. 4 (a) uniform MTS and (b) defected MTS.*

**157**

**Figure 8.**

*(b) LTLR and (c) LTSR.*

*A Defected Metasurface for Field-Localizing Wireless Power Transfer*

controlled individually using a chip capacitor as shown in **Figure 8(a)**. **Figure 8(b)** depicts the LTLR with the metasurfaces. In case of LTLR (**Figure 8(b)**), the large receiving is not fixed at the center, but it is moved and located following the defected unit cell. **Figure 8(c)** shows the case of the LTSR with the metasurfaces when the receiving coil can move all the unit cell locations. The distance between the receiving coil and MTS is fixed and kept by using the plastic pipe. It is a thin and non-magnetic material; its effect is negligible. The connection is accomplished using standard SMAs through two identical low-loss cables. The standard SOLT (short-open-line-trough) calibration has been performed at the desired frequency range before measurement, so the end of the cables has been considered as a reference plane for S-parameters. **Figure 9** shows the measured results of LTLR and LTSR cases with the uniform and defected MTSs, respectively. **Figure 9(a)** shows variation of the measured efficiency depending on the defected positions and the defected cell at position No. 0 is a uniform MTS case. As seen, the efficiency shows a significant dependence on the receiving positions. The WPT system is directly measured at the operating frequency of 13.56 MHz and using two-port method with VNA. It is clearly seen in **Figure 9(b)** that the transfer efficiency of the defected MTS is quite flat; it means the defected MTS can enhance the efficiency regardless of the positions of the receiving coil with various distances. **Figure 9(b)** shows the simulated and measured power transfer efficiency of LTLR and LTSR cases with the uniform and defected

*Photograph of prototype of the proposed metasurface (a) and the system experimental setup for measurement:* 

*DOI: http://dx.doi.org/10.5772/intechopen.95812*

*A Defected Metasurface for Field-Localizing Wireless Power Transfer DOI: http://dx.doi.org/10.5772/intechopen.95812*

#### **Figure 8.**

*Wireless Power Transfer – Recent Development, Applications and New Perspectives*

**Figure 7** shows the magnetic field intensity distributions of LTSR with the uniform and defected MTSs at 13.56 MHz, respectively. On the uniform MTS in **Figure 7(a)**, the magnetic field spreads over a relative area, while the defected MTS shows that the focusing effect of the magnetic field from the cavity is presented, which can suppress the filed elsewhere. It is observed in **Figure 7(b)** that the strong magnetic field confinement is realized on the defected MTS at the receiving position and the field is relatively low with uniform outside the cavity. It means that the defected MTS creates the field localization, hence, it can enhance transfer efficiency for a small receiver and reduce leakage EMF. It is because the unit cell forming the cavity resonance while the surrounding cells resonance at lower frequency. When the resonant frequency of surrounding cells falls into the hybridization bandgap, the negative permeability of metasurface forms a stopband for the cavity. Thus, the magnetic fields are prohibited from propagation in an outside area than the cavity. For the uniform MTS, the magnitude of the magnetic field is distributed relatively evenly about 14–22 dB along the surface of the MTS whereas the defected MTS is below 6 dB. Therefore, the defected MTS can enhance not only the field at the receiving coil, but also suppress the field elsewhere without additional shielding

To experimentally validate the performance of the uniform and defected MTSs, several experimental studies are conducted. **Figure 8** shows the prototype of the proposed metasurface and experimental setup by using the VNA (Rohde & Schwarz model ZVB20). The fabricated MTS consists of 5 × 5 arrays of unit cells that are

*Magnetic field intensity distribution for LTSR when the receiver located at No. 4 (a) uniform MTS and* 

**156**

**Figure 7.**

*(b) defected MTS.*

box or ferrite.

*Photograph of prototype of the proposed metasurface (a) and the system experimental setup for measurement: (b) LTLR and (c) LTSR.*

controlled individually using a chip capacitor as shown in **Figure 8(a)**. **Figure 8(b)** depicts the LTLR with the metasurfaces. In case of LTLR (**Figure 8(b)**), the large receiving is not fixed at the center, but it is moved and located following the defected unit cell. **Figure 8(c)** shows the case of the LTSR with the metasurfaces when the receiving coil can move all the unit cell locations. The distance between the receiving coil and MTS is fixed and kept by using the plastic pipe. It is a thin and non-magnetic material; its effect is negligible. The connection is accomplished using standard SMAs through two identical low-loss cables. The standard SOLT (short-open-line-trough) calibration has been performed at the desired frequency range before measurement, so the end of the cables has been considered as a reference plane for S-parameters. **Figure 9** shows the measured results of LTLR and LTSR cases with the uniform and defected MTSs, respectively. **Figure 9(a)** shows variation of the measured efficiency depending on the defected positions and the defected cell at position No. 0 is a uniform MTS case. As seen, the efficiency shows a significant dependence on the receiving positions. The WPT system is directly measured at the operating frequency of 13.56 MHz and using two-port method with VNA. It is clearly seen in **Figure 9(b)** that the transfer efficiency of the defected MTS is quite flat; it means the defected MTS can enhance the efficiency regardless of the positions of the receiving coil with various distances. **Figure 9(b)** shows the simulated and measured power transfer efficiency of LTLR and LTSR cases with the uniform and defected

**Figure 9.** *Measured and simulated results of the transfer efficiency with the uniform or defected metasurface (a) LTLR and (b) LTSR.*

MTSs. We obtained the measured transfer efficiency of LTSR case of 51,5%, 50.1%, 48.3%,43.2%, 39.5% and 26.6% at the receiver positions of No. 1 to No. 6, respectively. Contrastingly, for the uniform MTS, the efficiency decreases obviously, when the receiving positions are moved far away from the center since the intensity of magnetic field at the edge is lower than at the center for the uniform MTS.
