# Practical Model for Metamaterials in Wireless Power Transfer Systems
## 3 Experimental Verification
### Experimental Verification of the MTM-Enhanced WPT System  
After obtaining the characteristics of the MTM slab, the MTM-enhanced WPT system is established to verify the proposed model. According to the optimization results, when the \(f_{M}\) is 6.5 MHz, the power transfer efficiency of the system is 26.4%. The efficiency of the system without MTMs is 8.6% according to (4). The efficiency of the WPT system has increased by 17.8% in theoretical analysis. Nevertheless, the coupling coefficients in this calculation are obtained by magnetic field simulation, which is difficult to measure and sensitive to external disturbances, and this inevitably results in the deviation in the experimental measurements.  
To verify the calculation results, the experimental transmission efficiency of WPT is calculated by (4). The input power is measured with a power meter, and the output power is calculated through  
Figure 10: The relative permeability of the experimental MTM slab. (**a**) The experimental results. (**b**) The simulation results.  
Figure 9: The impedance results of MTMs.  
the measurement of the output voltage. The designed MTM slab is added to the system afterwards and the parameters are the same as the simulation settings.  
First, when the operation frequency of the system changes, the variation of power transfer efficiency is shown in Figure 11. The distance between transceiver coils is 15 cm, and the MTM slab is placed 4 cm away from the Tx. The experimental results show that when the MTM slab is tuned to 6.5 MHz, the optimal working frequency of the system is 6.78 MHz. This is consistent with the previous simulation and numerical optimization results. Experimental results also demonstrate that the efficiency of the system is 18.2% when the distance between coils is 10 cm. Afterwards, the position of the slab is fixed and the distance between the transceiver coils is changed in the range of 5-20 cm. The variation of system efficiency with distance is shown in Figure 12. After adding the MTM slab, the transmission efficiency of the experimental WPT system has been greatly improved by about 10% at the transmission distance of 10 cm. Because of the loss in the input signal amplifier, the experimental results are slightly smaller than the results from optimization and theoretical calculations.  
Figure 11: Variation of power and efficiency with different frequencies.  
Figure 12: Variation of power and efficiency with different distances between Tx and Rx.  
In order to verify the accuracy of the proposed practical model, we compared the power efficiency results with experimental results and the high-frequency calculation results (in which efficiency is obtained by measuring S-parameters) and the comparison is made in Figure 13. The power efficiency of the WPT system with the MTM slab is calculated by \(|S_{21}|^{2}\) (\(S_{21}\) is the positive transfer factor. At radio frequency, \(|S_{21}|^{2}\) is usually used to represent the positive energy transfer.), and the results from the proposed model are calculated by (4). It is clearly shown that the results from the proposed practical model have much-improved accuracy than those obtained from the S-parameter method. Furthermore, the S-parameter-based simulation has rather high requirements on the computer performance and is extremely time-consuming.