Analysis of the Effects of Dielectric Media on Magnetic Coupling WPT Using Filter Theory

This study, we first analyzed the characteristics when only the relative permittivity was varied from 1 to 81 in air, using filter theory. We then compared the results with those obtained using water as the medium, which includes other electrical properties as well. As a result, it was clarified that when the conductivity is zero, the coupling coefficient <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> can be determined using filter theory, whereas in the case of water, this becomes difficult. Next, we investigated the S-parameters by varying the conductivity from 0 (air) to 0.01 S/m (water), and examined how the wireless power transfer efficiency, calculated from the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k Q$</tex> product, changes accordingly. The results showed that when the coil distance is 30 mm, bimodal characteristics caused by the proximity of the coils can be observed up to a conductivity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sigma$</tex> of approximately 0.005 S/m. However, when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sigma$</tex> reaches 0.01 S/m, the same as that of water, the resonant frequency shifts and the bimodal behavior disappears. Furthermore, even when the medium has a relative permittivity of 81 (the same as water), the transmission characteristic <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$S_{21}$</tex> can reach nearly 0 dB when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sigma=0$</tex>. However, as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sigma$</tex> increases, the value of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$S 21$</tex> decreases, and in the case of water, it becomes significantly small, falling below 30 dB. In contrast, the maximum wireless power transfer efficiency obtained from the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k Q$</tex> product theory indicates that even with a water conductivity of 0.01 S/m, an efficiency of 16% can be achieved. This suggests that by designing the matching circuit to maximize the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k Q$</tex> product, it is possible to improve wireless power transfer efficiency even in water.