## 1 Introduction  
Recent progress in the magnetic resonant based wireless power transfer (MRWPT) system has stimulated its usage in wide applications such as electric vehicles, consumer appliances, and wireless sensor networks [1; 2; 3]. Also, MRWPT technology could be the best choice for small power wearable or implanted healthcare devices, such as blood glucose monitors, hearing aids, electrocardiogram, micropumps, pacemakers and insulin pumps [4; 5]. Similarly, with the advent of microelectronics and semiconductor technology the size of these devices is shrinking drastically, which makes the device portable or even implantable [6; 7]. In the meantime, the number of personal electronic devices used by a person is increasing day by day, which needs to be charged efficiently from a single power source [8]. MRWPT system turns to be the suitable choice to simultaneously power multiple devices by a single source [9]. However, the simultaneous power transfer to multiple devices presents to be more challenging regarding coil optimization and uniform power distribution. Moreover, under dynamic conditions, the power delivered to the receiving units is reduced due to the presence of cross coupling and frequency splitting issues [10; 11]. In [12], single Tx and multiple Rx system are investigated for the static load conditions with fixed operating frequency. However, in the practical scenario, the power rating and operating frequency of the devices cannot be maintained at the same level. Likewise, the uniform power distribution to multiple loads is challenging to attain using a single Tx coil with fixed operating frequency. On the other hand, the multiple Tx's are examined to increase the power delivery capacity to multiple loads [13; 14]. Even though, multiple Tx's can provide stable power to all the loads, the increase in the number of Tx will not be the preferred solution for small-scale power applications [15]. To increase the power transfer efficiency (PTE), relay coils are normally employed in the single Tx and Rx WPT system [16; 17]. These relay coils can improve the quality factor of the Tx, Rx and load coils, thereby improvement in the PTE of WPT system. However, the addition of relay coils in multiple Rx system requires an optimal design of the coil structure and coupling between the Tx and Rx coils [18]. Meanwhile, the coil optimization and addition of ferrite core materials to improve the magnetic coupling are studied for high power applications [19; 20]. Nevertheless, in case of lower power devices addition of ferrite core material is restricted and requires an alternative way for power transfer technique. The three-dimensional Tx coil structure is investigated for the maximum power transfer to single dynamic Rx irrespective of the orientation [21; 22]. However, the uniform power distribution to multiple Rx with three-dimensional structure is difficult to control and requires additional control circuitry at the Tx coil. Time division multiplexing based power transfer to multiple Rx approach was examined to uniformly transfer the power to individual loads [23]. In this approach, the Rx coils are designed with different resonant frequency, and the Tx frequency is varied to match with the Rx coil frequency. However, in practical scenarios more than one Rx's might be designed with a same resonant frequency which leads to cross-coupling between the Rx coils [24; 25]. To eliminate the cross coupling between the coils, compensation circuits are employed for the multiple Rx system [26]. The capacitive compensation at the Rx coil was studied for static load conditions and proved to be an effective way to filter the non-resonant magnetic field from the adjacent Rx coils [27]. The capacitive compensation also takes less space and turns to be effective in low power device fabrication. However, under the dynamic condition, the continuous variation in the Rx position leads to the frequency splitting in the Rx coil power with cross-coupling among the Rx unit [28].