## 2 Configuration of the Proposed Wireless Battery Charging System for a Quadcopter
### Transmitter and Receiver Circuit Design and Description  
Figure 2 shows a simple wireless power transmission circuit. The circuit comprises a transmitter circuit, a receiving circuit, and the control part (voltage divider and analog-to-digital converter (ADC) of the microcontroller). The power amplifier drives the transmitting coil \(L_{t}\). When the receiving coil is brought near to the transmitting coil, the voltage at receiving coil \(L_{r}\) is induced and it is processed by a bridge rectifier to convert AC to DC voltage. To achieve the optimum performance, values of \(C_{t},\ L_{o},\ C_{o}\), and \(C_{r}\) are calculated using Equations (1) to (4).  
Figure 1: Block diagram of the proposed wireless battery charging system for a quadcopter.  
\[C_{r}=\frac{R_{0}L_{r}\pm\frac{1}{2}\omega M^{2}}{R_{0}\omega^{2}L_{r}^{2}}; \tag{1}\]  
\[C_{0}=\frac{\omega^{-1}}{\omega L_{t}(1-K^{2})+R_{0}(Q+1-\sec(\varphi))}; \tag{2}\]  
\[C_{t}=\frac{\left(2\omega^{-1}\right)}{1+\frac{\pi^{2}}{4}R}; \tag{3}\]  
\[L_{0}=\omega^{-1}QR_{0}. \tag{4}\]  
In the above equations, \(M\) is the mutual inductance, \(K\) is the coupling factor, \(Q\) is the quality factor between the transmitting and receiving coils, and \(\varphi\) is the phase angle ranging from 40\({}^{\circ}\) to 70\({}^{\circ}\). The derivation of the equations for a Class-E amplifier can be found in Reference [39]. Transmitting coils and the receiving coil are made of copper wire with 15 and 40 turns, respectively (Tables 1 and 2). According to the power transmission range capabilities, wireless power transmission can be categorized into three types [40; 41]. First is the inductive power transmission (IPT) and capacitive power transmission (CPT), used for short-range distances; second is the resonant inductive coupling power transmission, widely used for medium-range distances; and third is the laser beam or microwave power transmission, used for long-range distances. In order to achieve high efficiency, inductive coupling requires very close coupling between the transmitting and receiving coil. Whereas, in resonant inductive coupling, efficient power transmission can be achieved with some distance between the transmitting and receiving coil via the use of resonant circuits. Also, resonant inductive coupling has better tolerance than inductive coupling. Therefore, the resonant inductive coupling is considered an effective technique for coping with the coil misalignment issues, and for drone battery charging systems. Therefore, in this work, a resonance inductive coupling-based wireless power transmission technique was used for charging the drone battery. The detailed block diagram of the circuit for wireless power transmission is shown in Figure 3. At the transmitter side, Class-E power amplifiers are used to generate amplified AC voltages with a resonance frequency of 240 kHz for each coil.  
Figure 2: Basic circuit diagram for wireless power transmission.  
These amplifiers are driven by a high-frequency clock signal. The clock signal is provided to the gate driver of each amplifier of the respective transmitting coil simultaneously. A microcontroller is used for generating a high-frequency clock signal and it keeps measuring the output voltages of each transmitting coil using an ADC, and performs envelop detection of the measured voltages to identify which excitation coil is the closest to the receiving coil of the drone.  
At the receiving side, the receiving coil is installed on the drone and it is connected to a full bridge rectifier, which is used to convert the AC to DC. Finally, a battery charger (DC to DC converter) is used for battery charging. The system works by detecting the change in the voltage of any of the envelope-detected voltage signals of the transmitting coils, which (changes in voltage) refer to the presence of the receiving coil on the charging station. After detecting the receiving coil, a control algorithm is activated to align the coils and start wireless power transmission.