## 2 Methods  
The mathematical modeling and simulation (M&S) research method [26] formed the basis for implementing a prototype system to test the viability of a complete WPT circuit. M&S assisted in acquiring the necessary information about the behavior of the WPT prototype through simulation and mathematical equations before the physical implementation, testing, and deployment. The LTspice simulation software (Analog Devices Inc., Wilmington, MA, USA) was utilized to analyze the test results of the WPT prototype circuit [27]. The variables considered for the energy harvesting circuit were distance, antenna type, and amount of energy harvested based on the feasibility of the circuit model. The variables considered for the MRC [28] circuit were the resistance and conductivity of the copper wire. The relevant formulae were applied to display the quality factor aspect of the complete WPT prototype circuit. It is practical to take into consideration the RF energy harvesting system, the circuitry of the magnetic resonant system, and the signal strength of the receiving antenna (Yagi-Uda) with a frequency range from 30 MHz to 3 GHz. The factors affecting the efficiency of the wireless power system were based on the coil design configuration, transmission distance, and coupling. A less efficient system will generate more emissions and result in less power passing through to the receiver device or load [29]. The prototype system consisted of the RF energy harvesting circuit initially tested in a previous study [30], which represented the input to the WPT system utilizing MRC. Figure 1 presents the block diagram for the WPT prototype system. The received RF signals are converted to electrical power through the RF energy harvester circuit (A) [30]. The power management system (B) sends the converted electrical power to be used as the input load (C) to the transmitting coil (D) in the WPT system. It consists of single transistor oscillator attached to the transmitting coil [31]. The receiving coil (E) transfers the electrical power (AC), referred to as the load to be converted by the rectifier (F) into DC power, which is stored in the storage capacitor (G). The voltage regulator (H) transfers the required DC power wirelessly through the MRC to the battery of a miniaturized electronic device (I) for charging. The components used for the initial magnetic resonance prototype circuit consisted of 22 AWG magnetic wire, 15 turns magnetic wire (receiver coil (D)), 7.5 turns of the magnetic wire with a looped tap (3 cm), and another 7.5 turns of magnetic wire (transmitting coil (E)), each with a diameter of 5 cm. The resistivity, resistance, conductance, area, and length of coils were taken into consideration because they impact the flow of voltage through the circuit. The RF energy harvesting circuit included the rectifier component, similar to the full bridge rectifier circuit [30]. The block diagram (Figure 1) can be divided into two components--the RF energy harvesting circuit and wireless power charging circuit. The RF energy harvesting circuit consisted of a voltage rectifier component (full-wave), Yagi-Uda antenna connection with a frequency range of 30 MHz to 3 GHz (RG-5 coaxial cable), and ground connection, which is a straight copper cable attached to a metal pole inserted 6 m into the ground [30]. The rectifier component within the RF energy harvesting circuit is responsible for converting the RF signals from the antenna to DC voltage [25,30,32]. The wireless power charging circuit includes the magnetically coupled coils shown in Figure 2, the transmitting coil (D) connected to single transistor oscillator, the receiving coil (E) with the rectifier (F) to convert AC to DC [33], and a capacitor (G) to smooth or filter the pulsating DC output after rectification and to store the converted voltage. Rectification comprises a bridge rectifier attached to the receiving coil to make the conversion from AC to DC [34,35,36]. The responsibility of the voltage regulator is to normalize the voltage to the load.