# A Novel Bidirectional Wireless Power Transfer System for Mobile Power Application
## 4 System Analysis and Discussion  
With the aforementioned understanding of the proposed circuit operation principle and the circuit equivalent models, it is now straightforward to test and measured the proposed contactless bidirectional power transfer system in the experiments. The bidirectional power flow with dual-side duty ratio control will be tested and explained here. For convenient explanation, while the power is delivered form primary side to secondary side, one can call it forward mode operation. While the power is delivered from secondary side to the primary side, one can call it backward mode operation. In the proposed system the forward mode operation is controlled by the switch S\({}_{1}\) duty ratio and the backward mode operation is controlled by the switch S\({}_{2}\) duty ratio. The power flow direction can be controlled by the switch duty ratio always in the transmitter side.  
The averaged output voltage and output current values are recorded in this section and measured by the oscilloscope YOKOGAWA DLM2024. The duty ratio control for forward mode and backward mode operation test results are shown in Figure 12; Figure 13, respectively. As can be observed from Figure 12; Figure 13, the output voltage and current can be controlled almost linearly by the duty ratio and the maximum output power point is at the 0.9 duty ratio, regardless whether the circuit is operated in the forward or backward mode. This represents that the system output power can be obviously and easily adjusted to increase or decrease for applications.  
Figure 11: The (**a**) simulated waveforms and (**b**) measured waveforms of (Top) control signal of switch 1, (Middle) inductor voltage \(V_{L1}\), and (Bottom) inductor current \(i_{L1}\).  
Figure 12: Output voltage and current vs. duty ratio of switch \(S_{1}\) in the forward mode operation.  
The switching frequency variation test results for forward and backward mode operations are shown in Figure 14; Figure 15, respectively. The circuit resonant frequency is designed at 50 kHz and the measured optimal switching frequency is also located at 50 kHz. If the switching frequency is between 40 kHz and 60 kHz near the resonant frequency, the output voltage and current are not seriously affected in the proposed circuit. This means that the resonant capacitor and/or resonant inductor value variation in the system due to the environment causing resonant frequency offset is easily corrected by properly adjusting the switching frequency. To explain how the distance between the windings affects the power transfer, Figure 16; Figure 17 show the output voltage and current vs. distance in the forward mode and backward mode operations, respectively, where there is 180-degree direction in coil 2 compared to coil 1 which has 0-digree direction. Coils 1 and 2 are overlapped with distance R. As can be observed from Figure 16; Figure 17, the voltage and current are decayed with increasing distance R and the magnetic vector potential \(\overrightarrow{A}\) is decayed with the rate proportional to \(1/R^{2}\). The measured power conversion efficiency is about 50%, while the coils are very close to each other.  
Figure 14: Output voltage and current vs. switching frequency in the forward mode operation.  
Figure 13: Output voltage and current vs. duty ratio of switch \(S_{2}\) in the backward mode operation.  
Figure 15: Output voltage and current vs. switching frequency in the backward mode operation.  
According to the above test, the proposed wireless power transfer system can transfer the power flow bi-directionally and the output voltage and/or current can be adjusted through the switch duty ratios regardless whether the system is operated in the forward or backward mode. One low-power WPT application for mobile power is shown in Figure 18.