# Quasi-Wireless Capacitive Power Transfer for Wire-Free Robotic Joints +
## 3 Results  
Each tap location along the QWR was tested with the matching network, as shown in Figure 4a. The QWR was maintained at its resonant frequency for every tap location tested. These changes occur due to the reduction in the electrical length of the QWR. The total system efficiency (\(\eta\)) was calculated by measuring the DC power output at the rectifying PCB, and dividing it by the measured AC input power at the base plate.  
\[\eta=\frac{P_{Load(DC)}}{P_{in(AC)}}=\frac{V_{DC}I_{DC}}{V_{RMS}I_{RMS}\cos \theta}. \tag{25}\]  
Figure 9 shows the voltage and current waveforms input to the base plate of the robotic system. From Figure 10, it can be seen that the percentage of the QWR that is tapped has a direct relationship to the efficiency. The presence of a capacitor in the load-side of the impedance branch also had a significant impact on the system transfer efficiency.  
Figure 8: Thermal image investigating the power loss when using the motor housing and gearbox as part of the unilateral current path. The temperature on the motor housing rose \({}^{\circ}\)C above ambient after 1 h of 0.5 A passing through it at a frequency of 6.78 MHz.  
Figure 9: The input waveforms from the device used to deliver power to the robot.  
Without any capacitance to balance the load-side branch, the efficiency was the lowest of the experimental measurements, achieving a maximum transfer efficiency of 79%. Using a capacitor to balance load-side branch, the peak efficiency of 82% was achieved. As can be seen in the figure, for all the cases tested, the efficiency reached a point where it plateaued, while the efficiency increased by a marginal amount. This plateau occurs at a tap that spans roughly 25% of the coil's length for the tests that had a matched impedance. The plateau for the test without a capacitor occurred at 43% of the coil's length (nearly half the coil). Utilizing proper matching capacitance can reduce the amount of tap size required for power transfer on the QWR. This is significant since a higher efficiency can be achieved without shifting the frequency as much. This will allow for lower frequencies to be achieved with the same QWR.  
Figure 11 plots the change in the resonant frequency with tap location. The data sets for the three capacitors used show that the capacitance does not have any large bearing on the shift in frequency as more of the coil is tapped. However, the number of turns of a tap produces a linear change in the operating frequency as the tap size is increased (Figure 11). This result shows that shunting a portion of the QWR using a tap creates a reduction in the electrical length in the \(\mu\)cT-line. The linear response in frequency vs. tap size is beneficial for designing a QWR to operate at a desired frequency while maintaining an improved power transfer efficiency.  
The theory derived earlier in the manuscript assists in conveying what Figures 10 and 11 show, which is that this topology can be used to improve the transfer efficiency while minimally affecting the operating frequency of the system. This can be a new framework for  
Figure 11: Graph of the effect on the resonant frequency from tapping.  
Figure 10: Graph of efficiencies.  
designing much more complex robots using impedance matching QWR topology to achieve better power transfer in the field of QWic.  
The ability to transfer power wirelessly over a robotic chassis, in a unilateral fashion, offers a unique design approach that eliminates wires between joints. Figure 12 depicts how such a unilateral wiring design can be expanded upon to operate any number of linkages using the QWiC power method. The multi-joint approach in Figure 12 is currently under development and will be communicated in a future work.