# Wireless Power Transfer via Subterahertz-Wave
## 2 Wireless Power Beaming  
A rectenna is completed by integrating a fabricated antenna and the rectifier. The power transmission efficiency \(\eta\) of the entire wireless power supply is obtainable as \(\eta=P_{\text{out}}/P_{0}\) from the output power of the oscillation source by \(P_{0}\) and the DC output power \(P_{\text{out}}\) obtained using the rectenna. Furthermore, the power transmission efficiency \(\eta\) can be estimated theoretically using the following parameters: antenna gain \(G_{\text{tr}}\), wavelength \(\lambda\), the area actually occupied by the antenna on the circuit pattern \(A_{\text{act}}\), the antenna's effective area \(A_{\text{eff}}\), the aperture area of transmitting antenna \(A_{\text{t}}\), the aperture area of receiving antenna \(A_{\text{r}}\), transmitting distance \(d\), beam radius \(\omega\), beam waist \(\omega_{0}\) of the power transmission antenna, and power density \(S\) at the rectenna installation point, which is obtainable from the beam profile using an IR camera. The conceptual diagram of power transmission efficiency is shown in Figure 5. The transmission efficiency of the entire wireless power supply by the rectenna can be estimated theoretically using Equations (1)-(5). Total transmission efficiency  
\[\eta=\ \eta_{tr}\eta_{apr}\eta_{rp}\eta_{RFDC} \tag{1}\]  
Transmission antenna efficiency (normally 1, when a reflection exists, decrease by that amount)  
\[\eta_{tr}=1 \tag{2}\]  
Figure 4: Schematic diagram showing the oscillation source output range for frequencies [19]. Figure 5: Conceptual diagram of power transmission efficiency in wireless power transmission. Antenna aperture efficiency  
\[\eta_{apr}=\frac{A_{eff}}{A_{act}}=\frac{\left(\frac{\lambda^{2}}{4\pi}\right)G_{r} }{A_{act}} \tag{3}\]  
Beam efficiency  
\[\eta_{rp}=1-\exp\left(-\frac{A_{t}A_{r}}{\lambda^{2}d^{2}}\right) \tag{4}\]  
RF-DC conversion efficiency  
\[\eta_{RFDC}=\frac{P_{DC}}{P_{in}}=\frac{P_{DC}}{S\times A_{eff}}=\frac{P_{DC}} {S\times\left(\frac{\lambda^{2}}{4\pi}\right)G_{r}} \tag{5}\]  
From the equations presented above, one can estimate the amount of specified amount of wireless power supply to the object at a distance \(d\) away using the antenna gain, RF-DC conversion efficiency, output power of the power generation source, and beam profile. From Equations (4), it is apparent that if the aperture area of the transmitting and receiving antenna is always constant, raising the frequency is sufficient to increase the beam efficiency. These factors clarify the merit of using millimeter waves for wireless power supply. Particularly, the diode performance determines the rectenna's maximum RF-DC conversion efficiency and the DC output power. The value \(RC\) (The RC time constant) multiplied by the series resistance \(R\) and the junction capacitance \(C\) expresses the time constant of switching. The smaller this value becomes, the more the cutoff frequency and the RF-DC conversion efficiency can be increased at high frequencies. Equation (6), which expresses the diode efficiency \(\eta_{d}\) and relational expression (7) of the RC time constant and the breakdown voltage \(V_{\text{MAX}}\) using the following parameters: The angular frequency \(\omega\), Dielectric breakdown electric field \(E_{\text{c}}\), Electron mobility \(\mu\). \[\eta_{d}=\frac{1}{1+\frac{1}{4}\omega^{2}\left(RC\right)^{2}} \tag{6}\]  
\[RC=\frac{2V_{MAX}}{\mu E_{c}} \tag{7}\]  
From Equation (6), one can infer the possibility of improving the RF-DC conversion efficiency as the RC time constant decreases. However, simultaneously, the breakdown voltage decreases because of the relation shown in Equation (7). When a wireless power transmission unit with the rectenna is mounted on a small aircraft such as a drone, a wireless sensor to the IoT, a mobile device, etc., some concerns arise that the power transmission efficiency will be remarkably lowered because many factors such as the radiation pattern, axial ratio, input power, optimum load, and the like deviate from optimal values.