# Low-Power Rectennas in Microwave Wireless Power Transmission
## 2 Low-Power Rectifiers  
A typical rectenna consists of an antenna and a rectifier, where the antenna serves as the medium for exchanging energy between ambient RF fields and the circuit, and the rectifier is responsible for converting the captured RF energy into dc power. Consequently, the overall efficiency of a rectenna is mainly determined by the rectification efficiency of the rectifier. Schottky barrier diodes are widely adopted in RF rectifier circuit design due to their low forward voltage drop and high switching speed characteristics. Numerous methods have been proposed to obtain closed-form models for diodes. The rectifying diode is ideal for medium to high input power levels. When forward-biased, diode impedance is extremely low and can be approximated by a series resistance Rs, whereas when reverse-biased, its impedance approaches infinity [10; 11]. However, the diode's nonlinearity weakens at low input power levels, and the ratio of reverse to forward impedance decreases, making the traditional on-off model no longer applicable [12]. The equivalent circuits corresponding to two states of the Schottky-diode-based rectifier are shown in Figure 1.  
In [13], [PERSON] et al. introduced an efficiency chain concept to characterize rectifiers' RF-dc conversion efficiency under low-power conditions. The overall efficiency can be described as the product of four efficiencies:  
\[\eta_{RF-dc}=\frac{p_{dc}}{P_{RF}}=\eta_{M}\cdot\eta_{p}\cdot\eta_{0}\cdot \eta_{DCT}\]  
where \(\eta_{M}\) stands for matching efficiency, representing the reflection loss caused by impedance discontinuity when the signal enters the nonlinear device, as well as additional insertion loss introduced by the matching network; \(\eta_{p}\) stands for parasitic efficiency, which accounts for the low-pass filtering effect of the diode junction capacitance \(C_{j}\), causing part of the current reaching the diode to be reflected and consumed by the series resistance. The inherent properties of the diode typically determine the following relationship: the  
Figure 1: Equivalent circuits corresponding to two states of Schottky-diode-based rectifier: (**a**) RF power absorber, (**b**) dc power provider [12].  
smaller the junction capacitance \(C_{j}\), junction resistance \(R_{j}\), and series resistance \(R_{s}\), the higher the parasitic efficiency. \(\eta_{0}\) is the RF-dc conversion efficiency of the diode, mainly governed by the current responsivity \(\Re_{10}\) of the nonlinear junction. A higher current responsivity indicates stronger nonlinearity and thus higher efficiency \(\eta_{0}\). The diode fabrication process primarily influences the current responsivity; \(\eta_{DCT}\) stands for dc-load transfer efficiency. The diode can be seen by the load as a dc source with the junction resistance considered the source impedance. The maximum dc-load efficiency \(\eta_{DCT}\) is obtained when the load resistance equals the diode's junction resistance.  
It can be seen that under low input power conditions, the energy loss in the rectifier mainly originates from two aspects. One is the loss caused by the diode's intrinsic parameters, primarily due to the weakened nonlinearity at low power levels. The other is the loss in the matching circuits, including impedance discontinuities resulting from imperfect matching network design, additional losses from transmission lines, and dc-load mismatches. It is worth noting that under low input power, the bias voltage \(V_{j}\) of the diode is less than the turn-on voltage \(V_{bi}\), causing the diode to operate in a zero-bias state. In this scenario, most of the energy is dissipated in the junction resistance, while energy loss at higher harmonics is minimal and can therefore be neglected.