## 3 Rectifier Efficiency Limitations  
Designing a rectifier with high efficiency and that operates over extensive dynamic input power levels is essential for harvesting energy and wireless power transfer systems. In fact, the rectifier circuits have a diversity of factors affecting the rectifier efficiency performance while attaining a wide range of input power levels, such as active device parasitics, low breakdown voltage, high threshold voltage, nonlinear effects, mismatched impedances, and sub-optimum output load [21]. As a result, a system with optimal PCE would require a thorough set of trade-offs among these parameters. Therefore, to understand the rectifier operation and the efficiency limitations, these parameters and their impact on the circuit performance need to be investigated. In fact, the parameters effecting the rectifier to be operated over a wide range of input powers are mainly the threshold voltage, \(V_{th}\), and the voltage breakdown, \(V_{br}\)[21; 22].  
However, note that the threshold voltage, which can be defined as the voltage value from where the diode can operate and detect the input signal, is controlled by the saturation current. Consequently,  
Figure 2: Illustration of the concept of efficiency. Here \(P_{RF}\) and \(P_{r}\) state the input radio frequency power and input reflected power, respectively.  
having a diode with a high saturation current is desirable in WPT and harvesting energy to attain and sense low signals. Therefore, the effect of the saturation current on the overall PCE is illustrated as in Figure 3, which shows that the loss at low input power is due to the lower saturation current and vice-versa.  
On the other hand, when the rectifier device is driven by a reverse bias, the electric field near the junction can reach its maximum allowable value. Once a breakdown occurs, the current will suddenly increase while the DC output voltage remains almost constant. Therefore, voltage breakdown leads to significant efficiency degradation and attaining a rectifier with a high breakdown voltage is required to achieve high efficiency [21; 23]. As noticed in Figure 4, as the voltage breakdown increases, the overall efficiency becomes broader and able to handle a wider input power range, thus achieving higher efficiency.  
For this aim, a matching circuit should be taken into account to minimize mismatch loss between the antenna and the rectifier as highlighted in Figure 1. In WPT and harvesting energy circuits, designing a matching network will be more challenging since the input impedance of the rectifier needs to be matched for a particular frequency operation while its input impedance varies with the input power level [21].  
Furthermore, since the diode is a nonlinear component, generating harmonics at the output can reduce the overall rectifier efficiency. In addition, the load resistance is an important parameter to  
Figure 4: Voltage breakdown effect on the overall PCE.  
Figure 3: Saturation current effect on the overall Power Conversion Efficiency (PCE).  
consider as well; as the output load changes, the output voltage varies as well as the overall PCE. Accordingly, an optimal output load should be applied [21].