## 4 Performance Comparison  
The choice of a specific rectifier topology depends upon the specific application, the used technology, and design specifications. The choice of a specific rectifier topology can be firstly done according to the input voltage range, as suggested in the following. * In ultra-low input voltage range (0.1-0.6 V) applications, such as micro-scale and battery-less biomedical implants, body driven circuits represent a good option because the threshold voltage of transistor is often relatively high and body driven topologies overcome this problem. Moreover, boost converters are often mandatory to adapt the rectified voltage at the levels conventionally required for functional block operations. * For low input voltage range (0.6-1.2 V) applications, passive rectifiers, such as cross-coupled and voltage doubler, are a good choice because the transistors work sufficiently well without additional circuits (that would reduce the _PCE_). * For mid and high input voltage range (higher than 1.2 V) applications, active rectifier topologies represent the best choice to optimize its performance in terms of power consumption (i.e., _PCE_). The solutions for implanted medical devices previously analyzed are compared in Table 1. Please note that the data shown in the table do not refer only to the adopted rectifier but to the overall PMLC. In Table 1, _PCE_ and _VCR_ are respectively defined as  
\[PCE=\frac{P_{OUT}}{P_{IN}}\cdot 100=\frac{V_{DC}^{2}/R_{L}}{\frac{1}{N\cdot T} \int_{I_{0}}^{I_{0}+N\cdot T}V_{AC}(t)\cdot I_{AC}(t)dt}\cdot 100 \tag{1}\]  
Figure 23: (**a**) Circuit implementation of digitally controlled on-off delay compensated full-wave rectifier and (**b**) control logic present in [51]. Reproduced with permission from [PERSON], IEEE Transactions on Circuits and System II: Express Briefs; published by IEEE, 2020. \[VCR=\frac{V_{OUT}}{V_{OUT,id}}\cdot 100 \tag{2}\]  
where \(V_{DC}\) is the averaged rectified output DC voltage, \(R_{L}\) is the output resistive load, \(T\) is the period of the input sinusoidal signal, \(N\cdot T\) is the integration range over \(P_{IN}\) is calculated, and \(V_{AC}(t)\), \(I_{AC}(t)\) are the instantaneous voltage and current of the AC input source, \(V_{out}\) and \(V_{out,id}\) are the actual and ideal output voltage of the system. Analysis of data reported in Table 1 reveals that the body driven rectifier proposed in [47] is the only solution for ultra-low input voltage range. However, such result was accomplished because the proposed BD-WTA is supplied by an auxiliary power source whose voltage is higher than the input signal amplitude. Actually, the circuit works as comparator where the resulting output voltage is always the maximum between the two inputted signals. Main drawbacks and limits of this circuit are strictly related to the needed of auxiliary supply and biasing sources and the use of the body-driven approach which allows working on very-low voltage input signals but limits their maximum amplitude values. Definetively, comparator in [47] is particularly suited as envelope detector for applications where the input signal amplitude contains information to be extracted, such as amplitude modulation receiver. On the other hand, the features of [44] confirm that active topologies are not suitable for low input voltage range since they have \(PCE<60\%\). Reasons of the relatively low power performance can be found in the loss of speed and driving capability of the auxiliaries, such as comparators and bias generators, when the transistors are constricted to work in sub-threshold region. This confirms the categorization done before, since typical values for the threshold voltage of a regular MOSFET is about 600 mV. The analysis of solutions in [35; 41; 45; 48; 49; 50; 51] further confirm the validity of the guidelines provided above, suggesting that mixed approaches are needed to extend the input voltage range.