*4.3. Power Efficiency*

The simulated power efficiency versus input voltage amplitude for different load resistors is presented in Figure 7. The definition of PCE is shown in (5):

$$PCE = \frac{\int\_{t}^{t+T} V\_{OUT}(t) \cdot I\_{OUT}(t) dt}{\int\_{t}^{t+T} V\_{IN}(t) \cdot I\_{IN}(t) dt} \cdot 100\%.\tag{5}$$

**Figure 7.** PCE versus input voltage amplitude simulated for different values of RLOAD

The maximum PCE value of 94% can be found at 0.6 V for a RLOAD of 500 Ω. When *Vin* is lower than this range, the PCE sharply decreases due to the low voltage efficiency, as noted in Section 4.1. Thus, the efficiency of the rectifier is poor in the ultra-low voltage range. Additionally, the PCE tends to decrease for higher input voltages because the power losses are mainly concentrated in the comparator. However, this case is not significant for ohmic loads lower than 15.5 kΩ. Moreover, for higher load resistors, the PCE tends to decrease due to the reduction of the output current, whereas the bias current that comes from the voltage source keeps almost constant. Regardless, from 0.45 V to 1 V, the power efficiency for low ohmic loads is considered as being good for this application. Additionally, the influence of the width of the NVC stage (M1–M4) and of M5 in both PCE and VCE can be observed in Figure 8. For this simulation test, the width of each stage was individually varied while the other was kept constant. This figure shows that the VCE and PCE features of both stages are at their maximum point for a width of 100 μm because the on-resistance of this transistor is directly influenced by the *W*/*L* ratio of the MOSFET. Even if the gate capacitance of M5 increases with the size, Figure 6 shows that the threshold cancellation circuit can drive this large transistor.

Figure 9 shows the power efficiency versus input voltage amplitude for different input frequencies. The load capacitor value was adapted to keep the output ripple voltage small depending on the input frequency. It is possible to observe that the proposed rectifier can achieve a high-power efficiency for low input frequencies in the operating voltage range. However, when the input voltage and frequency are high, the power efficiency tends to slightly decrease due to the power losses in the NVC and in the active diode, which in this case it is caused by the output signal of the comparator being too fast. Consequently, the working time of transistor M5 will be too short, which reduces the amount of power converted to the load. Nonetheless, at typical energy harvesting frequencies, the performance of the CMOS rectifier for the presented frequency range is suitable for this application.

**Figure 8.** VCE and PCE features with the variation of the width of the NVC transistors and M5 (L = 0.13 μm).

**Figure 9.** PCE versus input voltage amplitude simulated for different input frequencies for RLOAD = 5.5 kΩ.

To prove the robustness of the proposed CMOS rectifier, it was tested through the four known process corners, such as the typical ones, fast, slow, slow NMOS, and fast PMOS, and fast NMOS and slow PMOS. Figure 10 presents the PCE plots with the variation of the temperature depending on the process corner. According to the simulation results, it can be observed that PCE tends to decrease when a fast PMOS is used due to the high speed of the active diode, which reduces the ON time of the rectifier. Consequently, the power transferred to the load is affected. Nevertheless, as long as the temperature rises, the power consumption of the rectifier also increases because the MOS threshold voltage is an exponential function of the temperature.

The performance comparison between this work and previous rectifiers is presented in Table 2. It shows that the proposed configuration can achieve higher VCE and PCE for a low voltage range. Even if the PCE in [29] is higher for a high ohmic load, for this application, it is only expected a low impedance of the electronics to be powered. Thus, the achieved VCE and PCE in this work are higher than those in the reported literature, highlighting its added value [15,28,30]. In addition, this work presents a wider input voltage range compared to the previously noted article. Therefore, it can be concluded that

this rectifier can overcome the drawbacks of the structures discussed in Section 2, which means that this rectifier is very suitable for energy harvesting applications.

**Figure 10.** PCE variation with temperature depending on the process corner variation for a RLOAD = 5.5 kΩ.


