## 2 Conventional Topologies for AC-DC Conversion
the threshold voltage level. In such case, reverse and short-circuit currents are extremely reduced, but the on-resistance is increased, making the rectifier useful for very-low power applications (e.g., sub-uW power level). If the input voltage is larger than the threshold voltage of the transistors, the leakage current becomes relevant and the efficiency decreases, but the channel becomes more conductive decreasing the on-resistance and enabling mW -power level operations. The active rectifier shown in Figure 7 has the same structure of the passive full-wave rectifier but diodes are replaced by _active-diodes_. Active diodes are essentially comparator-controlled MOSFETs. The operation principle of the active full-wave rectifier can be described as follows. Let us assume that the process starts with \(V_{AC1}\) going down and \(V_{AC2}\) going up. When \(V_{AC2}-V_{AC1}>V_{TH,P}\) (threshold voltage of M\({}_{P1,2}\)), M\({}_{P1}\) is turned on and therefore \(V_{AC2}=V_{DC}\). Then \(V_{AC1}\) swings below the ground voltage, the comparator CMP1 turns on the switch M\({}_{N1}\), and \(I_{AC1}\) charges up \(V_{DC}\) through the AC source. When \(V_{AC1}\) swings above zero, M\({}_{1}\) is then turned off by CMP1, finishing one half cycle of the full-wave rectification period. During the next half of the AC input cycle, the other half of the rectification circuit will conduct in a similar manner as described above. Active diodes do not exhibit the large forward dropout voltage of conventional diodes and prevent the reverse leakage current. However, the implementation of an active diode entails additional area and power consumption for comparators. Moreover, they suffer in start-up at low input voltage because, generally, the comparator is powered by the output voltage of the rectifier. As already mentioned, the output voltage of the transducer or the rectifier may be too low to directly supply any electronics system. A possible solution is to exploit blocks which boost the voltage to the needed level (e.g., voltage multipliers or charge pumps). Such circuit can constitute a different building block of the conversion chain or replace the rectifier, acting as AC-DC boost converter [8; 30; 31]. Figure 8 shows the simplified schemes of the most used charge pump circuits. As with the rectifier topologies, diodes are often replaced by MOS-based passive and active diodes [6]. Signals which clock the circuit, named \(V_{CK}\) and \(V_{\overline{CK}}\) in the figure, can be generated internally the IMDs, for example by using a controlled oscillator, or can be provided directly by the transducer. In the first case, the Dickson CP is the topology widely adopted and it acts as DC-DC boost convert, moreover, in order to decrease the capacitance value of the pumping capacitor, \(C\), and improve the PCE, high frequency counter-phase square-wave signals are used. In the second case, where the frequency of the clock signal is imposed by the adopted piezoelectric transducer, the widest adopted is Cockcroft-Walton CP, and it implements the AC-DC conversion. Figure 7: Active full-wave rectifier with NMOS active diode. It is worth noting that also the cross-coupled structure can be exploited to realize diodes for CPs [32; 33]. They are essentially latch-configured inverters with \(V_{OUT}\) similar to the dual-branch charge pumps [6], but the pumping capacitances of a single stage are halved. These dual compensated structures introduce many benefits akin to the dual-branch structures. It improves pumping efficiency and reduces ripples in the output voltage. Moreover, while in a Dickson CP the voltage drop across each switch is equal to the diode threshold voltage, \(V_{TH}\), in the cross coupled charge pump the voltage drop is equal to the drain-to-source voltage \(V_{DS}\), which is lower than \(V_{TH}\). The output voltage of the charge pump depends on the power required by the load, therefore this voltage can be change dynamically. To prevent changes in this voltage, some type of feedback control can be implemented.