## 2 Conventional Topologies for AC-DC Conversion  
As mentioned above, the systems of interest harvest energy by means of a piezoelectric transducer, which converts ultrasound (US) waves into alternate electrical quantities, voltage and current. For medical devices, Food and Drug Administration (FDA) limits for power transmission into tissue to be the U.S. lesser than 7.2 mW/mm\({}^{2}\). Therefore, with the compact size requirements, power induced by US sources results to be limited in the order of few milliWatts. Typically, attenuations due to the US link (in this case, human tissues) further decreases these values. Thus, the system requires a very efficient conversion from AC to a DC voltage and a regulator to supply the biomedical functional circuits. To convert the AC voltage into a DC voltage a circuit (called _rectifier_) is required. The basic elements of a rectifier are _diodes_, historically realized with PN junctions, but they can also be implemented by using transistors (i.e., diode-connected transistors, PMOS diodes and NMOS diodes). These diodes are made by connecting gate and drain of the transistor and the current flows as indicated by the arrow. This type of diode may exhibit a relatively high leakage current when realized by means of a short-channel transistor, therefore, to reduce the reverse leakage, a composite CMOS diode can be adopted [29]. Nonetheless, this topology increases the conduction resistance which in turn increases the forward dropout voltage. The choice of a specific diode is mainly driven by the  
Figure 4: Simplified block diagram of a power management integrated circuit for ultrasound-based energy harvesting. characteristics of the adopted technology, the minimum amplitude of the input signal and realization costs. However, the MOS-based diode, in its simple or composite version, seems to be a valid trade-off in many cases and it is the widely adopted device in AC-DC converters. The main rectifier topologies are classified as passive and active rectifiers. In passive rectifiers, the transistors work as simple diodes while in active rectifiers, auxiliary circuits are added to decrease the voltage drop and improve the performance of the transistors used as diodes. Two traditional passive rectifier topologies are shown in Figure 5[29]. Focusing on Figure 5a, in the first half cycle \(V_{AC}\) is positive and the diode \(D_{1}\) will conduct when \(V_{AC1}\) goes higher than the DC output voltage \(V_{DC}\). During the second half cycle \(V_{AC}\) is negative and \(D_{1}\) is surely reverse-biased. Therefore, this circuit delivers current from the AC source to the DC output, at the maximum, during a half cycle, therefore it is called _half-wave rectifier_. On the other hand, in the rectifier shown in Figure 5b, during the first half cycle, the diodes \(D_{1}\) and \(D_{4}\) will conduct when \(V_{AC}\) is higher than \(V_{DC}\). In next half cycle, \(D_{2}\) and \(D_{3}\) will conduct when the voltage \(V_{AC2}-V_{AC1}\) is higher than \(V_{DC}\). Therefore, this circuit delivers current to the output twice a cycle, it is so-called _full-wave rectifier_. These solutions of rectifiers are very simple but have high dropout voltage and require an input voltage greater than one or two threshold voltage. Another passive rectifier is the _Cross Coupled_ topology, whose simplified diagram is shown in Figure 6[29]. The cross-coupled rectifier is widely used for its low-voltage and auto-switching characteristics. For high input voltage \(V_{AC}\), the MOS transistors will act as switches with low on-resistance for rectification, and the forward voltage drop is minimized. However, a high leakage current may occur if the input voltage, during the transition instants, is too high because the PMOS and NMOS will be turned on simultaneously short-circuiting the two supply rails. This rectifier operates efficiently with low input voltage, also below  
Figure 5: Schematics of (**a**) the half-wave rectifier and (**b**) the full-wave rectifier. Figure 6: Cross-coupled rectifier [6].