## 3 The State-of-the-Art of AC-DC Converters  
Many solutions have been proposed in the literature to improve the performance of the PMIC for IMDs. Since the output voltage of the transducer is an AC signal whose frequency ranges from some kHz to about 30 MHz [5], AC-DC converters topologies exploited for radiofrequency energy harvesting within low frequency range (e.g., below 100 MHz) could be adopted. For this reason, in this review some works based on radiofrequency energy harvesting are also included. Moreover, although all the solutions analyzed in this paper are equally interesting, for the sake of of conciseness only the topologies suitable for ultrasound energy harvesting are considered. As a first example, [PERSON] et al., in [34], presented an ultrasonically powered implantable micro-oxygen generator (IMOG) that is capable of in situ tumor oxygenation through water electrolysis. Wireless ultrasonic powering (2.15 MHz) was employed to increase the penetration depth and eliminate the directional sensitivity associated with magnetic methods. The block diagram of the overall system is shown in Figure 9. In this case the receiver is constituted of a passive full-wave rectifier, a filter and the interdigitated electrodes which act as micro-oxygen generator. Although an output voltage up to 6.4 V and an output current equal to 300 uA is reported [34], the system performance is limited mainly by the passive rectifier. Figure 8: Simplified schemes of Dickson (above) and Cockcroft-Walton charge pumps. Figure 9: Block diagram of the system proposed in [34]. Reproduced with permission from [PERSON], IEEE Transaction on Biomedical Engineering; published by IEEE, 2011. [PERSON] et al. proposed a generic rectifier system for biomedical implants [35]. As shown in Figure 10, the full-wave rectifier is composed of two cross-coupled PMOS and two active NMOS-diodes. As compared to the classic topology, it implements a real-time NMOS on/off calibration to make sure the rectifier always operates at near-optimum conditions with circuit-delay elimination under different (process, voltage and temperature) corners and loading conditions, thus both power conversion efficiency (\(PCE\)) and voltage conversion ratio (\(VCR\)) are significantly improved. Moreover, NMOS adaptive sizing is also introduced for \(PCE\) optimization over a wide loading range. However, this system operates at 13.56 MHz and requires a relatively high input voltage (from 1.2 V to 2.4 V). It is worth noting that a lot of solutions proposed in the literature adopt AC-DC with at the least one couple of active diodes, NMOS- or PMOS-type, because they allow heavily reducing reverse and short-circuit current losses, which are the main drawbacks of the conventional cross-coupled structure (i.e., currents flowing from the output to the ground when transistors are switched-off or switched-on simultaneously). Improved versions of active diodes have been continuously introduced with the aim of further increasing the power efficiency of the whole converter. Generally three aspects, namely turn-on instant, conduction angle and MOSFET channel conductivity, mainly affect the \(PCE\). Turn-on instant, defined as the time when the active diode is turned-on, can affect cross-conduction of MOSFETs constituting a single leg (for instance, transistors M\({}_{N1}\) and M\({}_{P2}\) or, alternately, M\({}_{N2}\) and M\({}_{P1}\), which constitute a vertical section of Figure 7). This time must be calibrated in order to avoid any time slot where transistors of the same leg are on simultaneously. In a simple implementation, it is sufficient to make sure that the active diode switches when the complementary MOSFET is cut-off. Contextually, conduction angle, defined by the effective angular portion of input signal which is converted, has to be maintained as wide as possible to preserve the highest power transferring. Therefore, solutions on this way can be categorized based on the adopted strategy to modulate turn-on instant and conduction angle.