## 3 Low-Power Electronic Converters
### Single-Phase Rectifiers
#### 3.1.2 Bridge Rectifier
For the time interval when the switch is closed, the system of equivalent current source \(i_{p}(t)\), the capacitor \(C_{p}\), and the inductor \(L_{s}\) form an oscillator. When the switch is opened, the oscillations decrease in a pseudo-periodic process. To reduce the voltage drops across the diodes and increase the efficiency of the bridge circuit (Figure 12), MOS transistors can be used instead of diodes [8; 51], as shown in Figure 15. Thus, for the circuit in Figure 15, a voltage drop across each of the transistors of up to several tens of millivolts can be achieved. The electronic circuit is made of two nMOS  
Figure 14: Functional circuit of an SSHI: (**a**) circuit variant in which an inductor \(L_{S}\) is added in series to the switch; (**b**) timing diagrams of the piezoelectric voltage when no load is connected. Figure 11:0 Functional circuit of a piezoelectric element with additional switch, connected in parallel: (**a**) circuit variant; (**b**) timing diagrams of the voltage drop over the switch. transistors and two pMOS transistors, and like the circuit with diodes, for each half-cycle of the input voltage \(e_{p}(t)\), two of the transistors are in a linear mode of operation, and the other two are turned off. For example, for the indicated polarity of the input voltage \(e_{p}(t)\), a positive voltage is supplied to the gate of \(M_{3}\) and a negative voltage to the gate of \(M_{1}\). For the same polarity, voltages are applied to the gates of \(M_{2}\) and \(M_{4}\), for which they are turned off. At a negative polarity of the \(e_{p}(t)\), transistors \(M_{2}\) and \(M_{4}\) operate in linear mode, while \(M_{1}\) and \(M_{3}\) are turned off. Typical representatives of discrete nMOSFETs and pMOSFETs suitable for building voltage rectifiers are BSS138 and NTR1P02L (from ONSEMI), respectively. A further increase in energy efficiency can be achieved by connecting the piezoelectric generator in the secondary diagonal of an H-bridge with four MOS transistors working as electronic switches, using a combination of pre-biasing and synchronous charge extraction [57]. The simplified circuit diagram of such a converter is shown in Figure 11:1 As can be seen in Figure 16, the inductors \(L_{1}\) and \(L_{2}\) are connected in series to the transistors \(M_{1}\) and \(M_{2}\) with additional pairs of diodes. Thus, the transistors are controlled as follows: \(M_{1}\) and \(M_{4}\) provide current through inductor \(L_{1}\), and then \(M_{2}\) and \(M_{3}\) provide current through inductor \(L_{2}\). The voltage of the secondary diagonal is supplied to the electronic switches implemented with transistors \(M_{5}\) and \(M_{6}\). In this case of converting the mechanical vibrations, the resulting electrical voltage obtained can be approximately twice as high as the voltage obtained by the standard bridge rectifier (Figure 12). The output DC voltage is obtained by algebraically summing the currents at the drains of the \(M_{5}\) and \(M_{6}\) and regulating with a step-down DC-DC converter. Figure 11:2 Simplified circuit diagram of a pre-bias H-bridge. Figure 11:3 Circuit diagram of a bridge rectifier employing MOS transistors.