## 3 Low-Power Electronic Converters
### Single-Phase Rectifiers
#### 3.1.2 Bridge Rectifier
During each time interval of recharging the capacitor, a current flow occurs with a peak value, according to [PERSON]'s law, equal to  
\[I_{L,\text{max}}=\frac{V_{om,0}-2V_{D}-V_{om,\infty}}{r_{p}}\approx\frac{V_{om,0}-V_{om,\infty}}{r_{p}}. \tag{13}\]  
After substituting Formula (12) into (13), the following is found [46]:  
\[I_{L,\text{max}}=\frac{V_{om,0}}{\sqrt{2r_{p}R_{L}}}. \tag{14}\]  
The maximum average power \(\hat{P}_{PEH,\text{max}}\) that can be obtained from a piezoelectric element is found at half the no-load rectified voltage [24; 25]:  
\[\hat{P}_{PEH,\text{max}}=\frac{C_{p}\omega V_{om,0}^{2}}{2\pi}\text{ at }V_{om,\infty}=\frac{V_{om,0}}{2}. \tag{15}\]  
In comparison with the basic circuit in the bridge rectifier, the peak current value is smaller by a factor of \(\sqrt{2}\). However, for both rectifier circuits, the internal resistance of the signal source has a significant effect on the peak current value. This means that a relatively high internal resistance, which at the same time changes its value, in some cases, can lead to a decrease in the current through the load. Examples of Si diodes that can be used to implement the basic and bridge rectifier circuits are 1N4148 and 1N914 (from Vishay Semiconductors(r) (Malvern, PA, USA)). Also, to obtain a smaller voltage drop across the diodes, Schottky diodes such as the BAT17-04, BAT54S, BAT81S, or BAT83S (from Infineon Technologies(r) (Neubiberg, Germany)) can be used. Due to its superior performance, the single-phase bridge circuit is one of the most commonly used rectifier circuits and is preferred in many cases where there is no obstacle to its use. In addition, there are a large number of example circuits that partially or fully use the bridge rectifier circuit [49; 50; 51; 52; 53]. For some circuits, the bridge rectifier is partially used to form AC-to-DC electronic converters [24; 50; 51; 53]. In cases where the voltage \(v_{p}(t)\) generated by the piezoelectric element is not of sufficiently high amplitude, a technique in which an electronic switch (implemented with a single or a pair of MOSFETs) is connected in parallel to the input port of the voltage rectifier (Figure 13a) is used [54]. As can be seen in Figure 13b, when the signal produced by the piezoelectric generator as a result of mechanical vibrations reaches, for example, its maximum value, the electronic switch is closed for a short time interval (for example, for a time interval that is about one-hundredth of the period of the \(v_{p}(t)\)), and the voltage decreases to zero. After this time interval, the switch is opened again, and the voltage again starts to vary according to the waveform of the voltage generated by the piezoelectric element. In this case, if proper control of the electronic switch is provided, so that exactly for the maximum and minimum values of the generated voltage, a control signal is provided to close the switch, as well as to ensure a sufficiently short interval of the closed state, the amplitude of the voltage that will be periodically applied to the input of the rectifier can be approximately twice-increased. Moreover, it is noticeable that the resulting AC voltage is distorted and delayed in phase with respect to the generated one based on the vibrations. An example block diagram for automatic self-powered switches can be found in [55]. As such, a \"self-powered\" switch means that the control circuit of the electronic switch is powered by the output DC voltage, i.e., by the voltage across the energy storage element. Based on the proposed technique with an additional electronic switch, a modification is presented in [56] in which an inductor is added in series to the switch (known as SSHI (_synchronized switch harvesting on inductor_)). In this way, signal distortions can be reduced (the first harmonic component is \(v^{(1)}_{p}(t)\)), as shown in Figure 14, allowing a further increase in the efficiency.