## 3 Low-Power Electronic Converters
### Single-Phase Rectifiers
#### 3.1.2 Bridge Rectifier  
A smaller value of the ratio between the recharge and discharge time intervals of the capacitor \(C\) as well as a larger average value of the rectified current can be obtained for the bridge rectifier, given in Figure 12. This circuit is a bridge, in the branches of which four rectifier diodes are connected [25; 46]. One diagonal of the bridge is connected to the input source \(e_{p}\) of the signal, and the other diagonal is connected to the grounded load \(R_{L}\) of the rectifier. The diodes are connected in such a way that during each half-cycle two of them operate simultaneously--the diode with the most positive anode potential (\(D_{1}\) or \(D_{2}\)) and the diode with the most negative cathode potential (\(D_{3}\) or \(D_{4}\)). As a result, the current through the load flows in the same direction. The positive pole of the rectifier is obtained at the common point of the cathodes of the diodes (\(D_{1}\) or \(D_{2}\)), and the negative pole--at the common point of the anodes of the diodes (\(D_{3}\) or \(D_{4}\)). During the recharge time interval of the capacitor \(C\) connected in parallel with the load \(R_{L}\), the positive terminal of the input source \(e_{G}\) is connected to the output and the negative terminal to the ground. The input signal source can be for example the ABT-441-RC Piezo Element or ABT-448-90-RC Piezo Element, as for ABT-448-90-RC the additional wire (marked in blue) can be connected to the ground. In this way, a reduction in parasitic common-mode voltages that would occur on the load can be ensured. Figure 11: Circuit diagram of a basic half-wave rectifier with two Schottky diodes. Figure 12: Circuit diagram of a bridge rectifier. For the output voltage of the circuit, with no load connected at the output of the circuit in Figure 6, the following can be written [46]:  
\[V_{om,0}=V_{pm,0}-2V_{D}=\sqrt{2}V_{p,rms,0}-2V_{D}. \tag{11}\]  
It can be seen from the above formula that the output voltage will be smaller compared to the value of the basic circuit (Figure 10), but when using Schottky diodes for the circuit, in some cases, this reduction can be neglected. When connecting a load with resistance \(R_{L}\) in the output port, the voltage decreases because the internal resistance of the source and diodes is taken into account. The value of the output voltage for a capacitor \(C\) of infinitely large capacitance can be determined as follows [46]:  
\[V_{om,\infty}=V_{om,0}\bigg{(}1-\sqrt{\frac{r_{p}}{2R_{L}}}\bigg{)}. \tag{12}\]  
As can be seen from Formula (12), at a larger load, i.e., with a smaller value of \(R_{L}\), the output voltage decreases. This results in a longer time interval for recharging the capacitor. At a periodic input signal with equal peak values, a steady-state operation is reached, with the incoming charge equal to the outgoing charge. In comparison with the basic circuit (Figure 10) in the bridge rectifier, due to the way of connecting the diodes, the voltage drop arising from the internal resistance \(r_{p}\) of the input source \(e_{p}\) is twice as small when connecting a load. As a result, there is less variation in the output voltage when the load changes. This is especially important in cases with higher internal resistance of the source \(e_{p}\).