## 3 Low-Power Electronic Converters
### Voltage Multipliers (Doublers and Quadruplers)
#### 3.2.2 Voltage Quadruplers  
In cases where a higher output voltage is required, multipliers with a larger multiplication factor are used. Figure 19 shows a circuit diagram of a voltage quadrupler [45; 60; 61]. Compared to the voltage-doubler circuit, the voltage-quadrupler circuit results in a lower energy efficiency value because it contains a larger number of passive components.  
Figure 19: Circuit diagram of a rectifier with a voltage multiplication factor of four (voltage-quadrupler circuit).  
Figure 18: Input and output voltages and currents of the voltage-doubler rectifier in Figure 6.  
The principle of operation is similar to that of the circuit given in Figure 17. For the third half-period (the polarity of the input voltage is without brackets), the diode \(D_{1}\) is turned on and the \(C_{1}\) is recharged to voltage \(\approx V_{pm,0}\). The capacitor \(C_{3}\) is also charged through the diode \(D_{3}\) up to the voltage [45]  
\[v_{C3}=V_{pm,0}+v_{C2}=3V_{pm,0}. \tag{18}\]  
In the same time interval, the \(D_{2}\) is turned off, and the voltage drop of the \(C_{2}\) is applied over it, as a reverse voltage, with the value \(v_{C2}=2V_{pm,0}\). During the fourth half-cycle (the polarity of the input voltage is in brackets), the capacitance \(C_{2}\) is recharged up to \(v_{C2}=2V_{pm,0}\) and the capacitor \(C_{4}\) is charged through the capacitor \(C_{3}\) and the diode \(D_{4}\) up to voltage \(v_{C4}=V_{pm,0}+v_{C3}=4V_{pm,0}\).  
For the implementation of electronic circuits of voltage multipliers intended for thin-film alternative sources of energy, Schottky diodes are basically used, with a voltage drop between the anode and cathode in the forward mode of operation below 200 mV at a current of up to about 1 mA. Moreover, the total power dissipation obtained is not greater than 300 mW. Examples of Schottky diodes suitable for certain types of electronic circuits are PMEG3002 TV and PMEG3015 EV from Nexperia(r) (Nijmegen, The Netherlands), NSR1020 MW2 from ON Semiconductor(r) (Phoenix, AZ, USA), FM130 EG from NXP Semiconductors(r) (Eindhoven, The Netherlands), and BAT54 (BAT54A, BAT54C, or BAT54S) from Nexperia(r). Some of the exemplary diodes are single in a package, while others are two in a package, which may facilitate use in wearable electronic devices. When the S\({}_{\text{the}}\) input voltage is of a larger value (more than 2 V), Schottky diodes can be used, which have a larger voltage drop in the forward direction, such as 1N5817 and 1N5818. For them, the forward voltage has a typical value of about 500 mV, as the maximum value of the average forward rectified current is 1 A.  
The capacitors are determined by the specific operating conditions, depending on the type of input signal source and the load. In this case, the total charge and discharge current flows through each of the capacitors. In this case, the last capacitor \(C_{4}\) has the smallest current, and the first capacitor \(C_{1}\) has the largest current. Due to the small voltage ripples \(\Delta U\), it can be assumed that the following expression applies to each capacitor [45]:  
\[I_{ch}=C\frac{\Delta U}{t_{ch}}, \tag{19}\]  
where \(t_{ch}\) is the charging time interval of each capacitor.  
The output voltage ripples (or fluctuations) should not be relatively large, and a typical value should not exceed 5% [60] of the nominal DC voltage for a given load. From a constructive and technological point of view, it is convenient for all capacitors to have the same values, and their capacity can be determined as follows [45]:  
\[C=\frac{I_{om,0}}{f\times V_{om,0}}2(k+2)\times 10^{6}\ [\mu F] \tag{20}\]  
at \(k=4\).