## 1 Introduction
### Design Consideration of the Output Capacitors \(C_{o1}\) and \(C_{o2}\)  
The amount of charge variation \(\Delta Q\) stored in the output capacitor is related to the amount of voltage variation \(\Delta V\) at both ends of the capacitor and the capacitance value \(C\). Thus, the peak-to-peak value of the output voltage ripple of the output capacitor, which is denoted as \(\Delta V_{OUT}\), can be expressed by the following equation. \[\Delta V_{OUT}=\frac{\Delta Q}{\frac{C_{O1}}{2}}=\frac{2}{C_{O1}}\cdot\frac{1 }{2}\cdot\frac{\Delta I_{LM}}{2}\cdot\frac{T_{S}}{2}=\frac{\Delta I_{LM}\cdot T _{S}}{4\cdot C_{O1}} \tag{6}\]  
By inserting Equation (3) into Equation (6), the output voltage ripple \(\Delta V_{OUT}\) is given by  
\[\Delta V_{OUT}=\frac{V_{OUT}\cdot Np\cdot(1-D)\cdot T_{S}{}^{2}}{8\cdot L_{M} \cdot C_{O}\cdot N_{S}} \tag{7}\]  
The percentage of the output voltage ripple \(\Delta V_{OUT}/V_{OUT}\) can be expressed as  
\[\frac{\Delta V_{OUT}}{V_{OUT}}=\frac{N_{P}\cdot(1-D)\cdot T_{S}{}^{2}}{8\cdot L _{M}\cdot C_{O}\cdot N_{S}}\cdot 100\% \tag{8}\]  
Figure 9: Magnetizing inductor in boundary conduction mode \(L_{MB}\) versus the switching frequency \(f_{S}\) under different duty cycles \(D\). After sorting out Equation (8), the design formula of output capacitors \(C_{O1}\) and \(C_{O2}\) can be obtained as follows:  
\[C_{O1}=C_{O2}=\frac{N_{P}\cdot(1-D)\cdot V_{OUT}}{8\cdot L_{M}\cdot N_{S}\cdot f _{S}^{2}\cdot\Delta V_{OUT}} \tag{9}\]  
As stated by Equation (9), Figure 10 displays the relationship between the output capacitor and the switching frequency \(f_{S}\) under different output voltage ripples \(\Delta V_{OUT}\). Substituting the circuit parameters into Equation (9) with a \(V_{OUT}\) of 10 V, an \(N_{P}\) of 1, an \(N_{S}\) of 1, an \(f_{S}\) of 50 kHz, an \(L_{M}\) of 85 uH, and a \(\Delta V_{OUT}\) of 0.02 V, the values of capacitors \(C_{O1}\) and \(C_{O2}\) are found as follows:  
\[C_{O1}=C_{O2}=\frac{N_{P}\cdot(1-D)\cdot V_{OUT}}{8\cdot L_{M}\cdot N_{S}\cdot f _{S}^{2}\cdot\Delta V_{OUT}}=\frac{1\cdot(1-0.3)\cdot 10}{8\cdot 85\cdot 10^{-6} \cdot 1\cdot 50000^{2}\cdot 0.02}=205.9\ \mathrm{\mu F}\]  
In addition, the output capacitors \(C_{O1}\) and \(C_{O2}\) are set to 220 uF for the purpose of decreasing the ripple of the output voltage when implementing the circuit. Experimental Results of Prototype UV-C LED Lamp Driver Circuit Applied to DC-Input Voltage Source for Sterilization and Germicidal Applications  
Figure 11 presents a photograph of the UV-C LED module for sterilization and germicidal applications used in the experiment. Table 1 presents the specifications of the UV-C LED module for sterilization and germicidal applications used in the experiment, and its information is as follows: the rated power is 0.33 W, the rated voltage is 10 V, the rated current is 33 mA, the wavelength is 275 nm, and the viewing angle is 120 degrees. Additionally, the \"viewing angle\", which is also called the \"azimuth angle\", is the luminous range of the LED light source, and the unit is \"degree\". When the package of the LED light source is tilted to observe the change in the light output, the angle from the peak output value to the characteristic value of the angle that can be recognized, and the angle of half of the brightness of the peak output value, are multiplied by 2 (front side as the basis for left-right symmetry), which is known as the viewing angle. Figure 10: Output capacitor versus switching frequency \(f_{S}\) under different output voltage ripples \(\Delta V_{OUT}\). Figure 12 displays a photograph of the UV-C LED lamp for sterilization and germicidal applications used in the experiment. Referring to Figure 10, ten UV-C LED modules were connected in parallel to establish the UV-C LED lamp for sterilization and germicidal applications used in the experiment in this paper, and their information is shown in Table 2; they had a rated output power \(P_{O}\) of 3.3 W, a rated output voltage \(V_{O}\) of 10 V, and a rated output current \(I_{O}\) of 330 mA.