## 2 Advantages and Design Procedure of Capacitive Isolated Series Resonant Converter
The series resonant converter still retains the other desirable traits of the resonant converter, such as soft switching and galvanic isolation, which will be discussed in the next section. The main  
Figure 3: Normalized voltage gain curves for a series resonant converter. The highlighted region represents the possible operation range where the converter operates at ZVS and could handle any PV or battery voltage variation. Figure 2: The irradiance level and the output maximum power–voltage curve for a PV panel. advantages of the series resonant converter with capacitive isolation will be presented by first examining the main operating principle of the converter. The configuration in Figure 1a will be taken as an example. The converter has four active switches (Q1-Q4) and four diodes (D1-D4). The switches are operated in pairs, meaning each pair is turned on and off at the same time. When Q1 and Q3 are on, a positive DC voltage is applied to the resonant tank, and a sinusoidal or semi-sinusoidal current will flow through the resonant tank in the outgoing direction. The current will pass through diodes D1 and D3 to charge the output capacitor and load. When Q2 and Q4 are on, a negative DC voltage is applied to the resonant tank, and a sinusoidal or semi-sinusoidal current will flow through the resonant tank in the incoming direction. The current will pass through D2 and D4, also charging the output capacitor and load. The main operation states and the key waveforms are shown in Figure 5, and it can be seen that the current has a semi-sinusoidal waveform. The converter switching frequency can be above, below, or equal to the resonant frequency. When the converter operates above the resonant frequency, it provides zero-voltage switching. This means that when the voltage of the active switch drops to zero before it turns on, and the turn-on switching loss is eliminated. Figure 4: A typical characteristic curve for a 24 volt battery: voltage vs. SOC. Figure 5: Switching states and key waveforms of series resonant converter with capacitive isolation. Figure 6 shows the switch voltage and current waveforms when operated above the resonant frequency. It can be seen that the switch voltage drops to zero before the switch is turned on. Figure 7 shows that if the converter is operated below the resonant frequency, zero current switching is achieved and the current goes to zero before the switch is turned off, meaning that it is not forced to turn off and turn-off losses are eliminated. Figure 6: The ZVS action when the converter is operated above the switching frequency. Figure 7: The ZCS action when the converter is operated below resonant frequency. Since the resonant tank only passes a sinusoidal current, a first harmonic approximation (FHA) can be used to analyze the converter. The input voltage can be taken as the fundamental component of the square wave, and the load can be represented as an equivalent series resistance that draws the same amount of power as the load. The system is then simplified to the simple circuit shown in Figure 8.  
The fundamental voltage, the equivalent series resistance, and the voltage gain equations can be defined as follows:  
\[v_{1}=\frac{4}{\pi}V_{dc} \tag{1}\]  
\[R_{eq}=\frac{8}{\pi^{2}}R_{Load} \tag{2}\]  
Figure 3:0  
And the voltage gain equation can be re-written as a function of the quality factor (Q) and the normalized switching frequency factor (\(F_{n}\)), as follows:  
Figure 3:1  
where the Q and \(F_{n}\) are defined as  
Figure 3:2  
Figure 3:3  
Figure 3:4  
Based on these equations, a design procedure can be synthesized for battery charging applications. If the nominal battery voltage is slightly less than the PV voltage, the configuration in Figure 1a can be used. If the battery voltage is higher than the PV voltage, the configuration in Figure 1b can be used because it has the ability to double the output.