# Hybrid LLC Converter with Wide Range of Zero-Voltage Switching and Wide Input Voltage Operation
## 4 Circuit Characteristics and Design Example  
Based on the input voltage regions, Sac1 and Sac2 are controlled at on or off state. Therefore, the converter can be operated at three input voltage regions. Full bridge (half bridge) LLC converter is operated to have low (high) voltage gain for low (high) voltage input region. The equivalent resonant  
Figure 5: Presented converter under low voltage input region (**a**) PWM signals (**b**) mode 1 equivalent circuit (**c**) mode 2 equivalent circuit (**d**) mode 3 equivalent circuit (**e**) mode 4 equivalent circuit (**f**) mode 5 equivalent circuit (**g**) mode 6 equivalent circuit. circuit is derived in Figure 6a. According to the PWM signals of S1-S4, the square wave voltage Vac is generated. If full bridge LLC converter with S1-S4 is operated, the voltage Vac has voltage values \(\pm\)Vin in Figure 2c,d. If the half bridge LLC converter with S3 and S4 shown in Figure 2b is operated, the voltage Vac has voltage values \(\pm\)Vin/2. For medium and high voltage input regions shown in Figure 2b,c, Sac is off. It can obtain the inductor voltage VLM = nV0/2 or -nV0/2, where n = nP/ns, if D3 or D4 is conducting. For low voltage input region (Figure 2d), the inductor voltage VLM = nV0/4 or -nV0/4 if D1 or D2 is conducting. In Figure 6a, the input-side and output-side of the resonant tank are all square voltage waveforms. Based on the Fourier Series Analysis (FSA), the square voltage waveform is expressed as the summation of the fundamental frequency component and the higher order harmonic frequency components. Thus, the circuit analysis of the resonant circuit in Figure 6a is related to the nonlinear and nonsinusoidal circuit analysis. If the output voltage at higher order harmonic frequencies are less than the fundamental harmonic voltage, then only the fundamental harmonic of square voltage wave is considered in Figure 6b to simply the circuit analysis and design the resonant converter. The fundamental harmonic approximation (FHA) approach has acceptable design results if the LLC converter is operated at or close to the resonant frequency f. In Figure 6b, the rms values of fundamental harmonic voltage at input and output side are given as. \[\text{V}_{\text{ac,f}}\ =\ \left\{ \begin{array}{l}\frac{2\sqrt{2}\text{V}_{ \text{in}}}{\pi},\text{ }S_{\text{ac,1}}\text{ off}\\ \frac{\sqrt{2}\text{V}_{\text{in}}}{\pi},\text{ }S_{\text{ac,1}}\text{ on}\end{array} \right. \tag{1}\]  
\[\text{V}_{\text{Lm,f}}\ =\ \left\{ \begin{array}{l}\sqrt{2}\text{nV}_{ \text{o}}/\pi,\text{ }S_{\text{ac2}}\text{ off}\\ \text{nV}_{\text{o}}/\left(\sqrt{2}\pi\right),\text{ }S_{\text{ac2}}\text{ on}\end{array} \right. \tag{2}\]  
The ac equivalent load resistance Re,ac can be obtained according to power balance between primary and secondary sides of trnasformer. \[\text{P}_{\text{ac}}\ =\ (\text{V}_{\text{Lm,f}})^{2}/\text{R}_{\text{e,ac}}\ =\ \text{P}_{\text{o}}\ =\ (\text{V}_{\text{o}})^{2}/\text{R}_{\text{o}}. \tag{3}\]  
From Equations (2) and (3), the ac equivalent load resistance is calculated as. \[\text{R}_{\text{e,ac}}\ =\ \left\{ \begin{array}{l}2\text{n}^{2}\text{R}_{ \text{o}}/\pi^{2},\text{ }S_{\text{ac2}}\text{ off}\\ \text{n}^{2}\text{R}_{\text{o}}/\left(2\pi^{2}\right),\text{ }S_{\text{ac2}}\text{ on}\end{array} \right.. \tag{4}\]  
From the linear circuit in Figure 6b, the voltage transfer function can be approximated by using the fundamental input and output voltages. \[\text{G}_{\text{ac}}(\text{f}_{\text{sw}})\ =\ \left|\left(\text{j}\text{X}_{ \text{Lm}}//\text{R}_{\text{e,ac}}\right)\right/\left[\left(\text{j}\text{X}_ {\text{Lm}}//\text{R}_{\text{e,ac}}\right)+\text{j}\text{X}_{\text{Lr}}-\text {j}\text{X}_{\text{Cr}}\right]\right|\ =\ (\text{V}_{\text{Lm,f}})^{2}/(\text{V}_{\text{ac,f}})^{2}, \tag{5}\]  
where XLm = 2\(\pi\)f\({}_{\text{sw}}\)Lm, XLF = 2\(\pi\)f\({}_{\text{sw}}\)Lr and XCr =1/(2\(\pi\)f\({}_{\text{sw}}\)C\({}_{\text{r}}\)).