## 2 Basic Principle
### Basic Analysis of the Proposed Design Method  
The SS topology with the proposed design method has a similar configuration to the conventional compensation topology design [33] that resonated with primary and secondary self-inductances. However, the SS topology with the proposed design method divides the primary self-inductance into a magnetizing inductance \(L_{m}\) and a virtual leakage inductance \(L_{llp}\) to compensate for partial resonance. The primary side capacitor resonates with the leakage inductance. The secondary side has the same resonant conditions as the SS topology with the conventional design method that resonated with \(L_{s}\). The equivalent impedance expressions for the secondary side is provided in (10)-(15). \(C_{r}\) is the capacitance that resonates with \(L_{llp}\), and \(Z_{in}\) is the equivalent input impedance.  
\[C_{s}=\frac{1}{\omega^{2}L_{s}} \tag{10}\]  
\[\frac{1}{j\omega C_{s}}+j\omega L_{s}=0 \tag{11}\]  
\[L_{m}=kL_{p} \tag{12}\]  
\[L_{llp}=(1-k)L_{p} \tag{13}\]  
\[C_{r}=\frac{1}{\omega^{2}L_{llp}} \tag{14}\]  
\[Z_{in}=j\omega L_{m}+\frac{\left(\omega k\sqrt{L_{p}L_{s}}\right)^{2}}{R_{o}} \tag{15}\]  
In (15), the imaginary value of the equivalent circuit impedance is always positive, and the proposed topology has inductive loads regardless of the load resistance. Thus, the proposed topology can be operated with zero-voltage switching (ZVS) over the entire load range. ZVS has the advantage of a reduced turn-on loss under MOSFET switching.  
The primary current \(l_{p}\), output current \(l_{o}\), and output voltage \(U_{o}\), respectively, are given in (16)-(18). As indicated by (17) and (18), the output current and voltage have complex components that show nonlinear output characteristics.  
\[I_{p}=\frac{U_{s}}{Z_{in}}=\frac{U_{s}}{j\omega L_{m}+\frac{\left(\omega M \right)^{2}}{R_{o}}} \tag{16}\]  
\[I_{o}=\frac{j\omega M\U_{s}}{Z_{in}\ R_{o}}=\frac{\omega M^{3}U_{s}}{\omega^{2 }M^{4}+\left(L_{m}R_{o}\right)^{2}}-j\frac{M\U_{s}L_{m}R_{o}}{\omega^{2}M^{4} +\left(L_{m}R_{o}\right)^{2}} \tag{17}\]  
\[U_{o}=I_{o}R_{o}=\frac{\omega M^{3}U_{s}R_{o}}{\omega^{2}M^{4}+\left(L_{m}R_{ o}\right)^{2}}-j\frac{M\U_{s}L_{m}R_{o}{}^{2}}{\omega^{2}M^{4}+\left(L_{m}R_{o} \right)^{2}} \tag{18}\]  
In (17), the smaller the load resistance becomes, the more the real part converges and the imaginary part becomes zero. In (18), the larger the load resistance becomes, the more the imaginary part converges and the real part becomes zero.  
Table 1 shows the practical parameters of the proposed design method used in Figures 2 and 4, which were measured using an IM 3536 LCR Meter from HIOKI. Figure 4a,b show the graphs of the voltage gains and phase, respectively, from short to open state in the proposed design method. The operation frequency is equal to the resonance frequency, i.e., 85 kHz. As shown in Figure 4a, the voltage gains converge to a constant value under open load.  
As shown in Figure 4b, there is a phase difference in the charging area. A small phase difference is required for ZVS but owing to the nature of the proposed design method, the phase increases with the increase in load resistance.