# Design of WPT System Based on Interleaved Boost Converter
## 3 Efficiency Improvement Strategy Analysis  
In this section, through the quantitative analysis of the copper loss of the primary and secondary sides of the secondary side miniaturized wireless charging system, the strategy for improving the system efficiency and the reasonable value of the boost ratio are obtained. For the convenience of analysis, the relative voltage gain \(G_{0}\) is defined as:  
\[G_{0}=\frac{1}{1-D}\cos\left(\pi D-\frac{\pi}{2}\right) \tag{5}\]  
Assuming that the resistances on the primary and secondary coils of the loosely coupled transformer are \(R_{\text{LP}}\) and \(R_{\text{LS}}\), respectively, the copper loss on the primary and secondary sides before the pre-stage boost conversion can be expressed as:  
\[P_{\text{loss}}={I_{\text{LP}}}^{2}R_{\text{LP}}+{I_{\text{LS}}}^{2}R_{\text {LS}} \tag{6}\]  
When the interleaved boost converter is used for boost conversion in the front stage, the fundamental RMS value of the output voltage after the inverter is increased by \(G_{0}\) times, and the primary current is reduced by \(G_{0}\) times:  
\[{I_{\text{LP}}}^{\prime}=\frac{1}{G_{0}}{I_{\text{LP}}} \tag{7}\]  
According to Formula (4), before and after the boost conversion, in order to keep the output voltage unchanged, the self-inductance of the primary and secondary sides needs to be increased, so the self-inductance relationship before and after the conversion is:  
\[\sqrt{L_{\text{P}}{{}^{\prime}}L_{\text{S}}{{}^{\prime}}}=G_{0}\sqrt{L_{\text {P}}L_{\text{S}}} \tag{8}\]  
For the convenience of analysis, let the self-inductance of the primary side increase to \(a\) times the original, and the self-inductance of the secondary side increase to \(b\) times the original. Then the relationship between the two is:  
\[b=\frac{{G_{0}}^{2}}{a} \tag{9}\]  
The square of the number of turns on the primary and secondary sides is proportional to the self-inductance value, and the parasitic resistance on the primary and secondary coils is proportional to the number of turns, so the square of the parasitic resistance on the coil is proportional to the self-inductance value. After the boost conversion, the parasitic resistance of the primary and secondary sides can be expressed as:  
\[\left\{ \begin{array}{l}{R_{\text{LP}}}^{\prime}=\sqrt{a}R_{\text{LP}}\\ {R_{\text{LS}}}^{\prime}=\sqrt{b}R_{\text{LS}}=\frac{G_{0}}{\sqrt{a}}R_{\text {LS}}\end{array} \right. \tag{10}\]  
At this time, the copper loss of the primary and secondary sides of the loosely coupled transformer is:  
\[ \begin{array}{l}{P_{\text{loss}}}^{\prime}={I_{\text{LP}}}^{\prime 2}{R_{\text{LP}}}^{ \prime}+{I_{\text{LS}}}^{\prime 2}{R_{\text{LS}}}^{\prime}\\ =\left(\frac{1}{G_{0}}{I_{\text{LP}}}\right)^{2}\sqrt{a}R_{\text{LP}}+{I_{\text {LS}}}^{2}\frac{G_{0}}{\sqrt{a}}R_{\text{LS}}\end{array}  \tag{11}\]According to Equations (6) and (11), the reduction in the primary and secondary side copper losses before and after the boost conversion is:  
\[ \begin{split}\Delta P_{\text{loss}}&=P_{\text{loss}}-P_{ \text{loss}}^{\prime}\\ &=\left(1-\frac{\sqrt{a}}{C_{0}2}\right)I_{\text{LP}}{}^{2}R_{ \text{LP}}+\left(1-\frac{G_{0}}{\sqrt{a}}\right)I_{\text{LS}}{}^{2}R_{\text{LS} }\\ &=\left(1-\frac{\sqrt{a}}{C_{0}2}\right)P_{\text{loss-pri}}+\left(1- \frac{G_{0}}{\sqrt{a}}\right)P_{\text{loss--sec}}\end{split}  \tag{12}\]  
In the above formula, \(P_{\text{loss-pri}}\) and \(P_{\text{loss--sec}}\) represent the losses of the primary and secondary sides, respectively. In the traditional wireless power transmission system, the voltage levels of the input and output voltages are generally the same. When using the S/S compensation, the currents on the primary and secondary sides are generally the same. In the miniaturized WPT system on the secondary side, the parasitic resistance on the primary coil is greater than the secondary side, so the primary side loss is greater than the secondary side loss. Figure 3 shows the relationship between the loss reduction and the primary and secondary side losses under different relative voltage gains.