## 2 Power Loss Analysis of Integrated Si LDMOSFET  
In PSiPs, integrated Si MOSFETs have the most severe heat dissipation and the easiest thermal breakdown of all power devices. For PSiP, power loss caused by high frequency is a great challenge in terms of designing power switches. Power losses of integrated Si LDMOSFETs mainly include switching loss, driving loss, conduction loss and other power losses [35; 36]. The equivalent model and switching process of an integrated Si LDMOSFET is shown in Figure 4. In Figure 4,c, the gate voltage \(V_{GS}\) exits the miller platform due to the inductor in the output filter. Figure 4: Equivalent model and switching process of an integrated Si LDMOSFET: (**a**) equivalent model (**b**) turn-on process (**c**) turn-off process. Figure 3: Initial relative magnetic permeabilities of TDK Mn-Zn ferrites, MAGNETICS nanomaterial and alloy powders. Switching loss: At the period \(t_{1}\)-\(t_{3}\) in turn-on and turn-off processes, the triangular overlapping area of drain-source current and voltage are switching losses. Therefore, according to the overlapping area, the switching loss is given by  
\[ \begin{split}& P_{on}=\frac{1}{2}f_{s}V_{in}I_{o}R_{G}\left[\frac{C_{ ISS}(V_{pl}-V_{th})}{V_{DD}-\frac{V_{PL}+V_{th}}{V_{DL}+V_{th}}}+\frac{C_{RSS}V_{in}}{V_{DD}-V_{ PL}}\right]\\ & P_{off}=\frac{1}{2}f_{s}V_{in}I_{o}R_{G}\left[\frac{C_{RSS}V_{in }}{V_{PL}}+\frac{2C_{ISS}(V_{pl}-V_{th})}{V_{PL}+V_{th}}\right]\end{split} . \tag{1}\]  
Driving loss: At the period \(t_{0}\)-\(t_{5}\) in turn-on and turn-off processes, gate voltage, \(V_{GS}\), rises or falls via the charge, \(C_{GS}\), or discharge, \(C_{GD}\). The stored energies of \(C_{GS}\) and \(C_{GD}\) are dissipated by the driving resistor, \(R_{G}\), which depends on the gate charge, \(Q_{G}\). The driving loss is given by  
\[P_{G}=f_{s}Q_{G}V_{DD}. \tag{2}\]  
Conduction loss: In on-state, the Si LDMOSFET is equivalent to the on-resistor, \(R_{on}\), dissipating the energy. Conduction loss is given by  
\[P_{cond}={I_{o}}^{2}R_{on}\frac{V_{out}}{V_{in}}. \tag{3}\]  
Other power losses: Other power losses mainly include output capacitance power loss and body diode power loss. The output capacitor stores the energy in off-state and releases the energy via the conducting channel in on-state. Based on the stored and released energies in a switching cycle, the output capacitance power loss is given by  
\[P_{ds}=\frac{1}{2}f_{s}C_{OSS}{V_{in}}^{2}. \tag{4}\]  
The body diode power loss includes forward conduction loss and reverse recovery loss. The forward conduction loss is caused by the forward body diode current during the dead time. It is given by  
\[P_{d\_f}=f_{s}V_{F}I_{o}t_{d}, \tag{5}\]  
where \(V_{F}\) and \(t_{d}\) are the forward conduction voltage and forward conduction time of the body diode. The reverse recovery loss is caused by the body diode reverse recovery after carrying the forward current. It is expressed as  
\[P_{d\_r}=f_{s}V_{DR}Q_{rr}, \tag{6}\]  
where \(V_{DR}\) and \(Q_{rr}\) are the reverse recovery voltage and reverse recovery charge of the body diode. Combining (1)-(6), the total power loss of \(M\) switches in parallel is given as  
\[ \begin{split}& P_{switch}=M(P_{on}+P_{off}+P_{G}+P_{ds}+P_{d\_f}+P_{d\_r})+ \frac{P_{cond}}{M}\\ &=Mf_{s}(X_{1}I_{o}C_{ISS}+X_{2}I_{o}C_{RSS}+X_{3}C_{OSS}+X_{4}I_{ o}+X_{5})+X_{6}I_{o}^{2}\frac{R_{on}}{M}\\ & X_{1}=V_{in}R_{G}\frac{2V_{DD}(V_{pl}-V_{th})}{(2V_{DD}-(V_{PL}+ V_{th}))(V_{PL}+V_{th})}\\ & X_{2}=\frac{1}{2}V_{in}R_{G}\frac{V_{in}V_{DD}}{(V_{DD}-V_{PL})V _{PL}}\\ & X_{3}=\frac{1}{2}V_{in}^{2},X_{4}=V_{F}d_{d},X_{5}=Q_{G}V_{DD}+Q _{rr}V_{DR},X_{6}=\frac{V_{out}}{V_{in}}\end{split} , \tag{7}\]  
where \(X_{1}\), \(X_{2}\), \(X_{3}\), \(X_{4}\), \(X_{5}\) and \(X_{6}\) represent coefficients in total power loss that do not depend on switching frequency and output current. Based on the capacitance value per unit length and area, \(C_{ISS}\), \(C_{OSS}\) and \(C_{RSS}\) of the integrated Si LDMOSFET are given by [37]  
\[