## 1 Introduction
Changes of convection coupling will be induced when the thermal environment is changed in the converters. Due to these factors, thermal convection cannot be ignored [18], and the thermal models should incorporate the convection thermal coupling resistances (\(R_{cccp}\)) among the heating components. These thermal models in the literature ignore the effect of convection coupling [19]. Furthermore, the method is not extensively discussed and analyzed for the purposes of calculating the thermal coupling resistances (\(R_{cp}\)) which include \(R_{cdcp}\) and \(R_{cccp}\). The major contributions of this paper are as follows: thermal analysis of a boost converter system has been given to compare the junction temperatures and the increments under different working conditions; a multi-variable thermal analysis resistances network has been built which includes \(R_{cdcp}\) and \(R_{cccp}\); the coupling resistances, MOSFET to the diode (\(R\underset{\mathcal{Q}\to\mathcal{MD}}{\overset{-}{\underset{-}{\underset{-}{ \underset{-}{\underset{-}{\underset{-}{\underset{-}{\underset{-}{\underset{-}{ \underset{-}{\underset{-}{\underset{-}{\underset{-}\underset{-}{\underset{-}{ \underset{-}{\underset{-}  
In a DC-DC boost converter, the MOSFET and the diode are two key heating components which can affect the performance of the overall converter systems [22]. PLECS has its advantages to simulate the dynamic systems for power converters [23]. The simulation schematics are shown in Figure 6. These figures give basic thermal models which are used for thermal descriptions and the \(T_{j}\) increments' (\(\Delta T_{j}\)) comparisons. The thermal model simulates the boost converter at different frequencies (10 kHz, 20 kHz, and 50 kHz) and different loading resistances (5 \(\Omega\), 8 \(\Omega\), and 10 \(\Omega\)). Figure 7 gives the \(\Delta T_{j}\) at different frequencies (load: 5 \(\Omega\)) for the MOSFET (duty cycle: 0.5) and the diode with a shared heatsink (System 1) and two separate heatsinks (System 2), respectively. Figure 8 gives the \(\Delta T_{j}\) at different loads (frequency: 20 kHz). The load voltage, load current, and inductor current under different working conditions are also given in Figures 7 and 8. Figure 5: Thermal map of a basic boost DC-DC converter in three cases: (**a**) large temperature difference with two components; (**b**) large temperature difference with three components; and (**c**) small temperature difference. Figure 6: PLECS thermal models: System 1 is with a shared heatsink; System 2 is with two separate heatsinks. Figure 7: \(\Delta T_{j}\) at different frequencies (duty cycle: 0.5; load: 5 \(\Omega\)): (**a**) at a frequency of 10 kHz; (**b**) at a frequency of 20 kHz; and (**c**) at a frequency of 50 kHz. Figure 8: \(\Delta T_{j}\) at different loading resistances (f: 20 kHz): (**a**) at a load of 5 \(\Omega\); (**b**) at a load of 8 \(\Omega\); and (**c**) at a load of 10 \(\Omega\). Based on the simulation results, the value of \(\Delta T_{j}\) increases while the frequency increases which indicates a greater thermal coupling effect at a higher frequency. The value of \(\Delta T_{j}\) decreases with the smaller operating current (by increasing loading resistance). In other words, the greater thermal coupling effect will be induced by a larger current passing through the MOSFET and the diode, and vice versa. Moreover, the \(T_{j}\) of the MOSFET and the diode with a shared heatsink are relatively higher than the ones with separate single heatsinks. The major reason for causing these is the conduction thermal coupling between the two devices, since they share the same heatsink. However, these kinds of models cannot calculate the convection coupling.