## 2 Variation of Ambient Temperature
### Thermal Coupling Experiments  
In this section, a thermal coupling testing platform for the power converter is established as shown in Figure 4, and its circuit diagram is shown in Figure 5. In this experimental platform, the selected switching frequencies of the power converters are commonly used, which are 10 kHz, 25 kHz and 50 kHz, respectively. The duty cycle is set to 0.5, and the load resistances are 8 \(\Omega\), 6 \(\Omega\) and 5 \(\Omega\), respectively. The type of the power device MOSFET is IRF540 NPBF, the diode model is MBR20100 CT, and both the semiconductor devices are in the TO-220 package. The capacitor is MAL215050472E3-35 V and the value of its capacitance is 4700 UF. The inductance is MCAP115018047A and the value of its inductance is 250 \(\mu\)H.  
In order to study the influence of the thermal coupling effect (the convection thermal coupling and conduction thermal coupling are included) of adjacent devices under different working conditions, the two different types of power converters are tested and compared as follows, type I with large device spacing and type II with small device spacing, as shown in Figure 6. The MOSFET is controlled by the PWM wave and its on state and off state are controlled by the given duty cycle and switching frequencies. During the testing of the converter system, the input voltage and output voltage of the circuit is 12 V and 24 V,  
Figure 4: Thermal coupling testing platform of the power converter. Figure 5: The circuit diagram of the power converter. respectively. The case temperature of the power devices of the converter system is collected by changing the load resistances. Figure 7 shows the measurement results of the case temperatures and the calculation results of the temperature difference of the two power devices with different types of spacing. In this figure, the case temperature of the MOSFET and diode with two types of devices spacing (type I: large spacing, dot mark on the blue and cyan solid line; type II: small spacing, six-star mark on red and green solid line) are compared at the switching frequency of 25 kHz and the load resistances which are 8 \(\Omega\), 6 \(\Omega\) and 5 \(\Omega\), respectively. It can be seen from the comparisons that, for both MOSFET and diode, with the decrease in device spacing the case temperature of the device increases under the same working condition. This shows that the thermal coupling effect between adjacent devices is affected by the device spacing, and with the decrease in the spacing, the thermal coupling effect increases. In addition, according to the comparison results of the case temperature difference in Table 1, when the load resistance decreases, the current flowing through the semiconductor device increases. At this time, the case temperature difference of the two devices changes with the change of current, which shows that the thermal coupling  
Figure 6: Two different types of power converters: (**a**) type I with large device spacing; (**b**) type II with small device spacing. Figure 7: The comparisons of the case temperatures and the temperature differences of the power devices with different spacing types. effect between adjacent devices is affected by the working current, and with the increase in the current the thermal coupling effect increases. It is verified that the thermal coupling effect obtained from the thermal coupling testing platform (the MOSFET and diode are tested) of devices can also be applied to the case where multiple devices exist in the power converter system. The calculation formula of the steady-state case-to-ambient thermal resistance, \(R_{ca}\) in the convection thermal transfer is obtained as  
\[R_{ca}=\frac{\Delta T}{P} \tag{5}\]  
The steady-state thermal resistance of the devices under different working conditions is analyzed. By bringing the measured steady-state \(T_{c}\) into (5), the \(R_{ca}\) of the MOSFET and diode can be obtained. The calculation results are shown in Tables 2 and 3, respectively.