# Thermal Mapping of Power Semiconductors in H-Bridge Circuit +
## 4 Thermal Stresses of Power Devices at Various Loading Conditions
### Dominating Factors for Device Loading  
The key parameters of the power converter are listed in Table 1, where a 1200 V/50 A power module with a maximum junction temperature of 150 \({}^{\circ}\)C is selected for both the test and load legs [23]. Figure 4: Thermal model of power semiconductor for thermal cycling caused by the fundamental frequency. The converter under the inverter mode, i.e., the Power Factor (PF) equals \(-1\), is regarded as the rated condition. Moreover, the rated current, fundamental frequency, and switching frequency are summarized in Table 1 as well. The rated peak current of 20 A and the dc-link voltage of 400 V are selected in order to leave the sufficient current and voltage margin. Moreover, the selection of the filter inductor and the switching frequency are determined by the current ripple requirement. As this configuration is able to emulate various loading conditions, the impact of different power factors, peak current, fundamental frequencies, and switching frequencies on the loss dissipation and thermal stress of the power devices can be evaluated. In the case of various power factors, the PF of \(-1\), \(1\), and \(0\) indicates the converter operating as the inverter, rectifier, and reactive power generator. With the parameters of loss and thermal models of power semiconductors listed in Table 2, the loss dissipation and thermal stress of the IGBT and the diode is presented in Figure 5. It is noted that the conduction loss changes between the IGBT and the diode, while the switching loss remains the same. The conduction loss of the IGBT is dominant in the inverter mode, but the conduction loss of the diode prevails in the rectifier mode. As a result, the mean junction temperature and the junction temperature swing of the IGBT and the diode changes in accordance with their loss dissipation. \begin{table}
\begin{tabular}{c c} \hline Rating of Power Device & 1200 V/50 A \\ \hline Filter inductor \(L_{f}\) & 300 \(\mu\)H \\ \hline DC-link voltage \(V_{dc}\) & 400 V \\ \hline Rated power factor \(PF\) & \(-1\) \\ \hline Rated peak current \(l_{lo}\) & 20 A \\ \hline Rated fundamental frequency \(f_{1}\) & 10 Hz \\ \hline Rated switching frequency \(f_{sw}\) & 10 kHz \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters and Rated Condition of Converter. \begin{table}
\begin{tabular}{c c c} \hline  & **IGBT** & **Diode** \\ \hline \multirow{6}{*}{Loss model} & V\({}_{\text{CE}}\) @ 50 A, T\({}_{\text{j}}\) = 150 \({}^{\circ}\)C (V) & 2.25 & / \\ \cline{2-3}  & V\({}_{\text{F}}\) @ 50 A, T\({}_{\text{j}}\) = 150 \({}^{\circ}\)C (V) & / & 1.65 \\ \cline{2-3}  & E\({}_{\text{on}}\) @ 50 A, T\({}_{\text{j}}\) = 150 \({}^{\circ}\)C (mJ) & 7.7 & / \\ \cline{2-3}  & E\({}_{\text{off}}\) @ 50 A, T\({}_{\text{j}}\) = 150 \({}^{\circ}\)C (mJ) & 4.8 & / \\ \cline{2-3}  & E\({}_{\text{rr}}\) @ 50 A, T\({}_{\text{j}}\) = 150 \({}^{\circ}\)C (mJ) & / & 3.7 \\ \hline \multirow{6}{*}{Thermal model} & \multirow{6}{*}{
\begin{tabular}{c} Fourth order thermal \\ resistance R\({}_{\text{th}}\) (\({}^{\circ}\)C/KW) \\ \end{tabular} } & 0.0324 & 0.0486 \\ \cline{2-3}  & & 0.1782 & 0.2673 \\ \cline{1-1} \cline{2-3}  & & 0.1728 & 0.2592 \\ \cline{1-1} \cline{2-3}  & & 0.1566 & 0.2349 \\ \cline{1-1} \cline{2-3}  & & 0.01 & 0.01 \\ \cline{1-1} \cline{2-3}  & Fourth order thermal time & 0.02 & 0.02 \\ \cline{1-1} \cline{2-3}  & constant \(\tau_{\text{th}}\) (s) & 0.05 & 0.05 \\ \cline{1-1} \cline{2-3}  & & 0.1 & 0.1 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters Used in Loss Model and Thermal Model of Power Semiconductors [23]. To investigate the impact of various loading currents, the current amplitude of 20 A, 10 A, and 5 A are used. As shown in Figure 6, it is obvious that the smaller loading current, the lighter conduction and switching losses in both the IGBT and diode. Accordingly, their mean junction temperature and the junction temperature swing are lower.