The Heating NPN component is a simple Ebers-Moll model of a bipolar NPN junction transistor with temperature dependency.

An optional heatport can be used to connect the device to a heatsink.

$T_{\mathrm{int}}\=\{\begin{array}{cc}{T}_{\mathrm{heatPort}}& \mathrm{Use\; Heat\; Port}\\ T& \mathrm{otherwise}\end{array}$

$i_B\=\frac{i_{\mathrm{BE}}}{{\mathrm{\beta }}_{F_T}}\+\frac{i_{\mathrm{BC}}}{{\mathrm{\beta }}_{R_T}}\+C_{\mathrm{BC}}{\stackrel{\.}{v}}_{\mathrm{BC}}\+C_{\mathrm{BE}}{\stackrel{\.}{v}}_{\mathrm{BE}}$

$i_C\=\left(i_{\mathrm{BE}}-i_{\mathrm{BC}}\right)q_{\mathrm{BK}}-\frac{i_{\mathrm{BC}}}{{\mathrm{\beta }}_{R_T}}-C_{\mathrm{BC}}{\stackrel{\.}{v}}_{\mathrm{BC}}\+C_{\mathrm{CS}}{\stackrel{\.}{v}}_C$

$C_{\mathrm{CJC}}\&equals;\{\begin{array}{cc}{C}_{\mathrm{JC}}\left(1\&plus;M_C\frac{v_{\mathrm{BC}}}{{\mathrm{\phi }}_C}\right)& 0<\frac{v_{\mathrm{BC}}}{{\mathrm{\phi }}_C}\\ C_{\mathrm{JC}}\mathrm{pow}\left(1-\frac{v_{\mathrm{BC}}}{{\mathrm{\phi }}_C}\&comma;-M_C\right)& \mathrm{otherwise}\end{array}$

$C_{\mathrm{CJE}}\&equals;\{\begin{array}{cc}{C}_{\mathrm{JE}}\left(1\&plus;M_E\frac{v_{\mathrm{BE}}}{{\mathrm{\phi }}_E}\right)& 0<\frac{v_{\mathrm{BE}}}{{\mathrm{\phi }}_E}\\ C_{\mathrm{JE}}\mathrm{pow}\left(1-\frac{v_{\mathrm{BE}}}{{\mathrm{\phi }}_E}\&comma;-M_E\right)& \mathrm{otherwise}\end{array}$

$i_E\&equals;-i_B-i_C\&plus;C_{\mathrm{CS}}{\stackrel{\&period;}{v}}_C$

${\mathrm{Ex}}_{\max }\&equals;\exp \left(E_{\max }\right)$

${\mathrm{Ex}}_{\min }\&equals;\exp \left(E_{\min }\right)$

${\mathrm{\beta }}_{F_T}\&equals;{\mathrm{\beta }}_F\mathrm{pow}\left(\frac{T_{\mathrm{int}}}{T_{\mathrm{nom}}}\&comma;\mathrm{XTB}\right)$

${\mathrm{\beta }}_{R_T}\&equals;{\mathrm{\beta }}_R\mathrm{pow}\left(\frac{T_{\mathrm{int}}}{T_{\mathrm{nom}}}\&comma;\mathrm{XTB}\right)$

$C_{\mathrm{BC}}\&equals;\{\begin{array}{cc}{\mathrm{\tau }}_R\frac{I_{\mathrm{ST}}}{\mathrm{NR}{V}_T}{\mathrm{Ex}}_{\min }\left(\frac{v_{\mathrm{BC}}}{\mathrm{NR}{V}_T}-E_{\min }\&plus;1\right)\&plus;C_{\mathrm{CJC}}& \frac{v_{\mathrm{BC}}}{\mathrm{NR}{V}_T}<E_{\min }\\ {\mathrm{\tau }}_R\frac{I_{\mathrm{ST}}}{\mathrm{NR}{V}_T}{\mathrm{Ex}}_{\max }\left(\frac{v_{\mathrm{BC}}}{\mathrm{NR}{V}_T}-E_{\max }\&plus;1\right)\&plus;C_{\mathrm{CJC}}& E_{\max }<\frac{v_{\mathrm{BC}}}{\mathrm{NR}{V}_T}\\ {\mathrm{\tau }}_R\frac{I_{\mathrm{ST}}}{\mathrm{NR}{V}_T}\exp \left(\frac{v_{\mathrm{BC}}}{\mathrm{NR}{V}_T}\right)\&plus;C_{\mathrm{CJC}}& \mathrm{otherwise}\end{array}$

$C_{\mathrm{BE}}\&equals;\{\begin{array}{cc}{\mathrm{\tau }}_F\frac{I_{\mathrm{ST}}}{\mathrm{NF}{V}_T}{\mathrm{Ex}}_{\min }\left(\frac{v_{\mathrm{BE}}}{\mathrm{NF}{V}_T}-E_{\min }\&plus;1\right)\&plus;C_{\mathrm{CJE}}& \frac{v_{\mathrm{BE}}}{\mathrm{NF}{V}_T}<E_{\min }\\ {\mathrm{\tau }}_F\frac{I_{\mathrm{ST}}}{\mathrm{NF}{V}_T}{\mathrm{Ex}}_{\max }\left(\frac{v_{\mathrm{BE}}}{\mathrm{NF}{V}_T}-E_{\max }\&plus;1\right)\&plus;C_{\mathrm{CJE}}& E_{\max }<\frac{v_{\mathrm{BE}}}{\mathrm{NF}{V}_T}\\ {\mathrm{\tau }}_F\frac{I_{\mathrm{ST}}}{\mathrm{NF}{V}_T}\exp \left(\frac{v_{\mathrm{BE}}}{\mathrm{NF}{V}_T}\right)\&plus;C_{\mathrm{CJE}}& \mathrm{otherwise}\end{array}$

$h_{\exp }\&equals;\left(\frac{T_{\mathrm{int}}}{T_{\mathrm{nom}}}-1\right)\frac{E_G}{V_T}$

$i_{\mathrm{BC}}\&equals;\{\begin{array}{cc}{I}_{\mathrm{ST}}\left({\mathrm{Ex}}_{\min }\left(\frac{v_{\mathrm{BC}}}{\mathrm{NR}{V}_T}-E_{\min }\&plus;1\right)-1\right)\&plus;v_{\mathrm{BC}}{G}_{\mathrm{BC}}& \frac{v_{\mathrm{BC}}}{\mathrm{NR}{V}_T}<E_{\min }\\ I_{\mathrm{ST}}\left({\mathrm{Ex}}_{\max }\left(\frac{v_{\mathrm{BC}}}{\mathrm{NR}{V}_T}-E_{\max }\&plus;1\right)-1\right)\&plus;v_{\mathrm{BC}}{G}_{\mathrm{BC}}& E_{\max }<\frac{v_{\mathrm{BC}}}{\mathrm{NR}{V}_T}\\ I_{\mathrm{ST}}\left(\exp \left(\frac{v_{\mathrm{BC}}}{\mathrm{NR}{V}_T}\right)-1\right)\&plus;v_{\mathrm{BC}}{G}_{\mathrm{BC}}& \mathrm{otherwise}\end{array}$

$i_{\mathrm{BE}}\&equals;\{\begin{array}{cc}{I}_{\mathrm{ST}}\left({\mathrm{Ex}}_{\min }\left(\frac{v_{\mathrm{BE}}}{\mathrm{NF}{V}_T}-E_{\min }\&plus;1\right)-1\right)\&plus;v_{\mathrm{BE}}{G}_{\mathrm{BE}}& \frac{v_{\mathrm{BE}}}{\mathrm{NF}{V}_T}<E_{\min }\\ I_{\mathrm{ST}}\left({\mathrm{Ex}}_{\max }\left(\frac{v_{\mathrm{BE}}}{\mathrm{NF}{V}_T}-E_{\max }\&plus;1\right)-1\right)\&plus;v_{\mathrm{BE}}{G}_{\mathrm{BE}}& E_{\max }<\frac{v_{\mathrm{BE}}}{\mathrm{NF}{V}_T}\\ I_{\mathrm{ST}}\left(\exp \left(\frac{v_{\mathrm{BE}}}{\mathrm{NF}{V}_T}\right)-1\right)\&plus;v_{\mathrm{BE}}{G}_{\mathrm{BE}}& \mathrm{otherwise}\end{array}$

$I_{\mathrm{ST}}\&equals;I_S\mathrm{pow}\left(\frac{T_{\mathrm{int}}}{T_{\mathrm{nom}}}\&comma;\mathrm{XTI}\right)h_{{\mathrm{temp}}_{\exp }}$

$q_{\mathrm{BK}}\&equals;-\mathrm{Vak}{v}_{\mathrm{BC}}\&plus;1$

$v_{\mathrm{BC}}\&equals;v_B-v_C$

$v_{\mathrm{BE}}\&equals;v_B-v_E$

$V_T\&equals;\frac{K}{q}{T}_{\mathrm{int}}$

$\mathrm{LossPower}\&equals;v_{\mathrm{BC}}\frac{i_{\mathrm{BC}}}{{\mathrm{\beta }}_{R_T}}\&plus;v_{\mathrm{BE}}\frac{i_{\mathrm{BE}}}{{\mathrm{\beta }}_{F_T}}\&plus;\left(i_{\mathrm{BE}}-i_{\mathrm{BC}}\right)q_{\mathrm{BK}}\left(v_C-v_E\right)$

$h_{{\mathrm{temp}}_{\exp }}\&equals;\{\begin{array}{cc}{\mathrm{Ex}}_{\min }\left(h_{\exp }-E_{\min }\&plus;1\right)& h_{\exp }<E_{\min }\\ {\mathrm{Ex}}_{\max }\left(h_{\exp }-E_{\max }\&plus;1\right)& E_{\max }<h_{\exp }\\ \exp \left(h_{\exp }\right)& \mathrm{otherwise}\end{array}$

The component described in this topic is from the Modelica Standard Library. To view the original documentation, which includes author and copyright information, click here.