Heating PNP

Simple PNP BJT according to Ebers-Moll with heating port

 Description The Heating PNP component is a simple Ebers-Moll model of a bipolar PNP junction transistor with temperature dependency. An optional heatport can be used to connect the device to a heatsink.
 Equations ${T}_{\mathrm{int}}=\left\{\begin{array}{cc}{T}_{\mathrm{heatPort}}& \mathrm{Use Heat Port}\\ T\phantom{\rule[-0.0ex]{4.5ex}{0.0ex}}& \mathrm{otherwise}\end{array}$ ${i}_{B}=-\frac{{i}_{\mathrm{EB}}}{{\mathrm{\beta }}_{{F}_{T}}}-\frac{{i}_{\mathrm{CB}}}{{\mathrm{\beta }}_{{R}_{T}}}-{C}_{\mathrm{EB}}{\stackrel{.}{v}}_{\mathrm{EB}}-{C}_{\mathrm{CB}}{\stackrel{.}{v}}_{\mathrm{CB}}$ ${i}_{C}=\frac{{i}_{\mathrm{CB}}}{{\mathrm{\beta }}_{{R}_{T}}}+{C}_{\mathrm{CB}}{\stackrel{.}{v}}_{\mathrm{CB}}+{C}_{\mathrm{CS}}{\stackrel{.}{v}}_{C}+\left({i}_{\mathrm{CB}}-{i}_{\mathrm{EB}}\right){q}_{\mathrm{BK}}$ ${C}_{\mathrm{CJC}}=\left\{\begin{array}{cc}{C}_{\mathrm{JC}}\left(1+{M}_{C}\frac{{v}_{\mathrm{CB}}}{{\mathrm{\Phi }}_{C}}\right)& 0<\frac{{v}_{\mathrm{CB}}}{{\mathrm{\Phi }}_{C}}\\ {C}_{\mathrm{JC}}\mathrm{pow}\left(1-\frac{{v}_{\mathrm{CB}}}{{\mathrm{\Phi }}_{C}},-{M}_{C}\right)& \mathrm{otherwise}\end{array}$ ${C}_{\mathrm{CJE}}=\left\{\begin{array}{cc}{C}_{\mathrm{JE}}\left(1+{M}_{E}\frac{{v}_{\mathrm{EB}}}{{\mathrm{\Phi }}_{E}}\right)& 0<\frac{{v}_{\mathrm{EB}}}{{\mathrm{\Phi }}_{E}}\\ {C}_{\mathrm{JE}}\mathrm{pow}\left(1-\frac{{v}_{\mathrm{EB}}}{{\mathrm{\Phi }}_{E}},-{M}_{E}\right)& \mathrm{otherwise}\end{array}$ ${i}_{E}=-{i}_{B}-{i}_{C}+{C}_{\mathrm{CS}}{\stackrel{.}{v}}_{C}$ ${\mathrm{Ex}}_{\mathrm{max}}=\mathrm{exp}\left({E}_{\mathrm{max}}\right)$ ${\mathrm{Ex}}_{\mathrm{min}}=\mathrm{exp}\left({E}_{\mathrm{min}}\right)$ ${\mathrm{\beta }}_{{F}_{T}}={\mathrm{\beta }}_{F}\mathrm{pow}\left(\frac{{T}_{\mathrm{int}}}{{T}_{\mathrm{nom}}},\mathrm{XTB}\right)$ ${\mathrm{\beta }}_{{R}_{T}}={\mathrm{\beta }}_{R}\mathrm{pow}\left(\frac{{T}_{\mathrm{int}}}{{T}_{\mathrm{nom}}},\mathrm{XTB}\right)$ ${C}_{\mathrm{CB}}={C}_{\mathrm{CJC}}+{\mathrm{Τ}}_{R}\frac{{I}_{\mathrm{ST}}}{\mathrm{NR}{V}_{T}}\left\{\begin{array}{cc}{\mathrm{Ex}}_{\mathrm{min}}\left(\frac{{v}_{\mathrm{CB}}}{\mathrm{NR}{V}_{T}}-{E}_{\mathrm{min}}+1\right)& \frac{{v}_{\mathrm{CB}}}{\mathrm{NR}{V}_{T}}<{E}_{\mathrm{min}}\\ {\mathrm{Ex}}_{\mathrm{max}}\left(\frac{{v}_{\mathrm{CB}}}{\mathrm{NR}{V}_{T}}-{E}_{\mathrm{max}}+1\right)& {E}_{\mathrm{max}}<\frac{{v}_{\mathrm{CB}}}{\mathrm{NR}{V}_{T}}\\ \mathrm{exp}\left(\frac{{v}_{\mathrm{CB}}}{\mathrm{NR}{V}_{T}}\right)& \mathrm{otherwise}\end{array}$ ${C}_{\mathrm{EB}}={C}_{\mathrm{CJE}}+{\mathrm{Τ}}_{F}\frac{{I}_{\mathrm{ST}}}{\mathrm{NF}{V}_{T}}\left\{\begin{array}{cc}{\mathrm{Ex}}_{\mathrm{min}}\left(\frac{{v}_{\mathrm{EB}}}{\mathrm{NF}{V}_{T}}-{E}_{\mathrm{min}}+1\right)& \frac{{v}_{\mathrm{EB}}}{\mathrm{NF}{V}_{T}}<{E}_{\mathrm{min}}\\ {\mathrm{Ex}}_{\mathrm{max}}\left(\frac{{v}_{\mathrm{EB}}}{\mathrm{NF}{V}_{T}}-{E}_{\mathrm{max}}+1\right)& {E}_{\mathrm{max}}<\frac{{v}_{\mathrm{EB}}}{\mathrm{NF}{V}_{T}}\\ \mathrm{exp}\left(\frac{{v}_{\mathrm{EB}}}{\mathrm{NF}{V}_{T}}\right)& \mathrm{otherwise}\end{array}$ ${h}_{\mathrm{exp}}=\left(\frac{{T}_{\mathrm{int}}}{{T}_{\mathrm{nom}}}-1\right)\frac{\mathrm{EG}}{{V}_{T}}$ ${i}_{\mathrm{CB}}={v}_{\mathrm{CB}}{G}_{\mathrm{BC}}+{I}_{\mathrm{ST}}\left\{\begin{array}{cc}\left({\mathrm{Ex}}_{\mathrm{min}}\left(\frac{{v}_{\mathrm{CB}}}{\mathrm{NR}{V}_{T}}-{E}_{\mathrm{min}}+1\right)-1\right)& \frac{{v}_{\mathrm{CB}}}{\mathrm{NR}{V}_{T}}<{E}_{\mathrm{min}}\\ \left({\mathrm{Ex}}_{\mathrm{max}}\left(\frac{{v}_{\mathrm{CB}}}{\mathrm{NR}{V}_{T}}-{E}_{\mathrm{max}}+1\right)-1\right)& {E}_{\mathrm{max}}<\frac{{v}_{\mathrm{CB}}}{\mathrm{NR}{V}_{T}}\\ \left(\mathrm{exp}\left(\frac{{v}_{\mathrm{CB}}}{\mathrm{NR}{V}_{T}}\right)-1\right)& \mathrm{otherwise}\end{array}$ ${i}_{\mathrm{EB}}={v}_{\mathrm{EB}}{G}_{\mathrm{BE}}+{I}_{\mathrm{ST}}\left\{\begin{array}{cc}{\mathrm{Ex}}_{\mathrm{min}}\left(\frac{{v}_{\mathrm{EB}}}{\mathrm{NF}{V}_{T}}-{E}_{\mathrm{min}}+1\right)-1& \frac{{v}_{\mathrm{EB}}}{\mathrm{NF}{V}_{T}}<{E}_{\mathrm{min}}\\ {\mathrm{Ex}}_{\mathrm{max}}\left(\frac{{v}_{\mathrm{EB}}}{\mathrm{NF}{V}_{T}}-{E}_{\mathrm{max}}+1\right)-1& {E}_{\mathrm{max}}<\frac{{v}_{\mathrm{EB}}}{\mathrm{NF}{V}_{T}}\\ \mathrm{exp}\left(\frac{{v}_{\mathrm{EB}}}{\mathrm{NF}{V}_{T}}\right)-1& \mathrm{otherwise}\end{array}$ ${I}_{\mathrm{ST}}=\mathrm{Is}\mathrm{pow}\left(\frac{{T}_{\mathrm{int}}}{{T}_{\mathrm{nom}}},\mathrm{XTI}\right){h}_{{\mathrm{temp}}_{\mathrm{exp}}}$ ${q}_{\mathrm{BK}}=-{V}_{\mathrm{ak}}{v}_{\mathrm{CB}}+1$ ${v}_{\mathrm{CB}}={v}_{C}-{v}_{B}$ ${v}_{\mathrm{EB}}={v}_{E}-{v}_{B}$ ${V}_{T}=\frac{K}{q}{T}_{\mathrm{int}}$ $\mathrm{LossPower}={v}_{\mathrm{CB}}\frac{{i}_{\mathrm{CB}}}{{\mathrm{\beta }}_{{R}_{T}}}+{v}_{\mathrm{EB}}\frac{{i}_{\mathrm{EB}}}{{\mathrm{\beta }}_{{F}_{T}}}+\left({i}_{\mathrm{CB}}-{i}_{\mathrm{EB}}\right){q}_{\mathrm{BK}}\left({v}_{C}-{v}_{E}\right)$ ${h}_{{\mathrm{temp}}_{\mathrm{exp}}}=\left\{\begin{array}{cc}{\mathrm{Ex}}_{\mathrm{min}}\left({h}_{\mathrm{exp}}-{E}_{\mathrm{min}}+1\right)& {h}_{\mathrm{exp}}<{E}_{\mathrm{min}}\\ {\mathrm{Ex}}_{\mathrm{max}}\left({h}_{\mathrm{exp}}-{E}_{\mathrm{max}}+1\right)& {E}_{\mathrm{max}}<{h}_{\mathrm{exp}}\\ \mathrm{exp}\left({h}_{\mathrm{exp}}\right)& \mathrm{otherwise}\end{array}$

Connections

 Name Description Modelica ID $C$ Collector C $B$ Base B $E$ Emitter E $\mathrm{Heat Port}$ heatPort

Parameters

 Name Default Units Description Modelica ID ${\mathrm{\beta }}_{F}$ $50$ $1$ Forward beta Bf ${\mathrm{\beta }}_{R}$ $0.1$ $1$ Reverse beta Br ${I}_{S}$ $1·{10}^{-16}$ $A$ Transport saturation current Is ${V}_{\mathrm{AK}}$ $0.02$ $\frac{1}{V}$ Early voltage (inverse) Vak ${\mathrm{\tau }}_{F}$ $1.2·{10}^{-10}$ $s$ Ideal forward transit time Tauf ${\mathrm{\tau }}_{R}$ $5·{10}^{-9}$ $s$ Ideal reverse transit time Taur ${C}_{\mathrm{CS}}$ $1·{10}^{-12}$ $F$ Collector-substrate capacitance Ccs ${C}_{\mathrm{JE}}$ $4·{10}^{-13}$ $F$ Base-emitter zero bias depletion capacitance Cje ${C}_{\mathrm{JC}}$ $5·{10}^{-13}$ $F$ Base-coll. zero bias depletion capacitance Cjc ${\mathrm{\phi }}_{E}$ $0.8$ $V$ Base-emitter diffusion voltage Phie ${M}_{e}$ $0.4$ $1$ Base-emitter gradation exponent Me ${\mathrm{\phi }}_{C}$ $0.8$ $V$ Base-collector diffusion voltage Phic ${M}_{c}$ $0.333$ $1$ Base-collector gradation exponent Mc ${G}_{\mathrm{BC}}$ $1·{10}^{-15}$ $S$ Base-collector conductance Gbc ${G}_{\mathrm{BE}}$ $1·{10}^{-15}$ $S$ Base-emitter conductance Gbe ${E}_{\mathrm{min}}$ $-100$ $1$ if $x<{E}_{\mathrm{min}}$, $\mathrm{exp}\left(x\right)$  is linearized EMin ${E}_{\mathrm{max}}$ $40$ $1$ if $x>{E}_{\mathrm{max}}$, $\mathrm{exp}\left(x\right)$ is linearized EMax ${T}_{\mathrm{nom}}$ $300.15$ $K$ Parameter measurement temperature Tnom $\mathrm{XTI}$ $3$ $1$ Temperature exponent for effect on ${I}_{s}$ XTI $\mathrm{XTB}$ $0$ $1$ Forward and reverse beta temperature exponent XTB ${E}_{G}$ $1.11$ $V$ Energy gap for temperature effect on ${I}_{s}$ EG $\mathrm{NF}$ $1$ $1$ Forward current emission coefficient NF $\mathrm{NR}$ $1$ $1$ Reverse current emission coefficient NR $T$ $293.15$ $K$ Fixed device temperature if Use Heat Port is false T Use Heat Port $\mathrm{false}$ True (checked) means heat port is enabled useHeatPort

 Modelica Standard Library 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.