PNP

Simple BJT according to Ebers-Moll

 Description The PNP component is a simple Ebers-Moll model of a bipolar PNP junction transistor. An optional heatport can be used to connect the device to a heatsink, however, the electrical parameters are not temperature dependent.
 Equations ${i}_{B}=-\frac{{i}_{\mathrm{BE}}}{{\mathrm{\beta }}_{F}}-\frac{{i}_{\mathrm{BC}}}{{\mathrm{\beta }}_{R}}-{C}_{\mathrm{BC}}{\stackrel{.}{v}}_{\mathrm{BC}}-{C}_{\mathrm{BE}}{\stackrel{.}{v}}_{\mathrm{BE}}$ ${i}_{C}=-\left({i}_{\mathrm{BE}}-{i}_{\mathrm{BC}}\right){q}_{\mathrm{BK}}+\frac{{i}_{\mathrm{BC}}}{{\mathrm{\beta }}_{R}}+{C}_{\mathrm{BC}}{\stackrel{.}{v}}_{\mathrm{BC}}+{C}_{\mathrm{CS}}{\stackrel{.}{v}}_{C}$ ${C}_{\mathrm{CJC}}=\left\{\begin{array}{cc}{C}_{\mathrm{JC}}\left(1+\mathrm{Mc}\frac{{v}_{\mathrm{BC}}}{{\mathrm{\phi }}_{C}}\right)& 0<\frac{{v}_{\mathrm{BC}}}{{\mathrm{\phi }}_{C}}\\ {C}_{\mathrm{JC}}\mathrm{pow}\left(1-\frac{{v}_{\mathrm{BC}}}{{\mathrm{\phi }}_{C}},-\mathrm{Mc}\right)& \mathrm{otherwise}\end{array}$ ${C}_{\mathrm{CJE}}=\left\{\begin{array}{cc}{C}_{\mathrm{JE}}\left(1+\mathrm{Me}\frac{{v}_{\mathrm{BE}}}{{\mathrm{\phi }}_{E}}\right)& 0<\frac{{v}_{\mathrm{BE}}}{{\mathrm{\phi }}_{E}}\\ {C}_{\mathrm{JE}}\mathrm{pow}\left(1-\frac{{v}_{\mathrm{BE}}}{{\mathrm{\phi }}_{E}},-\mathrm{Me}\right)& \mathrm{otherwise}\end{array}$ ${i}_{E}=-{i}_{B}-{i}_{C}+{C}_{\mathrm{CS}}{\stackrel{.}{v}}_{C}$ ${\mathrm{Ex}}_{\mathrm{max}}=\mathrm{exp}\left({E}_{\mathrm{max}}\right)$ ${\mathrm{Ex}}_{\mathrm{min}}=\mathrm{exp}\left({E}_{\mathrm{min}}\right)$ ${C}_{\mathrm{BC}}=\left\{\begin{array}{cc}{\mathrm{\tau }}_{R}\frac{\mathrm{Is}}{{V}_{T}}{\mathrm{Ex}}_{\mathrm{min}}\left(\frac{{v}_{\mathrm{BC}}}{{V}_{T}}-{E}_{\mathrm{min}}+1\right)+{C}_{\mathrm{CJC}}& \frac{{v}_{\mathrm{BC}}}{{V}_{T}}<{E}_{\mathrm{min}}\\ {\mathrm{\tau }}_{R}\frac{\mathrm{Is}}{{V}_{T}}{\mathrm{Ex}}_{\mathrm{max}}\left(\frac{{v}_{\mathrm{BC}}}{{V}_{T}}-{E}_{\mathrm{max}}+1\right)+{C}_{\mathrm{CJC}}& {E}_{\mathrm{max}}<\frac{{v}_{\mathrm{BC}}}{{V}_{T}}\\ {\mathrm{\tau }}_{R}\frac{\mathrm{Is}}{{V}_{T}}\mathrm{exp}\left(\frac{{v}_{\mathrm{BC}}}{{V}_{T}}\right)+{C}_{\mathrm{CJC}}& \mathrm{otherwise}\end{array}$ ${C}_{\mathrm{BE}}=\left\{\begin{array}{cc}{\mathrm{\tau }}_{F}\frac{\mathrm{Is}}{{V}_{T}}{\mathrm{Ex}}_{\mathrm{min}}\left(\frac{{v}_{\mathrm{BE}}}{{V}_{T}}-{E}_{\mathrm{min}}+1\right)+{C}_{\mathrm{CJE}}& \frac{{v}_{\mathrm{BE}}}{{V}_{T}}<{E}_{\mathrm{min}}\\ {\mathrm{\tau }}_{F}\frac{\mathrm{Is}}{{V}_{T}}{\mathrm{Ex}}_{\mathrm{max}}\left(\frac{{v}_{\mathrm{BE}}}{{V}_{T}}-{E}_{\mathrm{max}}+1\right)+{C}_{\mathrm{CJE}}& {E}_{\mathrm{max}}<\frac{{v}_{\mathrm{BE}}}{{V}_{T}}\\ {\mathrm{\tau }}_{F}\frac{\mathrm{Is}}{{V}_{T}}\mathrm{exp}\left(\frac{{v}_{\mathrm{BE}}}{{V}_{T}}\right)+{C}_{\mathrm{CJE}}& \mathrm{otherwise}\end{array}$ ${i}_{\mathrm{BC}}=\left\{\begin{array}{cc}\mathrm{Is}\left({\mathrm{Ex}}_{\mathrm{min}}\left(\frac{{v}_{\mathrm{BC}}}{{V}_{T}}-{E}_{\mathrm{min}}+1\right)-1\right)+{v}_{\mathrm{BC}}{G}_{\mathrm{BC}}& \frac{{v}_{\mathrm{BC}}}{{V}_{T}}<{E}_{\mathrm{min}}\\ \mathrm{Is}\left({\mathrm{Ex}}_{\mathrm{max}}\left(\frac{{v}_{\mathrm{BC}}}{{V}_{T}}-{E}_{\mathrm{max}}+1\right)-1\right)+{v}_{\mathrm{BC}}{G}_{\mathrm{BC}}& {E}_{\mathrm{max}}<\frac{{v}_{\mathrm{BC}}}{{V}_{T}}\\ \mathrm{Is}\left(\mathrm{exp}\left(\frac{{v}_{\mathrm{BC}}}{{V}_{T}}\right)-1\right)+{v}_{\mathrm{BC}}{G}_{\mathrm{BC}}& \mathrm{otherwise}\end{array}$ ${i}_{\mathrm{BE}}=\left\{\begin{array}{cc}\mathrm{Is}\left({\mathrm{Ex}}_{\mathrm{min}}\left(\frac{{v}_{\mathrm{BE}}}{{V}_{T}}-{E}_{\mathrm{min}}+1\right)-1\right)+{v}_{\mathrm{BE}}{G}_{\mathrm{BE}}& \frac{{v}_{\mathrm{BE}}}{{V}_{T}}<{E}_{\mathrm{min}}\\ \mathrm{Is}\left({\mathrm{Ex}}_{\mathrm{max}}\left(\frac{{v}_{\mathrm{BE}}}{{V}_{T}}-{E}_{\mathrm{max}}+1\right)-1\right)+{v}_{\mathrm{BE}}{G}_{\mathrm{BE}}& {E}_{\mathrm{max}}<\frac{{v}_{\mathrm{BE}}}{{V}_{T}}\\ \mathrm{Is}\left(\mathrm{exp}\left(\frac{{v}_{\mathrm{BE}}}{{V}_{T}}\right)-1\right)+{v}_{\mathrm{BE}}{G}_{\mathrm{BE}}& \mathrm{otherwise}\end{array}$ ${q}_{\mathrm{BK}}=-\mathrm{Vak}{v}_{\mathrm{BC}}+1$ ${v}_{\mathrm{BC}}={v}_{C}-{v}_{B}$ ${v}_{\mathrm{BE}}=\mathrm{E.v}-{v}_{B}$ $\mathrm{LossPower}=\left(\mathrm{E.v}-{v}_{C}\right)\left({i}_{\mathrm{BE}}-{i}_{\mathrm{BC}}\right){q}_{\mathrm{BK}}+{v}_{\mathrm{BC}}\frac{{i}_{\mathrm{BC}}}{{\mathrm{\beta }}_{R}}+{v}_{\mathrm{BE}}\frac{{i}_{\mathrm{BE}}}{{\mathrm{\beta }}_{F}}$

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 ${V}_{T}$ $0.02585$ $V$ Voltage equivalent of temperature Vt ${E}_{\mathrm{min}}$ $-100$ $1$ 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 $T$ $293.15$ $K$ 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.