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Heating PMOS

Simple PMOS Transistor with heating port

Description

The Heating PMOS model is a simple model of a n-channel metal-oxide semiconductor FET. The model does not contain capacitances. A high drain-source resistance RDS is included to avoid numerical difficulties.

The electrical parameters are temperature dependent. An optional heat port may be connected to a heatsink.

 On-Resistance When used as a switch, the on-resistance of the transistor is approximately ${R}_{\mathrm{on}}\approx \frac{1}{\mathrm{\beta }\left(W/L\right)\left({v}_{\mathrm{GS}}-{V}_{T}\right)}$ where ${v}_{\mathrm{GS}}$ is the applied gate-to-source voltage. Because the default parameter values yield a relatively high on-resistance. the product $\mathrm{\beta }\left(W/L\right)$ should be increased by several orders of magnitude when using this device in a high-power application.
 Equations ${i}_{B}={i}_{G}=0$ ${i}_{\mathrm{D}}=-{i}_{S}=\left\{\begin{array}{c}-{i}_{\mathrm{D}},{v}_{S}<{v}_{\mathrm{D}}\\ \phantom{\rule[-0.0ex]{0.5ex}{0.0ex}}{i}_{\mathrm{D}}& \mathrm{otherwise}\end{array}$ ${i}_{\mathrm{D}}={u}_{\mathrm{DS}}{g}_{\mathrm{DS}}+\left\{\begin{array}{cc}0& 0\le {u}_{\mathrm{GST}}\\ -v{u}_{\mathrm{DS}}\left({u}_{\mathrm{GST}}-\frac{1}{2}{u}_{\mathrm{DS}}\right)& {u}_{\mathrm{GST}}<{u}_{\mathrm{DS}}\\ \frac{-1}{2}v{u}_{\mathrm{GST}}^{2}& \mathrm{otherwise}\end{array}$ ${g}_{\mathrm{DS}}=\left\{\begin{array}{cc}\frac{1}{{R}_{\mathrm{small}}}& -{R}_{\mathrm{small}}<{R}_{\mathrm{DS}}<{R}_{\mathrm{small}}\\ \frac{1}{{R}_{\mathrm{DS}}}& \mathrm{otherwise}\end{array}$ ${u}_{\mathrm{BS}}=\left\{\begin{array}{cc}0& {v}_{B}<{u}_{S}\\ {v}_{B}-{u}_{S}& \mathrm{otherwise}\end{array}$ ${u}_{\mathrm{D}}=\left\{\begin{array}{cc}{v}_{S}& {v}_{S}<{v}_{\mathrm{D}}\\ {v}_{\mathrm{D}}& \mathrm{otherwise}\end{array}$ ${u}_{\mathrm{DS}}={u}_{\mathrm{D}}-{u}_{S}$ ${u}_{\mathrm{GST}}=\left({K}_{{2}_{T}}{u}_{\mathrm{BS}}+{v}_{G}-{u}_{S}-{V}_{{\mathrm{th}}_{T}}\right){K}_{5}$ ${u}_{S}=\left\{\begin{array}{cc}{v}_{\mathrm{D}}& {v}_{S}<{v}_{\mathrm{D}}\\ {v}_{S}& \mathrm{otherwise}\end{array}$ ${K}_{{2}_{T}}={K}_{2}\left(1+\left({T}_{\mathrm{int}}-{T}_{\mathrm{nom}}\right)\mathrm{kk2}\right)$ $v={\mathrm{\beta }}_{T}\frac{W+\mathrm{dW}}{L+\mathrm{dL}}$ ${\mathrm{\beta }}_{T}=\mathrm{\beta }{\left(\frac{{T}_{\mathrm{int}}}{{T}_{\mathrm{nom}}}\right)}^{-\frac{3}{2}}$ ${V}_{{\mathrm{th}}_{T}}={V}_{\mathrm{th}}\left(1+\left({T}_{\mathrm{int}}-{T}_{\mathrm{nom}}\right)\mathrm{kvt}\right)$ ${T}_{\mathrm{int}}=\left\{\begin{array}{cc}{T}_{\mathrm{heatPort}}& \mathrm{Use Heat Port}\\ T& \mathrm{otherwise}\end{array}$ $\mathrm{LossPower}={i}_{\mathrm{D}}\left({v}_{\mathrm{D}}-{v}_{S}\right)$

Variables

 Name Units Description Modelica ID $\mathrm{LossPower}$ $W$ Loss power leaving component via HeatPort LossPower ${T}_{\mathrm{heatPort}}$ $K$ Temperature of HeatPort T_heatPort

Connections

 Name Description Modelica ID $\mathrm{D}$ Drain D $G$ Gate G $S$ Source S $B$ Bulk B $\mathrm{Heat Port}$ heatPort

Parameters

 Name Default Units Description Modelica ID $W$ $2·{10}^{-5}$ $m$ Width of channel W $L$ $6·{10}^{-6}$ $m$ Length of channel L $\mathrm{dW}$ $-2.5·{10}^{-6}$ $m$ Narrowing of channel dW $\mathrm{dL}$ $-2.1·{10}^{-6}$ $m$ Shortening of channel dL $\mathrm{\beta }$ $1.05·{10}^{-5}$ $\frac{A}{{V}^{2}}$ Transconductance parameter Beta ${V}_{\mathrm{th}}$ $-1$ $V$ Zero bias threshold voltage Vt ${K}_{2}$ $0.41$ $1$ Bulk threshold parameter K2 ${K}_{5}$ $0.839$ $1$ Reduction of pinch-off region K5 ${k}_{{V}_{T}}$ $-0.0029$ $1$ fitting parameter for Vt kvt ${k}_{{K}_{2}}$ $6.2·{10}^{-4}$ $1$ Fitting parameter for kk2 kk2 ${R}_{\mathrm{DS}}$ $1·{10}^{7}$ $\mathrm{\Omega }$ Drain-Source resistance RDS ${T}_{\mathrm{nom}}$ $300.15$ $K$ Parameter measurement temperature Tnom $T$ $293.15$ $K$ Fixed device temperature if Use Heat Port is false T $\mathrm{Use Heat Port}$ $\mathrm{true}$ 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.