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2.6 Modeling and Analysis of Nonlinear Circuits 101
in the model definition.
Variables −>
{Current[B, C], Voltage[B, C],
Current[B, E], Voltage[B, E]},
It remains to write the model equations in terms of the port branch variables, paying attention to
the different positive reference directions assumed for the port currents as compared to I C and I E in
the Ebers-Moll equations. While the latter are defined to be positive for currents flowing into the
collector and emitter, positive values of Current[B, C] and Current[B, E] denote currents flowing
out of these terminals. We account for this difference by changing the sign on the right-hand side of
the model equations.
Definition −>
Equations[
Current[B, C] == −Is*(Exp[Voltage[B, E]/Vt] − 1)
+ Is/alphar*(Exp[Voltage[B, C]/Vt] − 1),
Current[B, E] == Is/alphaf*(Exp[Voltage[B, E]/Vt] − 1)
− Is*(Exp[Voltage[B, C]/Vt] − 1)
],
To store the transistor model in the global database we wrap the complete Model definition into a
Circuit structure and expand it with ExpandSubcircuits (Section 3.4.1).
In[10]:= Circuit[
Model[
Name −> NPNBJT,
Selector −> EbersMoll,
Scope −> Global,
Ports −> {C, B, E},
Parameters −>
{betaf, betar, Js, Area, Global[Temperature]},
Translation −>
{alphaf −> betaf/(1+betaf),
alphar −> betar/(1+betar),
Is −> Js*Area, Vt :> ThermalVoltage[Temperature]},
Variables −>
{Current[B, C], Voltage[B, C],
Current[B, E], Voltage[B, E]},
Definition −>
Equations[
Current[B, C] == −Is*(Exp[Voltage[B, E]/Vt] − 1)
+ Is/alphar*(Exp[Voltage[B, C]/Vt] − 1),
Current[B, E] == −Is*(Exp[Voltage[B, C]/Vt] − 1)
+ Is/alphaf*(Exp[Voltage[B, E]/Vt] − 1)
]
]
] // ExpandSubcircuits;