Page 42 - Complementarity and Variational Inequalities in Electronics

32 Complementarity and Variational Inequalities in Electronics

Let us now consider a more general mathematical model in assuming that
there exist proper convex lower semicontinuous functions ϕ E , ϕ C such that the
ampere–volt characteristics of the two diodes of the Ebers–Moll model can be
formulated as

V E ∈ ∂ϕ E (I), V C ∈ ∂ϕ C (I ).
The function ϕ E is called the emitter electrical superpotential of the transistor,
whereas the function ϕ C is named the collector electrical superpotential. The
mathematical model of the transistor reads

∂ϕ E (I)
V E
∈ , (2.8)

V C ∂ϕ C (I )

I 1 α I I E
= , (2.9)
I α N 1 I C
and
I B =−(I E + I C ). (2.10)

The different models of diodes discussed in the previous sections can be here
used to define the corresponding models of transistors.