Page 51 - Complementarity and Variational Inequalities in Electronics

The Variational Inequality Problem Chapter | 3 41

FIGURE 3.6 Stabilizer circuit.

FIGURE 3.7 Ideal Zener Diode.

Kirchhoff laws yield the system
⎧
−V z = V − R 1 (i Z + i E + i C ),
⎪
⎪
⎨
−V z − V C = V,
⎪
⎪
V E − V C = V − R 2 i E .
⎩
The NPN transistor behavior is described by means of the Ebers–Moll model as
given in the previous section, whereas the ideal Zener diode behavior is depicted
in Fig. 3.7.
Setting

V ze = V z − V s ,
we see that the ideal Zener diode is then described by the complementarity re-
lation
0 ≤ V ze ⊥ i z ≥ 0.