Page 36 - Complementarity and Variational Inequalities in Electronics

26 Complementarity and Variational Inequalities in Electronics

FIGURE 2.16 Zener diode model.

diode (see Fig. 2.16) is a good voltage regulator to maintain a constant voltage
regardless of minor variations in load current or input voltage. There is a current
point I Z , called the Zener knee current, which is the minimum value of the Zener
current required to maintain voltage regulation and a maximum allowable value
of Zener current I M . Currents above this value damage or destroy the system.
The graph corresponding to the ampere–volt characteristic (i,V ) is maximal
monotone, and there exists a proper convex continuous electrical superpotential
ϕ Z : R → R such that
(∀i ∈ R) : V ∈ ∂ϕ Z (i).
The ideal Zener diode model (see Fig. 2.17) is given by the practical diode
model (see Fig. 2.14) with appropriate values for V 1 and V 2 . This means that
the voltage across the diode is constant over a wide range of device current
values.
The practical Zener diode model (see Fig. 2.18) is a piecewise linear model
that includes the effects of the Zener impedance.
Let us use the notation of Fig. 2.18. Here it is implicitly assumed that
I 1 < 0 <I 2 ,V 1 <V 3 < 0 <V 4 <V 2 .
The electrical superpotential of the Zener diode is

⎧
⎨ (V 1 −V 3 ) 2 if x< 0
x + V 3 x
2I 1
ϕ Z (x) =
⎩ (V 2 −V 4 ) 2
x + V 4 x if x ≥ 0.
2I 2