Page 151 - Complementarity and Variational Inequalities in Electronics

P. 151

142 Complementarity and Variational Inequalities in Electronics

FIGURE 4.15 Zener diode + Operational ampliﬁer.

FIGURE 4.16 Small signals model.

4.17 OPERATIONAL AMPLIFIER
An operational ampliﬁer is a great versatile circuit element based on transistors,
which is used to design audio equipments, oscillators and waveform generators,
ﬁlters, and many other applications. Let us consider the system of Fig. 4.15
involving an ideal Zener diode D and a noninverting ampliﬁer circuit with re-
sistors R 1 > 0 and R 2 > 0. We denote by R i > 0 the input resistor, by R o the
output resistor, and by γ> 0 the differential gain of the operational ampliﬁer.
Note that R i is very large (a few M ), whereas R o is very small (a few ). The
differential gain γ is very large ( 100,000).
Considering, as in Fig. 4.16, a small-signal model for the operational ampli-
ﬁer, the Kirchhoff laws give

146 147 148 149 150 151 152 153 154 155 156