# Operational Amplifier as a Black Box

The term “operational amplifier” (op amp) was coined in the 1940s, well before the invention of the transistor and the integrated circuit. Op amps realized by vacuum tubes^{1} served as the core of electronic “integrators,” “differentiators,” etc., thus forming systems whose behavior followed a given differential equation. Called “analog computers,” such circuits were used to study the stability of differential equations that arose in fields such as control or power systems. Since each op amp implemented a mathematical *operation* (e.g., integration), the term “operational amplifier” was born.

Op amps find wide application in today’s discrete and integrated electronics. In the cellphone studied in Chapter 1, for example, integrated op amps serve as building blocks in (active) filters. Similarly, the analog-to-digital converter(s) used in digital cameras often employ op amps.

In this chapter, we study the operational amplifier as a black box, developing opamp-based circuits that perform interesting and useful functions. The outline is shown below.

**Figure 8.1** (a) Op amp symbol, (b) equivalent circuit.

## 8.1 GENERAL CONSIDERATIONS

The operational amplifier ...