Operational amplifier

An operational amplifier is an integrated circuit containing many transistors, sold as a single component, that behaves as a differential amplifier with extremely high gain. Every amplifier before this was one MOSFET or BJT whose gain depended sensitively on bias point, $g_m$, $\beta$, and temperature. The op-amp is a different beast: somebody else designed the internals, and the characteristics are so close to ideal that we treat them as exact. The remarkable consequence is that the gain of a circuit built around an op-amp depends almost entirely on external resistor ratios, not on the op-amp itself. That is the gift of Negative feedback — the engineering miracle that makes analog signal processing accessible without designing a single transistor.

Terminals

The op-amp has three signal terminals and two power-supply terminals.

• Inverting input $v_{-}$ (also written $v_1$): conventionally drawn with a minus sign.
• Non-inverting input $v_{+}$ (also written $v_2$): drawn with a plus sign.
• Output $v_O$.
• Positive supply rail $V_{CC}$ and negative supply rail $-V_{EE}$. The point midway between the two supplies, where they meet, is the circuit ground. Every signal voltage in the circuit is measured with respect to this node.

Three signal terminals + two supply rails; the supply midpoint is the circuit ground.

Two facts about the supply terminals cause endless confusion, so state them now. First, although $V_{CC}$ and $-V_{EE}$ appear on the schematic symbol, they are almost always omitted from circuit diagrams to keep them readable — but the op-amp does nothing without them. The chip needs power; the schematic just hides the wires. Second, the output voltage $v_O$ can never exceed $V_{CC}$ nor fall below $-V_{EE}$; it is physically pinned between the rails. With a typical lab supply of $V_{CC}=+15\text{V}$ and $V_{EE}=15\text{V}$, the usable output swing is only about $\pm 13\text{V}$ — a volt or two of headroom is lost inside the chip. This is Op-amp output saturation.

What it actually does

At its heart the op-amp computes the difference of its two inputs and multiplies by a huge number:

$v_O=A(v_2-v_1)$

where $A$ is the Open-loop gain, typically $10^5$ to $10^6$ for a real device. $v_2$ is the non-inverting input voltage, $v_1$ the inverting input voltage, both measured to ground. The op-amp responds only to the difference between its inputs; in principle it ignores any signal common to both (see Differential and common-mode signals).

That gain is far too large to use directly. A gain of $10^5$ means a $100\mu \text{V}$ input difference slams the output to $10\text{V}$ — the faintest noise saturates the output to a rail. The op-amp is useless open-loop. It only becomes a controllable amplifier when wrapped in Negative feedback: feed a fraction of the output back to the inverting input so the device drives its own input difference toward zero. The two ways to do this — the Inverting amplifier (op-amp) and the Non-inverting amplifier (op-amp) — are the foundation of every op-amp circuit. Their gains, derived from the Ideal op-amp model, depend only on resistor ratios. See Closed-loop gain.