# Operational Amplifier

The operational amplifier (op amp) is a powerful and versatile device with innumerable applications. The op amp takes two voltages as inputs

• Non-inverting input ($V_+$)
• Inverting input ($V_-$)

and supplies an output voltage, $V_{out}$. Essentially, $V_{out}=A(V_+ - V_-)$, where $A$ is the open loop gain of the amplifier – that is, the gain when there is no feedback around the op amp (more on this later).

The op amp is an active element, which means is requires a power supply. Here, it is connected to $V_{dd}$ and $V_{ss}$.

## Ideal Op Amp

For most applications, the inputs draw so little current (order nanoAmps) and the gain is so high (order $1,000,000$) that we can ignore the exact values for both and make these assumptions:

• Infinite gain ($A\to\infty$)
• No current into $V_+$ or $V_-$ ($R_{in}\to\infty$)

thus describing the ideal op amp model. This model makes op-amp circuits much easier to analyze while making accurate predictions. When we account for the op amp’s power supply (which ensures $V_{ss} \leq V_{out} \leq V_{dd}$) and simplify the op amp’s inputs to a single input ($V_{in} = V_+ - V_-$), we can plot $V_{out}$ vs. $V_{in}$ as shown below.

### Op Amp Open Loop Behavior

The plot on the right shows the three regions of op amp open loop operation. It is the behavior that $V_{out}$ of the op amp on the left would show if $V_-$ were fixed between $V_{dd}$ and $V_{ss}$ and $V_+$ was swept. This plot shows the three regions characteristic of the ideal op amp:

• Region 1: $V_+ > V_-$ in which $V_{out} = V_{dd}$
• Region 2: $% $ in which $V_{out} = V_{ss}$
• Region 3: $V_+ = V_-$

In the open loop configuration, region 3 is essentially infinitely thin because the open loop gain of the op amp is infinite. To show the power of this model, we can use it to analyze a configuration of the op amp that expands region 3.

### Op Amp as a Buffer

The only difference between this circuit and the above one is that $V_-$ and $V_{out}$ have been connected. The circuit path between the output ($V_{out}$) and the inverting input ($V_-$) is called negative feedback, and it means that region 3 of the op amp (where $V_+ = V_-$) is expanded.

To understand why, consider how the equality $V_+ = V_-$ is affected when $V_- = V_{out}$. Combining, $V_+ = V_{out}$ – that is, the one free input to the op-amp, $V_+$, is equal to the output, $V_{out}$. Thus, the $V_{out}$ vs. $V_+$ plot shows a line with slope 1 (unity) from the negative supply rail to the positive one.