Inverting Amplifier

A circuit diagram of an opamp in a inverting amplifier configuration is shown in Figure 15.

**Figure 15:** Inverting amplifier.
$\begin{figure} \begin{center} \epsfig{file=images/opampimg3.eps}\end{center}\end{figure}$

The basic input-output formula is

$\begin{displaymath}v_{out} = -\frac{R_2}{R_1} v_{in} . \end{displaymath}$

(14)

The term inverting comes from the minus sign (it corresponds to a $180^\circ$ phase shift).

Let's use the virtual model to derive (14).

The + node is connected to ground, so v₊ = 0. By the virtual model, v₊ = v_- and so v₊=0. Also i₊ = 0.

The - node is connected to two resistors, so we apply KCL:

$\begin{displaymath}\frac{v_{in}- v_+}{R_1} + \frac{v_{out} - v_+}{R_2} - i_- = 0 . \end{displaymath}$

By the virtual model, i_-=0, and we get

$\begin{displaymath}\frac{v_{in}}{R_1} + \frac{v_{out}}{R_2} = 0 . \end{displaymath}$

Solving for v_out gives (14).

PSPICE file: inva1.sch.

ANU Engineering - ENGN2211