# Difference Between Inverting and Noninverting Amplifier

## Main Difference – Inverting vs. Noninverting Amplifier

Inverting and noninverting amplifiers are two configurations that operational amplifiers can be set up in. The main difference between inverting and noninverting amplifier is that an inverting amplifier produces an output which is 180o out of phase with the input, whereas a noninverting amplifier produces an output which is in phase with the input.

## What is an Inverting Amplifier

An inverting amplifier is a differential amplifier that amplifies a small difference in voltage between its input terminals to a large voltage on its output terminal. The output voltage is at 180o out of phase compared to the input voltage. The setup of an inverting amplifier is shown below.

An operational amplifier.

For amplifiers, the output voltage $V_{out}$ is given in terms of the two input voltages $V^+$ and $V_-$ as:

$V_{out}=A\left( V_+-V_-\right)$

where $A$ is the gain of the operational amplifier. Since $V_+$ is connected to Earth, $V_+=0$. The point marked $X$ is virtual Earth so the potential at this point is almost 0 V. No current passes through this point. Therefore the current that flows through the resistor $R_2$ is the same as the current $I$ that flows through the resistor $R_1$.

If the potential difference across  $R_1$ is $V_1$, then,

$I=\frac{V_1}{R_1}=\frac{V_{in}-0}{R_1}=\frac{V_{in}}{R_1}$

Similarly for $R_2$

$I=\frac{V_2}{R_2}=\frac{0-V_{out}}{R_2}=-\frac{V_{out}}{R_2}$

Then the gain $A$ can be expressed as:

$A=\frac{V_{out}}{V_{in}}=\frac{-IR_2}{IR_1}$

$A=-\frac{R_2}{R_1}$

The negative sign here indicates that the output is at a 180o phase difference with the input.

## What is a Noninverting Amplifier

A noninverting amplifier is an amplifier that produces an output which is in phase with the input. The setup of a non-inverting amplifier is shown below:

A noninverting amplifier.

In the noninverting amplifier, $V_{in}=V_+$. The gain in a noninverting amplifier is quite large, so the difference between $V_+$ and $V_-$ is negligible. So we can say that $V_-\approx V_+ \left( =V_{in}\right)$. Using the idea of a potential divider, we can write

$V_-=V_{out}\times \frac{R_2}{R_1+R_2}$. Equating the two expressions for $V_-$, we have:

$V_{in}=V_{out}\times \frac{R_2}{R_1+R_2}$. Then, we can write the gain as:

$A=\frac{V_{out}}{V_{in}}=\frac{R_1+R_2}{R_2}$. Dividing both the numerator and the denominator by $R_2$, we get:

$A=1+\frac{R_1}{R_2}$

## Difference Between Inverting and Noninverting Amplifier

### Phase Difference:

In an inverting amplifier, the output voltage is 180o out of phase with the input voltage.

In a noninverting amplifier, the output voltage is in phase with the input voltage.

### Amplifier Gain:

For an inverting amplifier, the gain is simply the ratio between the two resistors.

For a noninverting amplifier, the gain is 1 + the ratio between resistors.