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A circuit is said to be **linear**, if there exists a linear relationship between its input and the output. Similarly, a circuit is said to be **non-linear**, if there exists a non-linear relationship between its input and output.

Op-amps can be used in both linear and non-linear applications. The following are the basic applications of op-amp −

- Inverting Amplifier
- Non-inverting Amplifier
- Voltage follower

This chapter discusses these basic applications in detail.

An inverting amplifier takes the input through its inverting terminal through a resistor $R_{1}$, and produces its amplified version as the output. This amplifier not only amplifies the input but also inverts it (changes its sign).

The **circuit diagram** of an inverting amplifier is shown in the following figure −

Note that for an op-amp, the voltage at the inverting input terminal is equal to the voltage at its non-inverting input terminal. Physically, there is no short between those two terminals but **virtually**, they are in **short** with each other.

In the circuit shown above, the non-inverting input terminal is connected to ground. That means zero volts is applied at the non-inverting input terminal of the op-amp.

According to the **virtual short concept**, the voltage at the inverting input terminal of an op-amp will be zero volts.

The **nodal equation** at this terminal's node is as shown below −

$$\frac{0-V_i}{R_1}+ \frac{0-V_0}{R_f}=0$$

$$=>\frac{-V_i}{R_1}= \frac{V_0}{R_f}$$

$$=>V_{0}=\left(\frac{-R_f}{R_1}\right)V_{t}$$

$$=>\frac{V_0}{V_i}= \frac{-R_f}{R_1}$$

The ratio of the output voltage $V_{0}$ and the input voltage $V_{i}$ is the voltage-gain or gain of the amplifier. Therefore, the **gain of inverting amplifier** is equal to $-\frac{R_f}{R_1}$.

Note that the gain of the inverting amplifier is having a **negative sign**. It indicates that there exists a 180^{0} phase difference between the input and the output.

A non-inverting amplifier takes the input through its non-inverting terminal, and produces its amplified version as the output. As the name suggests, this amplifier just amplifies the input, without inverting or changing the sign of the output.

The **circuit diagram** of a non-inverting amplifier is shown in the following figure −

In the above circuit, the input voltage $V_{i}$ is directly applied to the non-inverting input terminal of op-amp. So, the voltage at the non-inverting input terminal of the op-amp will be $V_{i}$.

By using **voltage division principle**, we can calculate the voltage at the inverting input terminal of the op-amp as shown below −

$$=>V_{1} = V_{0}\left(\frac{R_1}{R_1+R_f}\right)$$

According to the **virtual short concept**, the voltage at the inverting input terminal of an op-amp is same as that of the voltage at its non-inverting input terminal.

$$=>V_{1} = V_{i}$$

$$=>V_{0}\left(\frac{R_1}{R_1+R_f}\right)=V_{i}$$

$$=>\frac{V_0}{V_i}=\frac{R_1+R_f}{R_1}$$

$$=>\frac{V_0}{V_i}=1+\frac{R_f}{R_1}$$

Now, the ratio of output voltage $V_{0}$ and input voltage $V_{i}$ or the voltage-gain or **gain of the non-inverting amplifier** is equal to $1+\frac{R_f}{R_1}$.

Note that the gain of the non-inverting amplifier is having a **positive sign**. It indicates that there is no phase difference between the input and the output.

A **voltage follower** is an electronic circuit, which produces an output that follows the input voltage. It is a special case of non-inverting amplifier.

If we consider the value of feedback resistor, $R_{f}$ as zero ohms and (or) the value of resistor, 1 as infinity ohms, then a non-inverting amplifier becomes a voltage follower. The **circuit diagram** of a voltage follower is shown in the following figure −

In the above circuit, the input voltage $V_{i}$ is directly applied to the non-inverting input terminal of the op-amp. So, the voltage at the non-inverting input terminal of op-amp is equal to $V_{i}$. Here, the output is directly connected to the inverting input terminal of opamp. Hence, the voltage at the inverting input terminal of op-amp is equal to $V_{0}$.

According to the **virtual short concept**, the voltage at the inverting input terminal of the op-amp is same as that of the voltage at its non-inverting input terminal.

$$=>V_{0} = V_{i}$$

So, the output voltage $V_{0}$ of a voltage follower is equal to its input voltage $V_{i}$.

Thus, the **gain of a voltage follower** is equal to one since, both output voltage $V_{0}$ and input voltage $V_{i}$ of voltage follower are same.

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