Op-Amp-Apppcations

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

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

Inverting Amppfier

Non-inverting Amppfier

Voltage follower

This chapter discusses these basic apppcations in detail.

Inverting Amppfier

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

The circuit diagram of an inverting amppfier 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 appped 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 −

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

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

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

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

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

Note that the gain of the inverting amppfier is having a negative sign. It indicates that there exists a 180⁰ phase difference between the input and the output.

Non-Inverting Amppfier

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

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

In the above circuit, the input voltage $V_{i}$ is directly appped 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 spanision principle, we can calculate the voltage at the inverting input terminal of the op-amp as shown below −

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

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.

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

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

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

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

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

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

Voltage follower

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

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 amppfier 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 appped 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.