**Operational Amplifier**

Cover Image by: Martincco, Aurora Borealis – polar lights 3, CC BY-SA 4.0

**Contents**

**Introduction****Operational amplifier****Why is it Called Operational Amplifier ?****Working Principle of Operational Amplifier****Basic Operational Amplifier circuit diagram****Non-inverting operational amplifier****Op amp gain****Comparator****Integrator****Non-Inverting Op-Amp with negative feedback****Equivalent circuit of an Op-Amp****Pin-Diagram of an Op-amp IC chip.****Op-amp ideal Characteristics****What is offset voltage ?****Input offset voltage of Op Amp****Frequency Response****Applications of Operational Amplifier**

**What is op amp?**

Op-amp is an abbreviation of the Operation amplifier, a direct-coupled high gain amplifier. In the term Operational Amplifier, ‘Operational’ represents that the amplifier can perform certain operations like – summation, subtraction, comparison, etc. The word ‘Amplification’ suggests that it can amplify the input signal.

**Ideal op Amp**

An ideal op amp is not practically existed but has the best characteristics. All the practical Operational Amplifiers are built to achieve close characteristics as an ideal op amp. Let us discuss some of the features of an ideal op-amp.

**Ideal op amp characteristics**

- Ideal op amp provides infinite voltage gain.
- It has infinite input impedance.
- It has zero output resistance.
- It has infinite bandwidth.
- Common Mode Rejection Ratio is infinite.
- The power Supply Rejection ratio is infinite.
- The slew rate is 0.

**Inverting op amp**

Op-amp has various modes of operations. Inverting Operational Amplifier represents the type of process in which the input signal is provided through the inverting terminal of the op-amp. The phase of the amplifier’s output gets inverted in the amplification process. The inverting op-amp has a higher gain than non-inverting Operational Amplifier.

**Non inverting op amp**

Non-inverting is another mode of operation using an op amp. Here, the input signal is provided using the op amp’s non-inverting terminal. Thus, the output phase remains the same and does not get inverted in operation. That is why this operation using an op amp is known as a ‘non-inverting op amp.’ This op amp provides higher system stability due to the negative feedback system, but it has lesser gain than an inverting op amp. Between a non-inverting op amp and an inverting op amp, an inverting amplifier is given more preferences.

**Op amp circuits | Basic op amp circuits**

The circuits of op-amps are specific for their operations. An Operational Amplifier is capable of performing several mathematical operations. Circuits are made according to the need. The below image represents a typical circuit symbol of an op-amp.

We can observe that an op-amp has two inputs (marked as 1 and 2). The input labeled with the ‘-‘ is the inverting terminal. The input labeled with the ‘+’ sign is the non-inverting terminal. The voltage connection couple, shown as +Vsat and -Vsat, are the positive saturation voltage and negative saturation voltage, represent the highest and lowest Operational Amplifier limit; those can be observed at the output.

The saturation voltages are applied to the op-amp to balance the operational amplifier concerning the ground. The output is collected from the ‘O’ terminal.

**741 op amp**

Op-amps are now available in markets via ICs. One such IC is the 741 Operational Amplifier. It is a monolithic IC (all the connections are formed on a single piece of crystalline silicon). The IC consists of one op-amp. Fairchild Semiconductor in the early sixties first developed it. The number 741 indicates that the IC has seven functional pins, four input pins, and one output pin.

**741 op amp pinout**

The following diagram gives the pinout of the IC. The IC’s terminology consisting of an operational amplifier describes the pins as well. The number 7 from 741 represents seven functional pins, four input pins, and one output pin.

**741 op amp schematic**

The following mage represents the schematic diagram of a 741Operational Amplifier.

**Op amp integrator**

We have mentioned earlier, and an Operational Amplifier can do several mathematical operations. Let us find out how an Operational Amplifier can do an ‘integration’ operation over an input signal. To implement the integrator using an op-amp, we need a capacitor and a couple of resistors, and an op-amp! The below circuit diagram depicts the op amp integrator circuit.

**Operation of integrator**

The concept of virtual ground – works because of assuming the OP AMP’s infinite gain. That is why the ‘A’ node in the image is a virtual ground. Let the current ‘i’ flow through the resistance R. So, the current could be measured as i = V1/R.

Here, V1 is the input voltage provided in the inverting terminal, and the non-inverting terminal is grounded with a resistor and due to high input impedance, the same current will flow thru the feedback path, having a capacitor in that. So, the output voltage can be written as:

Vo = – 1/C 0 t [i dt ]

Or, Vo = – 1/RC 0 t [V1 dt]

Thus, we can say that the output voltage is proportional to the input voltage’s time integral and That is why the circuit is termed as integrator or Miller integrator.

**Op amp comparator**

An op-amp comparator or a voltage comparator, or a comparator, is an electronics device that compares two input voltages and provides an indicative output. The output indicates which of the two inputs voltage is more extraordinary in values.

The op-amp is designed in open circuit configurations to use an Operational Amplifier as a comparator.

- If the voltage in the non-inverting terminal is higher than the voltage in the inverting terminal, the output is switched to the op-amp’s positive saturation voltage.
- If the inverting terminal voltage is greter than the voltage in the non-inverting terminal, the o/p is switched to the -ve saturation voltage of the Operational Amplifier.

**Op amp comparator circuit**

The below image represents the Operational Amplifier comparator circuit.

**Op amp gain**

The op-amp gain refers to the ratio of the output voltage to the input voltage and Operational Amplifier has two types of gain as follows.

**Closed-loop Gain:**If the Operational Amplifier system has a feedback system associated with it, then the system’s gain is known as the closed-loop gain.**Open Looped Gain:**If the Operational Amplifier circuit doesn’t have a feedback system associated with it, then the gain is open-loop gain.

For an ideal Operational Amplifier, the gain is infinite for any frequencies. For real amplifiers, the gain is an absolute constant. Gain is the parameter of performance for the amplifier.

**Non inverting op amp gain**

The general expression of the non-inverting amplifier’s output voltage is: **Vout = k * Vin**

The output equation of the non-inverting amplifier is: **V0 = [ 1 + (Rf/R1)] * Vin**

So, comparing both the equation, the value of k will be

**k =** **[ 1 + (Rf/R1)]**

This expression of the resistor is known as the non-inverting amplifier’s gain. We can observe that if Rf = R1, Vo = 2 * Vin. So, the input voltage gets amplified by a factor of 2. The (Rf/R1) ratio typically controls the gain. Increasing Rf increases the gain value.

**Op amp buffer**

An op-amp buffer or a unity gain buffer, or a voltage follower circuit is a specially designed non-inverting amplifier model. Observe the circuit of the non-inverting amplifier given above. If we made the feedback resistance zero and the inverting terminal infinite resistance, the amplifier’s gain would be unity. That is why this circuit is known as unity gain buffer. This buffer is used for impedance matching.

**Differential op amp**

Differential Operational Amplifier or difference amplifier is the op-amp that amplifies the difference between the two input voltages and provides that as output and performs the subtraction operation, unlike a summing amplifier which adds up the input voltages.

The below circuit depicts the circuit of a differential amplifier.

**Operations**

Using the concept of virtual ground, we can conclude that the voltage at node A is the same as the voltage at node B. Using KCL, we can write that –

**(V1 – Vx) / R1 = (Vx – VO) / R2**

& **(V2 – Vx) / R1 = Vx /R2**

Here, V1 is the input voltage. Vx is the voltage at A node (as well as B). Vo is the output voltage. Now we assume that the Operational Amplifier has high input impedance. Comparing and using both the equations, we can write –

**Vo = (V2 – V1) * R2 / R1**

This output equation justifies the operation.

**Inverting op amp gain**

The general expression of the inverting amplifier’s output voltage is: **Vout = -k * Vin**

The output equation of the inverting amplifier is: **V0 = – (Rf/R1) * Vin**

Now, comparing both the equation, we can say –

**k =** **(Rf/R1)**

It is the closed-loop gain of the inverting amplifier.

**Summing op amp**

Summing Operational Amplifier or adder op-amp is the amplifier that amplifies the input voltages’ summation and provides as output. It performs summation or addition operation, unlike a differential amplifier which performs subtraction operations.

The below image represents the summing Operational Amplifier.

**Operation**

Using the virtual ground concept, the potential at the A node is the same as the potential at the B node. Applying KCL, we can write –

**I1 +I2 +I3 +…+IN = IO**

**Or, V1 /R1 + V2/R2 + … +Vn/Rn = – Vo/Rf**

**Or, Vo = – [(V1*Rf/R1) + (Rf*V2/R2) + … + (Rf*Vn/Rn)**

**Now if R1 = R2 = … = Rn = Rf, then we can write –**

**Vo = – [V1 + V2 + … +Vn]**

**Voltage Follower op amp | Op amp follower**

A voltage follower op amp or a unity gain buffer, or a voltage follower circuit is a specially designed non-inverting amplifier model and if we made the feedback resistance zero and the inverting terminal infinite resistance, the amplifier’s gain would be unity. As the output voltage is just following the input voltage without amplification, the amplifier is known as voltage follower op ap. That is why this circuit is also known as a unity-gain buffer. This buffer is used for impedance matching.

**Discrete op amp**

The discrete op-amp is built to provide the minimal residual between the positive and negative inputs, thus further causes high gain. Discrete op-amps are generally used for audio applications rather than conventional op-amps. It has several advantages over the conventional op-amps as custom design is possible, needs lesser components, provides better temperature stability, etc.

**Lm741 op amp**

The lm741 is a monolithic IC that has one op amp inside it. It has eight pins. The IC doesn’t require external frequency compensation. It provides higher CMRR and consumes lesser power. The pinout of lm741 is given below.

Pin Number | Description |

1, 5 | Offset NULL for removal of offset and balancing with the ground. |

2 | Inverting Input terminal |

3 | Non-inverting terminal |

4 | Negative Saturation voltage |

6 | Output of the op amp |

7 | Positive Saturation voltage |

8 | No connection (NC) |

**Op amp differentiator**

Op-amp differentiator or differential op-amp performs the differentiation operation over an input voltage signal. To implement the differentiator using an op-amp, we need a capacitor and a couple of resistors, and an op-amp! The below circuit diagram depicts the op amp differentiator circuit.

<image: diff1>

**Op amp equations**

Op-amp equations are generally referred to as the output equations of an op-amp. The output equations represent the relation between the input and output voltages. The gain factor can also be determined from the output equations. Some of the output equations of some basic amplifiers are given below.

Non inverting op amp equations: **V0 = [ 1 + (Rf/R1)] * Vin**

Inverting op amp equations: **V0 = – (Rf/R1) * Vin**

**Op amp types**

Op-amp has several types rather than several modes of operations. Different types of op-amp perform various mathematical operations. Some of them are –

- Inverting op amp
- Non inverting op amp
- Difference op amp
- Summing amplifier
- Integrator
- Differential amplifier
- Logarithmic amplifier
- Comparator
- Current to voltage converter
- Voltage to current converter

**Inverting vs non inverting op amp**

Let us do a comparative analysis between inverting and non-inverting op amp.

Subject of Comparison. | Inverting op-amp | Non-inverting op-amp |

Input Terminal | Input is provided through the inverting terminal. | Input is provided through a non-inverting terminal. |

Output polarity | The polarity of the input voltage gets changed in the output. | The polarity of the input remains the same in the output. |

Gain | Gain is given as: Av = -(Rf/R1) | Gain is given as: Av = (1 + Rf/R1) |

Input impedances | The input impedance is lesser than the non-inverting op amp. | Input impedance is higher than inverting op amp. |

Output phase | The input and output are in phase. | The input and output are out of phase. |

**Negative feedback op amp**

For a closed-loop system of an op-amp, if the feedback system is connected to the inverting terminal of the op-amp, the feedback system is known as the negative feedback. An op-amp operating with negative feedback incorporated with it is known as negative feedback. Negative feedback op-amps have better system stability, but the gain is lower than positive feedback Operational Amplifier.

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