Op-amp stands for operational amplifier. It is basically an amplifier and because it performs many mathematical operations, so it is called an operational amplifier. In the past time when digital computers were not available at that time different mathematical operations like addition, subtraction, integration, differentiation, etc were performed on these amplifiers. The figure shown below is a symbol of an op-amp.

Op-amp has two input pins which are v1 and v2 in the figure and one output pin which is V_{out} in the figure. V+ and V- is the power pins. If you have noticed, there are positive and negative signs marked on input terminals. The positive sign mark represents the non-inverting input terminal and the negative sign mark represents the inverting input terminal. If we apply an alternating signal on the non-inverting input terminal, the output does not invert but if we apply the signal on the inverting input terminal, it gets inverted.

For example, see these figures.

In the above figure, an AC signal is applied on the non-inverting input terminal and the output is not inverted but amplified.

In this figure, the AC signal is applied to the inverting input terminal, the output is magnified but inverted.

This amplifier amplifies the potential difference between these two input terminals. If the gain of an amplifier is A then the

V_{out} =A(V_{1 }– V_{2})

Where A = open-loop gain

Here open loop gain means that no feedback from the output to the input terminal. In this condition, the op-amp is called open loop configuration.

A= 10^{5} to 10^{6}

V_{d} = 1mV

V_{OUT} = 1mV x 10^{5}

= 100 V

If V_{d} = 1V

V_{OUT} = 10^{5} V (not possible)

The output voltage is restricted by the biasing voltage that is applied to this to this op-amp.

Table of Contents

### Concept of virtual ground

A_{OL} =10^{6}

V_{O} = A x V_{d}

10 = 10^{6} x V_{d}

V_{d} = 10µV

V^{+} – V^{–} = 10µV

V^{+} – V^{–} » 10µV

V^{+ }= V^{–}

It means that inverting and non-inverting input terminals are at the same potential. There is a virtual short between these input terminals. Because both input terminals are not actually shorted but they virtually act as short. So, it is called virtual ground.

Op-amp will try to keep the voltage on both input terminals the same. It will do so by using feedback from output to input. It will set the output such as it matches the input on another input terminal so that the voltage on both terminals remains the same because the output is connected to one of the input terminals.

The figure below is the op-amp equivalent circuit.

### Ideal op-amp characteristics

- Infinite input impedance ( R
_{i}=∞) - Zero output impedance ( R
_{O}= 0) - Infinite open loop gain ( A = ∞)
- Zero offset voltage (V
_{OUT}=0 when V_{in}= 0) - Infinite bandwidth and slew rate
- Infinite common mode rejection ratio (CMRR)

Op-amp 741 specification

## Op-amp with negative feedback

### Inverting op-amp

As the name suggests this configuration of the op-amp will invert the signal we have given on the input terminal. For that, we have to give the signal to the inverting terminal.

Now let’s understand the logic behind the inversion of the input signal. As we know till now the op-amp wants to keep the voltage on both terminals the same. We have connected the non-inverting terminal to the ground (0 volts).

So op-amp will want inverting terminal also to be at ground. But we are giving an input signal at the inverting terminal. So op-amp will have to set its output such that the voltage on the node ‘x’ should be 0 volts.

Input resistor R_{i} and feedback resistor R_{f} are acting like voltage dividers and diving the voltage between the input voltage and output voltage. The divided voltage is being fed to inverting terminal. So voltage on the inverting terminal will be voltage divided between the input voltage and output voltage and it should be zero. So op-amp should change the output voltage according to the input signal.

For example, we have designed an op-amp inverting amplifier that has a gain of 1. So if we apply a 1v signal then the output will be -1v. Then it will cancel the input voltage.

R_{in} = ∞

I_{i} = I_{f}

### Non- inverting op-amp

Here input signal doesn’t get inverted. We have to give the signal at the non-inverting terminal. Here also, the amplification concept is the same. Op-am will want that both input terminals should be on the same potential. So let’s consider that Ri and Rf are the same. So it will divide the output voltage in half at node ‘x’.

If we give a 1-volt signal then the output will be 2 volts. Half of the output voltage which is 1 volt will be applied to inverting terminal. This way potential on both terminals is the same.

Now you can understand that we change the gain by changing the resistor values.

### Inverting summing amplifier

In the figure below, we can see the circuit for inverting the summing amplifiers using op-amp. This circuit adds the voltages which we apply through the resistors. This circuit uses the inverting input to take inputs from resistors, so the output gets inverted. That is why we call this circuit an “inverting summing amplifier”.

Applying KVL,

### Non-inverting summing amplifier

The figure shown below is the circuit diagram of a non-inverting summing amplifier. This amplifier also adds voltages but this circuit uses the non-inverting terminal to input the voltages. So, the output does not invert.

### Differential amplifier

As we know the op-amp amplifies the potential difference between the input terminals. If gain of op-amp becomes unity then it will give only potential difference. The figure shown below is the circuit of differential amplifier.

### Integrator op-amp

This circuit (given below) integrates the input signal. In this circuit, a capacitor is used as feedback.

**Frequency response of ideal integrator**

#### Practical integrator using op-amp

A_{V} = -R_{f}/R

Where f_{L} = 3dB or cut-off frequency

F_{o} = 0dB frequency

Proper integration of an input signal, its frequency should be between f_{L} and f_{o}.

### Op-amp as differentiator

This circuit gives a derivative of the input signal. In an integrator circuit, if we interchange the position of resistor and capacitor, we will get the differentiator circuit. This circuit is mostly used for edge detection purposes. This means if we apply a square wave to the input, it will give a spike at every transition on the output terminal.

Where F_{0} = 0dB frequency

#### Practical op-amp differentiator

This circuit contains two low-pass filters. So, this circuit will have two cut-off frequencies.

**If f _{1} > f_{2}**

**If f _{1} = f_{2}**

### Comparator

Comparator is nothing but an op-amp with open loop gain. The difference is just that op-amps are designed for linear applications but comparators have low propagation delay and fast rise and fall time. That means the transition of output is very fast in the comparators. It has two inputs – inverting and non-inverting input. It compares the voltages between these two inputs. If the voltage of the non-inverting terminal is greater than the inverting terminal then the output of the comparator will be high else its output will be low.

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