Table of Contents

**Operational amplifier:**

The basic job of an amplifier is to amplify the input signal. In early days when digital computers were not evolved, at that time the different mathematical functions like addition, subtraction, integration, and differentiation were performed using this operational amplifier. So, just by connecting few resistors and capacitors, it is possible to perform the different mathematical operations.

It consists of two inputs and one output. Most of the operational amplifiers consist of two power supplies. The positive and the negative power supply. But there are many op-amp IC’s which runs on the single power supply. So, now in this operational amplifier, the input terminal which is marked by this positive sign is known as the non-inverting input terminal and another input terminal which is marked by this negative sign is the known as the inverting input terminal.

So, now if you see this operational amplifier, it is one kind of differential amplifier with the singal output. It means that this amplifier amplifies the difference between the two input signals. So, let’s say V1 and V2 are the input signals which is being applied to this operational amplifier and let’s say the gain of this operational amplifier is A, then the output will be equal:

V_{out}=A (V_{1}– V_{2})

if we have applied the single input to this operational amplifier and we have grounded another input terminal then at the output you will get A times V1. Where A is the open loop gain of this operational Amplifier.

When there is no feedback from the output to the input side. So, suppose if you are applying the sinusoidal signal over here, then at the output that sinusoidal signal should be get multiplied

by the factor of this gain and at the output, you should get the amplified sinusoidal signal. Now, here the phase of this output voltage will be the same as the input voltage.

Likewise, whenever we are applying input to this negative terminal, and we are grounding another terminal then the output of this amplifier will be equal to minus A times the V2 because the difference between these two input terminals will be equal to 0 minus V2, that is equal to minus V2.

**Inverting terminal:**

So, suppose let’s say if we are applying the sinusoidal signal at the input then at the output we will get the amplified sinusoidal signal which is having a 180-degree phase with respect to the input signal. That means the output will be get inverted by 180 degrees. And that is why this input terminal is known

as the inverting terminal. Because the output will be get inverted with respect to the input.

So, now here suppose if we apply the input signal between these two positive and the negative terminals then at the output we will get A times this differential input signal. Where here this A represents the open-loop gain of this operational amplifier.

Now, this operational amplifier is a very high gain amplifier. The value of gain used to be in the range

Of 10^{5} to 10^{6} So, let’s say, even if we apply the 1 mV of a signal between these two terminals, and let’s say if the gain of this op-amp is then at the output theoretically we should get 1 mV signal that is multiplied by 10^{5 }that is equal to 100V. Or let’s say if we apply 1V of a signal, then theoretically, we should get the output as 10^{5 }volts but that is not possible.

The output of this op-amp is restricted by the biasing voltages that are being applied to this op-amp. So, the output voltage will be between these biasing voltages.

**Positive and negative Feedback of operational amplifier:**

We know that any circuit has two major parameters such as input and output. A condition in which some part of the output is fed back to the input is called as a feedback. In case of an op-amp we have two types of feedbacks such as positive feedback and a negative feedback. When some part of an output is fed back to a non-inverting terminal of an op-amp it is called as a positive feedback and when some part of an output is fed back to the inverting terminal of an op-amp it is called as a negative feedback resistor RF is called as a feedback resistor.

**Virtual ground:**

A virtual ground concept the input impedance of an op-amp is very high hence an op-amp never draws any current at its input an input current is always zero amperes for current to be 0 the voltage must be 0. Let’s assume that some input is applied to an inverting terminal keeping a non-inverting terminal at the ground even though the input is applied an inverting terminal also behaves as a ground terminal at node a this concept is called as a virtual ground concept.

**Op Amp Parameters:**

We will learn different parameters of op-amp as voltage gain, input impedance, output impedance, input offset voltage, input offset current, input bias current and bandwidth.

**Voltage gain:**

Let’s start with the voltage gain it is defined as the ratio of output voltage to input voltage.

**Input impedance:**

The second term is an input impedance the resistance offered by the input terminals of an op-amp is called as an input impedance. The voltage drop at the input of an op-amp must be very high hence the input impedance of an op-amp is always very high due to equation V equals I into R.

**Output impedance:**

The third term is an output impedance the resistance offered by the output of an op-amp is called as an output impedance generally an output device like a speaker is connected next to an op-amp hence it is necessary that all the output of an op-amp must be passed to the next device in other words the voltage drop at output must be zero hence output impedance must be as low as possible.

**Input offset voltage:**

The fourth term that we learn is an input offset voltage when input to an op-amp is zero the output should be zero ideally but if it’s not zero we need to apply some DC voltage at the input terminal to force the output voltage to be zero this applied voltage is called as an input offset voltage.

**Input offset current:**

The next term we study is an input offset current. The difference between the currents into the two input terminals when the output is held at zero is called as an input offset current.

**Bias current:**

The sixth term is an input bias current the average of the currents into the two input terminals with the output at zero volts is called as an input bias current.

**Bandwidth:**

The last term is a bandwidth the range of frequencies for which an op-amp can be used is called as a bandwidth of an op-amp.

**Operational Amplifier as wave form generator:**

An op-amp can also be used as a waveform generator. Here it generates different waveforms such as a square wave, triangular wave etc. First we will see an op-amp as a square wave generator. The schematic diagram for this application is as shown as we can see a capacitor C is connected to an inverting terminal and resistances and are connected to a non-inverting terminal.

Resistor R is connected as a negative feedback to the inverting terminal forming the RC circuit. As soon as the op-amp is supplied with the supply voltages +V and –V. We get some output as without any input applied the output should be zero but practically we get some nonzero output. R_a and R_b form a voltage divider network. Thus if initial V_out is nonzero. We get voltage across V_b also as nonzero thus we get a positive input at the non-inverting and inverting terminals and the output gets amplified by its gain say AV and reaches its maximum value V_{out} max thus we get the positive half of the square wave as we have a nonzero input at the inverting terminal. Now a capacitor also starts charging it will charge continuously till its voltage becomes greater than V_{b} as soon as voltage V_{c} is greater than V_{b} the inverting input becomes greater than the non-inverting input and hence op-amp output switches to negative voltage and gets amplified till minus vo max. Thus we get the negative half of the square wave this is the application of an op-amp as a square wave generator.

Now we see an op-amp as a triangular wave generator we have already seen that the output of the integrator is a triangular wave if the input given to it is a square wave thus to construct the triangular wave generator we combine two circuits such as a square wave generator followed by an integrator as shown and at the output of an integrator we get a triangular signal.

## Operational amplifier as differentiator:

An op-amp is a differentiator for this we replace the input resistor with the capacitor as shown applying KCl at node “A”

if I_{f} equals to I_{c} from the diagram the current I_{f} is equals to:

I_{f}= (V_{a}– V_{out} )/R

The current flowing through a capacitor:

I_{c}= (CdV_{c})/dt

(V_{a}– V_{out} )/R= (CdV_{c})/dt

(V_{a}– V_{out} )/R= (Cd(V_{in}-V_{a} ))/dt

But V_{a}=0 virtual ground concept.

(- V_{out} )/R= (Cd(V_{in} ))/dt

V_{out} = (RC*d(V_{in} ))/dt

If RC is equal to gain A_{v}.

V_{out} = (A_{v}*dV_{in})/dt

We can see if we take R into C as a gain of an amplifier then the output is the differentiation of an input hence it is called as a differentiator.

## Operational amplifier as Integrator:

The next use of an op-amp is an integrator. If we interchange the position of the capacitor and the resistor of a differentiator circuit. We get the circuit of an op-amp as an integrator applying KCl at node “A”.

**Operational amplifier as difference amplifier:**

The next application of an op-amp is a difference amplifier. Here we apply KCl at both the nodes node a and node B applying KCl at node B.

If we consider Z as a gain of op-amp then the output is an amplified version of the difference between two inputs hence it is called as a difference amplifier.

**Operational amplifier as summing amplifier:**

An op-amp is also used for mathematical operations we will start with an op-amp as a summing amplifier we have three inputs as v1 v2 and v3 given to an inverting terminal of an op-amp with the currents as i1 i2 and i3. Applying KCl at node “X”:

Vx = 0 virtual ground concept.

Rearranging the equation in terms of V out we get V out equals:

We can see an output is an amplified version of the sum of all the input signals it is called as a summing amplifier.