# Basics of Operational Amplifiers

## Introduction – Operational Amplifier

Operational-amplifiers is basically amplifier. And the basic job of an amplifier is to amplify the input signal.

### Why operational amplifiers ?

As the name itself suggests operational, operational amplifier performs different mathematical operations. For example addition, subtraction, integration, and differentiation. So, just by connecting few resistors and capacitors, it is possible to perform the different mathematical operations. Hence, known as the operational amplifier.

### Circuit Symbol

Now if you see this circuit symbol of the operational amplifier, it can be represented by this symbol.

Operational Amplifiers consists of two inputs and one output. And 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.

### Operational Amplifiers pin arrangements

In operational amplifier, there are different terminals. The positive marked input terminal is the non-inverting input terminal. And negative marked input terminal 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 single output. It means that this amplifier amplifies the difference between the two input signals. Input is applied with V1 and V2 on Op-amp. Let’s say the gain of this operational amplifier is A. So the output will be equal to A times the V1 minus V2.

Vout = A(V1-V2)

### Working of Operational Amplifiers

Assuming we have applied the single input to this operational amplifier and we have grounded another input terminal. At the output you will get A times V1.Where A is the open loop gain of this operational amplifier. Open loop gain has no feedback from the output to the input side. Suppose if you are applying the sinusoidal signal over here. The output you get is the multiplication of the Sinusoidal signal and the gain. Hence 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, when we apply input to this negative terminal, and grounding another terminal. The difference between these two input terminals will be equal to 0 minus V2, that is equal to -V2.The output of this operational amplifier will be equal to minus A times the V2 i.e. -V2.

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. Hence, the output is inverted. Due to inverting output it is the inverting terminal.

### Calculations

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. And the value of gain used to be in the range of 10^5 to 10^6. If we apply 1 mV of signal between these two terminals, and if the gain of this op-amp is 10^5. Then the output 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.

Therefor to restrict the output, biasing voltage is used. Hence, the output voltage will be between these biasing voltages.

### Voltage Transfer Curve of Operational Amplifiers

If you looking at the voltage transfer curve of op-amp then it will look like this.

Here the X-axis represents the differential input . Y-axis represents the output voltage of the amplifier. Here the slope represents the gain of the amplifier, used to be in the range of 10^5 to the 10^ 6. Now, here let’s say if the gain of the op-amps 10^6. And we are applying 1 microvolt of a signal. Then at the output, we should get 1V of signal. Likewise, let’s say if we apply 10 microvolts of a signal, then at the output, we will get10 V of output.

If we continuously increase the input signal. After certain value the output is under +Vsat. Which is less than the positive biasing supply.

This saturation is same for negative voltage also . So, as soon as the input voltage goes beyond some threshold value at the output you will get minus saturation voltage.

### Operational Amplifier Applications

When operational amplifier used in open loop configuration. When there is no feedback. If we apply small input signal between these two input terminals, then also you will find that the output will be get saturated towards the positive or the negative biasing voltages. This particular characteristic of the op-amp is particularly useful when we use this op-amp as a comparator.

But if you see this op-amp, this op-amp can also be used in some any other applications. Like, in designing the

• Active filters,
• Oscillators,
• Waveform converters
• Analog to digital converters
• Digital to analog converters.

And if we count the list, then the list will go on. The op-amp is very versatile IC and you will find this op-amp in so many applications because of its different characteristics. Different characteristics makes it very versatile and used in different applications.

Before we see that let’s see the equivalent circuit of the op-amp. So, as you can see here, this Ri is the input impedance of this op-amp. Likewise, this Ro represents the output impedance of this op-amp. And the output voltage of the op-amp will be the open-loop gain multiplied by the difference between the input signals V1 and V2. Now before we see the different characteristics of the op-amp, let’s see the different characteristics of the ideal op-amp.

### Characteristics of Ideal Operational Amplifiers

• The ideal op-amp should have this input impedance Ri that is equal to infinity. Because whatever input that is being applied between the input terminals will directly get applied to the op-amp.
• Similarly, the output impedance of this op-amp should be equal to zero. That means whenever we are applying the output load to this op-amp then the output voltage should directly come across this output load.
• The bandwidth of the idea lop-amp, the bandwidth of the ideal op-amp should also be equal to infinity. It means it should support all the frequencies starting from the zero Hertz to the infinite.
• The gain of the ideal op-amp should also be equal to infinite. Apart from that whenever these two input terminals are zero, that means the input to this op-amps zero, at that time the output of this idea lop-amp should be equal to zero.

Now, apart from these operational amplifier characteristics, there are few more characteristics of the idea lop-amp that is slew rate and the common mode rejection ratio.

#### Slew rate and common mode rejection ratio

So, will see more about these different characteristics in detail in separate post. But let’s see the basics of this different characteristics.

In a simple way, the slew rate is basically how fast the op-amp is able to reach its final value. In that is particularly useful when we are applying a square wave to the op-amp.

So, let’s say we have applied the square wave to the input of this op-amp and at the output, we are getting this output waveform. That is varying from zero volts to the V saturation voltage. The ideal op-amp should be able to reach from the zero volts to the Vsat volt in zero time.

• The ideal op-amp, the slew rate should be equal to infinity.

Generally, this slew rate is defined in the unit of Volt per microseconds. That means the how fast the op-amp is able to respond to the output voltage.

Then there is another parameter, which is known as the common mode rejection ratio. Let’s understand very briefly what do we mean by this common mode rejection ratio.

If we are applying the same input voltage to this V1 and V2 then the difference between these two voltages will be equal to zero and at the output, we should get zero volts. Likewise, when we are applying different input voltages V1 and V2 to this op-amp then at the output the difference between these two voltages will be get amplified by certain amplifier gain.

So, this common mode rejection ratio basically defines how well the op-amp is able to reject the common input voltages that are being applied to both its input terminals and how well it is able to amplify the difference between the two voltages.

And it is generally defined as the ratio of differential gain divide by the common mode gain.

• The ideal op-amp, the value of this common mode rejection ratio should be equal to infinity.

### Ideal Vs practical Operational Amplifiers

So, here is the list of different ideal operational amplifier characteristics. The ideal op-amp has infinite input impedance, zero output impedance, infinite open loop gain and infinite bandwidth and slew rate.

And in this ideal op-amp, whenever the input is equal to zero then at that time the output is also zero. And this ideal op-amp has infinite common mode rejection ratio. But if you see any practical op-amps, they used to have finite input as well as the output impedance. Generally, this input impedance is in the range of megaohms, while the output impedance is in the range of few ohms. Similarly, the open loop gain of the op-amp is not infinity but it used to be in the range of 10^5 to the 10^6. Likewise, for the practical op-amps, when the input is equal to zero, at that time also you will get some output at the op-amp. Generally, it used to be in the range of few mV. That is known as the offset voltage.