# Inverting Op-Amp and The Concept of Virtual Ground in Op-Amp

Inverting Op-Amp Hey friends, Welcome to the Kohiki ALL ABOUT ELECTRONICS. So, in this article, we are going to talk about the inverting input configuration of the operational amplifier.

Inverting Op-Amp we will see the concept of virtual ground in the Op-Amp. Now, in the last article, we have seen the basics of this operational amplifier and we had seen that this op-amp is a very high gain differential amplifier.

Inverting Op-Amp and The Concept of Virtual Ground in Op-Amp

## What Is Op-Amp

Inverting Op-Amp The gains of the op-amp used to be in the range of 10 to the power 5 to the 10 to the power 6.

Inverting Op-Amp And we had seen that even if apply a very small amount of differential input voltage between the input terminals of the op-amp, then also the output will be get saturated towards the biasing points.

## Voltage Transfer Curve Of This Op-Amp

we had seen the voltage transfer curve of this op-amp. And then we had seen that even if we apply the small input voltage to this op-amp then also the output will get saturated either towards the positive or the negative saturation voltages.

Now, let’s say the saturation voltage for the op-amp is 10V, and the open-loop gain of this opamp is let’s say 10 to the power6. So, this op-amp will get saturated at 10 microvolts of a differential input voltage.

So, now whenever we want to use this op-amp as an amplifier, we need to use it in the linear region. That means in this region. So, the input and output have a linear relationship. But whenever we are using this op-amp in an open-loop configuration, then this linear range is very small.

## Op-Amp As An Amplifier

• One is providing feedback from output to this positive input terminal
• second is providing the feedback from output to this inverting input terminal

So, if we want to use this op-amp as an amplifier, then we need to somehow control the gain of this amplifier. And we can do so, by applying the feedback from the output to the input side.

So, there are two ways, by which we can apply this feedback. One is providing feedback from output to this positive input terminal. Or let’s say non-inverting input terminal. And the second is providing the feedback from output to this inverting input terminal.

### One is providing feedback from output to this positive input terminal

Now, whenever we are providing the feedback from this output to this non-inverting input then that kind of feedback is known as positive feedback.

Because here the fraction of an output voltage is getting added to this non-inverting input.

##### second is providing the feedback from output to this inverting input terminal

Now, whenever in any system we are using positive feedback, then this positive feedback leads that system to instability. So, we can not use this positive feedback alone. So now here to control the gain of the op-amp, we need to go for this negative feedback.

That means we need to feed the fraction of the output voltage to this inverting input terminal. Now, here three ways by which we can apply the input to this op-amp. The first is applying the input to this non-inverting input terminal and grounding this negative input terminal.

The second is providing the input to this inverting input terminal and grounding this positive terminal. And third is providing the input to both non-inverting as well as inverting input terminals. So, first, we will see the case when we are applying the input to this inverting input terminal.

## Inverting Op-Amp configuration

So, let’s say we have applied input to this inverting input terminal through one resistor R1.

Inverting Op-Amp And we are providing negative feedback from output to this inverting input terminal via this feedback resistor Rf.

So, now whenever op-amp is used in this configuration then this configuration is known as the inverting op-amp configuration.

So, now in this configuration let’s find out the relationship between this output and the input voltages. And let’s see how we can control the gain of op-amp by using this feedback resistor Rf and this resistor R1.

So, let’s find the relationship between this output and input in terms of this feedback resistor Rf and R1.

## Concept of Virtual Ground in Op-Amp

• So, now before we derive this expression, let’s understand the concept of virtual ground in the op-amp. And this concept of the virtual ground is applicable when we are providing negative feedback to this op-amp.
• Now, let’s say for the given op-amp the open-loop gain of this op-amp is 10 to the power 6.
• we know that the output voltage Vout of the op-amp can be given as A times the differential input voltage.
• That is the input voltage between these inverting and the non-inverting input terminals.
• Now, here let’s assume that through this negative feedback we are controlling the output voltage of this op-amp in such a way that the output voltage is always less than the saturation voltage.
• Or we can say that we are operating this op-amp in a linear region. So, let’s assume that the output voltage is 10 V.

So, we can say that 10V that is equal to 10to the power 6 times this differential input voltage. Or we can say that the differential input voltage is equal to 10 microvolts. Now, here this differential input voltage is nothing but the difference between this inverting and the non-inverting input terminals.

So, we can write this differential input voltage as (Vplus ) – (Vminus) that is equal to 10 microvolts. Now, here these 10 microvolts are a very small signal and we can almost neglect it. So, we can write this (Vplus) – (Vminus) approximately equal to zero volts. Or we can say that Vplus is equal to Vminus.

• inverting and the non-inverting

It means that the inverting and the non-inverting input terminals are at the same potential. Or we can say that there is a virtual short between this inverting and the non-inverting input terminals. Now, here the term virtual means that these two terminals are not actually short-circuited but they are virtually short-circuited.

So, whatever voltage appears at one terminal, the exact same voltage will appear at another terminal. So, now in this configuration, this non-inverting input terminal is grounded. So, we can say that Vplus is equal to zero. So, according to this conclusion, Vminus should be equal to zero. It means that this terminal is not actually grounded but it will act as a virtual ground.

• negative feedback

So, this negative feedback will ensure that the difference between this inverting and the non-inverting input is very small or we can say that it is almost negligible. And because of that, we can consider both input terminals at the same potential. So, this concept is known as the virtual ground concept. So, now let’s use this concept of the virtual ground and let’s derive the expression between this Vout and Vin.

## Derivation of Inverting Op-Amp Configuration

Now, here let’s say the current I1 is the current that is flowing through this resistor R1. And let’s say this node is node X. And let’s say the current that is flowing through this resistor Rf is If. Now, in the last article, we had seen that the op-amp has very high input impedance. Or if we consider the ideal op-amp then the input impedance of the op-amp is infinite.

It means that no current is entering into this op-amp. Or we can say that the current I am equal to zero. It means that I1 is equal to If. So, now we can write this I1 as, Vin minus Vx, divided by R1. Where Vx is the voltage at this particular node. Likewise, we can write this current If as Vx minus Vout, divide by Rf.

### concept of virtual ground

Now, if we apply the concept of virtual ground, then this node x should have zero potential. Because this non-inverting input terminal is grounded.

So, the value of Vx should be equal to zero. So, we can write this expression as Vin divided by R1 that is equal to minus Vout divide by Rf.

If we rearrange it then we can write it as Vout by Vin, which is equal to minus Rf divide by R1.

This expression is known as the closed-loop gain for this inverting op-amp configuration.

So, as you can see here, just by changing the value of this Rf and R1 we can control the gain of this op-amp.

We can use this op-amp as an amplifier. Now, here the negative sign indicates that the output voltage is 180 degrees out of phase with respect to the input voltage.

So, let’s say, if we have applied 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 is why this configuration of the op-amp is known as the inverting configuration. Because the output will be get inverted with respect to the input voltage.

So, let’s say in this case if Rf is equal to 2 kilo-ohms and R1 is equal to 1 kilo-ohm, then the gain of the op-amp will be equal to 2. and suppose if we apply the 1 volt of a signal, then at the output, we will get 2Vof a signal which is 180 degree out of phase with respect to 1V signal.

So, in this way, by controlling the value of Rf and R1, we can control the gain of this op-amp and we can use this op-amp as an amplifier.

So, I hope in this article, you understood the inverting op-amp configuration and the concept of virtual ground.

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