Concept of Virtual Ground

Concept of Virtual Ground in Operational Amplifiers

Virtual Ground concept forms the basics of most of the Op-Amp applications. Often most of us know the definition of the virtual ground concept. i.e. the voltage at inverting terminal is equal to the voltage at not inverting terminal but the definition here is not complete. It does not specify the conditions where the virtual ground concept can be applied, or what are the limitations of the virtual ground concept. So here in this blog today we will discuss everything about the virtual ground starting from the basics and see the applications and utility of this concept.

An Op-Amp amplifies the difference of the voltages between the non-inverting and inverting terminal.

The gain of a practical open loop Op-Amp is infinite.

Mathematically:

For A_OL to be infinite there are two possibilities:

V_o can be infinite or

V_id can be zero

Since the output voltage of the Op-Amp is limited by its operating voltages (+V_cc and -V_EE),

The output voltage cannot be infinity.

The only possibility left is to make V_id approach zero:

V_id  =  V ⁺ – V ^– = 0

V ⁺  =  V ^–

i.e. voltage at inverting terminal follows the voltage non-inverting terminal.

This is only the half-truth, there are conditions when this statement is valid and there are conditions when this condition is not valid. Those conditions will be discussed in the blog.

Test Yourself Question:

Question. If the voltage at inverting and non-inverting terminal are the same, then the difference voltage is mathematically (V ⁺ – V ^– = 0) zero. Then what voltage does Op-Amp amplifies?

Note* Answer to this question is at the end of the blog.

Application of Virtual Ground in Analyzing Op-Amp Circuits

1. Inverting Amplifier:

Consider an ideal Op-Amp circuit connected below in a negative feedback configuration:

Since the inverting terminal is connected to ground ( V ⁺  = 0 ), using the virtual ground concept:

V ^– = V ⁺  = 0

Apply Nodal Analysis to the inverting terminal V ^–

The negative sign shows the output and input have a phase shift of 180°

i.e. the output voltage is inverted of the input voltage.

Hence the Op-Amp in this configuration is known as “Inverting Amplifier”

Note:

The important point to note here is that the gain of the Op-Amp is no longer infinite.

It is the ratio of resistances.

As a designer, you can control the gain of the Op-Amp by choosing appropriate values of R₁ and R₂

When R₂ < R₁ the gain of the amplifier is less than 1.

This is the advantage of inverting amplifier over non-inverting amplifier where the gain less than 1 can be achieved.

2. Non-Inverting Amplifier:

In this application, the input voltage is applied to the non-inverting input of the Op-Amp.

Let us evaluate the gain of the Op-Amp for this configuration using a virtual ground concept.

Since the inverting terminal is connected to voltage V_s ( V ⁺  = V_s ), using the virtual ground concept:

V ^– = V ⁺  = V_s

Apply Nodal Analysis to the inverting terminal V ^–

The output voltage is in phase with the input voltage.

Hence the Op-Amp in this configuration is called “Non-Inverting amplifier”.

Note:

The important point to note here is that the gain of the Op-Amp is no longer infinite here also.

It is the ratio of resistances.

As a designer you can control the gain of the Op-Amp by choosing appropriate values of R₁ and R₂

The minimum gain that can be achieved in non-inverting Op-Amp configuration is 1.

The above two applications explain how the analysis of the Op-Amp circuits can be easily done using the virtual ground concept.

It is time now that we discuss here, where the virtual ground concept is applicable and where it not.

In the above two examples, the Op-Amp was considered ideal (i.e. it has infinite gain and infinite input resistance) and connected in a negative feedback configuration

What if the Op-Amp was non-ideal i.e. with finite gain?

What if the Op-Amp had positive feedback or No – feedback?

Let us discuss these points here:

A) A Practical Op-Amp/ Op-Amp with Finite Gain (A_OL) and Negative Feedback :

Consider an Op-Amp circuit connected in negative feedback:

Case 1: Ideal Op-Amp with infinite gain (A_OL  = ∞ )

In this case the open is ideal and the gain is:

This is the case where our virtual ground is valid, and gain is calculated directly.

Case 2: Practical Op-Amp with finite gain (A_OL = 20 )

The gain, in this case, is finite and small to evaluate the gain we do not use the virtual ground here.

We go by the circuit analysis and if the gain comes equal to gain calculated by the virtual ground concept in case 1, then we say the virtual ground concept is valid otherwise not.

To find V ^– , apply Nodal Analysis

Substitute value of V ^– from (2) in (1)

Solving the above equation gives

Conclusion:

The gain in this case of a non-ideal Op-Amp with a finite gain is not the same as that of an ideal Op-Amp.

The closed loop gain of a practical Op-Amp is less than that of an ideal Op-Amp

Hence virtual ground concept is not valid in case of a practical Op-Amp with finite gain.

Case 3: Practical Op-Amp with finite but very large gain (A_OL = 10⁶ )

From the discussion of case 2

Substituting (2) in (1)

Conclusion:

Even though the gain of the amplifier is not infinite, but it is large enough to be considered as an ideal amplifier.

Hence practical Op-Amp with very high gain can be analyzed using virtual ground concept.

B) Ideal Op-Amp in Open Loop Configuration:

Consider an Op-Amp circuit in an open loop configuration with input terminal voltages as shown in the figure:

V ^– = 1 V

V ⁺ = 0 V

The voltages at inverting and non-inverting terminals are forced to a value.

1 V and 0 V can never be equal

In general V ^– ≠ V ⁺

For the above Op-Amp

V ^– > V ⁺  , the Op-Amp will go into negative saturation

When

V ^– < V ⁺ , the Op-Amp goes into positive saturation

Conclusion:

Even though the gain of the amplifier is not infinite, but it is large enough to be considered as an ideal amplifier.

Hence practical op-amp with very high gain can be analyzed using virtual ground concept.

C) Ideal Op-Amp in a Positive Feedback Configuration:

Positive feedback provides the feedback voltage that is in phase with the input voltage.

The net effect of positive feedback is increase in the voltage at the non-inverting terminal.

The feedback voltage aids the input voltage

Thus, the difference voltage keeps on increasing

For virtual ground we need V ^– = V ⁺ , i.e. difference voltage should eventually decrease

Conclusion:

Virtual ground concept is not valid here in a positive feedback configuration.

Overall Conclusion:

Virtual ground concept is valid for :

Negative feedback system with infinite gain

Negative feedback system with a very large gain

Virtual ground concept is not valid for:

Positive feedback system.

Open loop system

You can also download Concept on Virtual Ground as PDF for last minute preparation

Concept on Virtual Ground Study Notes – Download as PDF

Test Yourself Solution:

Solution: Virtual ground concept is valid only for a negative feedback system.
Mathematically it can be said:
V ^– = V ⁺
But practically they are not the same, there is a very very small difference between the two voltages which is amplified by the Op-Amp.

Practice Question:

Following figures show 5 different cases in which Op-Amp is connected. Find out in which of the configuration is the virtual ground concept valid.