# Non-Inverting Op-Amp Gain

A non-inverting amplifier is a type of amplifier that is designed to amplify the input signal without changing its phase. In this post, we will discuss non-inverting op-amp gain, but before that, we need to know some theories about Non-Inverting amplifiers.

The non-inverting amplifier is another mode of operation of a standard amplifier. it is an op-amp circuit that is designed to provide a positive voltage gain. As we know, simple amplifiers have two terminals – inverting and non-inverting. When the input is supplied through non-inverting terminals, the mode of operation is known as a non-inverting amplifier. Look at the above picture of the non-inverting amp.

## Theory about Non-inverting Amplifier:

The working principle or theory behind a non-inverting amplifier is the same as an inverting amplifier. For a non-inverting amplifier, the input is supplied to the non-inverting terminal. The amplifier amplifies the output with a certain gain and produces it. The gain is dependent on the values of reference and feedback resistance. The feedback system is connected to the inverting amplifier to create negative feedback in the system. As the system has negative feedback, this amplifier has more stability but lower gain than inverting amplifiers with the same resistance values.

### Circuit Diagram of Non-inverting Amplifier:

The above figure depicts the circuit diagram of a non-inverting amplifier. In the diagram, carefully study the ‘I’ current diagram with the input voltage, R1 primary resistance, and Rf feedback resistance.

### Non-inverting Amplifier Design.

A quite simple and straightforward task is designing a non-inverting amplifier. Initially, the Op-Amp is set with its positive, and a Reference voltage and ground contacts are made as required.

Now as this is a non-inverting amplifier, the input voltage is supplied to the non-inverting, the inverting terminal is connected to the ground through a resistance, and the standard feedback resistor is connected to the output pin from the inverting amplifier supply.

### How does a Non-Inverting Amplifier Work?

The non-inverting amplifier amplifies the input signal supplied to the non-inverting amplifier and resistances in the amplifier design act as a gain factor of a certain mathematical equation.

Due to virtual grounding, the voltage at point B also appears at point ‘A’ in the end. Thus a node has the same voltage as the input voltage. Again, the same current will flow through the inverting terminal as in the feedback path.

## Derivation of Non-inverting Amplifier.

Let us take the non-inverting amplifier equation and other necessary formulas. Let’s consider the virtual shorting portion first.

So, the voltage at node B will be equal to the voltage at node A. So, we can write as-

VB = VA

And, VB = Vin.

Vin will thus appear at node A. Therefore, we can say,

VA = Vin.

Let us assume the output voltage is Vo. The feedback resistance is called Rf. The current presenter is ‘I’ through the reaction path. ‘I’ can be written below at Node “A”.

I = (Vo – VA) / Rf

Or, I = (Vo / Rf) – (VA / Rf) ———– (i)

The same current flows through the inverting terminal. Hence, the equation of this terminal,

I = (VA – 0) / R1 = VA / R1 = Vin / R1 ———– (ii)

Now, to Analysis the equations (i) & (ii), we can write –

```
(Vo / Rf) - (VA / Rf) = VA / R1
=> (Vo / Rf) - (Vin / Rf) = Vin / R1 [Replaced, VA= Vin]
=> Vo / Rf = Vin / R1 + (Vin / Rf)
=> Vo / Rf = Vin [(1 / R1) + (1 / Rf)]
=> Vo / Rf = Vin [(Rf + R1) / (R1 Rf)]
=> Vo = Vin [(Rf + R1) / R1]
=> Vo = Vin [1 + (Rf / R1)] ----------- (iii)
```

For the non-inverting amplifier, this is the final output equation or formula.

## Equation of Non-inverting Amplifier:

In the above discussion, we have got equation (iii). It is the final output equation of the non-inverting amplifier circuit that is known as the non-inverting amplifier equation. The equation gives the relationship between the input and output voltages. The gain factor can also be noticed in the equation.

Vo = Vin [1 + (Rf / R1)]

This is the non-inverting amplifier equation. Rf is the feedback resistance, and R1 is the resistance connected to the inverting terminal. These resistance values affect the input voltage. Here, we can observe that if the value of (Rf/R1) is greater than 1, then we have gained in the system. So, we can say the (Rf/R1) factor needs to be increased as much as possible.

## Non-Inverting Amplifier Vout.

The volt or output voltage of a non-inverting amplifier tells us why this operation set in the amplifier is called a non-inverting amplifier. The equation of the non-inverting amplifier output is given as –

Vo = Vin [1 + (Rf / R1)].

From the above equation, we can observe that the output and input voltage are in the same operation. Unlike inverting terminals, the output of the amplifier is not inverted to a negative phase. For that reason, the operation set is well-known as a non-inverting amplifier.

## Input Impedance of Non-Inverting Amplifier:

An ideal op-amp has the property of high input impedance and that is why every amplifier is designed to produce a higher input impedance. Non-inverting amplifiers are no exception. They show higher input impedance in operations.

## Non-Inverting Amplifier Gain:

The non-inverting amplifier output is the product of the amplifier’s input and gain. The gain of the amplifier depends on the impedance values and the type of feedback of the amplifier. For a negative feedback system, the gain is decreased, and the system stability is increased and for positive feedback, the gain is higher, but the power of the system is decreased.

For the equation: Vo = K * Vin, Where “K” is the gain of the amplifier.

**Points to note:** Gain is the ratio of the supplied input voltage to the output voltage. That’s why it has no units.

## Non-inverting Amplifier Gain, Vo.

We discussed earlier what gain is for a non-inverting amplifier. Let us find the exact expression for the gain of a non-inverting amplifier.

The general expression for the output voltage of an amplifier is –

Vo = K * Vin ————- (iv)

From the non-inverting amplifier output equation, we know that-

Vo = [1 + (Rf / R1)] * Vin ————- (iii)

So, K can be calculated by comparing the above two equations.

K = [1 + (Rf / R1)] ————- (v)

This expression of the register is known as the gain of the non-inverting amplifier and from this, we can observe that if Rf = R1, Vo = 2 * Vin.

So, the input voltage is amplified by a factor of 2, (Rf/R1) ratio which usually controls the gain. Increasing the Rf increases the gain value.

#### Recommended:

- Characteristics of an Ideal Operational Amplifier
- 741 Operational Amplifier
- Basic Concept of Inverting Amplifier,
- Summing Amplifier,
- Difference Amplifier,
- Multiplication Amplifier,
- Division Amplifier,
- Concept of Integrating Operational Amplifier,
- The basic concept of Differentiating operational amplifiers,

## Negative Gain of Non-inverting Op-Amp.

A detailed analysis of the gain of the non-inverting op-amp is done before. The negative gain of the non-inverting op-amp is referred to as the correct gain of the amplifier. It is given a different name because the op-amp provides negative feedback. Although the term is confusing, many readers think it indicates that a non-inverting amplifier provides negative levels of gain.

## Bottom Line:

This amplifier is used for its higher impedance values and better stability due to negative feedback and gain. And the property of non-inverting amplifiers that give gain or resistance at the output makes them famous for circuit differentiation for cascade systems. So, to know more about this circuit keep your research continue and stay with us.

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