# Inverting Operational Amplifier – Inverting Op Amp

In this lecture, we are going to discuss the Inverting Operational Amplifier. We will discuss the operation of inverting Op Amp, derivation of the closed-loop voltage gain of inverting operational amplifier, and input and output resistance.

There are three basic op-amp configurations:

Note that the inverting operational amplifier configuration discussed in this section, we assume that the used operational amplifier in this section is ideal.

Table of Contents

## Inverting Operational Amplifier

The circuit diagram of an inverting operational amplifier is shown in the figure below.

The signal which is to be the amplifier is applied at the inverting (-) terminal of Op-amp.

The amplified output signal will be 1800 out of phase with the input signal.

In other words, the output signal is inverted. Therefore this amplifier is known as the inverting operational amplifier.

Also Read: what is Op-amp? |Block diagram of op-amp

## Operation of Inverting Op Amp

The signal to be amplified (Vs) has been connected to the inverting terminal via the resistance R1. The other resistor RF, connected between the output and inverting terminals is called the feedback resistance. It introduced negative feedback.

The non-inverting (+) terminal is connected to the ground.

As the op-amp is an ideal operational amplifier, its open loop voltage gain Av = -∞ and input resistance Ri = ∞.

The input and output voltage waveforms are shown in the below figure. Output is an amplified and inverted version of the input signal Vs.

## Closed Loop Voltage Gain of Inverting Op Amp

• Looking at the figure of the inverting amplifier, we can write that,

\mathbf{V_0 = \left | A_V \right | \times V_d }

\therefore \mathbf{V_d = \frac{V_0} {\left | A_V \right |}}

Where Av = open loop voltage gain of Op-Amp

• As we know Av of an open loop Op-amp is ∞.

\therefore \mathbf{V_d = \frac{V_0} {\infty } = 0}

But, Vd = V1 – V2

∴ V1 – V2 = 0

• As the non-inverting (+) terminal is connected to the ground, V1 = 0. Sp from above equation V2 = 0. Thus V2 is as ground potential.
• Since the input resistance Ri = ∞, the current going into the Op-amp will be zero. Therefore the current I that passes through R1 will also pass through RF as shown in the figure. As voltage V2 = 0, the input voltage Vs is the voltage across R1 and the voltage across RF is the output voltage.
• The input voltage, Vs is given by,

Vs = I R1

And the output voltage V0 is given by,

V0 = – I RF

• Closed loop voltage gain \mathbf{A_{VF} = \frac{V_0}{V_s}}

Substituting the expression for V0 and Vs, we get

\boxed{\mathbf{A_{VF} = - \frac{IR_F}{IR_1} = -\frac{R_F}{R_1} }}

Note: The negative sign indicates that there is a phase shift between te input and output voltages.

From the above equation, we can draw the following important conclusions:

1. The value of closed-loop voltage gain AVF does not depend on the value of open-loop voltage gain Av.
2. The value of AVF can be very easily adjusted by adjusting the values of the resistor RF and R1. generally, the feedback resistor RF is a potentiometer to adjust the gain to its desired value.
3. The output is an amplified inverted version of an input.

Also Read: Ideal Differential Amplifier

## Ideal Closed Loop Characteristics of Inverting Op Amp

We have already obtained the value of the ideal closed-loop voltage gain on inverting operational amplifiers. Now let us obtain the ideal closed-loop input resistance and output resistance values of inverting op-amp.

### Closed loop input resistance RiF

Referring to the above figure, we can conclude that the input resistance Ri is the resistance seen by the source Vs. Since V2 = 0 due to the virtual ground concept.

Ri = R (between point A and GND)

RiF = R1

Note: This shows that the input resistance of the inverting operational amplifier with ideal op-amp is equal to only R1, (instead of ∞). This is the biggest disadvantage of inverting configuration.

### Closed loop output resistance RoF

Referring to the above figure, we can write that,

RoF = 0

This is because the output resistance of an ideal op-amp i.e. R0 = 0

## FAQs on Inverting Op Amp

Why is it called an inverting amplifier?

because the op-amp changes the phase angle of the output signal exactly 1800 degrees out of phase with respect to the input signal.

What are the main advantages of inverting amplifiers?

One advantage of the inverting amp is the offset voltage is added to the output so is < a few mV

What are the applications of inverting op-amp?

Inverting operational amplifiers are used in a number of applications like phase shifters, integration, signal balancing, mixer circuits, etc.

Is an inverting amplifier AC or DC?

DC amplifier

Hello friends, my name is Trupal Bhavsar, I am the Writer and Founder of this blog. I am Electronics Engineer(2014 pass out), Currently working as Junior Telecom Officer(B.S.N.L.) also I do Project Development, PCB designing and Teaching of Electronics Subjects.

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