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:

- Inverting operational amplifier
- Non-inverting operational amplifier
- Buffer amplifier or Voltage follower

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

## 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 180^{0} 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 (V_{s}) has been connected to the inverting terminal via the resistance R_{1}. The other resistor R_{F}, 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 A_{v} = -∞ and input resistance R_{i} = ∞.

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

Also Read:What is CMRR? | Common Mode Rejection Ratio

## 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 A_{v} = open loop voltage gain of Op-Amp

- As we know A
_{v}of an open loop Op-amp is ∞.

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

But, V_{d} = V_{1} – V_{2}

∴ V_{1} – V_{2} = 0

- As the non-inverting (+) terminal is connected to the ground, V
_{1}= 0. Sp from above equation V_{2}= 0. Thus V_{2}is as ground potential.

- Since the input resistance R
_{i}= ∞, the current going into the Op-amp will be zero. Therefore the current I that passes through R_{1}will also pass through R_{F}as shown in the figure. As voltage V_{2}= 0, the input voltage V_{s}is the voltage across R_{1}and the voltage across R_{F}is the output voltage.

- The input voltage, V
_{s}is given by,

V_{s} = I R_{1}

And the output voltage V_{0} is given by,

V_{0} = – I R_{F}

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

Substituting the expression for V_{0} and V_{s}, 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:

- The value of closed-loop voltage gain A
_{VF}does not depend on the value of open-loop voltage gain A_{v}. - The value of A
_{VF}can be very easily adjusted by adjusting the values of the resistor R_{F}and R_{1}. generally, the feedback resistor R_{F}is a potentiometer to adjust the gain to its desired value. - 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 R_{iF}

Referring to the above figure, we can conclude that the input resistance R_{i} is the resistance seen by the source V_{s}. Since V_{2} = 0 due to the virtual ground concept.

R_{i} = R (between point A and GND)

R_{iF} = R_{1}

Note:This shows that the input resistance of the inverting operational amplifier with ideal op-amp is equal to only R_{1}, (instead of ∞). This is the biggest disadvantage of inverting configuration.

### Closed loop output resistance R_{oF}

Referring to the above figure, we can write that,

R_{oF} = 0

This is because the output resistance of an ideal op-amp i.e. R_{0} = 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 180^{0} 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