What is an Inverting Op Amp : Working & Its Applications

The configuration of an op-amp or operational amplifier can be done in two ways like inverting op-amp and non-inverting op-amp. In either of these  configurations, the output is given back to its input which is called feedback. This feedback is used in different functional circuits like oscillators, filters, amplifiers, different types of voltage regulators, rectifiers, etc. We know that operational amplifiers include two input terminals like positive & negative but the connection of feedback can be either to the positive or negative terminal.

Once the output is connected to the positive terminal of the operational amplifier, then the feedback is called positive. Similarly, if it is connected to a negative terminal then it is called a negative. The connection of output to the input can be done through an external resistor or feedback resistor. So feedback connection is used to control the gain accurately based on the application.

What is an Inverting Op-Amp?

The inverting op-amp or operational amplifier is an essential op-amp circuit configuration that uses a negative feedback connection. As the name suggests, the amplifier inverts the input signal and changes it.

An inverting op-amp is a type of operational amplifier circuit used to generate an output that is out of phase as compared to its input through 180 degrees which means, if the input signal is positive (+), then the output signal will be opposite. The inverting op-amp is designed through an op-amp with two resistors.

Inverting Operational Amplifier Configuration

The circuit diagram of an inverting op-amp is shown below. In this circuit, the negative terminal is connected through feedback to create a closed-loop operation. While working with op-amps, we need to remember two essential rules like there is no flow of current in the input terminal & the other one is V1 is always equal to V2.

Inverting Op Amp Circuit
Inverting Op Amp Circuit

This is because the positive input terminal is at OV as it is  Grounded.  In the above configuration, the op-amp is connected by using feedback to create a closed-loop operation. When dealing with operational amplifiers there are two very important rules to remember about inverting amplifiers, these are: “No current flows into the input terminal” and that “V1 always equals V2”.


However, in practical op-amp circuits, the above-mentioned two rules are broken to some extent because the input junction and feedback signal ‘X’ are at equal potential. When the positive input is at zero volts, then the junction is called a “Virtual Earth”. So due to this virtual earth, the op amp’s input resistance is equivalent to the input resistor value (Rin).

Here, the inverting op amp’s closed-loop gain can be fixed through the ratio of the two exterior resistors.
Once we apply the input signal through the ‘Ri’ resistor to the inverting terminal of the op-amp, the non-inverting terminal is connected to the ground. Further, a feedback is provided to stabilize the circuit. Now , the output can be controlled through a feedback resistor ‘Rf’.

Inverting Op-Amp Working & Operations

The voltage gain provided from the above circuit is given as

Av = Vo/Vi


Vi-V1 = IiRi

V1-V0 = IfRf

But, we know that a perfect operational amplifier includes unlimited input impedance because there is no flow of current into its input terminals. I1 = I2 = 0. Therefore, Ii is equivalent to If. So,

Vi-V1 = IfRi

V1-V0 = IfRf

We already know that in a perfect operational amplifier, the voltage at two inputs in the op-amp is always equivalent.

Because the non-inverting terminal is grounded, so the voltage that appeared at the noninverting terminal is V1 = V2= 0. So, the equation will be,

Vi-0 = IfRi

0-Vo = IfRf

From the above equations, we can get,

-Vo/ Vi = IfRf/ IfRi

Vo/ Vi = – (IfRf/ IfRi)

Vo/ Vi = – (Rf/Ri)

This equation can be changed to get Vout is

Vout/ Vi = – (Rf/Ri)

Vout = – (Rf/Ri) x Vin

The inverting op-amp’s voltage gain is,

Inverting Op Amp Gain (Av) = – (Rf/Ri)

This specifies that the inverting amplifier’s voltage gain can be decided through the fraction of the ‘Rf’ to the ‘Ri’ including the negative sign that indicates the reversal phase. In addition, the inverting amplifier’s input impedance is ‘Ri’.

Like DC amplifiers, these amplifiers provide outstanding linear characteristics to make them ideal. In addition, they are frequently used to change the i/p current to the o/p voltage in the Transresistance form otherwise Transimpedance Amplifiers form.

The output voltage (Vout) equation shows that the op-amp circuit is linear for a fixed gain of an amplifier like Vout = Vin x Gain. So this property is very helpful in changing a small sensor signal to a better voltage.

Voltage Characteristics

The voltage characteristics of inverting amplifier are shown in the below graph. It can be noted that once the input signal is positive like Vin, then the output voltage like Vout is negative. In addition, the output voltage will be changed linearly once the input voltage is applied.

Voltage Characteristics
Voltage Characteristics

This characteristic will saturate otherwise the output will become constant, once the amplitude of the input signal goes ahead of both the applied power supplies to the op-amp.

+VCC = + VSAT & –VCC = -VSAT

Inverting Op Amp Waveforms

The inverting op-amps input & output waveforms are shown below. The following waveforms can be drawn by assuming the gain of the amplifier & the sine wave is an input signal. From the following waveforms, it is very clear that the output is double in magnitude as compared to the input like Vout = Av * Vin & phase is reverse to the input.

Inverting Op Amp Waveforms
Inverting Op Amp Waveforms

Inverting Op-Amp Solved Problems

1). For the following inverting amplifier circuit, calculate the input impedance and output voltage.

Inverting Amplifier Example Circuit
Inverting Amplifier Example Circuit

The input impedance is set through input resistance Ri which is 4kΩ. So Zin=4kΩ.

Vout=Vin Av

Av = −Rf/Ri



Vout=100mV * (−5)

Vout = −500mV

2). An inverting amplifier including a gain = 8 & 10 k Ω of an input impedance. The input impedance (Zi) tells us what ‘Ri’ must be?

Zin = Ri


So Rf =?

We know that, Av =−Rf/Ri

Rf = 10 (−8)

Rf= 80k

3). For the following inverting amplifier circuit, please calculate the closed-loop gain.

Op Amp Circuit Example
Op Amp Circuit Example

The gain formula for the above circuit is

Gain (Av) = Vout/Vin = -Rf/Rin

Now we have to substitute the above-given values within the circuit are

Rin = 20kΩ and Rƒ = 80kΩ

The circuit gain can be measured as Av = -Rƒ/Rin = -80k/20k = -4

So, for inverting amplifier circuit, the closed-loop gain is -4.

Why Inverting Op Amps are better than Non-Inverting Op Amps?

In inverting op-amp, the offset voltage is included in the output thus it is less than a few mV whereas, in a non-inverting op-amp, the offset voltage can be changed through the non-inverting gain & again this voltage is included in the output voltage.

Inverting amplifiers give additional stability to the system as compared to non-inverting amplifiers. In inverting amplifiers, negative feedback is utilized that is required always for a stable system.


The advantages of inverting amplifiers include the following.

  • These are not expensive
  • Its size is small
  • Versatility
  • Dependability
  • Flexibility
  • The two input terminals of this op-amp are zero always. In addition, simply the differential mode signal will exist.
  • The device with inverting amplifier includes strong anti-interference capacity.
  • It uses negative feedback.
  • The gain factor is extremely high.
  • The output of this op-amp will be out of phase through the input signal.


The disadvantages of inverting amplifiers include the following.

  • It has a small input impedance (equal to r1)
  • It has high gain but the feedback must be maintained distortion less.
  • The input signal should not include the noise because the small value will be multiplied & attained at the output.
  • The signal is reversed.

Inverting Op-Amp Applications

The applications of inverting amplifiers include the following.

  • An inverting amplifier can be used as a trans resistance amplifier which is also called a trans-impedance amplifier. This amplifier works as a current to voltage converter, used in less power-based applications.
  • Inverting amplifier is used at the output stage when any system is designed with different types of sensors.
  • This op-amp maintains the equal potential of voltage at two terminals, so it can be used in many fields.
  • These op-amps are used in the mixers concept where the RF signals are present.
  • It can be utilized as a phase shifter.
  • These types of op-amps are used where the balancing of the signal is necessary.
  • It is used practically in integration applications.
  • The op-amp-based inverting circuits are more stable; distortion is fairly lower & provide a superior transitory response.
  • Op-amps are used in every electronic device where linear ICs are used
  • These are used in analog filtering and signal processing.
  • These are used in various fields like communications, process control, displays, computers, measuring systems, power sources & signal sources.
  • These are applicable in linear op-amp applications.

Why is the inverting amplifier used?

Inverting amplifier is used mostly for high frequency based applications wherever high i/p impedance is not used because; Inverting Op-Amp’s slew rate is high as compared to non-inverting type configuration.

Why is a unity gain amplifier used?

A voltage follower is also known as a unity gain amplifier, an isolation amplifier, or a voltage buffer. The output voltage (Vo) within a voltage follower circuit is equivalent to the input voltage (Vin). So, the gain of this amplifier is 1 & does not change the incoming signal.

What is the formula of inverting amplifier?

The formula of inverting amplifier (Av) = – (Rf/Ri)

How can an op-amp be used as a non-inverting amplifier?

An op-amp can be used as a noninverting amplifier by applying the input to the positive terminal of the op-amp and connecting the output voltage signal of the op-amp as feedback to the input of the inverting terminal.

Thus, this is all about an overview of inverting op-amp or inverting operational amplifier. Generally, operational amplifiers are used as basic components in analog electronic circuits. So, it is used in filtering, signal conditioning & to perform different arithmetic operations. There are different electronic components are used in between the two terminals of the operational amplifier for amplifying the level of voltage for the signal applied. Here is a question for you, how many terminals are there in an op-amp?