Inverting Operational Amplifier

Operational amplifiers are an important category of instruments used in electronics engineering. Often they are used for the task of amplifying the output. In this category of instruments, there is a subcategory known as Inverting Operational Amplifiers. They are typically used when we need an opposite phase for the input waveform. In this article, we will discuss what is Inverting Operational Amplifier. We will discuss their work and the equation used for calculating the gain of an Inverting Operational Amplifier. We will also discuss the advantages and disadvantages of Inverting Operational Amplifier. To understand the real-life usage of these, we will also discuss some applications of Inverting Operational Amplifiers. The article will also aim to provide a comparative analysis between an Inverting operational Amplifier and a Non-Inverting Operational Amplifier. We will conclude the article with some frequently asked questions.

What is Inverting Operational Amplifier?

An Inverting operational Amplifier is a device used in electronics engineering for amplifying the output and generating an output voltage that has a phase opposite to the input waveform. It is usually built using an operational amplifier and some resistors. Let us see the formal definition of

The inverting operational amplifier can be described as an amplifier with fixed-gain which produces a negative output voltage as its gain is always negative.

We can say that the output of inverting operational amplifier is out of phase with respect to its input by 180⁰. This can be interpreted that for a negative input pulse, the output will be positive and for a positive input pulse, the output wave will be negative.

Working of Operational Amplifier

Let us see the working of operational amplifier through the circuit.

An inverting operational amplifier

• The inverting terminal of inverting operational amplifier is fed with the input signal whereas the non-inverting terminal is usually connected to ground or some reference voltage.
• Next a feedback circuit is applied. In this a feedback resistor is connected between the output of op-amp and inverting input terminal. This resistor primarily controls the gain.
• Now an ideal op-amp amplifies the input voltage applied. The negative feedback from the output to the inverting input creates a stable condition. This helps us to control the output generated. The whole time op-amp works to ensure that the voltage at the inverting input is equal to the voltage at the non-inverting input.
• Due to the inverting nature, the input signal is inverted .This means if input signal increases then output will decrease and vice-versa. The gain in final output is calculated using the formula gain=R_F/R_in.
• After the amplification and inversion of input signal along with phase inversion ,the output wave is generated at the junction. The output voltage is denoted by V_out.

Inverting Amplifier Equation and Gain

Let us derive the gain of an op-amp

Gain calculation for inverting op-amp

Mathematically, we can write voltage gain as

A_v=V_out/V_in

Where ,V_in-V₂= I_inR_in and V₂-V_out=I_FR_F

Observe that an ideal op amp has infinite input impedance due to which the currents flowing into its input terminals are zero.

Thus, I_in = I_f. We also know that in an ideal op amp the voltage at inverting and non-inverting inputs are always equal. Hence,

Due to virtual ground V₁=0

Also,V₂=V₁=0

So ,V_in-0= I_FR_in and 0-V_out=I_FR_F

We combine the last two equations

-V_out/V_in= I_FR_F/I_FR_in

so, -V_out/V_in= R_F/R_in

∴ V_out/V_in= -R_F/R_in

This is how we derive the gain of inverting operational amplifier.

Advantages of Inverting Operational Amplifier

There are various advantages of Inverting Operational Amplifier some of which have been stated below:

• the configuration of Inverting Operational Amplifier makes them stable as compared to the non-Inverting Operational Amplifier. The stability and predictability of these op-amps makes them more easier to analyse.
• The output gain in-case of Inverting Operational Amplifier is dependant on resistances used so by selecting appropriate resistance values, we can achieve high gains with large amplifications of input waveforms.
• The non-inverting input of this Operational Amplifier is grounded therefore the inverting input acts as a virtual ground. This simplifies the task of circuit designing and circuit-analysis.
• One important advantage of Inverting Operational Amplifier is their ability of phase-inversion. This helps to give an output which is out of phase with input wave at 180⁰. Thus it can be used in phase-shift circuits.
• Inverting Operational Amplifiers have high input impedance and low output impedance. The high input impedance helps to drain very little current from input waveform and low output impedance helps to carry low-input impedance loads without the loss of signal.

Disadvantages of Inverting Operational Amplifier

There are certain disadvantages of Inverting Operational Amplifier some of which have been stated below:

• Due to the configuration of Inverting Operational Amplifier, it often exhibits more noise as compared to non-Inverting Operational Amplifier. This noise performance can an important consideration when designing circuits.
• Designing of circuits with Inverting Operational Amplifier can be a complicated procedure. Sometimes one can require specific gain for the circuit and in order to achieve this the feedback circuits can be complex. This can increase the components and therefore the cost.
• We can’t use Inverting Operational Amplifier when we require precise output .This is because Inverting Operational Amplifier are sensitive to input offset voltage. This leads to certain errors in final output produced.
• Inverting Operational Amplifier has some limitations when using it in common mode. The common mode limits the input range and any voltage beyond or below this range will distort the output voltage.
• Sometimes the inversion from Inverting Operational Amplifier is undesirable. This can cause unnecessary phase shifting and as a result some extra circuits might be needed for correction.

Application of Inverting Operational Amplifier

Let us see some real-life applications of Inverting Operational Amplifier.

• Inverting Operational Amplifier are used as a part of phase-shifter circuit. This is because they have an inherent tendency to generate an output which is in 180⁰ phase shift with input voltage.
• They are also used in oscillator circuits due to their ability of shifting phase. They can be used to generate sinusoidal waves in such circuits by varying the phase as a function of time.
• In electronics engineering, Inverting Operational Amplifier are used as Integrator and Differentiator Circuits. This property is used in signal-processing to integrate or differentiate electrical signals as per requirement.
• The most common application of Inverting Operational Amplifier is its use as inverting amplifier where the input signals (mostly voltages) can be inverted and amplified by a certain factor(gain) which is determined by the set of resistors used. Hence they are used for signal amplification.
• Inverting Operational Amplifier are largely used in Schmitt trigger circuits. There ,they are used for signal conditioning. Some noisy and slow-varying signals are converted to another forms.

Difference Between Inverting and Non-Inverting Op-Amp

Let us compare inverting and non-inverting op-amplifiers.

	Inverting op-amplifier	Non-Inverting op-amplifier
Gain	-RF/Rin	1+RF/Rin
Phase Shift	Output is 1800 out of phase with input signal.	Output is in-phase with input.
Range of Gain	The gain can be less than ,equal to or greater than 1.	Gain is always greater than 1.
Output	Output voltage is high for Vin less than Vref.	Output voltage is high for Vin higher than Vref.
Input applied	Input is applied to the inverting terminal of op-amp.	Input is applied to the non-inverting terminal of op-amp.

Solved Examples of Inverting Operational Amplifier

Q1. Determine the gain for the given circuit.

Solved Examples of Inverting Operational Amplifier

The above circuit is of inverting operational amplifier

Hence the gain will be

gain= -R_f/R_in

On putting values

gain=-R₂/R₁

Q2. Derive the value of output voltage from previously derived results if R₂ is 10 ohm R₁ is 2 ohms and input voltage is 0.2V.

Calculating the gain from previously derived result

gain=-(10)/2= -5

Hence gain is -5

Now we define gain as the factor by which input signals gets amplified

Hence

gain=V_out/V_in

Hence V_out= gain* V_in

On putting the values

V_out= -5 * 0.2 V= -1V

Hence output voltage is -1V

Conclusion

We have seen that Inverting Operational Amplifier is an essential component in electronics engineering primarily because of its ability to invert a signal and generate a 180⁰ phase shift in output signal as compared to input signal. This makes Inverting Operational Amplifier a major tool in signal processing .Although, it is quite significant yet it has some limitations like high noise generation and complicated designing. Therefore ,it is necessary to keep the research up in this field and bring in some developments in this field. It has been advised to readers to go through the solved questions for better understanding and refer to the necessary links for clear concepts.

FAQs on Inverting Operational Amplifier

What is the gain of Inverting Operational Amplifier?

Inverting Operational Amplifier are used for amplifying an input signal. The gain of an amplifier is defined as factor by which the input signal is amplified to generate the output signal. Gain is negative for Inverting Operational Amplifier.

What is the use of two resistors used in Inverting Operational Amplifier?

The inverting op-amp has two resistors. The feedback resistor is connected between the output and the inverting input of the op-amp and input resistor is connected between the inverting input of the op-amp and the input signal source. Together R_f/R_in is used to determine gain.

What is the concept of virtual earth in Inverting Operational Amplifier?

This concept is applicable to an ideal op-amp as a result of negative feedback applied. It states that for an ideal op-amp with negative feedback, the voltage difference between the inverting and non-inverting input terminals is virtually zero.