# Inverting Amplifier Gain

Basically, an inverting op-amp reverses the polarity of the input signal while amplifying it. It is a constant or fixed-gain amplifier that produces a negative output voltage as inverting amplifier gain is always negative. Also, at DC the phase shift from the inverting input terminal to output is 180°.

In this post, we are going to discuss the inverting amplifier gain. But before starting the discussion about gain, we have to know some basics like we have to understand the circuit diagram, function, and derivation. So, let’s start with a circuit diagram.

## Pin Diagram of Inverting Amplifier.

This is the pin diagram of Inverting Operational Amplifier. As we know, in op-amp Pin-2 is inverting input and Pin-3 is non-inverting input.

In the above picture is an inverting amplifier shown. Here in the circuit, the noninverting input is directly grounded, Vi or Input Voltage is connected to the inverting input through reference Resistor Ri, and the feedback Resistor is Rf. Here the Rf is connected between the inverting input and output. Also here V1 is inverting voltage and V2 is non-inverting voltage, I1 is input current and I2 is the feedback current, and “A” is used to point to a node.

In the case of inverting amplifiers, our goal is to obtain the relationship between the input voltage Vi and the output voltage Vo.

## Derivation of Inverting Amplifier.

Once this amplifier is assumed to be ideal, then we need to apply the virtual short concept to the I/P terminals of the op-amp. So the voltage across the two terminals (V1 and V2) is equal.

So, From the characteristic of the ideal Op-Amp, we can write-

V1 = V2; ——— (i)

The above circuit has a node point as “A”.

So, Applying KCL at node A, we can write-

I1 = I2; ——— (ii)

=> Vi – V1/Ri = V1 – Vo/Rf

=> Vi /Ri = – Vo/Rf [V1 = 0; Since V1 = V2 and V2 directly connected to the ground, so V2 = 0]

=> (Vi-0) / Ri = (0 – Vo) / Rf

=> Vi /Ri = – Vo/Rf

Simplifying the above terms we get the following formula.

Voltage gain, (V) = Vo / Vi = – (Rf / Ri); ——— (iii)

or, Vo = – Vi(Rf / Ri); ——— (iv)

Here, equation (iii) is the inverting operational amplifier voltage gain, and equation (iv) is the output equation of inverting operational amplifier.

Where Inverting amplifier gain is, Av = Rf / Ri;

## Application of Inverting Amplifier.

• As a trans-resistance amplifier, an inverting amplifier can be used which is also known as a trans-impedance amplifier. This amplifier is used in less power-based applications and it works as a current to voltage converter.
• When any system is designed with different types of sensors inverting amplifier is used at the output stage.
• At two terminals this op-amp maintains the equal potential of voltage, so it can be used in many fields.
• Inverting operational amplifiers is used in the mixers concept where the RF signals are present.
• As a phase shifter, it can be utilized.
• This type of op-amp is used where signal balancing is required.
• In integration applications, it is used practically.
• Op-amp-based inverting circuits are more stable, Distortion is fairly low, and provides a superior transient response.
• In electronics devices where linear ICs are used, op-amps are also used in these electronic devices.
• They are used in signal processing and analog filtering.
• They are used in various fields like process control, communication, display, measurement system, computer, power sources, and signal sources.

## Why Inverting Amplifier is Used?

Mostly this type of amplifier is used for high frequency-based applications where high input impedances are not used because it has a higher slew rate than a non-inverting type configuration.

## Bottom Line:

Thus, this is all about an overview of inverting operational amplifiers. Generally, as basic components of analog electronic circuits, operational amplifiers are used. Hence, it is used to perform signal conditioning, filtering, and various mathematical operations. To increase the voltage level for the applied signal various electronic components are used between the two terminals of an operational amplifier.