The inverting amplifier is a basic operational amplifier (op-amp) configuration that relies on a few assumptions to operate correctly. Here are the main assumptions of the inverting amplifier:

- Negligible Input Current.
- Virtual Ground at the inverting terminal.
- Negligible Differential Input Voltage.
- Negative feedback.
- Negligible Input Bias Current.

## What is Inverting Amplifier?

An inverting amplifier is a constant or fixed-gain amplifier where only one input is applied to the inverting input terminal, producing a negative output voltage. So, its gain is always negative.

**Assumptions of Inverting Amplifier and Corresponding Functions**

The inverting amplifier consists of an operational amplifier (op-amp) and two external components: a feedback resistor, R_{F,} and an input resistor R_{in}. The input signal, V_{S}, is applied to the inverting terminal of the op-amp, and the output voltage, V_{O}, is taken from the op-amp’s output terminal.

**Fig.1 Circuit diagram of Inverting Amplifier.**

### Negligible Input Current

In an ideal op-amp, the input impedance is assumed to be infinitely high, meaning that the input terminals draw almost zero current. This assumption allows us to neglect the current flowing into the inverting terminal of the inverting amplifier.

### Gain of Inverting Amplifier

The gain of the inverting amplifier is determined by the ratio of the feedback resistor R_{F} to the input resistor R_{in}. Using Kirchhoff’s voltage law, we have,

Using Kirchhoff’s current law at the inverting terminal, we get,

So, the gain of the inverting amplifier becomes,

### Negative Feedback and Virtual Ground Concept

R_{F} is used to feed the output voltage back to the inverting terminal of the op-amp, creating a negative feedback loop. This negative feedback causes the op-amp to adjust its output voltage so that the voltage difference between the two terminals, V_{d}, becomes close to zero or Ground. This junction is thus called “Virtual Ground”.

**Fig.2 Virtual Ground in Inverting Amplifier.**

### Negligible Input Bias Current

In the inverting amplifier configuration, the input bias current can be negligible because it flows into the virtual ground at the inverting terminal of the operational amplifier.

## Why Understanding Assumptions of Inverting Amplifiers Are Important?

The assumptions, such as the ideal operational amplifier and virtual ground, simplify the mathematical analysis of the circuit, allowing for easier calculation of voltage and current relationships.

By assuming negligible input current and bias current, the inverting circuit can be designed with minimal loading effects and reduced offset voltages, resulting in improved overall performance.

Negative feedback, assumed in the inverting circuit, ensures stability and linearity by reducing distortion and maintaining the amplifier within its linear operating range.

## Frequently Asked Questions (FAQs)

### What are the Two Assumptions of Op-Amp?

Answer: Two assumptions of Op-amp are

- The open-loop gain of an op-amp is assumed to be infinitely large.
- The input impedance of an op-amp is assumed to be infinitely high, allowing us to treat the input current as negligible.

### What are the Characteristics of an Ideal Op Amp?

Answer: An ideal op-amp exhibits 5 characteristics:

- Infinite voltage gain A.
- Infinite input resistance and output resistance
- Zero output voltage when the input voltage is zero.
- Infinite slew rate.
- Infinite common mode rejection ratio (CMRR).

### What Two Circuit Assumptions Are Used to Analyze Op-Amp Circuits?

Answer: Two circuit assumptions are used to analyze op-amp circuits:

- Op-amp to have an extremely high gain.
- The voltage difference between the op-amp’s input terminals is negligible, effectively considering the inverting terminal as a virtual ground.

## To Conclude

The assumptions of the inverting circuit are because they simplify the analysis, optimize design, ensure stability, and enable predictable behavior. By assuming a virtual ground, negligible input current, negligible input bias current, and the presence of negative feedback, engineers can confidently analyze and design inverting circuits, resulting in improved performance and reliable operation.

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