## Theory

An inverting amplifier is a fundamental configuration in the field of operational amplifiers (op-amps). It is widely used in various electronic applications due to its ability to invert and amplify input signals. In this explanation, we will explore the theory behind an inverting amplifier using an op-amp, two resistors (R1 and R2), with the input voltage denoted as V_{in} and the output voltage as V_{out}.

##### Circuit Configuration

The inverting amplifier circuit consists of:

**Operational Amplifier (Op-Amp)**: The central component that amplifies the input signal.**Resistors R1 and R2**: These resistors set the gain of the amplifier.

In this configuration:

- The input voltage V
_{in}is applied to the inverting input terminal (-) of the op-amp through resistor R1. - The non-inverting input terminal (+) is connected to ground.
- The feedback loop connects the output V
_{out}to the inverting input through resistor R2.

##### How It Works

**Input Stage**: The input signal V_{in}is applied to the inverting input of the op-amp through resistor R1. The non-inverting input is grounded, creating a virtual ground at the inverting input due to the high gain of the op-amp.**Feedback Loop**: The output voltage V_{out}is fed back to the inverting input through resistor R2, forming a negative feedback loop.**Current Flow**: The current I flowing through R1 is the same as the current through R2, as the input impedance of the op-amp is very high, causing negligible current to flow into the inverting input.**Voltage at Inverting Input**: The voltage at the inverting input is virtually zero (virtual ground), leading to:I = V

_{in}/ R1 = -V_{out}/ R2**Output Voltage Equation**: Solving for V_{out}, we get:V

_{out}= -V_{in}× (R2 / R1)

This equation shows that the output voltage V_{out} is the input voltage V_{in} multiplied by the gain factor and inverted in phase, which is determined by resistors R1 and R2.

##### Gain of the Amplifier

The gain A_{v} of an inverting amplifier is given by:

A_{v}= -R2 / R1

This indicates that the output voltage is the input voltage scaled by the gain factor and inverted in phase. The gain can be adjusted by changing the values of resistors R1 and R2.

##### Summary

An inverting amplifier using an op-amp, two resistors R1 and R2, inverts and amplifies the input voltage V_{in} to the output voltage V_{out}.

The gain of the amplifier is -R2 / R1, making it a versatile and essential component in many electronic circuits. Understanding this theory is fundamental for designing effective amplification systems in various applications.

Mathematically, we can express the Inverting Amplifier equations as:

V_{out}= -V_{in}× (R2 / R1)

V_{in}= -V_{out}× (R1 / R2)

R1 = (-V_{in}/ V_{out}) × R2

R2 = (-V_{out}/ V_{in}) × R1

The Inverting Amplifier Calculator uses the equations above to find each parameter that's required as long as three out of four of the parameters are provided.