## Theory

A non-inverting amplifier is a basic yet powerful configuration in the field of operational amplifiers (op-amps). It is widely used in various electronic applications due to its ability to amplify input signals without inverting the phase. In this explanation, we will explore the theory behind a non-inverting amplifier using an op-amp, two resistors (R1 and R2), with the input voltage denoted as V_{in} and the output voltage as Vout.

##### Circuit Configuration

The non-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 non-inverting input terminal (+) of the op-amp. - The inverting input terminal (-) is connected to a voltage divider formed by R1 and R2, with the feedback loop connecting the output Vout to this voltage divider.

##### How It Works

- Input Stage: The input signal V
_{in}is applied directly to the non-inverting input of the op-amp. This means the input voltage is the same as the voltage at the non-inverting terminal. - Feedback Loop: The output voltage V
_{out}is fed back to the inverting input through the voltage divider formed by resistors R1 and R2. The voltage at the inverting input (V_{-}) is a fraction of V_{out}determined by the ratio of R1 and R2. - Voltage at Inverting Input: The voltage V
_{-}at the inverting input is given by:V

_{-}= V_{out}*(R1/(R1+R2)) - Op-Amp Behavior: The op-amp adjusts V
_{out}to make the voltages at the inverting and non-inverting inputs equal. Therefore, V_{-}= V_{+}. Given V_{+}= V_{in}, we have:V

_{in}= V_{out}*(R1/(R1+R2)) - Output Voltage Equation: Rearranging the above equation to solve for V
_{out}, we have:

V

This equation shows that the output voltage V_{out}= V_{in}*(1+(R2/R1))_{out}is the input voltage Vin multiplied by the gain factor, which is determined by resistors R1 and R2.

##### Gain of the Amplifier

The gain A_{v} of a non-inverting amplifier is given by:

AThis indicates that the output voltage is the input voltage scaled by the gain factor. The gain can be adjusted by changing the values of resistors R1 and R2._{v}= V_{out}/V_{in}= 1 + (R2/R1)

##### Summary

A non-inverting amplifier using an op-amp, two resistors R1 and R2, amplifies the input voltage V_{in} without inverting its phase.

Mathematically, we can express the Non-Inverting Amplifier equations as:

V_{out}= V_{in}× (1 + (R2 / R1))

V_{in}= V_{out}/ (1 + (R2 / R1))

R1 = R2 / ((V_{out}/ V_{in}) - 1)

R2 = ((V_{out}/ V_{in}) - 1) × R1

The Non-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.