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:

1. Operational Amplifier (Op-Amp): The central component that amplifies the input signal.
2. 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

1. 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.


2. 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.


3. Voltage at Inverting Input: The voltage V_- at the inverting input is given by:
   

   V- = Vout*(R1/(R1+R2))

4. 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:
   

   Vin  = Vout*(R1/(R1+R2))

5. Output Voltage Equation: Rearranging the above equation to solve for V_out, we have:
   

   Vout = Vin *(1+(R2/R1))

   This equation shows that the output voltage V_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:

Av  = Vout/Vin  = 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:

Vout = Vin × (1 + (R2 / R1))

Vin  = Vout / (1 + (R2 / R1))

R1 = R2 / ((Vout / Vin) - 1)

R2 = ((Vout / Vin) - 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.