Question

What is a non-inverting amplifier and how is its gain calculated?

Answer 1

A non-inverting amplifier is a type of electronic amplifier circuit that amplifies an input signal without inverting its polarity. In simpler terms, the output signal is in phase with the input signal. It is widely used in various electronic applications, including audio amplifiers, signal conditioning circuits, and instrumentation systems.

The basic configuration of a non-inverting amplifier consists of an operational amplifier (op-amp) with two external resistors: one connected between the amplifier's non-inverting input and the input signal, and the other connected between the amplifier's output and its non-inverting input. The input signal is applied to the non-inverting input (+) of the op-amp, and the output is taken from the output of the op-amp.

The gain (A_v) of a non-inverting amplifier is calculated using the following formula:



=
1
+

2

1
A
v
    ​

=1+
R
1
    ​

R
2
    ​

    ​


where:


1
R
1
    ​

 is the resistance of the resistor connected between the non-inverting input (+) of the op-amp and the input signal.

2
R
2
    ​

 is the resistance of the resistor connected between the output of the op-amp and its non-inverting input (+).

To understand how this gain formula is derived, let's briefly analyze the circuit's operation:

The non-inverting input (+) of the op-amp is a high-impedance node, which means that no current flows into the input. This ensures that the input impedance of the non-inverting amplifier is very high, making it suitable for interfacing with various sources without loading them significantly.

The voltage at the inverting input (-) of the op-amp is assumed to be equal to the voltage at the non-inverting input (+) due to the high open-loop gain of the op-amp and the assumption of negative feedback.

Applying Kirchhoff's voltage law around the loop formed by the input resistor (

1
R
1
    ​

), the feedback resistor (

2
R
2
    ​

), and the op-amp output, we can derive the gain equation as follows:



=

out

in
=

out

non-inv
A
v
    ​

=
V
in
    ​

V
out
    ​

    ​

=
V
non-inv
    ​

V
out
    ​

    ​


where

in
V
in
    ​

 is the voltage at the non-inverting input (+) and

non-inv
V
non-inv
    ​

 is the voltage at the output of the op-amp, which is equal to the voltage at the non-inverting input (+).



=

out

non-inv
=

2

1
+
1
A
v
    ​

=
V
non-inv
    ​

V
out
    ​

    ​

=
R
1
    ​

R
2
    ​

    ​

+1

The
+
1
+1 term in the gain formula signifies that the output is in phase with the input, indicating non-inverting operation.