A non-inverting amplifier is an op amp circuit designed to provide a positive voltage gain.
The input voltage \(v_i\) is applied directly at the non-inverting input terminal, and resistor \(R_1\) is connected between the ground and the inverting terminal.
Application of KCL at the inverting terminal gives
\(\displaystyle i_1 = i_2 \to \frac{0 - v_1}{R_1} = \frac{v_1 - v_o}{R_f}\)
But \(v_1 = v_2 = v_i\) for an ideal op amp. Hence,
\(\displaystyle -\frac{v_i}{R_1} = \frac{v_i - v_o}{R_f}\)
\(\displaystyle \boxed{v_o = \left(1 + \frac{R_f}{R_1}\right) v_i}\)
Closed-loop voltage gain \(A_v\)
\(\boxed{A_v = \frac{v_o}{v_i} = 1 + \frac{R_f}{R_1}}\)
If feedback resistor \(R_f = 0\) (short circuit) or \(R_1 = \infty\) (open circuit) or both, the gain becomes 1. This is called a voltage follower (or unity gain amplifier) because the output follows the input.