Non-Inverting Amplifier

Governed by:

$$V_{\text{out}}=V_{\text{in}}\times \left(1+\frac{R_f}{R_i}\right)$$

Basically, how this work is:

• Signal is applied to $V_{+}$
• Negative feedback means the op-amp is trying to minimize $V_{+}-V_{-}$
  • Since $A_0$ is huge, we can assume that $V_{+}-V_{-}=0$ or that $V_{+}=V_{-}$.
  • Called the “virtual ground”
• Thus, we have:

$$\begin{array}{rl}{V}_{+}& =V_{in}\\ V_{-}& =V_{\text{out}}\frac{R_i}{R_i+R_f}\\ V_{+}& =V_{-}\\ \therefore \frac{V_{\text{out}}}{V_{\text{in}}}& =\frac{R_i+R_f}{R_i}=1+\frac{R_f}{R_i}\end{array}$$

• This is called the “closed-loop gain”, $A\left[\frac{V}{V}\right]$.