Voltage Gain

The circuit in Fig 1.8 is the noninverting amplifier configuration, which has the signal V_in to be amplified going into V⁺ and the feedback going to V^-.

  

Figure 1.8: Basic Noninverting Amplifier

Setting V⁺=V^-, and realizing that

V⁺=V_in

The simple voltage divider expression gives

$$V^-=V_{out}\frac{R_1}{R_1 + R_f}$$ (10)

Since feedback forces V⁺=V^-, equating the two previous expressions and solving for $\frac{V_{out}}{V_{in}}$ gives the following expression for closed loop voltage gain A_v for a noninverting amp:

$$A_{v}=\frac{V_{out}}{V_{in}}=1 + \frac{R_f}{R_1}$$ (11)