What is the closed-loop gain of a non-inverting op-amp configuration with resistors R1 and R2 in the feedback network?

What is the closed-loop gain of a non-inverting op-amp configuration with resistors R1 and R2 in the feedback network?

• A. Av = 1 + (R1 / R2)
• B. Av = 1 + (R2 / R1)
• C. Av = 1 - (R2 / R1)
• D. Av = R2 / R1

Answer: (B)

Non-inverting amplifiers rely on negative feedback to set the output so that the inverting input sits at the same voltage as the non-inverting input. The feedback network between output, the inverting input, and ground forms a divider that sets the voltage at the inverting input. If the resistor from output to the inverting input is the one labeled R2 and the resistor from the inverting input to ground is R1, then the voltage at that node is V- = Vout · (R1 / (R1 + R2)). With negative feedback, V- equals V+ (which is Vin), so Vin = Vout · (R1 / (R1 + R2)). Solving for the gain Vout/Vin gives Vout/Vin = (R1 + R2) / R1 = 1 + (R2 / R1). So the closed-loop gain is 1 plus the ratio of the feedback resistor to the resistor to ground. This corresponds to a gain greater than one and aligns with the resistor labeling where R2 is the feedback resistor.

Non-inverting amplifiers rely on negative feedback to set the output so that the inverting input sits at the same voltage as the non-inverting input. The feedback network between output, the inverting input, and ground forms a divider that sets the voltage at the inverting input. If the resistor from output to the inverting input is the one labeled R2 and the resistor from the inverting input to ground is R1, then the voltage at that node is V- = Vout · (R1 / (R1 + R2)). With negative feedback, V- equals V+ (which is Vin), so Vin = Vout · (R1 / (R1 + R2)). Solving for the gain Vout/Vin gives Vout/Vin = (R1 + R2) / R1 = 1 + (R2 / R1). So the closed-loop gain is 1 plus the ratio of the feedback resistor to the resistor to ground. This corresponds to a gain greater than one and aligns with the resistor labeling where R2 is the feedback resistor.