Derive the transfer function for a non-inverting op-amp with feedback network R_f (from output to - input) and R_g (from - input to ground).

• A. V_out = V_in (1 + R_f/R_g)
• B. V_out = V_in
• C. V_out = V_in (1 + R_g/R_f)
• D. V_out = V_in /(1 + R_f/R_g)

Answer: (A)

The main idea is how negative feedback sets the gain of a non-inverting amplifier. In an ideal op-amp, the input currents are zero and the open-loop gain is infinite, so the voltages at the two inputs become equal when feedback is present. The input signal Vin is applied to the non-inverting input, so the inverting input sits at V- ≈ Vin.

Now look at the currents at that inverting node. The current through the feedback resistor from output to the node is (Vout − V-)/R_f, and the current through the resistor from the node to ground is V- / R_g. Because no current flows into the op-amp input, these two currents must be equal: (Vout − V-)/R_f = V- / R_g. Substituting V- with Vin gives (Vout − Vin)/R_f = Vin / R_g. Solve for Vout: Vout = Vin [1 + R_f/R_g]. This is the transfer function of a non-inverting amplifier. It also shows how the gain increases with the feedback ratio R_f/R_g, and that if R_f is zero the gain is 1.