Non-Inverting Op-Amp Gain
Non-Inverting Op-Amp Gain
A non-inverting op-amp configuration amplifies a signal without flipping its sign, and its gain is set entirely by the ratio of two external resistors — the feedback resistor and the resistor to ground — assuming the op-amp itself behaves ideally.Because gain depends only on a resistor ratio and not on the op-amp’s internal open-loop gain (which is large but imprecise), this configuration gives a predictable, stable, and easily adjustable gain, which is why it is one of the most common building blocks in analog signal conditioning circuits.
The voltage gain is A_v = 1 + R_f/R_in, one plus the ratio of the feedback resistor to the input resistor. where R_f is the feedback resistor and R_in is the resistor from the inverting input to ground.
Inputs
R_f := 10 kOhm=10000 Ω
R_in := 1 kOhm=1000 Ω
The op-amp forces its two inputs to the same voltage, so the ratio of the feedback and ground resistors directly sets how much the output voltage is amplified above the input.
A_v := 1 + R_f/R_in=11
Results
A gain of 11 from a 10:1 feedback-to-input resistor ratio is exactly what the formula predicts, and this kind of round-number gain is typical in practice since designers usually pick standard resistor values that give a clean, easy-to-remember gain. Because gain is set purely by this resistor ratio, using precision resistors matters far more for gain accuracy than the op-amp’s own datasheet tolerances.
Assumptions & limitations
- Ideal op-amp assumed (infinite open-loop gain, infinite input impedance, zero output impedance).
- DC or low-frequency gain; bandwidth/slew-rate limits not modeled.
- Resistors assumed at their nominal values (tolerance not included).