The formula
Inverting: A_v = −R_f / R_in | Non-inverting: A_v = 1 + R_f / R_in
- A_v
- closed-loop voltage gain
- R_f
- feedback resistor, output to inverting input (ohms)
- R_in
- input resistor (inverting) or lower feedback leg (non-inverting)
- V_out
- output voltage = A_v × V_in
Worked example
R_f = 90 kΩ, R_in = 10 kΩ, input 0.5 V.
- Non-inverting: A_v = 1 + 90/10 = 10, so V_out = 0.5 × 10 = 5 V
- Inverting with the same parts: A_v = −90/10 = −9
- V_out = 0.5 × −9 = −4.5 V
Gain of 10 (non-inverting) or −9 (inverting) — the same resistors, differing by exactly one.
Where you'll use it
Amplifying sensor outputs, building filters and buffers. A non-inverting stage cannot have a gain below 1, and its input impedance is enormous; the inverting stage's input impedance is just R_in, which is often the deciding factor.