Library / Electrical / ELE-22
Electrical
Inverting op-amp gain
Closed-loop gain of an inverting op-amp amplifier.
- Ref
- ELE-22
- Rev
- v1
- Field
- Electrical
- Result
- A
Ainv the voltage gain (negative: output is inverted), Rf the feedback resistor from output to inverting input, Ri the input resistor. Ideal op-amp, negative feedback, linear region.
With negative feedback, an op-amp’s gain depends only on two resistors. The signal comes out inverted, multiplied by the ratio of feedback to input resistance.
Calculator
- Gain magnitude10
- Gain in decibels20 dB
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The gain depends only on the resistor ratio, not on the op-amp itself, provided the open-loop gain is high.
- The input impedance equals Ri, so a very high gain from a tiny Ri loads the source.
- Ideal behaviour fails near the amplifier’s gain-bandwidth limit and when the output saturates at the supply rails.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| Rf Feedback resistor | 1 to 1,000 kΩ | −100 | −0.1 | 99.9 | +10% | +10 % |
| Ri Input resistor | 1 to 100 kΩ | −100 | −1 | 99 | +10% | −9.09 % |
Sweep of Feedback resistor
| Feedback resistor (kΩ) | Voltage gain |
|---|---|
| 1 | −0.1 |
| 2.371 | −0.2371 |
| 5.623 | −0.5623 |
| 13.34 | −1.334 |
| 31.62 | −3.162 |
| 74.99 | −7.499 |
| 177.8 | −17.78 |
| 421.7 | −42.17 |
| 1,000 | −100 |
Sweep one variable
Variables and how each one contributes
Voltage gain
What the equation gives you. Everything else feeds it.
Feedback resistor
Resistor from output to the inverting input. Directly proportional to the gain magnitude.
Input resistor
Resistor from the signal to the inverting input; it also sets the input impedance. Inversely proportional.
Worked example with the values above
- Both resistors are in kΩ, so the units cancel in the ratio.
- Rf/Ri = 100 / 10 = 10.
- The gain is −10, so the output is inverted.
Assumptions and limits
- Ideal op-amp: infinite open-loop gain and input impedance.
- Negative feedback, linear range (output below the rails).
- Frequencies well below the gain-bandwidth limit.
Common mistakes
- Forgetting the minus sign.
- Using the non-inverting formula.
- Ignoring the loading of the signal source by Ri.
Statistics and uncertainty
With ±1% resistors the worst-case gain error is about ±2% (the two errors add). Matched pairs or thin-film networks reduce this to ±0.1%. The ratio is scale-free, so temperature drift matters only if the two resistors drift differently.
Where it is used
- Sensor signal conditioning.
- Summing amplifiers and audio mixers.
- Active filters.
Maths you need
- Ohm’s law: resistor ratios
- Feedback: output fed back to the input