Library / Electrical / ELE-23
Electrical
Non-inverting op-amp gain
Closed-loop gain of a non-inverting op-amp amplifier.
- Ref
- ELE-23
- Rev
- v1
- Field
- Electrical
- Result
- A
Anon-inv the voltage gain, Rf the feedback resistor from output to the inverting input, Rg the resistor from the inverting input to ground. Ideal op-amp, negative feedback.
The signal goes into the non-inverting input and comes out larger, with the same polarity. The gain is always at least 1, set by the ratio of two resistors.
Calculator
- Gain in decibels20 dB
- Unity-gain buffer (Rf = 0)1
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 input impedance is very high (the op-amp input itself), so the source is barely loaded, unlike the inverting circuit.
- Setting Rf = 0 (and removing Rg) gives a gain of exactly 1: a voltage follower buffer.
- The minimum gain is 1; to attenuate you need a different circuit.
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 | 1.1 | 101 | 99.9 | +10% | +9 % |
| Rg Ground resistor | 1 to 100 kΩ | 1.9 | 91 | 89.1 | +10% | −8.18 % |
Sweep of Feedback resistor
| Feedback resistor (kΩ) | Voltage gain |
|---|---|
| 1 | 1.1 |
| 2.371 | 1.237 |
| 5.623 | 1.562 |
| 13.34 | 2.334 |
| 31.62 | 4.162 |
| 74.99 | 8.499 |
| 177.8 | 18.78 |
| 421.7 | 43.17 |
| 1,000 | 101 |
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. Raises the gain in proportion.
Ground resistor
Resistor from the inverting input to ground. Lowers the gain as it increases.
Worked example with the values above
- The ratio Rf/Rg = 90 / 10 = 9.
- Add 1 for the direct path: 1 + 9.
- Gain 10, output in phase with the input.
Assumptions and limits
- Ideal op-amp: infinite gain and input impedance.
- Negative feedback in the linear range.
- Frequencies below the gain-bandwidth limit.
Common mistakes
- Forgetting the +1.
- Swapping Rf and Rg.
- Expecting a gain below 1.
Statistics and uncertainty
With ±1% resistors and a gain of 10, the worst-case error in Rf/Rg is about ±2%, giving ±1.8% on the gain. Higher gain makes the result track the resistor ratio more closely.
Where it is used
- Amplifying thermocouple, strain gauge and microphone signals.
- Buffering a high-impedance sensor.
- ADC input drivers.
Maths you need
- Ohm’s law: resistor ratios
- Feedback: output fed back to the input