Library / Circuits, electronics and noise / ELN-34
Circuits, electronics and noise
Output error from input offset voltage
Size of the output error caused by the input offset voltage Vos alone, when the amplifier stays in its linear range.
- Ref
- ELN-34
- Rev
- v1
- Field
- Circuits, electronics and noise
- Result
- |\Delta Vo| [V]
The input offset voltage Vos is a small DC voltage that appears at the input of every real op amp. The feedback network amplifies it by the DC noise gain NG = 1 + Rf/Rg, so the output error is about NG·|Vos|. A gain of 100 with a 1 mV offset gives 0.1 V. The sign of Vos is not known in advance, so the formula uses the magnitude. Bias currents add a separate error.
Size of the output error caused by the input offset voltage Vos alone, when the amplifier stays in its linear range. The noise gain NG at DC multiplies the offset.
Calculator
- Error referred back to the input2×10−4 V
- Error as a share of a 1 V full-scale output0.42 %
- Largest offset for a 1 mV output error4.762×10−5 V
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.
- A 0.2 mV offset with a noise gain of 21 causes up to 0.0042 V (4.2 mV) of output error.
- Halving the gain halves the error, which is why the first stage of a chain should have a low offset or a low gain.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (V) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Vos Input offset voltage | −0.01 to 0.01 V | 0 | 0.21 | 0.21 | +0.01 V | +4,800 % |
| NG DC noise gain | 1 to 1,000 V/V | 2e-4 | 0.2 | 0.1998 | +10% | +10 % |
Sweep of DC noise gain
| DC noise gain (V/V) | Output error magnitude (V) |
|---|---|
| 1 | 2e-4 |
| 2.371 | 4.743e-4 |
| 5.623 | 0.001125 |
| 13.34 | 0.002667 |
| 31.62 | 0.006325 |
| 74.99 | 0.015 |
| 177.8 | 0.03557 |
| 421.7 | 0.08434 |
| 1,000 | 0.2 |
Sweep one variable
Variables and how each one contributes
Output error magnitude
What the equation gives you. Everything else feeds it.
DC noise gain
The DC noise gain of the stage, no units. A larger noise gain amplifies the offset, so the error rises in direct proportion. Raising it by 10 % (to 23.1) moves the result by +10 %, from 0.0042 to 0.00462 V.
Input offset voltage
The input offset voltage, in V (data sheets give mV or µV). A larger magnitude of offset raises the output error in direct proportion. Raising it by 10 % (to −2.2×10−4) moves the result by +10 %, from 0.0042 to 0.00462 V.
Worked example with the values above
- Offset magnitude: |Vos| = 2×10−4 V.
- Multiply by the noise gain: 21 × 2×10−4.
- |ΔVo| = 0.0042 V.
Assumptions and limits
- A voltage-feedback op amp with a single dominant pole and a constant feedback network.
- Small-signal formulas used below the slew limit and with the output in its linear range.
Common mistakes
- Using the closed-loop gain where the noise gain is needed: they differ, for instance, in an inverting stage.
- Entering a peak-to-peak voltage in the slew-rate formula, which needs the peak.
- Forgetting that input offset adds to the output through the noise gain.
Statistics and uncertainty
Open-loop gain, offset voltage, bias current and gain-bandwidth product all vary a lot between parts and with temperature, and data sheets give typical and maximum values. Use the worst case for error budgets.
Where it is used
- Choosing an op amp for gain, bandwidth, output swing and DC accuracy.
- Estimating the errors of a precision amplifier circuit.
Maths you need
- Noise gain: 1 + Rf/Rg for a non-inverting stage; the gain seen by the amplifier’s own errors
- Gain-bandwidth product: gain times bandwidth is constant
- Slew rate: the largest rate of change of the output