Library / Circuits, electronics and noise / ELN-35
Circuits, electronics and noise
Bias-current compensation resistor
Resistor from the non-inverting input to ground of an inverting amplifier that balances the DC resistances at the two inputs, so the bias currents cause nearly equal voltages.
- Ref
- ELN-35
- Rev
- v1
- Field
- Circuits, electronics and noise
- Result
- Rb [Ω]
An op amp’s two inputs draw small bias currents. If the resistance to ground at the non-inverting input equals the resistance seen at the inverting input, which is Ri in parallel with Rf (with the source resistance included in Ri), the two currents cause nearly equal voltages and their effects at the output cancel. The compensation resistor is Rb = Ri∥Rf. Offset current is what remains.
Resistor from the non-inverting input to ground of an inverting amplifier that balances the DC resistances at the two inputs, so the bias currents cause nearly equal voltages. Input offset current remains.
Calculator
- Resistance seen at the inverting input9,000 Ω
- Inverting-stage gain, −Rf/Ri−9 V/V
- Output error from bias current without Rb, Ib Rf at 100 nA0.009 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.
- For Ri = 10,000 Ω and Rf = 90,000 Ω, a 9,000 Ω resistor from the non-inverting input to ground balances the bias-current drops.
- Without it, a 100 nA bias current would cause an output error of about 0.009 V; with it only the offset current of a few nA remains.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Ω) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Ri Input resistance including the source resistance | 10 to 1,000,000 Ω | 9.999 | 82,570 | 82,560 | +10% | +8.91 % |
| Rf Feedback resistor | 10 to 1,000,000 Ω | 9.99 | 9,901 | 9,891 | +10% | +0.917 % |
Sweep of Feedback resistor
| Feedback resistor (Ω) | Compensation resistor (Ω) |
|---|---|
| 10 | 9.99 |
| 42.17 | 41.99 |
| 177.8 | 174.7 |
| 749.9 | 697.6 |
| 3,162 | 2,403 |
| 13,340 | 5,715 |
| 56,230 | 8,490 |
| 237,100 | 9,595 |
| 1,000,000 | 9,901 |
Sweep one variable
Variables and how each one contributes
Compensation resistor
What the equation gives you. Everything else feeds it.
Input resistance including the source resistance
The input resistance seen at the inverting input, including the source resistance, in Ω. A larger Ri raises Rb, but never above Rf. Raising it by 10 % (to 11,000) moves the result by +8.91 %, from 9,000 to 9,802 Ω.
Feedback resistor
The feedback resistor, in Ω. A larger Rf raises Rb, but never above Ri. Raising it by 10 % (to 99,000) moves the result by +0.917 %, from 9,000 to 9,083 Ω.
Worked example with the values above
- Product: Ri Rf = 10,000 × 90,000 = 9×108 Ω².
- Sum: Ri + Rf = 100,000 Ω.
- Rb = 9×108 / 100,000 = 9,000 Ω.
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