Library / Circuits, electronics and noise / ELN-32
Circuits, electronics and noise
Closed-loop bandwidth from gain-bandwidth product
Approximate small-signal closed-loop bandwidth of a voltage-feedback op amp with a dominant pole, from its gain-bandwidth product and the noise gain.
- Ref
- ELN-32
- Rev
- v1
- Field
- Circuits, electronics and noise
- Result
- fb [Hz]
A voltage-feedback op amp with a single dominant pole has a nearly constant gain-bandwidth product, so the closed-loop −3 dB bandwidth is about GBW divided by the noise gain NG = 1/β. A gain of 20 from a 2 MHz part has a bandwidth of only 100 kHz. Use the noise gain, not the signal gain, so an inverting stage of gain −10 has NG = 11. This is for small signals only.
Approximate small-signal closed-loop bandwidth of a voltage-feedback op amp with a dominant pole, from its gain-bandwidth product and the noise gain. A higher gain means a narrower bandwidth.
Calculator
- Bandwidth at unity noise gain2,000,000 Hz
- Rise time, 0.35/bandwidth3.5×10−6 s
- Highest noise gain for 100 kHz bandwidth20 V/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 2,000,000 Hz part with a noise gain of 20 gives 100,000 Hz (100 kHz) of closed-loop bandwidth.
- Splitting a high gain over two stages, each of the square root of the gain, gives a wider total bandwidth than a single stage would.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Hz) | Local step | Change in result |
|---|---|---|---|---|---|---|
| GBW Gain-bandwidth product | 100,000 to 1e9 Hz | 5,000 | 5e7 | 5e7 | +10% | +10 % |
| NG Noise gain | 1 to 1,000 V/V | 2,000 | 2,000,000 | 1,998,000 | +10% | −9.09 % |
Sweep of Noise gain
| Noise gain (V/V) | Closed-loop bandwidth (Hz) |
|---|---|
| 1 | 2,000,000 |
| 2.371 | 843,400 |
| 5.623 | 355,700 |
| 13.34 | 150,000 |
| 31.62 | 63,250 |
| 74.99 | 26,670 |
| 177.8 | 11,250 |
| 421.7 | 4,743 |
| 1,000 | 2,000 |
Sweep one variable
Variables and how each one contributes
Closed-loop bandwidth
What the equation gives you. Everything else feeds it.
Gain-bandwidth product
The gain-bandwidth product of the op amp, in Hz. Raises the bandwidth in direct proportion. Raising it by 10 % (to 2,200,000) moves the result by +10 %, from 100,000 to 110,000 Hz.
Noise gain
The noise gain 1/β, no units. A larger noise gain lowers the bandwidth in inverse proportion. Raising it by 10 % (to 22) moves the result by −9.09 %, from 100,000 to 90,910 Hz.
Worked example with the values above
- Noise gain: NG = 20.
- Divide: GBW / NG = 2,000,000 / 20.
- fb = 100,000 Hz.
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