Library / Circuits, electronics and noise / ELN-33
Circuits, electronics and noise
Full-power bandwidth from slew rate
Highest frequency at which a sine wave of peak voltage Vp can be produced without slew-rate distortion.
- Ref
- ELN-33
- Rev
- v1
- Field
- Circuits, electronics and noise
- Result
- fmax [Hz]
A sine wave Vp sin(2πft) has a maximum slope of 2πf Vp. The op amp cannot follow it if this exceeds the slew rate SR, so the full-power bandwidth is fmax = SR/(2πVp). Beyond it the output turns triangular and distorts. Use the peak voltage Vp, not peak-to-peak; entering the peak-to-peak value halves the result.
Highest frequency at which a sine wave of peak voltage Vp can be produced without slew-rate distortion. Use the peak voltage, not peak-to-peak; entering peak-to-peak would halve the result.
Calculator
- Maximum slope of the sine wave at 1 kHz12,570 V/s
- Largest peak voltage at 100 kHz1.592 V
- Slew rate in V/µs1 V/µs
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 1 V/µs op amp can reproduce a 2 V peak sine up to 79,580 Hz (79.58 kHz).
- At half the peak voltage, the same op amp gets to twice the frequency, 159,200 Hz.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Hz) | Local step | Change in result |
|---|---|---|---|---|---|---|
| SR Slew rate | 10,000 to 1e9 V/s | 795.8 | 7.958e7 | 7.958e7 | +10% | +10 % |
| Vp Required peak output voltage | 0.1 to 20 V | 7,958 | 1,592,000 | 1,584,000 | +10% | −9.09 % |
Sweep of Required peak output voltage
| Required peak output voltage (V) | Full-power bandwidth (Hz) |
|---|---|
| 0.1 | 1,592,000 |
| 2.587 | 61,510 |
| 5.075 | 31,360 |
| 7.562 | 21,050 |
| 10.05 | 15,840 |
| 12.54 | 12,690 |
| 15.02 | 10,590 |
| 17.51 | 9,088 |
| 20 | 7,958 |
Sweep one variable
Variables and how each one contributes
Full-power bandwidth
What the equation gives you. Everything else feeds it.
Slew rate
The slew rate, in V/s (1 V/µs is 10⁶ V/s). Raises the full-power bandwidth in direct proportion. Raising it by 10 % (to 1,100,000) moves the result by +10 %, from 79,580 to 87,540 Hz.
Required peak output voltage
The required peak output voltage, in V. A larger swing needs a steeper slope, so the full-power bandwidth falls in inverse proportion. Raising it by 10 % (to 2.2) moves the result by −9.09 %, from 79,580 to 72,340 Hz.
Worked example with the values above
- Maximum slope for a unit sine at 1 Hz: 2π Vp = 2π × 2 = 12.566 V/s.
- Divide the slew rate by it: 1,000,000 / 12.566.
- fmax = 79,577 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 peak-to-peak voltage in place of the peak, which halves the answer.
- Entering the slew rate in V/µs without converting to V/s.
- Assuming the small-signal bandwidth applies to large signals.
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